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https://www.math.princeton.edu/events/conformally-warped-manifolds-and-quasi-einstein-metrics-2010-02-26t200002	# Conformally Warped Manifolds and quasi-Einstein metrics - Jeffrey Case, University of California, Santa Barbara Fine Hall 314 The concept of a smooth metric measure space has recently arisen as a useful object within Riemannian geometry, for example in Perelman's formulation of Ricci flow as a gradient flow. In this setting, a key objective is to find a suitable generalization of Ricci curvature, and to understand the associated quasi-Einstein'' metrics. Taking two different perspectives, Lott, Villani, Sturm and Chang, Gursky and Yang have found two distinct approaches to studying smooth metric measure spaces. While the formulations are different, they both introduce an extra dimensional parameter $m$ which, in the limit $m\to\infty$, recovers the curvatures that arise in Perelman's treatment of the Ricci flow. In this way it becomes interesting to see if the two approaches are related. As the quasi-Einstein metrics of these approaches include conformally Einstein metrics, the bases of Einstein warped products, and gradient Ricci solitons, finding a relation between them might also allow us to find interesting connections between these metrics.In this talk, I will introduce what I call conformally warped manifolds'' as a way to unite the approaches of Lott-Villani-Sturm and Chang-Gursky-Yang. I will discuss three results which suggest that this notion is indeed the best'' approach. First, I will discuss the variational problem associated to quasi-Einstein metrics, which naturally relates the Yamabe constant to Perelman's shrinker entropy. Second, I will discuss a Liouville-type theorem which illustrates the usefulness of studying the limit $m\to\infty$ as a way to overcome difficulties in the $m=\infty$ comparison theory. Third, I will discuss a compactness theorem for compact quasi-Einstein metrics analogous to Anderson's theorem for Einstein metrics, which is independent of the parameter $m$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9019294381141663, "perplexity": 393.9161936492767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948517181.32/warc/CC-MAIN-20171212134318-20171212154318-00564.warc.gz"}
https://aviation.stackexchange.com/questions/45904/how-are-cd-and-cl-calculated-from-cp-data?noredirect=1	# How are Cd and Cl calculated from Cp data? Given pressure coefficient data for corresponding x/c (position along chord) values on a wing, I am looking to calculate coefficients of drag and lift. Here's what I have: b, MAC, S, sweep angles at LE & c/4, and Cp vs. x/c data for 6 different stations (span position given). Angle of attack is 0 degrees. I understand that to calculate Cl, I can numerically integrate Cp with respect to x/c from 0 to 1. (ignoring skin friction [which, I know, is not best practice]) To calculate Cd (again ignoring skin friction), I believe I need to perform the same integration but with the Cp values being first multiplied by dz/dx inside the integrand, where z corresponds with the airfoil thickness. My problem is that I do not have any information on the airfoil thickness. Any thoughts on approaching this? Is this problem possible? If it matters, I'm sourcing my equations from Anderson's Fundamentals of Flight, Ch. 1. Without the local inclination of the airfoil surface you will not be able to achieve exact results for drag. You need to integrate just the component orthogonal to the flow direction at infinity for the lift coefficient (because it is defined that way) and parallel to that direction for the pressure part of the drag coefficient. While it is OK to neglect friction for lift, it does contribute about half of total drag when the flow is attached, so it should not be neglected for calculating total drag. To illustrate how important the local inclination is, here the c$_{\text p}$ plot of the Eppler 502 at a moderate angle of attack (3°): And now the same thing, plotted with vectors. Arrows pointing away from the surface denote suction and vice versa. Since the c$_{\text p}$ plot should use the projected length along the X-axis, this inclination effect is already considered when you integrate the pressure coefficient over chord. Treat chord length as a dimensionless number that runs from 0 to 1. Since the angle of attack is 0°, you need no other correction and the net surface under the c$_{\text p}$ plot is your lift coefficient. Use the results at the six known span positions and interpolate between them. In principle, the same applies to the drag coefficient, but now you would need a plot which projects the pressure coefficient on a coordinate which runs orthogonal to the flow direction. In inviscid flow, the pressure differences equal out, so it is only the friction-induced changes in the pressure distribution between inviscid and viscous flow which cause drag. My best advice is to find airfoils with the same pressure distribution and use their drag coefficient values. Make sure you know the Reynolds and Mach numbers, because both have a higher effect on drag than on lift. Some quirks in the pressure distribution can give them away, like the location of the laminar separation bubble on the lower side of the c$_{\text p}$ plot above or the magnitude of the stagnation point pressure coefficient. Regarding the relative thickness of the airfoil: The amount of suction on both sides of an airfoil grows with its relative thickness. • Thanks for the detailed answer here, Peter. It sounds like I'm on the right track for getting the approximate lift coefficient, but I may out of luck for Cd unless I can determine the airfoil somehow. I'll have to look into that. I'll add that my AoA=0 comment in my original question was for the sake of simplicity - I actually have data for two separate angles (2 and 4 deg). I'm currently attempting to find the normal and axial force coefficients, then will rotate those w/alpha to find Cd and Cl. Are you aware of any methods to find airfoil shape (or z variation) that could use this data? – user26989 Nov 19 '17 at 21:38 • @user26989: There is free software which allows to reverse-engineer (actually, design) an airfoil from a desired pressure distribution. It is called XFOIL and heavily used by model enthusiasts. I used it years ago to create the images in this answer. – Peter Kämpf Nov 19 '17 at 22:11 • This looks very interesting, thanks for the link (and all the help here!). – user26989 Nov 19 '17 at 22:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8531571626663208, "perplexity": 756.3692318542654}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347413624.48/warc/CC-MAIN-20200531182830-20200531212830-00501.warc.gz"}
https://www.lesswrong.com/users/sniffnoy	# Sniffnoy I'm Harry Altman. I do strange sorts of math. Highly upvoted posts: Underappreciated points about utility functions (of both sorts) Ahh, thanks for clarifying. I think what happened was that your modus ponens was my modus tollens -- so when I think about my preferences, I ask "what conditions do my preferences need to satisfy for me to avoid being exploited or undoing my own work?" whereas you ask something like "if my preferences need to correspond to a bounded utility function, what should they be?" [1] That doesn't seem right. The whole point of what I've been saying is that we can write down some simple conditions that ought to be true in order to avoid being exploitable or otherwise incoherent, and then it follows as a conclusion that they have to correspond to a [bounded] utility function. I'm confused by your claim that you're asking about conditions, when you haven't been talking about conditions, but rather ways of modifying the idea of decision-theoretic utility. Something seems to be backwards here. I agree, one shouldn't conclude anything without a theorem. Personally, I would approach the problem by looking at the infinite wager comparisons discussed earlier and trying to formalize them into additional rationality condition. We'd need • an axiom describing what it means for one infinite wager to be "strictly better" than another. • an axiom describing what kinds of infinite wagers it is rational to be indifferent towards I'm confused here; it sounds like you're just describing, in the VNM framework, the strong continuity requirement, or in Savage's framework, P7? Of course Savage's P7 doesn't directly talk about these things, it just implies them as a consequence. I believe the VNM case is similar although I'm less familiar with that. Then, I would try to find a decisioning-system that satisfies these new conditions as well as the VNM-rationality axioms (where VNM-rationality applies). If such a system exists, these axioms would probably bar it from being represented fully as a utility function. That doesn't make sense. If you add axioms, you'll only be able to conclude more things, not fewer. Such a thing will necessarily be representable by a utility function (that is valid for finite gambles), since we have the VNM theorem; and then additional axioms will just add restrictions. Which is what P7 or strong continuity do! A summary of Savage's foundations for probability and utility. Here's a quick issue I only just noticed but which fortunately is easily fixed: Above I mentioned you probably want to restrict to a sigma-algebra of events and only allow measurable functions as actions. But, what does measurable mean here? Fortunately, the ordering on outcomes (even without utility) makes measurability meaningful. Except this puts a circularity in the setup, because the ordering on outcomes is induced from the ordering on actions. Fortunately this is easily patched. You can start with the assumption of a total preorder on outcomes (considering the case of decisions without uncertainty), to make measurability meaningful and restrict actions to measurable functions (once we start considering decisions under uncertainty); then, for P3, instead of the current P3, you would strengthen the current P3 by saying that (on non-null sets) the induced ordering on outcomes actually matches the original ordering on outcomes. Then this should all be fine. Underappreciated points about utility functions (of both sorts) (This is more properly a followup to my sibling comment, but posting it here so you'll see it.) I already said that I think that thinking in terms of infinitary convex combinations, as you're doing, is the wrong way to go about it; but it took me a bit to put together why that's definitely the wrong way. Specifically, it assumes probability! Fishburn, in the paper you link, assumes probability, which is why he's able to talk about why infinitary convex combinations are or are not allowed (I mean, that and the fact that he's not necessarily arbitrary actions). Savage doesn't assume probability! So if you want to disallow certain actions... how do you specify them? Or if you want to talk about convex combinations of actions -- not just infinitary ones, any ones -- how do you even define these? In Savage's framework, you have to prove that if two actions can be described by the same probabilities and outcomes, then they're equivalent. E.g., suppose action A results in outcome X with probability 1/2 and outcome Y with probability 1/2, and suppose action B meets that same description. Are A and B equivalent? Well, yes, but that requires proof, because maybe A and B take outcome X on different sets of probability 1/2. (OK, in the two-outcome case it doesn't really require "proof", rather it's basically just his definition of probability; but the more general case requires proof.) So, until you've established that theorem, that it's meaningful to combine gambles like that, and that the particular events yielding the probabilities aren't relevant, one can't really meaningfully define convex combinations at all. This makes it pretty hard to incorporate them into the setup or axioms! More generally this should apply not only to Savage's particular formalism, but any formalism that attempts to ground probability as well as utility. Anyway yeah. As I think I already said, I think we should think of this in terms not of, what combinations of actions yield permitted actions, but rather whether there should be forbidden actions at all. (Note btw in the usual VNM setup there aren't any forbidden actions either! Although there infinite gambles are, while not forbidden, just kind of ignored.) But this is in particular why trying to put it it in terms of convex combinations as you've done doesn't really work from a fundamentals point of view, where there is no probability yet, only preferences. Underappreciated points about utility functions (of both sorts) Apologies, but it sounds like you've gotten some things mixed up here? The issue is boundedness of utility functions, not whether they can take on infinity as a value. I don't think anyone here is arguing that utility functions don't need to be finite-valued. All the things you're saying seem to be related to the latter question rather than the former, or you seem to be possibly conflating them? In the second paragraph perhaps this is just an issue of language -- when you say "infinitely high", do you actually mean "aribtrarily high"? -- but in the first paragraph this does not seem to be the case. I'm also not sure you understood the point of my question, so let me make it more explicit. Taking the idea of a utility function and modifying it as you describe is what I called "backwards reasoning" above -- starting from the idea of a utility function, rather than starting from preferences. Why should one believe that modifying the idea of a utility function would result in something that is meaningful about preferences, without any sort of theorem to say that one's preferences must be of this form? Underappreciated points about utility functions (of both sorts) Oh, so that's what you're referring to. Well, if you look at the theorem statements, you'll see that P=P_d is an axiom that is explicitly called out in the theorems where it's assumed; it's not implictly part of Axiom 0 like you asserted, nor is it more generally left implicit at all. but the important part is that last infinite sum: this is where all infinitary convex combinations are asserted to exist. Whether that is assigned to "background setup" or "axioms" does not matter. It has to be present, to allow the construction of St. Petersburg gambles. I really think that thinking in terms of infinitary convex combinations is the wrong way to go about this here. As I said above: You don't get a St. Petersburg gamble by taking some fancy convex combination, you do it by just constructing the function. (Or, in Fishburn's framework, you do it by just constructing the distribution; same effect.) I guess without P=P_d you do end up relying on closure properties in Fishburn's framework, but Savage's framework just doesn't work that way at all; and Fishburn with P=P_d, well, that's not a closure property. Rather what Savage's setup, and P=P_d have in common, is that they're, like, arbitrary-construction properties: If you can make a thing, you can compare it. Underappreciated points about utility functions (of both sorts) Savage does not actually prove bounded utility. Fishburn did this later, as Savage footnotes in the edition I'm looking at, so Fishburn must be tackled. Yes, it was actually Fishburn that did that. Apologies if I carelessly implied it was Savage. IIRC, Fishburn's proof, formulated in Savage's terms, is in Savage's book, at least if you have the second edition. Which I think you must, because otherwise that footnote wouldn't be there at all. But maybe I'm misremembering? I think it has to be though... In Savage's formulation, from P1-P6 he derives Theorem 4 of section 2 of chapter 5 of his book, which is linear interpolation in any interval. I don't have the book in front of me, but I don't recall any discussion of anything that could be called linear interpolation, other than the conclusion that expected utility works for finite gambles. Could you explain what you mean? I also don't see the relevance of intervals here? Having read (and written a summary of) that part of the book I simply don't know what you're talking about. Clearly, linear interpolation does not work on an interval such as [17,Inf], therefore there cannot be any infinitely valuable gambles. St. Petersburg-type gambles are therefore excluded from his formulation. I still don't know what you're talking about here, but I'm familiar enough with Savage's formalism to say that you seem to have gotten quite lost somewhere, because this all sounds like nonsense. From what you're saying, the impression that I'm getting is that you're treating Savage's formalism like Fishburn's, where there's some a-prior set of actions under consideration, and so we need to know closure properties about that set. But, that's not how Savage's formalism works. Rather the way it works is that actions are just functions (possibly with a measurability condition -- he doesn't discuss this but you probably want it) from world-states to outcomes. If you can construct the action as a function, there's no way to exclude it. I shall have to examine further how his construction works, to discern what in Savage's axioms allows the construction, when P1-P6 have already excluded infinitely valuable gambles. Well, I've already described the construction above, but I'll describe it again. Once again though, you're simply wrong about that last part; that last statement is not only incorrect, but fundamentally incompatible with Savage's whole approach. Anyway. To restate the construction of how to make a St. Petersburg gamble. (This time with a little more detail.) An action is simply a function from world-states to outcomes. By assumption, we have a sequence of outcomes a_i such that U(a_i) >= 2^i and such that U(a_i) is strictly increasing. We can use P6 (which allows us to "flip coins", so to speak) to construct events E_i (sets of world-states) with probability 1/2^i. Then, the action G that takes on the value a_i on the set E_i is a St. Petersburg gamble. For the particular construction, you take G as above, and also G', which is the same except that G' takes the value a_1 on E_0, instead of the value a_0. Savage proves in the book (although I think the proof is due to Fishburn? I'm going by memory) that given two gambles, both of which are preferred to any essentially bounded gamble, the agent must be indifferent between them. (The proof uses P7, obviously -- the same thing that proves that expected utility works for infinite gambles at all. I don't recall the actual proof offhand and don't feel like trying to reconstruct it right now, but anyway I think you have it in front of you from the sounds of it.) And we can show both these gambles are preferred to any essentially bounded gamble by comparing to truncated versions of themselves (using sure-thing principle) and using the fact that expected utility works for essentially bounded gambles. Thus the agent must be indifferent between G and G'. But also, by the sure-thing principle (P2 and P3), the agent must prefer G' to G. That's the contradiction. Edit: Earlier version of this comment misstated how the proof goes Underappreciated points about utility functions (of both sorts) Fishburn (op. cit., following Blackwell and Girschick, an inaccessible source) requires that the set of gambles be closed under infinitary convex combinations. Again, I'm simply not seeing this in the paper you linked? As I said above, I simply do not see anything like that outside of section 9, which is irrelevant. Can you point to where you're seeing this condition? I shall take a look at Savage's axioms and see what in them is responsible for the same thing. In the case of Savage, it's not any particular axiom, but rather the setup. An action is a function from world-states to outcomes. If you can construct the function, the action (gamble) exists. That's all there is to it. And the relevant functions are easy enough to construct, as I described above; you use P6 (the Archimedean condition, which also allows flipping coins, basically) to construct the events, and we have the outcomes by assumption. You assign the one to the other and there you go. (If you don't want to go getting the book out, you may want to read the summary of Savage I wrote earlier!) A short answer to this (something longer later) is that an agent need not have preferences between things that it is impossible to encounter. The standard dissolution of the St. Petersberg paradox is that nobody can offer that gamble. Even though each possible outcome is finite, the offerer must be able to cover every possible outcome, requiring that they have infinite resources. Since the gamble cannot be offered, no preferences between that gamble and any other need exist. So, would it be fair to sum this up as "it is not necessary to have preferences between two gambles if one of them takes on unbounded utility values"? Interesting. That doesn't strike me as wholly unworkable, but I'm skeptical. In particular: 1. Can we phrase this without reference to utility functions? It would say a lot more for the possibility if we can. 2. What if you're playing against Nature? A gamble can be any action; and in a world of unbounded utility functions, why should one believe that any action must have some bound on how much utility it can get you? Sure, sure, second law of thermodynamics and all that, but that's just a feature of the paticular universe we happen to live in, not something that reshapes your preferences. (And if we were taking account of that sort of thing, we'd probably just say, oh, utility is bounded after all, in a kind of stupid way.) Notionally, it could be discovered to be wrong! It won't happen, but it's not probability literally 0. Or are you trying to cut out a more limited class of gambles as impossible? I'm not clear on this, although I'm not certain it affects the results. Anyway, yeah, as I said, my main objection is that I see no reason to believe that, if you have an unbounded utility function, Nature cannot offer you a St. Petersburg game. Or I mean, to the extent I do see reasons to believe that, they're facts about the particular universe we happen to live in, that notionally could be discovered to be wrong. Looking at the argument from the other end, at what point in valuing numbers of intelligent lives does one approach an asymptote, bearing in mind the possibility of expansion to the accessible universe? What if we discover that the habitable universe is vastly larger than we currently believe? How would one discover the limits, if there are any, to one's valuing? This is exactly the sort of argument that I called "flimsy" above. My answer to these questions is that none of this is relevant. Both of us are trying to extend our ideas about preferences from ordinary situations to extraordinary ones. (Like, I agree that some sort of total utilitarianism is a good heuristic for value under the conditions we're familiar with.) This sort of extrapolation, to an unfamiliar realm, is always potentially dangerous. The question then becomes, what sort of tools can we expect to continue to work, without needing any sort of adjustment to the new conditions? I do not expect speculation about the particular form preferences our would take under these unusual conditions to be trustworthy. Whereas basic coherence conditions had damn well better continue to hold, or else we're barely even talking about sensible preferences anymore. Or, to put it differently, my answer is, I don't know, but the answer must satisfy basic coherence conditions. There's simply no way that the idea that decision-theoretic utility has to increase linearly with number intelligent lives, is on anywhere near as solid ground as that! The mere fact that it's stated in terms of a utility function in the first place, rather than in terms of something more basic, is something of a smell. Complicated statements we're not even entirely sure how to formulate can easily break in a new context. Short simple statements that have to be true for reasons of simple coherence don't break. (Also, some of your questions don't seem to actually appreciating what a bounded utility function would actually mean. It wouldn't mean taking an unbounded utility function and then applying a cap to it. It would just mean something that naturally approaches 1 as things get better and 0 as things get worse. There is no point at which it approaches an asymptote; that's not how asymptotes work. There is no limit to one's valuing; presumably utility 1 does not actually occur. Or, at least, that's how I infer it would have to work.) Underappreciated points about utility functions (of both sorts) Huh. This would need some elaboration, but this is definitely the most plausible way around the problem I've seen. Now (in Savage's formalism) actions are just functions from world-states to outcomes (maybe with a measurability condition), so regardless of your prior it's easy to construct the relevant St. Petersburg gambles if the utility function is unbounded. But seems like what you're saying is, if we don't allow arbitrary actions, then the prior could be such that, not only are none of the permitted actions St. Petersburg gambles, but also this remains the case even after future updates. Interesting! Yeah, that just might be workable... Underappreciated points about utility functions (of both sorts) OK, so going by that you're suggesting, like, introducing varying caps and then taking limits as the cap goes to infinity? It's an interesting idea, but I don't see why one would expect it to have anything to do with preferences. Underappreciated points about utility functions (of both sorts) You should check out Abram's post on complete class theorems. He specifically addresses some of the concerns you mentioned in the comments of Yudkowsky's posts. So, it looks to me like what Abrams is doing -- once he gets past the original complete class theorem -- is basically just inventing some new formalism along the lines of Savage. I think it is very misleading to refer to this as "the complete class theorem" -- how on earth was I supposed to know that this was what was being referred to when "the complete class theorem" was mentioned, when it resembles the original theorem so little (and it's the original theorem that was linked to)? -- and I don't see why it was necessary to invent this anew, but sure, I can accept that it presumably works, even if the details aren't spelled out. But I must note that he starts out by saying that he's only considering the case when there's only a finite set of states of the world! I realize you weren't making a point about bounded utility here; but from that point of view, it is quite significant... Also, my inner model of Jaynes says that the right way to handle infinities is not to outlaw them, but to be explicit and consistent about what limits we're taking. I don't really understand what that means in this context. It is already quite explicit what limits we're taking: Given an action (a measurable function from states of the world to outcomes), take its expected utility, with regard to the [finitely-additive] probability on states of the world. (Which is implicitly a limit of sorts.) I think this is another one of those comments that makes sense if you're reasoning backward, starting from utility functions, but not if you're reasoning forward, from preferences. If you look at things from a utility-functions-first point of view, then it looks like you're outlawing infinities (well, unboundedness that leads to infinities). But from a preferences-first point of view, you're not outlawing anything. You haven't outlawed unbounded utility functions, rather they've just failed to satisfy fundamental assumptions about decision-making (remember, if you don't have P7 your utility function is not guaranteed to return correct results about infinite gambles at all!) and so clearly do not reflect your idealized preferences. You didn't get rid of the infinity, it was simply never there in the first place; the idea that it might have been turned out to be mistaken.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8680054545402527, "perplexity": 690.8157846938848}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251687958.71/warc/CC-MAIN-20200126074227-20200126104227-00480.warc.gz"}
http://mathhelpforum.com/calculus/38944-integral.html	# Math Help - Integral 1. ## Integral Will someone check my work....I think this is right $\int_0^{\infty}e^{-a^2x^2}dx,\forall{a}>0$ First $Let\text{ }u=a^2x^2\Rightarrow{dx=\frac{1}{2a\sqrt{u}}}$ and $u(0)=a^2\cdot{0^2}=0$ and $u(\infty)=a^2\cdot{\infty}=\infty$ So this would be $\frac{1}{2a}\int_0^{\infty}\frac{e^{-u}}{\sqrt{u}}du=\frac{1}{2a}\int_0^{\infty}u^{\fra c{-1}{2}}e^{-u}du=\frac{\Gamma\bigg(\frac{1}{2}\bigg)}{2a}=\fra c{\sqrt{\pi}}{2a}$ This doesnt seem right...I mean I think I did my calculations right but this was in a very simple book and this seems uncharcteristic of such a book .... Could someone verify? 2. Originally Posted by Mathstud28 Will someone check my work....I think this is right $\int_0^{\infty}e^{-a^2x^2}dx,\forall{a}>0$ First $Let\text{ }u=a^2x^2\Rightarrow{dx=\frac{1}{2a\sqrt{u}}}$ and $u(0)=a^2\cdot{0^2}=0$ and $u(\infty)=a^2\cdot{\infty}=\infty$ So this would be $\frac{1}{2a}\int_0^{\infty}\frac{e^{-u}}{\sqrt{u}}du=\frac{1}{2a}\int_0^{\infty}u^{\fra c{-1}{2}}e^{-u}du=\frac{\Gamma\bigg(\frac{1}{2}\bigg)}{2a}=\fra c{\sqrt{\pi}}{2a}$ This doesnt seem right...I mean I think I did my calculations right but this was in a very simple book and this seems uncharcteristic of such a book .... Could someone verify? $\int_{0}^{\infty}e^{-a^2x^2}\,dx \ \forall \ a>0$ $let \ u=a^2x^2 \implies du=2a^2x\,dx\implies dx=\frac{du}{2a^2\sqrt{\frac{u}{a^2}}}\implies dx=\frac{du}{2a\sqrt{u}}$ $u(0)=0 \ and \ u(\infty)=\infty$. $\therefore \frac{1}{2a}\int_{0}^{\infty}e^{-u}u^{-\frac{1}{2}}\,du=\frac{\Gamma\left(\frac{1}{2}\rig ht)}{2a}=\frac{\sqrt{\pi}}{2a}$. I get what you get. 3. Originally Posted by Chris L T521 $\int_{0}^{\infty}e^{-a^2x^2}\,dx \ \forall \ a>0$ $let \ u=a^2x^2 \implies du=2a^2x\,dx\implies dx=\frac{du}{2a^2\sqrt{\frac{u}{a^2}}}\implies dx=\frac{du}{2a\sqrt{u}}$ $u(0)=0 \ and \ u(\infty)=\infty$. $\therefore \frac{1}{2a}\int_{0}^{\infty}e^{-u}u^{-\frac{1}{2}}\,du=\frac{\Gamma\left(\frac{1}{2}\rig ht)}{2a}=\frac{\sqrt{\pi}}{2a}$... I get what you get. I didnt think this was right because this was juxtaposed beside this integral $\int_2^3\frac{dx}{1-\cos(x)}$ So I was like...hmm	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9865663051605225, "perplexity": 2616.565747428336}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507448896.34/warc/CC-MAIN-20141017005728-00114-ip-10-16-133-185.ec2.internal.warc.gz"}
http://mathhelpforum.com/advanced-statistics/67566-n-random-points-circle.html	# Math Help - N random points in a circle 1. ## N random points in a circle How can I calculate the minimum distance from the center to N points uniformly distributed in a circle? In other words, I want to find the distance to the closest point from the center. Does this distance decrease with N? 2. Originally Posted by hpinvent How can I calculate the minimum distance from the center to N points uniformly distributed in a circle? In other words, I want to find the distance to the closest point from the center. Does this distance decrease with N? The distance from the center to random points inside a disk is of course random, so that your question doesn't quite make sense... You can compute its distribution, or its mean for instance. As for the decrease, it is obvious that the minimum distance from the center to $N$ points decreases with $N$. Just give it a thought. I show you how to find the distribution of the minimum distance from the center to $N$ points uniformly chosen in a disk. First thing is to consider only one point $X$ uniformly distributed in a disk. I will consider a disk $D$ with center $O$ and radius $r$. Let $R=OX$ (i.e. $R$ is the distance from $O$ to $X$). For $t>r$, we have of course $P(R, and if $0 then $P(R (because $R means that $X$ is inside the circle with radius $t$, and the probability to be in a subset of the disk is proportional to its area). Using this computation, you can get the density of the distribution of $R$ (by differentiating, it is $\frac{2t}{r^2}$ on $[0,r]$ and 0 elsewhere), and the expectation of $R$. Now, suppose there are $N$ independent points uniformly chosen on the same disk, and let $d$ be the minimum distance from the center to the points, i.e. $d=\min(R_1,\ldots,R_N)$ where $R_1,\ldots,R_N$ are defined like the previous $R$, for each of the points. Then we have $P(d>t)=P(R_1>t,\ R_2>t,\ldots,\ R_N>t)=P(R>t)^N=\left(1-\frac{t^2}{r^2}\right)^N$, from which we can get the density of the distribution of $d$ : it is $\frac{2Nt}{r^2}\left(1-\frac{t^2}{r^2}\right)^{N-1}$ on $[0,r]$. 3. Can I say the distribution (pdf) of the maximum distance from the center to points uniformly chosen in a disk same as on ??. Also since the area of a sector is (1/2)r^2theta, the same distribution applies for N points uniformly chosen in a sector ?. Your thoughts. Thanks Arvind 4. Sorry, my question was if N points are uniformly distributed in a sector of area $1/2{r}^2\theta$, can i then write the pdf as $p(d>t) = \frac{Nt\theta}{\pi r^2}\left(1-\frac{\theta t^2}{2\pi r^2}\right)^{N-1}$ on [0,r]. Can I compute the expected value of d from the pdf by integrating over the area of sector ?(varying t from 0 to r and theta from 0 to thetamax - say pi/2). Also it doesn't matter (or does it ?) if d is minimum or maximum of R1, R2....RN ?. Please let me know. 5. Originally Posted by arvind Sorry, my question was if N points are uniformly distributed in a sector of area $1/2{r}^2\theta$, can i then write the pdf as $p(d>t) = \frac{Nt\theta}{\pi r^2}\left(1-\frac{\theta t^2}{2\pi r^2}\right)^{N-1}$ on [0,r]. Can I compute the expected value of d from the pdf by integrating over the area of sector ?(varying t from 0 to r and theta from 0 to thetamax - say pi/2). Also it doesn't matter (or does it ?) if d is minimum or maximum of R1, R2....RN ?. Please let me know. Of course it does matter if $d$ is the min or the max! The min is small, it obviously tends to 0, while the max is big, it tends to $r$ when $N\to\infty$... But you can find the distribution of the max using the same procedure as I did for the min: $P(d^, and deduce the expected value using for instance $E[d^]=\int_0^r P(d^*>t) dt$. Since the distribution of the points is rotation-invariant, this property is the same for any sector of radius $r$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 41, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9816853404045105, "perplexity": 175.49663298814747}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500830721.40/warc/CC-MAIN-20140820021350-00155-ip-10-180-136-8.ec2.internal.warc.gz"}
https://mathoverflow.net/questions/138287/maximize-weighted-vertex-sequence-subject-to-neighbour-inclusion	# Maximize weighted vertex sequence subject to neighbour inclusion Let $G=(V,E)$ be a simple undirected graph on $n$ nodes, with node weights $W = [w_1,w_2,\dots,w_n] \in \mathbb{R}^n$. Define the weight for a sequence of nodes $v_1,v_2,\dots,v_k$ by the average $\frac{1}{k}\sum_{i=1}^k w_i$. Given $k$, find the tightest possible upper bound on the maximum average weight. Consecutive vertices in the sequence are not constrained to be connected by an edge, and the vertices in the sequence do not have to be distinct. Instead, the sequence is required to satisfy the following property: • A vertex $v_i$ can only be appended to the end of the sequence if at least one of its neighbours has been added since the last occurence of $v_i$ (with the exception that a vertex that has never occurred in the sequence can be added at any time). • I take it from your final sentence that the $k$ vertices need not be distinct? And in your average formula, do you want $w_i$ in the summand rather than $v_i$? – Vidit Nanda Aug 1 '13 at 3:05 • Good point, question updated! – Mark Schmidt Aug 1 '13 at 4:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9298020601272583, "perplexity": 227.36397675136206}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627997508.21/warc/CC-MAIN-20190616002634-20190616024634-00111.warc.gz"}
http://mathhelpforum.com/advanced-algebra/171929-group-theory.html	1. ## Group theory Prove that $<\mathbb Q, +>$ group has no finite set of generators. Any help would be appreciated! 2. For the ease of notation, suppose there are two generators, $m_1/n_1, m_2/n_2$. Let $p$ be a prime such that $\gcd(n_1, n_2,p)=1$. Is it possible to write $1/p$ as a combination of $m_1/n_1, m_2/n_2$? You can generalize this argument for any supposed number of generators.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.952315092086792, "perplexity": 147.39040476210985}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164456039/warc/CC-MAIN-20131204134056-00051-ip-10-33-133-15.ec2.internal.warc.gz"}
https://kyushu-u.pure.elsevier.com/en/publications/friction-coefficient-of-well-defined-hydrogel-networks	# Friction Coefficient of Well-Defined Hydrogel Networks Midori Fujiki, Masaya Ito, Kell Mortensen, Shintaro Yashima, Masayuki Tokita, Masahiko Annaka Research output: Contribution to journalArticlepeer-review 17 Citations (Scopus) ## Abstract The friction coefficient between Tetronic gel and water is measured as a function of the polymer concentration of the gel and the temperature by a simply designed apparatus. Tetronic gel was prepared by cross-linking Tetronic macromonomers through activated ester chemistry. The gel is expected to have homogeneous network structure. The polymer concentration Cp dependence of the friction coefficient f is well expressed by a power law relationship f ∼ Cpν with the exponent of ν = 1.5, which is in a good agreement with the prediction of the scaling theory. The friction coefficient normalized by viscosity of water, f(T)/η(T), increases with temperature. When the network is homogeneous, the mesh size is given by the average distance between the nearest polymer-polymer contacts. Therefore, the increase in the ratio f(T)/η(T) with temperature attributed to the decrease in the average mesh size of the network due to the dehydration of the chains at higher temperature. The friction coefficient for randomly cross-linked Tetronic gel prepared by enzyme-mediated cross-linking reaction of tyrosin-modified Tetronic is compared with that of the homogeneous Tetronic gel. The friction coefficient for the randomly cross-linked gel is about an order of magnitude smaller than that for homogeneous gel. It suggests that the friction coefficient is mainly governed by the spatial inhomogeneity frozen in the gel rather than the average cross-linking density of the gel. Original language English 634-642 9 Macromolecules 49 2 https://doi.org/10.1021/acs.macromol.5b01997 Published - Jan 26 2016 ## All Science Journal Classification (ASJC) codes • Organic Chemistry • Polymers and Plastics • Inorganic Chemistry • Materials Chemistry ## Fingerprint Dive into the research topics of 'Friction Coefficient of Well-Defined Hydrogel Networks'. Together they form a unique fingerprint.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9334457516670227, "perplexity": 3648.4988005848695}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570767.11/warc/CC-MAIN-20220808061828-20220808091828-00328.warc.gz"}
https://arxiv.org/abs/1408.6389	astro-ph.HE # Title:Some Aspects of Strange Matter in Astrophysics Abstract: The present work is connected with the investigation of the origin and properties of compact astrophysical objects endowed with strangeness, with the objective of finding out their relevance in the formation and evolution of the universe. In the first part of the thesis, Chap.~1-3, we discuss a model, proposed by us, to describe the propagation of small lumps of Strange Quark Matter (SQM) or strangelets, through the Terrestrial atmosphere. The theoretical results were found to be well correlated with exotic cosmic ray events characterized by very low charge to mass ratio. In the next part, we have investigated the other end of the mass spectrum of SQM. In Chap 5, we have developed an analytical expression for the Chandrasekhar Limit of Strange Quark Stars. The limit is found to depend on the fundamental constants (including the bag constant). In the last chapter we have endeavored to show that the quark nuggets, surviving the quark-hadron phase transition in the millisecond era of the early Universe can provide the required closure density and can merge to form compact quark matter objects, whose maximum mass would be governed by the formulation laid out in the preceding chapter. We have also found that these Cold Dark Matter objects can explain the recent astronomical observations of MACHOS by gravitational micro-lensing techniques in the Large Magellanic clouds in the Halo of our Galaxy. Comments: Ph. D Thesis, Awarded by Jadavpur University, Calcutta, done under the supervision of Prof. Sibaji Raha, Bose Institute, Kolkata Subjects: High Energy Astrophysical Phenomena (astro-ph.HE) Cite as: arXiv:1408.6389 [astro-ph.HE] (or arXiv:1408.6389v1 [astro-ph.HE] for this version) ## Submission history From: Shibaji Banerjee [view email] [v1] Wed, 27 Aug 2014 11:56:04 UTC (1,084 KB)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8243921995162964, "perplexity": 1186.6532751632014}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027331228.13/warc/CC-MAIN-20190826064622-20190826090622-00447.warc.gz"}
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http://afterschoolhelp.com/pages/topics/topic-list.aspx?ConceptID=37	Forms of Rational Numbers ### Overview This chapter introduces rational numbers and their relation to ratios, rates, proportions, decimals, and percents. Scale drawings are introduced as an application. The chapter concludes with three different types of percent problems. ### What you can expect to learn After completing these activities you should be able to 1. Simplify rational expressions. 2. Write ratios and unit rates. 3. Determine whether two ratios form a proportion, and be able to solve for a missing term of a proportion. 4. Find measurements in scale drawings and, given the measurements, be able to find the scale. 5. Convert between rational numbers and decimal numbers. 6. Convert between percents and decimal numbers, and between percents and fractions or mixed numbers. 7. Find the percent of a number. 8. Find what percent one number is of another number. 9. Solve for the whole when given the percent and the part. Activity List	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8104455471038818, "perplexity": 2434.744901414336}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592579.77/warc/CC-MAIN-20180721125703-20180721145703-00437.warc.gz"}
http://math.stackexchange.com/questions/253168/how-to-prove-that-the-number-of-solutions-of-x2-equiv-a-pmodp-is-0-or-2	# How to prove that the number of solutions of $x^2 \equiv a \pmod{p}$ is 0 or 2? I want to prove that the equation $x^2 \equiv a \pmod{p}$ either doesn't have or has 2 solutions. (p is odd prime , a is integer , a $\ne pk$ ) - If $y$ is a solution of $x^2\equiv a\pmod p\implies y^2\equiv a\pmod p\implies (-y)^2\equiv a\pmod p\implies -y$ is also a solution. Let $z$ be another solution, so $z^2\equiv a\pmod p\equiv y^2\pmod p$ $\implies p\mid (z+y)(z-y)\implies z\equiv \pm y\pmod p$ So if there is a solution, there will be exactly one more. For the existence of solution for $p\ge 3$, we can try in the following way: if $g$ is a primitive root of $p,$ taking discrete logarithm with respect to $g$ on $x^2\equiv a\pmod p$ we get, $2 ind_gx\equiv ind_ga\pmod{p-1}$ as $\phi(p)=p-1$ As $p-1$ is even and $ind_gx$ must be some integer $\in[0,p-1],$ $ind_gx\equiv \frac{ind_ga}2\pmod{\frac{p-1}2}\implies ind_ga$ must be even to admit any solution. For example, if $a\equiv-1\pmod p, ind_ga=\frac{p-1}2 \implies 4\mid (p-1)$ - can you show me how to i prove that $x^2 \equiv a$ hasn't solution? – World Dec 7 '12 at 17:45 @World, please find the edited answer. – lab bhattacharjee Dec 7 '12 at 18:01 when we haven't solution? I don't understand. – World Dec 7 '12 at 18:18 @World, we need to identify a primitive root$g$ of $p$, the previous always exists for a prime, then find the index of $a$ with respect to $g\pmod p,$ which must be even to admit any solution. – lab bhattacharjee Dec 7 '12 at 18:22 1. If there is solution, then there is a second (different). Observe that $$(p-x)^2 = x^2 - 2px + p^2,$$ so $$(p-x)^2 = x^2 \pmod p.$$ Now assume that $x = p-x$, then $p = 2x$ and $p$ would be even (contradiction), so $x \neq p-x$. 2. There are at most two different solutions modulo $p$. Let $x^2 = a \pmod p$ and $y^2 = a \pmod p$ then $$x^2 - y^2 = 0 \pmod p,$$ $$(x+y)(x-y) = 0 \pmod p,$$ that is $y = x \pmod p$ or $y = -x \pmod p$. 3. This means that there may be more solutions like $x+p, x+2p, \ldots$, but at most two modulo $p$. Cheers! - Thanks. what is mean $p-x \ne x$ .can you explain more about this. – World Dec 7 '12 at 17:51 We proved that there is possibly a second solution. The problem is, what if the two solutions $x$ and $p-x$ coincide, i.e. $x = p-x$ (we would have only one solution then)? However, this would imply that $p$ is even and contradict the assumption that $p$ is odd, therefore it is impossible that $x = p - x$ and therefore $x \neq p - x$. Also, $a \neq 0 \pmod p$, so $x$ does not divide $p$ and therefore we have at least two different solutions. – dtldarek Dec 7 '12 at 18:22 $$x^2=a\pmod p\Longleftrightarrow (-x)^2=a\pmod p$$ and since $\,p\,$ is an odd prime, $\,x\neq -x\,$ whenever $\,x\neq 0\,$ - When you are working mod $p$, you are actually working in the field $\mathbb{Z}/p\mathbb{Z} = \mathbb{F}_p$. So, your statement translates to whether a polynomial of degree $2$ has roots in $\mathbb{F}_p$ (which is not guaranteed because $\mathbb{F}_p$ is not algebraically closed), and if it does have a root, how many roots can it have in total (namely $2$, because any quadratic polynomial has at most $2$ roots in any field, and if one root of a quadratic polynomial is in the field, the other root must also be in the field). - Suppose that $a$ is not divisible by the odd prime $p$. We show that if the congruence $x^2\equiv a$ has a solution, then it has exactly two. As shown by DonAntonio and Pambos, if there is a solution then there are at least two. We show that there are no more than two. Suppose that $r^2\equiv a\pmod{p}$. Then if $x^2\equiv a\pmod{p}$, we have $x^2\equiv r^2\pmod{p}$. It follows that $p$ divides $x^2-r^2$, that is, $p$ divides $(x-r)(x+r)$. But since $p$ is prime, it follows that $p$ divides $x-r$ or $p$ divides $x+r$. That says that $x\equiv r\pmod{p}$ or $x\equiv -r\pmod{p}$. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9688137173652649, "perplexity": 103.06795526999076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398463315.2/warc/CC-MAIN-20151124205423-00011-ip-10-71-132-137.ec2.internal.warc.gz"}
https://www.universetoday.com/87354/astronomy-without-a-telescope-granularity/	# Astronomy Without A Telescope – Granularity [/caption] The very small wavelength of gamma ray light offers the potential to gain high resolution data about very fine detail – perhaps even detail about the quantum substructure of a vacuum – or in other words, the granularity of empty space. Quantum physics suggests that a vacuum is anything but empty, with virtual particles regularly popping in and out of existence within Planck instants of time. The proposed particle nature of gravity also requires graviton particles to mediate gravitational interactions. So, to support a theory of quantum gravity we should expect to find evidence of a degree of granularity in the substructure of space-time. There is a lot of current interest in finding evidence of Lorentz invariance violations – where Lorentz invariance is a fundamental principle of relativity theory – and (amongst other things) requires that the speed of light in a vacuum should always be constant. Light is slowed when it passes through materials that have a refractive index – like glass or water. However, we don’t expect such properties to be exhibited by a vacuum – except, according to quantum theory, at exceedingly tiny Planck units of scale. So theoretically, we might expect a light source that broadcasts across all wavelengths – that is, all energy levels – to have the very high energy, very short wavelength portion of its spectrum affected by the vacuum substructure – while the rest of its spectrum isn’t so affected. There are at least philosophical problems with assigning a structural composition to the vacuum of space, since it then becomes a background reference frame – similar to the hypothetical luminiferous ether which Einstein dismissed the need for by establishing general relativity. Nonetheless, theorists hope to unify the current schism between large scale general relativity and small scale quantum physics by establishing an evidence-based theory of quantum gravity. It may be that small scale Lorentz invariance violations will be found to exist, but that such violations will become irrelevant at large scales – perhaps as a result of quantum decoherence. Quantum decoherence might permit the large scale universe to remain consistent with general relativity, but still be explainable by a unifying quantum gravity theory. On 19 December 2004, the space-based INTEGRAL gamma ray observatory detected Gamma Ray Burst GRB 041219A, one of the brightest such bursts on record. The radiative output of the gamma ray burst showed indications of polarisation – and we can be confident that any quantum level effects were emphasised by the fact that the burst occurred in a different galaxy and the light from it has travelled through more than 300 million light years of vacuum to reach us. Whatever extent of polarisation that can be attributed to the substructure of the vacuum, would only be visible in the gamma ray portion of the light spectrum – and it was found that the difference between polarisation of the gamma ray wavelengths and the rest of the spectrum was… well, undetectable. The authors of a recent paper on the INTEGRAL data claim it achieved resolution down to Planck scales, being 10-35 metres. Indeed, INTEGRAL’s observations constrain the possibility of any quantum granularity down to a level of 10-48 metres or smaller. Elvis might not have left the building, but the authors claim that this finding should have a major impact on current theoretical options for a quantum gravity theory – sending quite a few theorists back to the drawing board. Further reading: Laurent et al. Constraints on Lorentz Invariance Violation using INTEGRAL/IBIS observations of GRB041219A. ESA media release ## 48 Replies to “Astronomy Without A Telescope – Granularity” 1. IVAN3MAN_AT_LARGE says: At the ninth paragraph, there’s a missing preposition “of” in the second line: “… Gamma Ray Burst GRB 041219A, one [of] the brightest such bursts on record.” 1. Steve_Nerlich says: Check – thanks 2. Anonymous says: What does your statement have to do with anything on this forum? NOBODY CARES. People post from their phones and dont have time to make everything perfect, dont you get it? Once again, Ivan3man, what a douche. 1. IVAN3MAN_AT_LARGE says: I know the difference between formal and informal writing; therefore, I do not nitpick on any person’s comments! 2. Anonymous says: Steve, Bravo on the statement “There are at least philosophical problems with assigning a structural composition to the vacuum of space, since it then becomes a background reference frame – similar to the hypothetical luminiferous ether which Einstein dismissed the need for by establishing general relativity.” This is exactly the problem we face with this problem. This ended up being a bit long, with parts pieced in from other communications. However, this result and the results from the FERMI spaceraft 2-1/2 years ago are extremely important. I was wondering it this topic would make its way here. This subject has consumed a lot of discussion time on my part this past couple of weeks. In part I have worked for over 20 years on an idea that quantum mechanics and general relativity are on the level of category theory of mathematics the same thing. They are equivalent, but have an appearance according to a type of projection on varieties that makes them appear different. Everything is now up for “grabs.” A lot of theory is now probably worth little more than paper for recycling. There is no information pertaining to such vacuum physics: It does not exist. This has to be taken seriously, and the implications are troublesome for many in the theoretical world. These data are the Michelson-Morely experimental results of our age. Physics contains thousands of people out there, many with decent positions at universities, who have worked up theories that are now little more than crap. We seem to have a problem with this matter of the “vacuum.” A quantum vacuum is computed with the ZPE and this has generated lots of attention. Supersymmetry eliminates the vacuum in an interesting way with a graded Lie algebra which assigns to each fermion and boson a corresponding boson and fermion partner respectively. In the unbroken phase SUSY then cancels out the negative fermion vacuum with a positive boson vacuum. There was always something attractive about this, for it appeared to be a fundamental way of eliminating the vacuum physics. However, if you break supersymmetry the vacuum energy is increased and you have a vacuum of positive energy, including with SUGRA. However, we have no experimental evidence for this vacuum. In 2008 the results of the Fermi spacecraft were released. The time of arrival for gamma-rays and radio waves was the same over a distance of 10 billion light years. It was back then that I began having lots of doubts about these fluctuation ideas with the metric. 10 billion light years is 10^{27}cm. A change in the speed of light would mean that quantum fluctuations of the metric introduce a dispersion, which acts as a sort of mass. The wave equation for radiation is then Proca like ?^a?_aA – m^2A = 0, which translates to a dispersion term in a Green’s function 1/(k^2 – m^2). The metric fluctuations which induce this are ?L/L ~ L_p/L ~ 10^{-33}/10^{-4} ~= 10^{-29}, or a fluctuation induced mass of 10^{-29}M_p ~ 1ev. The dispersion induced mass is a k + ?k, and the area probed is then ?x =1/?k ~ 10^2L_p. However, the time of arrival had no spread, and so the fluctuation scale probed is close to the Planck length. So these results have to be taken into account as well Y. Jack Ng’s holgraphic fluctation results also are in question as well. This predicts ?L =L_p(L/L_p)^{1/3} and the numbers predicted are 10^{-33}cm(10^{60})^{1/3} = 10^{-13}, and clearly no fluctuations on that scale were found. The problem as I have seen over the last couple of years, in particular since FERMI gave similar results, is we are over counting the number of degrees of freedom (DoF) in the universe. The quantum vacuum has become sort of the aether space of our modern age. We may remember back then that it was presumed there was a “fluid” which inhabited space that was the medium electromagnetic radiation propagated on. There was then an implicit degree of freedom density, if we think of this fluid as made of particles of some type. None of this worked, and in the end the solution came down to 6 parameters of a symmetry group called the Lorentz group: 3 for rotations and 3 for boosts. None of this aether nonsense was needed. We are facing a similar shift in our perspectives on physics. Huge vacuum energies, with lots of modes and DoF, must be replaced by some simpler principle. Remember that the inflationary vacuum is enormous, up to 10^{110} times the current value estimated based on the small cosmological constant, and we still have this problem of 123 orders of magnitude with vacuum physics. The correspondence (worked by Duff, Dahanyake, Borsten, Rubens) between SLOCC groups for 3-partite entanglements and the STU moduli for 1/2-1/4-1/8 supersymmetric BPS black holes and between 4-partite entanglements and extremal black holes appears to suggest some element of this path. The actual spacetime physics is completely classical. The spacetime physics has underlying quantum physics, but this is not entirely known as yet. The standard 3-partite entanglement group decomposes into C^3/SL(2,C)^3, which has an STU spacetime moduli equivalency in R^3/SL(2,R)^3. The spacetime physics that is classical indicates a Copenhagen-like correspondence, and I think that underlying quantum physics for gravity involves SL(2,H) symmetries, where H is the quaterions. Quaternions are pairs of complex numbers, which is a dual system of observables associated with the entanglement group with SL(2,C). The direct measurement of these observables involves the classical realization, which is what we call spacetime physics. What this duality is exactly is tough to ferret out, but I think this involves a duality with respect to the Borel group representation of the AdS completion with discrete symmetries. These Borel groups define both the Heisenberg group and the parabolic group for null geodesics congruencies — lightcones, horizons etc. The AdS_n in a near horizon condition decomposes into AdS_2xS^{n-2}, and the AdS_2 has an interesting duality between soliton physics and fermion condensate physics. It may in the end by that the number of degrees of freedom in the universe is then reduced to a very small number for low dimensional spaces. The approach by Duff et al and these results with borel subgroups I am working on are aspect of how quantum mechanics and gravitation are categorically equivalent. If this is the case, then what we expect to come from LC 1. IVAN3MAN_AT_LARGE says: In 2008 the results of the Fermi spacecraft were released. The time of arrival for gamma-rays and radio waves was the same over a distance of 10 billion light years. Actually, that was on May 10, 2009, when Fermi’s LAT detected from a 2.1-second gamma-ray burst – designated GRB 090510 – two gamma-ray photons, possessing energies differing by a million times, which arrived just nine-tenths of a second apart after travelling 7.3 billion light-years. Universe Today featured an article, “Einstein Still Rules, Says Fermi Telescope Team“, on that subject, back in October 28, 2009. 1. Anonymous says: Indeed so, I had the year off by one. LC 1. Anonymous says: There are connections between graphene and the M2-brane, or at least there are similar properties. The AdS_4 spacetime which contains a black hole is perturbed near the horizon of the black hole into AdS_2xS^2. The AdS_2 has hyperbolic dynamics, which when perturbed by a Higg’s like field becomes a soliton. Zamalodchikov demonstrated how this is isomorphic to a fermion theory with a quartic potential. It is similar to superconductivity. The graininess might be removed, but this needs to sit in an E_8 group theory. The 8 dimensional space may be tessellated by the Gossett polytope of the E_8 roots. One of the curious things about E_8 is that the space of roots is isomorphic to the algebra, which has a continuous structure. In this case the mass spectra on the 2 dimensional space is the (8,1) of the E_8 in the Zamalodchikov s = 1/2 conformal theory. LC 3. Anonymous says: I’m fascinated by the way you are comparing this problem to the problem of the electromagnetic medium. The realizations that dispelled the problematic need for the ether were radical to the point of being difficult for some to accept at that time – I can imagine the reality of quantum gravity will be equally paradigm-shattering. 1. Torbjörn Larsson says: The question being of course if there is such a thing as “quantum gravity”. The ether was unnecessary. So is quantum gravity since we already know how to quantize gravity. It isn’t renormalizable, but I don’t think there is any requirement that an effective theory must be renormalizable and the idea of effective theory (such as general relativity) speaks against actually. There should be an underlying, quantized, theory that supplants gravity, but that can be much larger/different, say derived from cosmology in the way inflation is. Inflation has the necessary local degree of freedoms (its potential value, with fluctuations) to have variation in the same way gravity has. Whether you want to call such a theory “quantized gravity” of “quantized cosmology” I don’t know. But if it is much more than gravity, say string theory, why not let it be called what it is? Conversely, to say “quantum gravity” as this stage of the game is premature, a sign of immature imagination, and potentially harmful to investigation. 1. Anonymous says: Oh wow… that is very … deep. I am stuck in classical physics, you see. I have a very hard time with the spooky quantum world of probabilities and uncertainty and whatnot 🙂 thanks for the reply. 4. Wezley Jackson says: Wonderful article Mr Nerlich! The mystery of the universe has its own beauty and for me this is revealed by your simple explanations of humanity’s wonderful science methods. Being not schooled to a high degree on physics and math theory, I really appreciate it when people with higher knowledge such as yourself can distill things into more easily digestible chunks for me. Also great commentary by LC. I am going to bookmark this page now and do some serious googling on some of the terms here when I get time. Wow! 5. Yousuf Khan says: What I don’t quite get is why anybody thinks that space should polarize light waves? If photons are excitations of the space-time grains, then they should be vibrating at all random directions, the space-time grains won’t stop certain directions of vibrations, they will be part of the vibrations themselves. It’s like expecting water to polarize water. 1. Anonymous says: Water does polarize light. Any surface polarises light. 1. Yousuf Khan says: Water polarises light, but it doesn’t polarise other water. This is the point I’m making. Light is polarised by other substances, not by itself. 2. I understand exactly what you’re saying, though I haven’t got the information to clarify your question. In other words, it’s not you… you’re making perfect sense. I think others aren’t reading your statements carefully enough before they reply. 3. Anonymous says: lcrowell already gave you the answer above: “Photons are excitons of the QED vacuum. They are not excitons of spacetime quanta. Excitons of spacetime quanta would be gravitons.” 4. Torbjörn Larsson says: I think you misunderstand the described physics. The GRB signal is already (highly) polarized, see the paper, from physics of supernova/jet formation that have been discussed here many times. What is observed is how much a difference in polarization is seen after photons have been traveling cosmological distances. No one is claiming that photons are excitations of “the space-time grains” but of EM fields that live in a possibly granular spacetime. Hence you get the replies that point out that most anything external to the fields can polarize them further, water, surfaces, crystals, magnetic fields. And in principle, but as it seems not in practice, the vacuum. 2. Anonymous says: The energy of a photon is E = ?? and the momentum is p = ?k = ?/?. A dispersion relationship is ? = ?(k), which is a linear dispersion if ? = kc. However, if there is a dispersion relationship that is due to spacetime fluctuations there is a dispersion ?^2 = (kc)^2 +/- Ak^3/M_p, A = constant which are two solutions for ?, which is a birefringent property of quantum “foamy” spacetime. This splitting what involves the polarization of EM photons. It is in a way similar to the reflection of light off the surface of water. Certain crystals such as sapphire have this property. The splitting off of different dispersions induces a polarization splitting of light. These results give strong bounds on the occurrence of this, which tends to rule out a lot of grainy ideas about spacetime. LC 1. Yousuf Khan says: You misunderstand my point here. I’m not saying whether or not water can polarise light, I’m saying whether or not a substance can polarise itself. Light is excitations of space-time quanta, and light itself is made from space-time quanta. Can a substance polarise itself? Can light polarise light, or can water polarise water waves? 2. Anonymous says: Photons are excitons of the QED vacuum. They are not excitons of spacetime quanta. Excitons of spacetime quanta would be gravitons. I suspect there is a confusion between the vacuum as a source of curvature and curvature itself. The Einstein field equation G_{ab} = (8?G/c^4)T_{ab} has on the left hand side curvature stuff and on the right hand side mass-energy source stuff. The electromagnetic field defines the T_{ab}, which determine on the left curvature stuff G_{ab}. Now of course the coupling constant 8?G/c^4 is very small, so it takes a huge density of photons to generate curvature. On the other hand curvature can easily change the path that photons take. The spacetime curvature these observations are attempting to measure are due to quantum fluctuations on a very small scale. I will post a rather long discussion on this for those who are geeky enough to go through the mathematics — which is pretty basic actually. I will discuss the FERMI result more than these. The polarization effect is a bit subtle. LC 3. Do Da Do says: At question is wether and/or how much is the vacuum quatatized. If it is quatatized like the electron “orbits” and nucleous “shells”, light will incur a phase shift depending on wavelenght and interaction wether it is water of water or not. Light does inteact with itself anyway. Light is assumed to interact with the oscillations of the space-time grains wve if your ideas hold true. Your first sentence is the best question. 1. Anonymous says: The photon is quantized as a harmonic oscillator. A harmonic oscillator is a spring or pendulum with a small amplitude. The quantized version involves discrete energy steps of equal size E = ??(n + 1/2). The frequency ? is determined by the spring constant and just means this pertains to the generation of n photons with a certain frequency. The quantization of the Maxwell equations of electromagnetism works out to be a harmonic oscillator. If n = 0 there is still a residual energy left ??/2, which is called the zero point energy. To show this involves solving the Schrodinger equation for a system with a potential energy V = -kx^2/2 and working through Hermite polynomials — stuff one gets in an undergraduate quantum mechanics class. That zero point energy term can be removed by a little trick with quantum operators called normal ordering. However, if this system is coupled to another particle field, then so is this vacuum, and one can’t so easily eliminate the coupling of this other system to this vacuum. Something called the Lamb shift is a consequence of this. This also leads to the whole matter of renormalization. LC 2. Anonymous says: The photon is quantized as a harmonic oscillator. A harmonic oscillator is a spring or pendulum with a small amplitude. The quantized version involves discrete energy steps of equal size E = ??(n + 1/2). The frequency ? is determined by the spring constant and just means this pertains to the generation of n photons with a certain frequency. The quantization of the Maxwell equations of electromagnetism works out to be a harmonic oscillator. If n = 0 there is still a residual energy left ??/2, which is called the zero point energy. To show this involves solving the Schrodinger equation for a system with a potential energy V = -kx^2/2 and working through Hermite polynomials — stuff one gets in an undergraduate quantum mechanics class. That zero point energy term can be removed by a little trick with quantum operators called normal ordering. However, if this system is coupled to another particle field, then so is this vacuum, and one can’t so easily eliminate the coupling of this other system to this vacuum. Something called the Lamb shift is a consequence of this. This also leads to the whole matter of renormalization. LC 4. Anonymous says: It is hard to come up with an exact analogy, but here’s a water-based approximation. Suppose it is raining. The air contains lots of water droplets, but you can still see objects in the distance. Sometimes, a raindrop is in your line of sight, so you lose a bit of contrast, but the focus is still the same. However, your short-wave radio reception may go to pieces, because the radio wavelength is a good match for the spacing between the raindrops, and light isn’t. Long-wave radio may be too large to be affected one way or the other. Empty space may not be quite empty. It should be possible for a particle and an antiparticle to suddenly appear, and then annihilate again, paying back the energy they ‘borrowed’ to come onto existence in the first place. This may give a slight texture to ’empty’ space. If we found radiation with a wavelength that roughly matched was a the characteristic length of the texture of empty space, then we might expect that radiation to be deviated or delayed slightly. Radio waves, microwaves, visible light and X-rays all arrive at the same times. This research continues the search up to some enormous energies and tiny wavelengths, and still finds no significant effect. There may still be quantum granularity, but it will be really, really tiny, or the effects are really small. Why do we think there is any quantum granularity in the first place? That’s a bit harder to explain. 1. Anonymous says: This heuristic is commonly thought, and if there were dispersion for EM radiation things might be a bit like this. However, these particle heuristics of virtual particles, electron-positron pairs popping in and out of the vacuum and so forth are approximations which correspond to radiative correction terms. These results suggest that quantum uncertainty is something more fundamental than this sort of heuristic. LC 2. Torbjörn Larsson says: While I haven’t read quantum field theory I think radiative correction terms is a fancier way to say that virtual particles are already incorporated in the corresponding QFT. Indeed is the embodiment of interaction (as exchange of virtual particles). They appear as real when you accelerate (Unruh effect, Hawking radiation). And they appear as bona fide particles after pair production (of strong fields, say). The Unruh effect of the vacuum should incorporate all fields, even gravitation of flat space. I think “quantum uncertainty is something more fundamental than this sort of heuristic” is one good way of putting it, granularity is something over and beyond what you would naively expect. 6. Anonymous says: This comment has nothing to do with this actual article, instead it is a question that has been intriguing me. The Question: If all energy emitted into the universe is stretched by the expansion of this universe, what do gamma rays start out as? If they reach us from billions of light years away and still posses such high energy/frequency, what type of energy did the gamma ray start with? 1. Wezley Jackson says: 2. Torbjörn Larsson says: They start out as high energy gamma rays. There is no higher qualitative class, since they all behave the same. (Sufficiently high energy to interact with atomic nuclei.) Those observations are fairly backyard cosmological, though. Low z (0.02) means low stretch. The results depend on timing (Fermi) and polarization (Integral) differences over long distances. 3. Anonymous says: Your question is similar to the question above. This can be computed. The Hubble relationship is v = Hd, where H = 70km/sec/Mpc. This GRB is 300 million light years away, and 3.26 light years makes a parsec. Hence this GRB is at 9.2×10^7pc = 92Mpc. Now multiply this by H and you get v = 6440km/sec. This is equal to v = .0215c, for c the speed of light. The z-factor is v/c and the wavelength of any photon which escapes this GRB is stretched out be a factor of 1.02. This is not a whole lot. For the GRB detected by the FERMI spacecraft at 7.3 billion light years or d = 2239Mpc. Multiplication by H gives 1.57×10^5km/sec or about half the speed of light. The z factor is then ~ .5 and the wavelength of light is expanded by about 1.5. LC 7. Anonymous says: This comment has really nothing to do with this actual article. It is more of a question I would like to see answered. Question: If all light/energy emitted into the universe gets stretched by the expansion of said universe, what do gamma rays start out as at their source? If we are receiving these rays at such high energy frequencies, what is higher then gamma rays? 1. Wezley Jackson says: Stronger Gamma Rays. 2. Anonymous says: Or in more detail: Gamma rays form a VERY LARGE band. This band begins at a frequency of about 10^18 or 10^19 Hz. But we detect gamma rays with frequencies as high as 10^27 Hz or even higher. However, there is also a distance limit on such high frequencies. The farther the source the more background light (the combined light of the stars and galaxies, not the CMB in this case) is between the source and us. And this light causes some of the very high energetic gamma ray photons to “annihilate” with the background light into electron-positron-pairs. This reduces the amount of very high energetic photons we can detect. So the highest energetic photons come from sources nearby actually, where redshift is not so important. 8. Torbjörn Larsson says: Great article and comments, and of course LC expands this in all the great directions. I too was wondering if this result would make it here. The result is provocative if not robust. It relies on symmetries, or “softly broken” symmetries, such as supersymmetry to suppress vacuum birefringence factors of dimension 3. If that symmetry is supersymmetry, the dimension 5 result should be supplanted with a dimension 6 result that is nowhere near the earlier constraint Fermi puts. [“Constraints on Lorentz Invariance Violation using INTEGRAL/IBIS observations of GRB041219A”, p 4.] “We showed that, although astrophysical constraints are not yet really constraining, they are getting closer to the relevant regime (ξ of order 1 or smaller).” Fortunately supersymmetry seems to be pushed out of relevance by WIMP searches both on Earth and as astronomical pair production events, as well as direct LHC experiments. AFAIU soon predicting supersymmetry particles mass would engender more finetuning than the purported symmetry would solve. So it is promising and building on the Fermi results that pushed observations into the Planck sector for the first time. As the paper puts it: “written in the same way as we did in this work, this limit was ξ < 0.8". And there was one Fermi observation of < 0.01 planck length that was just shy of 3 sigma. As I understand it the theoretical physics community treats the results as interesting but arguable. But the observations, such as they are, adds up. As for the physics, there really isn't anything that suggests that spacetime itself should be granular on any scale. Special relativity predicts the converse. The Planck scale is connected to particle physics of fields, not directly spacetime physics. As such, general relativity is perfectly quantizable as an effective field theory and predicts gravitons and no more fully as expected. (The problem is that the quantized theory breaks down at higher energies, it is fundamentally non-renormalizable.) Quantum gravity ideas such as loop quantum gravity shows the problems with the ideas. As Nerlich notes they break special relativity. They break Lorentz invariance. They break lightcone gauge invariance. (Hence the "philosophical problem" has a very real physics alternate problem.) They have no lowest energy gap. And they don't admit harmonic oscillators so that one can derive dynamics. If we go to ideas such as string theory structures, they have none of these problems. The planck scale is simply a cut off that leads into a dual physics model. The structure does not show up as granularity but as continuity. Showing that in this case it is possible to have the cake and eat it too. 1. Anonymous says: The dimension 5 refers to the Kaluza-Klein dimension for electrodynamics. This has issues with supersymmetry, for Lorentz breaking is more commensurate with dimension 6. However, in dimension 5 if Lorentz symmetry fails at the Planck scale, for whatever rational or religious reasons, there is (almost) no reason why the following higher-dimension term (dimension-5 operator) in the Lagrangian coming from the Planckian physics shouldn’t occur in the effective action: L = (?/M_p)n^aF_{ab}F^bc n^d ?_e(n^eF_{bc}) This term is gauge-invariant and rotationally symmetric and it is suppressed by the right Planck energy scale where the Lorentz violation, picking a preferred unit 4-vector “n”, comes from by the assumption. The dimension 6 theory is similar, but with an additional internal index. Dimension 6 is such that Lorentz violations can be made to work with supersymmetry. All of these theories give a dispersion term ?^2 = (kc)^2 +/- 2 (?/M_p) k^{d – 2} where d = dimension. Generically in what ever theory you are working in the two solutions to the frequency is a birefringence, which has polarization effects. These observations of polarized light in the gamma ray burst found the rotation plane wasn’t rotating which allowed them to impose a remarkable upper bound on the dimensionless coefficient ” ? ” in the term ? < 1.1×10^{-14}. In the natural Planck units, the Lorentz violation linked to the chirality-dependence is smaller than one part per 100 trillion. I am placing here a general derivation of how a dispersion can arise from quantum fluctuations of spacetime. This covers more the results of the FERMI spacecraft, where I derive Torbjorn Larrson’s result on the limit below the Planck scale. I know the space shuttle has all the “spacenews” right now, but this is really more of a fundamental nature. LC 1. Torbjörn Larsson says: As I noted in my previous comment, the author’s themselves were unable to “impose” that constraint, but had to stop at the remark that such constraints are getting closer. You extend, but doesn’t change the conclusion that it is the dimension 6 term that is rigorous as of yet. Instead you summarize their conclusion to say the opposite of what they claim. Or at least, how I read it. If you don’t believe I quoted correctly, read the paper. For myself I am cautiously optimistic, as I noted these tests do add up and one is already pushing the Planck scale even if this didn’t do so rigorously.* I’m all for chucking the unnecessary, wildly counterphysical (well, counter relativity/gauge theory) idea that quantum effects show up as fluctuation of spacetime metric. That last sentence of yours seems misplaced in the context of my comments. ——— * Most natural string vacua are non-supersymmetric. Since the cosmological constant is so low, we sample a very little volume of string landscape. On these grounds I make the easy bet that our vacua is most likely non-supersymmetric, whether string theory is a fact or not. So I think the author’s made the correct decision in not going overboard with this, despite what articles such as this would like to do. And in any case they should point out the tentative nature of this result, and they did. 2. Anonymous says: Supersymmetry is the one thing which can unify internal and external symmetries. There is something called the Coleman-Mandula theorem which demonstrates that without graded symmetries such unifications are not possible. It would be very odd if supersymmetry turned out to be completely absent from reality. Now in our low energy world supersymmetry is broken. How it is broken is rather interesting. The inflationary universe had a huge vacuum energy, but also an enormous negative pressure. So the cosmological constant ? was determined as ?g^{ab} = 8?G/c^4(?g^ab} + pU^aU^b), and the total free energy dF = dE – dQ = 0 Supersymmetry loves this situation and is in the unbroken phase. However, with reheating there is a symmetry breaking of the state, which also breaks supersymmetry. The total 1 = ?_t = ?_{de} + ?_m + ?_r for dark energy, matter (including dark matter) and radiation means that some of the energy has gone into matter and radiation, which is compensated from in the vacuum density. Then supersymmetry is broken. Now again in all of this is mention of vacuum energy density and so forth. This is the stuff which gets us into trouble. These ideas are probably heuristics that do not capture the foundations of this problem. From an information theory perspective we might want to ponder what it means for a vacuum state to have any quantum information (qubit) content. I have this idea that the universe consists only of one of each type of particle. The occurrence of multiple copies of an elementary particle, such as an electron, is due to entanglements across event horizons, such as the cosmological horizon or Bousso bounding surfaces. So an electron here is the same as the one there. In fact there is only one of each type of elementary particle. In this perspective there is really no vacuum state. The vacuum state is only a place holder for the uncertainty of an elementary particle appearing with some particular configuration variable set in a horizon entanglement. This is a bit odd to think about. LC 9. Torbjörn Larsson says: If there is anything in the article I would nitpick, apart from the mentioned physics realization of a “philosophical problem”, it would be this: Light is slowed when it passes through materials that have a refractive index – like glass or water. However, we don’t expect such properties to be exhibited by a vacuum – except, according to quantum theory, at exceedingly tiny Planck units of scale. I would amend that to say that we don’t expect the vacuum to show dispersion, additional differential slowing, because EM theory revolves precisely around combining E & M through a finite interaction speed. (As Einstein realized.) Hence the EM vacuum has susceptibility and permittivity precisely as any other media, and that sets the “slowed light” speed. 1. Light is everpresent. Something makes it behave the way it does, a medium. “Electromagnetic” fabric….which on one hand can not be granular becuse the dimension which is rests in is similar to bose einstein condensates….Overlaying positions…but it is granular in the way that it emerges into this dimension as a point matrix of tiny black/white holes in which each one contains all information of all others. So when we see light ‘travel’ it is not traveling continuously…it is cycling in and out of each of these vortexes and reappearing as information until it is located by an interaction/relationship. Just theorizing outloud……… J. Eve 1. Torbjörn Larsson says: I am sorry, but I can’t make sense of the general idea of this. My response will be partial: “Light … a medium.” Relativity predicts precisely that there is no medium for light, no ether. It works. “dimension … similar to bose einstein condensates … positions.” Again: relativity predicts precisely that there can be no preferred frame such as a condensate would constitute. It works. “each one contains all information of all others” Again and again: relativity predicts precisely locality. It works. “reappearing as information” Information is relative a system and a chosen measure, say Shannon information used to analyze message channels. Nothing physical “is” information, it is a measure or a measure value, depending on context. Need I say it … it is information theory, and, hey: it works! “theorizing outloud” Theories makes testable predictions. It works: =D I didn’t see predictions here. Can you point to this missing piece? ———- Sometimes people identify degrees of freedom with information, say quantum variables. Then of course they can be said to exist as observables. 10. Anonymous says: The graininess of spacetime tested here is due to quantum fluctuations. If I invoke the Heisenberg uncertainty principle ?E?t = ? and use E = mc^2 there is then a fluctuation of mass given by ?m = ?/?tc^2. The uncertainty in time is and uncertainty in position ?t = ?r/c so that ?m = ?/?rc, and a metric ?g_{00} = 1 – 2G?/(r?r c^3), where the metric radius r >> ?r. Now let the length uncertainty be ?r ~ L_p = sqrt{G?/c^3}, and we substitute this into the metric uncertainty ?g_{00} = 1 – 2G?/(rL_p c^3) ~ 1 – 2L_p/r. This is a nice compact result. Now let the radius term be the probe length, which is given by the wavelength of the different radiation r = ?, and we assume ? >> L_p. The approximate metric for radiation of a certain wavelength is then ds^2 = c^2?g_{00}dt^2 – dx^2 – dy^2 – dz^2 = c^2(1 – 2L_p/?)dt^2 – dx^2 – dy^2 – dz^2. For EM radiation ds = 0 and for radiation propagating along one of the directions we have dx/dt = c sqrt{1 – 2L_p/?}. This predicts then a wavelength dependency on the speed of light c’ = c sqrt{1 – 2L_p/?} So if radiation travels a distance D = c’T the time of travel is T = D/(c sqrt{1 – 2L_p/?}) and I use the binomial theorem for ? >> L_p T ~ (D/c)(1 + L_p/?). So this is the effect of quantum fluctuations, really a naïve theory of such fluctuations, should have on radiation. Clearly very short wavelength radiation is slowed down. The FERMI spacecraft detected gamma rays of 33GeV and much radiation at the bottom of the bandwidth at about 10^3eV from a Gamma Ray Burst event GRB 090510 out 7.3 billion light years. We can use these to estimate the time of arrival for the two forms of radiation. L_p/? = E_?/E_p =~ 33GeV/1.2×10^{18}GeV = 2.7×10^{-17}. For the softer gamma ray this is E_?/E_p ~= 10^{-24}. Input this into our formula for the change in speed of light and we get T – T’ = (D/c)( 2.7×10^{-17} – 10^{-24}) =~ (7×10^{25}m/3×10^8m/sec) 2.7×10^{-17} = 6.7sec. The GRB event observed had a time spread of 2 seconds and the two photons which a 10^6 spread in energy arrived at the detector within .8 seconds. Given the error margins and so forth this puts some pretty tight constraints on the role of such fluctuations on physics. This type of spacetime fluctuation is basically ruled out, which are fluctuations that on a small scale violate Lorentz invariance. With heterotic string theory E_8 — > SU(3)xE_6, which gives a twistor type of theory. Twistor theory does not invoke this sort of energy dependency on light cone structure. Rather the uncertainty is in a null congruency, but where all null rays in the bundle, such as a null plane, all have the same spacetime direction. Cheers LC The energy of a photon is E = ?? and the momentum is p = ?k = ?/?. A dispersion relationship is ? = ?(k), which is a linear dispersion if ? = kc. However, if there is a dispersion relationship that is due to spacetime fluctuations there is a dispersion ?^2 = (kc)^2 +/- Ak^3/M_p, A = constant which are two solutions for ?, which is a birefringent property of quantum “foamy” spacetime. This splitting what involves the polarization of EM photons. It is in a way similar to the reflection of light off the surface of water. Certain crystals such as sapphire have this property. The splitting off of different dispersions induces a polarization splitting of light. These results give strong bounds on the occurrence of this, which tends to rule out a lot of grainy ideas about spacetime. LC 1. Torbjörn Larsson says: Ah, thanks! I wasn’t aware that one could tie specifically quantum gravity mass scale to these results, I was relying on the fact that the timing of these traveling photons prohibits any metric fluctuations to be Planck scale regardless of probe size. As a matter of fact you prompted me to find this recent summary of results of a coauthor of the concurrent Nature letter of Abdo et al. More methods and so more results: Confidence Mplanck —————- ———— very high 1.19 high 3.42 medium 5.12 low 10.0 low 102 lag analysis: very high 1.22 “Very high” confidence is 99 % 1. Anonymous says: Thanks for the paper reference. These results push the quantum gravity fluctuation scale into the trans-Planckian domain. LC 11. Peter peete says: Thank you for this really great article, and thanks to you guys who wrote interesting comments on this post. 12. Peter peete says: Thats a really nice article, I want to say thank you for it and i want to give thanks to those people who wrote very interesting comments on this post. 13. Do Da Do says: In somewhat agreement with what Jennifer Eve has said, I would agree totally if I knew for sure what she is thinking I think, I wonder if the interaction being sought cannot be expected to reveal itself in this space. Also, I conjecture that any action would be immediatly countered by a counter action. In addition, the vacuum between here and there here is not a unmolested one since it has been traveled through by a great leveling bulldozer, the exspansion of energy and mass. I have read the posts a couple of times to get the math and degree of freedom remarks correct. The math is not coming through well on my box but, I can fill in the incorrect characters. I am not a superstring reachers or string man. I just wonder if the experiment was looking for ghosts with dark shades on. Hate to see man years of work reduced to crap. It may have some function or use.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8423388600349426, "perplexity": 952.0884697375316}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988793.99/warc/CC-MAIN-20210507120655-20210507150655-00633.warc.gz"}
https://www.physicsforums.com/threads/problem-with-vectors.662934/	# Homework Help: Problem with vectors 1. Jan 7, 2013 ### MMCS Question Forces of magnitude 3 Newtons, 5 Newtons and 7 Newtons act along the vectors (-3,-2,-9) (8,5,-9) (4,-1,-9) Find the x component. I have the answer at 4.968 however i can not arrive at it, attached is my working out. d has been used instead of c. i have the x components as 2.531, -2.774 and -6.93 however these are not correct as they do not equal the answer of 4.968 **Im pretty sure the figures are correct, there is most probably error in the method Thanks #### Attached Files: • ###### Working.jpg File size: 26 KB Views: 117 Last edited: Jan 7, 2013 2. Jan 7, 2013 ### Joffan Normalize the given vectors to unit length. 3. Jan 7, 2013 ### MMCS Is that not what i have done.For example, on F1 i have divided it by the magnitude of AB (13.038) then multiplied it by the magnitude of newtons given in the question (3N) ? 4. Jan 7, 2013 ### Joffan I don't know why you chose to multiply the vectors together first - there was no need. 5. Jan 7, 2013 ### MMCS I didnt multiply them, it isnt clear from the working out sorry, where it says ab it represents the vector a to b. 6. Jan 7, 2013 ### Joffan Ah. The three triplets are the vectors - the forces act from the origin towards those coordinates. 7. Jan 7, 2013 ### NemoReally Does the following help? Notes: • str2mat is user-defined function that converts a string representation of a vector into a Mathcad array • the over-arrow is the vectorize operator (you probably know this, but ...) File size: 21.3 KB Views: 171 8. Jan 7, 2013 ### MMCS Im only new to mathcad so i wasnt aware of them functions but ill give them a go they look to solve the problem pretty easily thanks! 9. Jan 7, 2013 ### Joffan I recommend solving this without Mathcad, to get a feel for the process. Your initial problem with solution was not associated with Mathcad use, but with understanding what was specified in the problem. 10. Jan 7, 2013 ### Staff: Mentor Please do not do student's homework for them here on the PF. That is against our rules here. Instead, give hints, ask questions, find errors in their work, etc. We need to have the students doing the bulk of their schoolwork themselves.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8000741600990295, "perplexity": 2765.4923467586614}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590443.0/warc/CC-MAIN-20180719012155-20180719032155-00608.warc.gz"}
http://mathoverflow.net/questions/7921/failure-of-smoothing-theory-for-topological-4-manifolds	# Failure of smoothing theory for topological 4-manifolds Smoothing theory fails for topological 4-manifolds, in that a smooth structure on a topological 4-manifold $M$ is not equivalent to a vector bundle structure on the tangent microbundle of $M$. Is there an explicit compact counterexample, i.e., are there two compact smooth 4-manifolds which are homeomorphic, have isomorphic tangent bundles, but are not diffeomorphic? (The uncountably many smooth structures on $\mathbb{R}^4$ should give a noncompact counterexample, since $Top(4)/O(4)$ does not have uncountably many components.) I'm also interested in the other type of counterexample, of a nonsmoothable topological 4-manifold whose tangent microbundle does admit a vector bundle structure. Does someone know such an example? Tim Perutz's answer to my first question, below, says that homeomorphic smooth 4-manifolds have isomorphic tangent bundles. If it's not true that all topological 4-manifolds have vector bundle refinements of their tangent microbundle, what is the obstruction in the homotopy of $Top(4)/O(4)$? - For a pair of smooth, simply connected, compact, oriented 4-manifolds $X$ and $Y$, • Any isomorphism of the intersection lattices $H^2(X)\to H^2(Y)$ comes from an oriented homotopy equivalence $Y\to X$ (Milnor, 1958). • Any oriented homotopy equivalence is a tangential homotopy equivalence (Milnor, Hirzebruch-Hopf 1958). • Any oriented homotopy equivalence comes from an h-cobordism (Wall 1964). • Any oriented homotopy equivalence comes from a homeomorphism (Freedman). • It need not be the case that $X$ and $Y$ are diffeomorphic (Donaldson). Many examples are now known: e.g., Fintushel-Stern knot surgery on a K3 surface gives a family of exotic K3's parametrized by the Alexander polynomials of knots. Here's a sketch of why homotopy equivalences preserve tangent bundles: $X$ and $Y$ have three characteristic classes: $w_2$, $p_1$ and $e$. However, $e[X]$ is the Euler characteristic, and $p_1[X]$ three times the signature. By the Wu formula, $w_2$ is the mod 2 reduction of the coset of $2H^2(X)$ in $H^2(X)$ given by the characteristic vectors, hence is determined by the lattice. In trying to construct an isomorphism of tangent bundles over a given homotopy equivalence, the obstructions one encounters are in $H^2(X;\pi_1 SO(4))=H^2(X;Z/2)$ and in $H^4(X;\pi_3 SO(4))=Z\oplus Z$, and these can be matched up with the three characteristic classes. - John, if you look at chapter 8 of Freedman-Quinn's book on topological 4-manifolds, you'll find the following computation of the homotopy groups of Top(4)/O(4): $\pi_3 = Z/2$ and $\pi_i = 0$ for $i=0,1,2,4$. This implies that • a topological 4-manifold has a linear reduction of its tangent bundle if and only if the Kirby-Siebenmann invariant vanishes • if it exists, the reduction is unique. Donaldson's and Freedman's results imply lots of examples of non-smoothable 4-manifolds with trivial Kirby-Siebenmann invariant: any unimodular intersection form arises from a closed simply connected topological 4-manifold, and in the even case the Kirby-Siebenmann invariant is the signature/8 mod 2. If the form is definite, it cannot arise from a smooth manifold. Furuta even showed that Euler characteristic/signature must be $\geq 10/8$ in order to be realized smoothly. The conjectured bound is 11/8 and is realized by the Kummer surface. - I have always been mystified about handlebody structures on topological 4-manifolds. Already in 1970 Kirby and Siebenmann had established that topological n-manifolds have a handlebody structure for n>5 (see Essay III.2 in the 1976 K-S book), and Quinn proved this for n=5 in Ends of Maps III (1982). Finally I just sent an email to Kirby, who gave a simple argument that a topological 4-manifold has a handlebody structure if and only if it is smoothable. I have posted his email on the surgery pages of the Manifold Atlas Project. - PS. I am still mystified about CW structures: when is a topological 4-manifold a CW complex? Again, if and only if smoothable? – Andrew Ranicki Sep 15 '10 at 5:59 Take any two closed simply-connected homeomorphic smooth closed 4-manifolds that are not diffeomorphic. Then their products with $\mathbb R$ are diffeomorphic because the smooth structure on a such a product is unique. (Indeed, since PL/O is 6-connected, it is enough to show that the associated PL structure is unique, but the set of PL-structures on a PL-manifold $M$ of dimension $\ge 5$ is bijective to the set of homotopy classes of maps from $M$ to $TOP/PL$, and the latter space is $K(\mathbb Z_2, 3)$, so the set of PL structures on $M$ is bijective to $H^3(M,\mathbb Z_2)$, which vanishes by Poncare duality if $M$ is homotopy equivalent to a simply-connected $4$-manifold; in fact the argument shows that all we need is $H_1(M;\mathbb Z_2)=0$). It follows that the original closed simply-connected $4$-manifolds are tangentially homotopy equivalent, i.e. there is a homotopy equivalence that pulls stable tangent bundles to each other. - And do you know an example of distinct smooth, stably parallelizable, compact 4-manifolds that are homeomorphic? Also, I'm skeptical that topological 5-manifolds have unique smoothings; I believe smooth structures on a smoothable topological 5-manifold $M$ are distinguished by an invariant in $H^3(M, \mathbb{Z}/2)$. – John Francis Dec 6 '09 at 23:08 I think you are searching for the following: An exotic {4}-manifold by Selman Akbulut We construct two compact smooth 4-manifolds $Q_1, Q_2$ which are homeomorphic but not diffeomorphic to each other. In particular no diffeomorphism $\partial Q_1 \rightarrow \partial Q_2$ can extend to a diffeomorphism $Q_1 \rightarrow Q_2$ Alternatively the boundary case An exotic orientable 4-manifold by Robert E. Gompf In the present paper, we exhibit two compact orientable manifolds (with boundary), $M_1$ and $M_2$, which are homeomorphic, but not diffeomorphic. The minimal symplectic case. http://www.msp.warwick.ac.uk/gt/2008/12-02/p019.xhtml Finally you will perhaps like the following notes by David Gay This paper will outline in an informal way the construction of a family of 4manifolds which are homeomorphic but not diffeomorphic. The first section of the paper (after the introduction, so it is section 2 in the paper), describes the usual construction "of an infinite family of diffeomorphism classes of 4manifolds in two homeomorphism classes". (Roughly speaking, the basic examples of non diffeomorphic but homeomorphic 4-manifolds are constructed as follows : Let $E(1)$ be the algebraic surface, obtained by blowing up 9 points in $\mathbb{C}P^2$. This is an elliptic surface. Let $E(2)$ be the sum of two copies of $E(1)$ (how this is done, is explained in section 2). Define inductively $E(n)$ as the fiber sum of $E(n-1)$ and $E(1)$. By logarithmic transformations you can build from these $E(n)$'s the elliptic surfaces $E(n, m_1,...m_n)$, where $m_1,...,m_n$ are the orders of the transformation. The basic examples of not diffeomorphic but homeomorphic 4-manifolds are such $E(n,p,q)$'s where $p,q$ are relativly prime.) Since you asked for compact examples, this doesn't answer your question. Nevertheless I think (hope) that this last link is useful, since it provides a short overview and introduction to non diffeomorphic but homeomorphic 4-manifolds. - Do these papers deal with issue of whether the tangent bundles of these distinct smoothings are isomorphic? At first glance, I don't see that point considered. – John Francis Dec 6 '09 at 22:49 This is in response to John's addendum. As I understand it, one has the following hierarchy: • Any Poincare complex $X$ has a Spivak normal spherical fibration $S$. • If $X$ carries a topological manifold structure then $S$ has a microbundle reduction. • If $X$ carries a smooth manifold structure then $S$ has a vector bundle reduction refining the microbundle reduction. I'm going to concentrate on simply connected Poincare 4-complexes $X$ with even intersection form. These have Kirby-Siebenmann smoothing obstruction $ks\in H^4(X;\mathbb{Z}/2)=\mathbb{Z}/2$ equal to $\sigma(X)/8$ mod 2, where $\sigma$ is the signature. This is just the obstruction coming from Rochlin's theorem: $\sigma$ is divisible by $16$ if $X$ is smoothable. Freedman tells us that $X$ has a unique topological manifold structure, and hence $S$ has a canonical microbundle structure. So, to ask whether there is a vector bundle reduction of the microbundle is the same as asking whether $S$ has a vector bundle reduction. Let $BG$ be the classifying space for stable spherical fibrations. To solve the obstruction-theory problem of lifting $X\to BG$ to a map $X\to BO$, we need to know the low-dimensional homotopy groups of $BO$ and $BG$ - specifically, whether $\pi_i(BO)\to \pi_i(BG)$ is surjective. I read off from a table in Ranicki's book "Algebraic and geometric surgery" that this is so for $i=1$ and $2$, but that $\pi_3(BG)=\mathbb{Z}/2$ whereas $\pi_3(BO)=0$. So there is an obstruction $o\in H^4(X;\mathbb{Z}/2)$ to finding a vector bundle reduction. I'm a bit nervous of $ks$ due to my ignorance of topological manifold theory, but I think it should then be the case that $o=ks$ (they seem to be similar beasts; I'm thinking of $ks$ as coming from $\pi_3 (BTOP)$, where $o$ comes from $\pi_3(BG)$). What I actually want to use is the corollary, which if true should have a direct proof - that $o=\sigma/8$ mod 2. Anyone? Given any unimodular matrix $Q$, I can build a Poincare 4-complex with $Q$ as its intersection matrix (plumb together disc-bundles over $S^2$ according to $Q$, cone off the homology 3-sphere boundary). If it's correct that $o=\sigma/8$, then when $Q=E_8$, I get a complex with no tangent bundle, whereas when $Q=E_8\oplus E_8$ I get a complex which has a tangent bundle but which is not smoothable by Donaldson's diagonalizability theorem. - Assuming the $o=ks$ claim (that I, unfortunately, don't know how to show at the moment), this seems to me to give that the plumbing of $E_8\oplus E_8$ has a stable tangent bundle. This might be standard, but how do you go from that to the unstable statement? A priori, it's plausible that a microbundle $\tau_M \oplus \mathrm{R}^k$ could admit a vector bundle structure even if $\tau_M$ doesn't. – John Francis Dec 12 '09 at 18:13 Fair point. If I read Dold-Whitney (Annals 1959) correctly, I can create an $SO(4)$ vector bundle with $w_2=0$ and $p_1$ any even integer. Altering this over a 4-ball, via a map $S^3\to SO(4)$ that factors through $SU(2)$, I can adjust its Euler class freely. In this way I can cook up a "tangent bundle" that underlies the Spivak fibration, provided that $o=0$. One then ought to check, using $ks$, whether it underlies the microbundle. – Tim Perutz Dec 12 '09 at 20:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.889621376991272, "perplexity": 349.1921800827969}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207929899.62/warc/CC-MAIN-20150521113209-00022-ip-10-180-206-219.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/794382/if-q-and-p-are-distinct-p-sylow-subgroups-then-q-not-subseteq-n-gp	# if $Q$ and $P$ are distinct $p$-Sylow subgroups then $Q\not\subseteq N_G(P)$. I have been told to use the following to prove another claim, but I would like to prove this anyway for myself. However I can't tell why it's true. I think it's true, but can't see why! Here it is: If $P$ and $Q$ are distinct $p$-Sylow subgroups in a group $G$ then $Q\not\subseteq N_G(P)$. Could I use the theorem below? If so, how? I mean $Q$ isn't a $p$-subgroup, which is why I'm unsure. If $G$ is a group, $P \leq G$ is a $p$-Sylow subgroup, for some prime $p$, then for each $H \leq G$ a $p$-subgroup such that $H \leq N_G(P)$ then $H \leq P$. Thanks! • But $Q$ is a $p$-subgroup, so you can use it. – Derek Holt May 14 '14 at 11:54 Of course you can apply this theorem. Any $p$-Sylow group is a $p$-subgroup per definition. Here is a simple proof of your claim: If $Q \leq N_G(P)$ then its quotient $QP/P$ is a $p$-subgroup of $N_G(P)/P$. Since $\|N_G(P):P\|$ divides $\|G:P\|$ and $P$ is a $p$-Sylow group, $p$ does not divide the group order, so there is no nontrivial $p$-subgroup of $N_G(P)/P$. Hence $QP/P$ is trivial which means $Q \leq P$. • How do you know that $QP/P$ is a $p$-subgroup of $N_G(P)/P$? Thanks for your help, by the way. Algebra isn't my strong suit. – user148158 May 14 '14 at 13:04 • $QP/P$ is the image of $Q$ under the canonical epimorphism $N_G(P) \to N_G(P)/P$. Images of $p$-groups are $p$-groups (in general the order of an image of a subgroup $U$ divides the order of $U$). You can also see this by applying the second isomorphism theorem: $QP/P \cong Q/(Q \cap P)$. – Dune May 14 '14 at 14:05 There is still another approach. If $Q$ would normalize $P$, then $PQ$ is a subgroup of $N_G(P)$, since of course $P \subseteq N_G(P)$. But $\|PQ\|=\|P\|\|Q\|/\|P \cap Q\|$, which shows that $PQ$ is a $p$-subgroup of $N_G(P)$, so it must lie in some Sylow $p$-subgroup of $N_G(P)$. Since $P$ is normal in $N_G(P)$, it is the only Sylow $p$-subgroup of $N_G(P)$, so $PQ \subseteq P$, whence $PQ=P$, which is equivalent to $Q \subseteq P$. But $\|P\|=\|Q\|$, and we get $P=Q$, contradicting $P$ and $Q$ being distinct.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9475146532058716, "perplexity": 88.17635225069505}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347422803.50/warc/CC-MAIN-20200602033630-20200602063630-00402.warc.gz"}
https://www.physicsforums.com/threads/electric-field-in-a-hemisphere.529296/	# Electric Field in a Hemisphere 1. Sep 12, 2011 ### Jshumate 1. The problem statement, all variables and given/known data A nonconducting hemispherical cup of inner Radius R has a total charge Q spread uniformly over its inner surface. Find the electric field at the center of curvature. 2. Relevant equations $\sigma$ = $\frac{Q}{2piR^{2}}$ dq = $\sigma$ dA = $\sigma$ R$^{2}$Sin$\theta$d$\theta$d$\phi$ k = $\frac{1}{4\pi\epsilon_{}0}$ 3. The attempt at a solution dE = $\frac{kdq}{R^{2}}$ dE = $\frac{k \sigma R^{2} Sin\theta d\theta d\phi}{R^{2}}$ = $k \sigma Sin \theta d \theta d \phi$ E = $k \sigma \int^{2 \pi}_{0} \int^{\frac{\pi}{2}}_{0} Sin \theta d \theta d \phi$ E = k $\sigma 2 \pi$ = k $\frac{Q}{R^{2}}$ But for some reason, the answer is listed as k $\frac{Q}{3R^{2}}$. I have no idea why my answer is factor of 3 larger. Any help would be appreciated. 2. Sep 12, 2011 ### ehild Do not forget that the electric field is a vector quantity, so is dE. You can add the contributions as vectors: Determine the x, y and z components of dE and integrate. ehild 3. Sep 12, 2011 ### Jshumate Alright, so the x and y components of the field will cancel by symmetry correct? Therefore, only the z-component dEz = dECos$\theta$ will remain. Ez = $k \sigma \int^{2 \pi}_{0} \int^{\frac{\pi}{2}}_{0} Sin \theta Cos \theta d \theta d \phi$ Ez = $k \sigma \int^{2 \pi}_{0} \frac{1}{2} [Sin^{2} \theta]^{\frac{\pi}{2}}_{0} d \phi$ Ez = $k \sigma \int^{2 \pi}_{0} \frac{1}{2} d \phi$ Ez = $k \sigma \pi$ = k $\frac{Q}{2 R^{2}}$ This still seems to be off from the correct answer unless I did this wrong. 4. Sep 12, 2011 ### BruceW It looks correct to me. I don't know why the answer is listed differently... 5. Sep 12, 2011 ### Jshumate So the correct answer is k $\frac{Q}{2 R^{2}}$ ? 6. Sep 12, 2011 ### BruceW Yes, that's what I get the answer to be. 7. Sep 12, 2011 ### Jshumate My definition of the center of curvature is correct right? It would be the center of the bottom of the hemisphere? If so, I guess the book's answer is wrong. 8. Sep 12, 2011 ### BruceW Yes, I would have thought the centre of curvature was the centre of the bottom of the hemisphere. (since this point is equidistant from any point on the curve). It seems to me that the book is wrong. This does happen sometimes. (Rarely, though). 9. Oct 28, 2013 ### bakeneko If the cup is closed (with a cover), it adds /pi r^2 to the surface and the book's answer is correct. Draft saved Draft deleted Similar Discussions: Electric Field in a Hemisphere	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8379729390144348, "perplexity": 935.2098536540827}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806842.71/warc/CC-MAIN-20171123142513-20171123162513-00693.warc.gz"}
https://asmedigitalcollection.asme.org/MNC/proceedings-abstract/MNC2007/42657/15/326162	A three-dimensional (3-D) parametric model of Tesla-type valves is proposed. A geometrical relationship is derived for optimization study, and based on the model, performance investigations in terms of diodicity and pressure-flow rate characteristics of the valve are numerically carried out with same hydraulic diameter and different aspect ratios (of the model cross-sectional dimensions) ranging from 0.5 to 4. The 3-D computational simulations show that, for the same hydraulic diameter, the unity aspect ratio gives higher diodicity at Reynolds number less than 500 and higher will be achieved with bigger aspect ratio when the Reynolds number is above 500. Investigations of pressure-flow rate characteristics of the Tesla valve show that Tesla valve with high aspect ratio gives more flow control ability. This content is only available via PDF.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8451569080352783, "perplexity": 1422.3283873385665}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573699.52/warc/CC-MAIN-20220819131019-20220819161019-00143.warc.gz"}
https://ask.sagemath.org/questions/33441/revisions/	# Revision history [back] ### How to define a polynomial which can take matrix ? I want to define a matrix valued function. for example.. If I have a polynomial of a matrix with me say $f(x)$ and I want to check $f(A)$. What can be done better? The following will work for numbers but not for matrix. var('x') f(x)=2x^2+x+3 print f(A)# this is what I want as an answer.. ## In the above if I want to replace my x by a matrix what I have to do? So, ultimate aim is to find define a polynomial which can take matrix Thanks in advance... 2 No.2 Revision tmonteil 21078 ●25 ●152 ●390 http://wiki.sagemath.o... ### How to define a polynomial which can take matrix ? I want to define a matrix valued function. for example.. If I have a polynomial of a matrix with me say $f(x)$ and I want to check $f(A)$. What can be done better? The following will work for numbers but not for matrix. var('x') f(x)=2x^2+x+3 print f(A)# this is what I want as an answer.. answer.. ## In the above if I want to replace my x by a matrix what I have to do? So, ultimate aim is to find define a polynomial which can take matrix Thanks in advance...	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8300622701644897, "perplexity": 621.7405143631305}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250611127.53/warc/CC-MAIN-20200123160903-20200123185903-00359.warc.gz"}
http://www.sciforums.com/threads/galaxy-orbital-velocities-explained-without-dark-matter-halos.143491/	# Galaxy orbital velocities explained without 'dark matter' halos. Discussion in 'Pseudoscience' started by nebel, Dec 19, 2014. 1. ### nebel Messages: 2,076 Is it correct to say that the 'pulls' of gravity are zero at the 'center of mass' of an entity? and max at the surface/ perimeter?--- if this is so, One would expect the highest orbital velocities at the perimeter of galaxies, spirals, globular or ellipticals with even mass distribution; and the lowest speeds near the centers,- of at least of those accumulations without a great central mass. Results may vary, because of mass density variations, or central black holes, but even there, in the very center, should gravity not fall to zero ? and with it the need for balancing gravity by centrifugal forces? Last edited: Dec 19, 2014 to hide all adverts. 3. ### nebel Messages: 2,076 to hide all adverts. 5. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member Messages: 11,049 That would apply to a solid object. A diffuse matterial would not have the same attributes. to hide all adverts. 7. ### nebel Messages: 2,076 origin, could you explain why and how the action of gravity depends on whether an object is solid, a fluid, or particles? BSW I like your avatar, the roar of an Atlas shakes every organ in your body. 8. ### nebel Messages: 2,076 origin, granted, diffuse entities might not have a 'surface' or a well defined perimeter, but does not their force of gravity fall to zero at the center, even if not in a linear decline as in an 'ideal' sphere? 9. ### The. Ring.BannedBanned Messages: 111 If a black hole, exist at the center of a galaxy, and is in fact the center of the galaxy, it is irrational for an object, (black hole) that is created by gravity itself, to not have gravity. However, to test this, one presumably would need to enter and record the gravity at the center of the hole, and as far as I recall, theory does not permit this as the recording devise would be obliterated by gravity. nebel likes this. 10. ### nebel Messages: 2,076 The.Ring., thank you for pointing this out. Inside a black hole, conventional physics is thought to break down, and the OP deals with the gravity, orbital velocities outside such center regions, and with galaxies that do not even have a center bulge , nor even rotation, but must have distinct gravity -balancing orbits for all it's stars. (just like the jumping dolphin gets that 'zero gravity' feeling) One way or another the direction of the 'pull' of gravity reverses at the center of a black hole region, it follows that it has to go through the zero value, right? so, even where gravity is extreme, because of great density in the singularity, there has to be a zero gravity situation in there. (see the Ring/torus situation below). In the normal scheme of things, the earth, gravity in Montreal pulls you toward Australia, the Aussies tend to sink 'up' toward us in the North; somewhere in the interior that force is reversed, so there has to be a zero value, and what better place for that, than in the inner core's center? is this not so, even if we can not take a gravity gradient meter down there? BSW: if you understand gravity in 'The. Ring.' or an empty torus; -there is zero gravity from the inside surface all the way to the opposite inside, including -of course- the center. so there can be even a 'zero-gravity region', rather just a center point; -- with orbital velocities to match. Max on the outside, but free floating, or even stationary at the center. and: Inside the Ring or that torus the gravity gradient would fall from max at the outside to zero on the inside surface. Last edited: Dec 21, 2014 11. ### The. Ring.BannedBanned Messages: 111 There is no right, or wrong, you could have all the answers and not know it, in fact no one would know it. In another similar topic, have you heard that quantum teleportation of data, may be happening seriously faster than the speed of light, and might in reality be instantaneous, which if true, tosses Einstein's equations completely into the dumpster? http://www.livescience.com/49028-farthest-quantum-teleportation.html 12. ### nebel Messages: 2,076 T.R., yes I might have, but the OP deals with Keplerian orbits, Newtonian gravity. 13. ### The. Ring.BannedBanned Messages: 111 Newtonian gravity, is what Newton postulated about gravity, without ever leaving the Earth. His view might be flawless, or it might be flawed, however there is still no explanation for what gravity is, just it's noticeable effects, are described. Again, if spooky entanglement reigns true, the speed of light is no longer the max speed, and we need a new model..............again. So it seems that the more we learn, the less we know. 14. ### nebel Messages: 2,076 yes, but I am trying to deal with the effects of simple gravity, the 'flat' velocity graphs in galaxy observations; possibly flawed interpretations of MACRO EFFECTS. whether gravity is a tensioning of space time, exchange of gravitons, Hicks Boson results,-- is another story. The observed entanglement phenoma, are in another ballpark, real, but futuristic, beyond the immediate grasp of someone in the mid-eighties. 15. ### The. Ring.BannedBanned Messages: 111 Simple gravity, in galactic observations. This statement implies that you believe that galaxies, which are of currently unknowable complexity, can be made simple. Again, all equations pretty much go out the door, if spooky entanglement disproves that the velocity of light is not a maximum speed. There is also no right of humanity, to achieve a perfect mathematical model. It may be there, and it may not as there may be other realities, with completely different physics, that might be intermingling with our own. Nothing is known for sure. 16. ### nebel Messages: 2,076 T.R. :-- Newtonian laws, Kepler, with a little bit of general relativity thrown in, got us to the moon and back, Mars, the voyageurs, the comets, and this is the level of discussion the OP aimed for. are there future possibilities in the arcane field you are interested in? absolutely. have you exposed these topics in other/your own threads? 17. ### James RJust this guy, you know?Staff Member Messages: 34,419 Consider our solar system. The planet Neptune has a much lower velocity around the Sun than Mercury does. But then, our solar system has a great central mass, doesn't it? Galaxies also have great central masses, but their rotation curves look different to the ones of planets in our solar system. Galaxies seem to rotate more like rigid bodies (although not exactly like that). That's one reason why we need dark matter, by the way. 18. ### nebel Messages: 2,076 James, that is exactly my point, in an entity, the highest gravity values are in the perimeter, but zero in the center, matter in the perimeter would have to travel at higher velocities to generate the centrifugal forces to counter that maximum gravity there, and surprise! --matter orbiting at the outer reaches of galaxies does. How are star clusters comparing? it is difficult to get a doppler picture there, because of the lack of common rotation, but all these stars are in stable orbits and not whizzing through the center ( I am guessing here) , but conform to the pattern of inner orbit velocities that are slower and in outer orbit segments faster. In these globulars, it only appears that there are more "central" stars because in their orbits that traverse the central regions, stars are packed closer together, in gentler gravity. I predict, that in a situation, where the mass of the sun would be diffused equally into the space of the solar system, that in the short run, the orbital velocity of Neptune would be highest, and Mercury the slowest, without adding 'dark matter'. so: who needs dark matter here? Kepler's laws of planetary motion are predicated on a great central body, ignoring the masses of the planets, their field. edited: it is understood that you removed and dispersed the solar mass, that mercury would be off to the races, and so the other planets. I meant that if the present setup existed with the sun distributed, these inner bodies would have to orbit slower to have a measure of stability. Last edited: Dec 21, 2014 19. ### nebel Messages: 2,076 Sorry, I got caught editing past the time limit. In a stable solar system where the planets orbit at their present distances, but the solar mass is diffused equally into the space inside the Neptune orbit, the velocity values would be reversed. Neptune* , having the total system's mass 'below' it, would have to travel fastest, whereas Mercury, with hardly any matter below him, could proceed slowly, in that near-zero gravity central environment. no dark matter needed. dark matter would be a 'red herring' in that 'ideal mass distribution' situation. Galaxies, with their diffuse, but enhanced central masses, fall in between the above and the conventional 'central mass' planetary systems., and rotate more like solid bodies, but perhaps not because of dark matter in their halos either. assuming that we would ignore the gravitational effects of the planet's masses or have them dispersed too,- into toruses in those orbits, and while it could last. Last edited: Dec 21, 2014 20. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member Messages: 11,049 Deleted, I misread a post. Last edited: Dec 21, 2014 21. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member Messages: 11,049 I missed that you stated this in the OP. That is precisely the first evidence that was used in the dark matter hypothesis. It is obvious that stars in galaxies are NOT evenly distributed. There are many more stars towards the center of the galaxy than on the outer areas. That would mean that the stars in the galaxy should orbit the center like a solar system. But the stars orbit more closely to a solid (not exactly just closer to a solid) than a solar system. The only way that ould be possible would be if there is a fairly even distribution of matter through the galaxy. The more evenly distributed the matter the more the movement of the diffuse body moves and behaves gravitationally like a solid. But we do not see this even distribution, hence the obvious conclusion that there is matter that does not emit or reflect light so it is dark! Last edited: Dec 21, 2014 22. ### nebel Messages: 2,076 origin, in my above model of a solar system with a diffuse solar mass, the orbital velocity of neptune would not be changed, it still has to deal with all that matter calculated to act through the center. It is the speed of mercury, venus that would have to be reduced drastically. Thanks to your objection, can I make it clearer that the even, near 'solid body' galaxy velocity distribution is not about the faster perimeter alone, but the (by comparison to the Solar system) slower inner orbits. In any circular object, it is only the enclosed mass that generates an inward gravitational force, and with the more diffuse matter distribution of the inner regions of galaxies, (excluding of the central black holes) one would rightly expect relatively low speeds in the orbiting matter there. One could imagine a model of our solar system with a gradual, galaxy-like dispersion* of the the solar mass, that would result in ~equal velocities for all orbit locations, similar to the flat velocity distribution seen in galaxies, and that without adding dark energy inside the Neptune orbit. . More TNO's Oort cloud objects would not add gravity, or speed to Neptune. But I agree, the case would vary from one Galaxy to another, and these doppler-type surveys have to be done on near edge-on examples, that are hard to asses about their matter distribution. On the way down to the 'zero pull' in the center, gravity diminishes in step with the still enclosed, ever smaller mass, and with it the orbital velocity to balance it. compared with many galaxy images, the 'central' mass would be smeared out past the orbit of Saturn. Last edited: Dec 21, 2014 23. ### nebel Messages: 2,076 James R , - Newton's universal law of gravitation is always applied to show gravity acting from center of [total]mass 1, - to center of [total]mass 2. This is appropriate and true for situations outside these masses. In the case of galaxies, a substantial portion of their mass lies diffused outside their very center. For any body orbiting INSIDE a galaxy, only the portion of the mass that lies between mass 2 (the orbiting object) and the center of mass 1 (the galaxy) can contribute to the gravitational force on 2. so: While the outer orbit's denizen are pulled inward by the TOTAL mass of the galaxy, with the comparative resulting high velocities, by contrast, the inner orbiting objects are pulled toward the center only by that part of the galaxy that lies inward from them to the center. A big difference!, because If one assumes that the same mass pulls on both the inner and outer orbits, as happens in the Keplerian orbits of the Solar system, of course the inner appear to go too slow and the outer too fast; or rather the outer at the right speed, but too fast in comparison to the thus wrongly calculated inner orbits. Have you seen this reflected in any of the calculations that are used to derive the need for 'dark matter' in the outer halo? * much of the mass is only shining in the pressure- standing-wave that we see as spiral arms, for there is where stars are formed, the same amount of material exists also between the arms as it rotates toward them, only this material does not show up as light, as it does in the density of stars. I would like to hear good refutations, specific falsification of these ' pseudo' ideas, could this be moved to the main cosmology page, if it merits it? thank you. 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https://proofwiki.org/wiki/Definition:Algebraic_Dual	# Definition:Algebraic Dual It has been suggested that this page or section be merged into Definition:Dual Module. (Discuss) ## Definition Let $R$ be a commutative ring. Let $G$ be a module over $R$. The $R$-module $\mathcal L_R \left({G, R}\right)$ of all linear forms on $G$ is usually denoted $G^$ and is called the algebraic dual of $G$. ### Double Dual The double dual $G^{}$ of $G$ is the dual of its dual $G^$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8740333914756775, "perplexity": 254.8145664608793}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146342.41/warc/CC-MAIN-20200226115522-20200226145522-00054.warc.gz"}
https://mathoverflow.net/questions/253090/elementary-proof-of-riemann-roch-for-compact-riemann-surfaces	# Elementary Proof of Riemann-Roch for Compact Riemann Surfaces I am supposed to give a talk about the Riemann-Roch theorem to a seminar of first and second year graduate students. I want to do Riemann-Roch for compact Riemann surfaces, but I am open to perhaps doing the version for projective curves. I assume the crowd knows little algebraic geometry. I assume however, knowledge of elementary differential geometry, sheaves, cohomology and complex analysis. I am looking for an elementary proof (especially because I want time to be able to work out some examples). Any references? • Did you look at Forster, Lectures on Riemann Surface? – user31415 Oct 26 '16 at 1:40 • The proof in Rick Miranda's book is fairly elementary, and only uses the prereqs you list. It is a little long, but maybe you could condense it. – Steven Gubkin Oct 26 '16 at 1:41 • An entirely elementary proof (no sheaves or cohomology) can be found in Fulton's Algebraic Curves. However, I have to admit that I found the proof unenlightening, last time I looked at it. Since you want to do examples, you can also focus on the case of elliptic curves, where you can prove RR by counting Fourier coefficients of theta functions. The details are probably in some standard text such as Husemuller or Silverman. – Donu Arapura Oct 26 '16 at 13:07 • @JacobGross These students are familiar with differential geometry, sheaves, cohomology, and complex analysis, but are not familiar with the notion of the genus of a curve? This seems unbelievable. – Steven Gubkin Oct 28 '16 at 21:55 • I wound up finding also Nigel Hitchin's notes people.maths.ox.ac.uk/hitchin/hitchinnotes/… useful. – user100272 Dec 19 '16 at 8:09 RRT There is a big difference in difficulty between the compact Riemann surface case and the projective curve case, for reasons already mentioned. Namely a projective curve comes equipped with a large supply of meromorphic functions, but the proof that they exist for a compact Riemann surface is a major step. I suggest you decide what your goal is. E.g., do you want to make clear why the theorem is true, without giving all steps of verification, or do you want to show how some of the trivial steps are derived easily using modern sheaf techniques, or perhaps give complete derivations of some significant parts of the statement? if you use sheaf theory, it is trivial to show that chi(D)-chi(O) = deg(D) for any divisor D, where chi is the holomorphic Euler characteristic: chi(D) = h^0(D)-h^1(D). To get full RRT from this one needs to compute chi(O) = 1-g, where g is the topological genus, and then to prove duality, that h^1(D) = h^0(K-D), where K is the canonical divisor. In 4 pages of the notes on my web page, I take an argument from Bill Fulton to do one of these for plane curves, namely that chi(O) = 1-g, with some hand waving over the computation of topological Euler characteristics by deformation. see pages 38-42: http://alpha.math.uga.edu/%7Eroy/rrt.pdf If you just want to show why the result is true with some arguments omitted, I feel nothing beats Riemann’s own exposition. Riemann himself proved the theorem in clear natural stages: 1st the theorem in the special case of the canonical divisor, i.e. he proved that there are exactly g independent holomorphic differential forms on a compact Riemann surface of genus g. Then he proved that for each point p, there is one meromorphic differential with a double pole at p and zero residue, equivalently he proved the RRT for divisors of form K+2p, i.e. that h^0(K+2p) = g+1, so that in addition to the g holomorphic forms there is one with a double pole at p, (and necessarily zero residue). (Riemann also allows himself the simplification of assuming all points of the divisor considered are distinct.) Then, from the existence of these basic types of differentials, one deduces the converse of the residue theorem. Even if you barely read German, you can get the idea of what is most important just from deciphering the headings of the first two paragraphs in Riemann's treatment of the theorem in his great paper "On Abelian Integrals"; (since differentials the things you integrate, he speaks of their integrals): "Integrale erster Gattung" (integrals of first kind, i.e. of holomorphic differentials); "Integrale zweiter Gattung" (integrals of second kind, i.e. of differentials with double pole at one point).... With this information, one can deduce the RRT in two steps, as clearly explained in Griffiths and Harris’s book, (see in particular pages 233, 244-5). Namely for each effective divisor D, to compute the number of independent meromorphic functions with pole divisor dominated by D, is equivalent to computing the number of meromorphic differential forms that would occur as their differentials. The assumed facts give the number of meromorphic differentials with the right singularities, and then one has only to compute how many of those differentials are exact, which is a period computation. As in Riemann’s original paper they give this calculation in terms of the periods of integrals, and as in Roch’s follow-up these periods are computed in terms of residues using Green’s theorem. All this is done nicely in Griffiths Harris, where they depend on the Kodaira vanishing theorem for the requisite existence of differential forms of first and second kinds. (They also discuss this deep theorem earlier in their book.) The point is that the deduction of RRT from the known existence of the right number of differential forms of first and second kinds is very clear and elementary complex calculus. Hence it only remains to provide an elementary proof of these prerequisite facts about forms. Now if one restricts attention to plane curves, at least the holomorphic forms can be immediately written down in coordinates, as Riemann himself points out. He also says one can write them down in the meromorphic case as well, but does not do so. I believe this can indeed be done in an elementary way, as indicated in the book of Brieskorn and Knorrer, but I have not done it except in special cases. In fact one can finesse the existence of the forms of second kind by the trick of Brill and Noether; i.e. one can use duality to rely exclusively on the existence of holomorphic forms for the theorem. This argument is explained in the books of Arbarello, Cornalba, Grifiths and Harris (appendix A, chapter 1), and in the book on algebraic curves by Griffiths. I have also written out this argument in the notes for my course in pdf form, at the link below: http://alpha.math.uga.edu/%7Eroy/8320.pdf If you want a complete argument for compact Riemann surfaces, a nice treatment using sheaves is in the book Lectures on Riemann surfaces by Robert Gunning, including some nice Hilbert space arguments to deduce the finiteness of cohomology groups. I like the old book, but a more current version of his notes are posted on his web site at: https://web.math.princeton.edu/~gunning/ Finally David Mumford recommended reading the argument by George Kempf, in Crelle’s Journal, and reproduced in his book Algebraic Varieties, using sheaf theory heavily for the algebraic case. I found this rather terse, but aspire to understanding it. Here is a link to it: http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002194015&physid=PHYS_0046 Please forgive the somewhat rushed answer, I hope some of the references are useful. I apologize if my correction of an error causes a bump, but I hope it does not. • This is the sort of answer that makes MO the valuable asset it is. Thanks! – Mariano Suárez-Álvarez Oct 28 '16 at 7:55 • at the cost of bumping this, I have added a link to my course notes with a complete proof for smooth plane curves, as mentioned above. – roy smith Oct 31 '16 at 16:05 • @Mariano, this site is a privilege to participate in. I.e. this answer would not have survived a week on wikipedia, and I speak from experience. – roy smith Nov 18 '16 at 1:34 • your answer is characteristic of the best in MO: it communicates understanding and insight. Neither Wikipedia abounds in that nor, sadly, the majority of literature. I love finding counterexamples to my claim here! – Mariano Suárez-Álvarez Nov 18 '16 at 1:54 Joe Harris, as recorded in his course notes here, gives the following slick proof when both $D$ and $K-D$ are effective; it has the advantage of never mentioning $H^1$. See lecture 1 for this argument, and 6-7 for removing the effectiveness hypothesis. Let $X$ be a complete connected curve of genus $g$. Let $K$ be the canonical class, and let $D = x_1 + x_2 + \cdots + x_n$ be an effective divisor. For notational simplicity, assume the $x_i$ are distinct. Assume also that we already know $\dim H^0(X, \Omega^1)=g$ and $\deg K = 2g-2$. For each $x_i$, choose a uniformizer $z_i$ near $x_i$, so that we have a residue map $\mathrm{Res}_i$ from meromorphic functions on $X$ to $\mathbb{C}$. An element of $\mathcal{O}(D)$ which has no residue at any $x_i$ is a global holomorphic function, hence a constant, so we have an exact sequence: $$0 \to \mathbb{C} \to H^0(\mathcal{O}(D)) \to \mathbb{C}^n$$ where the last map is the direct sum of the residue maps. Similarly, we have a short exact sequence $$0 \to H^0(\Omega^1(-D)) \to H^0(\Omega^1) \to \mathbb{C}^n$$ where the $i$-th component of the last map sends a differential form $\omega$ to $\left. \tfrac{\omega}{d z_i} \right\|_{x_i}$. Here $\tfrac{\omega}{d z_i}$ is a ratio of $1$-forms, hence a meromorphic function, which is defined and hence evaluable at $x_i$. I claim that the images of these maps are perpindicular under the standard inner product on $\mathbb{C}^n$. This is because, for $f \in H^0(\mathcal{O}(D))$ and $\omega \in H^0(\Omega^1)$, the pairing $\sum \mathrm{Res}_i (f dz_i) \cdot \left(\left. \tfrac{\omega}{d z_i} \right\|_{x_i}\right)$ is simply the sum of the residues of $f \omega$, and hence $0$ by Stokes theorem. If we knew that the images were orthogonal complements, we would deduce $$(\ell(D)-1) + (g-\ell(K-D)) = n = \deg D.$$ Rearranging, we would get Riemmann-Roch and, in fact, Riemann-Roch is true and they are orthogonal complements. Without knowing this, simply the fact that they are orthogonal gives the inequality $$(\ell(D)-1) + (g-\ell(K-D)) \leq \deg D.$$ But, now consider the same argument for $K-D$ in place of $D$ (here is where we assume $K-D$ effective). We deduce $$(\ell(K-D)-1) + (g-\ell(D)) \leq \deg K-D.$$ Adding both sides, $2g-2 \leq \deg D+\deg K-D = \deg K = 2g-2$. So every step must have been equality, and we have proved the result. • Wow, very slick! Thanks. I actually am starting to like the idea of proving the theorem like this just for $D$ and $K-D$ effective, referring to these notes for the full proof and then just taking a close look at some elliptic curves. – user100272 Oct 27 '16 at 4:38 • Thanks! I think I'm going to make some cosmetic edits to make it a little prettier. – David E Speyer Oct 28 '16 at 13:48 There are (at least) 2 kinds of proofs: analytic ones (which use the existence of Abelian differentials with certain properties) and algebraic ones. The proofs of the first kind use powerful analytic machinery, so it is a question what are you willing to accept as prerequisites. The simplest analytic proof that I know is in Hurwitz-Courant (exists in German and Russian, but unfortunately not in English). Of course all prerequisites are in the same book, starting from definition of complex numbers. The proof of the Riemann-Roch itself is about 1 page, once existence of Abelian differentials is established. The simplest algebraic proof that I know is in Lang's book Algebraic and Abelian functions, which is almost self-contained (refers only to Algebra book of the same author). The proof given in Otto Forster, Lectures on Riemann Surfaces (Graduate Texts in Mathematics 81), chapter 16, seems very much suited to your list of prerequisites. I wrote up notes for the 4 lectures I did going through a completely algebraic proof at the end of a Shavarevich based algebraic geometry course. I think this is a nice approach in that it introduces in an elementary way the cohomological tools which will come up sophisticated ways in the following term. I didn't allocate nearly enough time to explain why we cared, though. There is a U of Chicago REU by a Valeriya Talovikova which does everything from the beginning in 10 pages. • Just to note, "everything" does not include what the paper labels Fact 2.1: that every compact Riemann surface has a nonconstant meromorphic function. This is, in my experience, harder than all the rest. For the purposes of your talk, I think you should also omit this, perhaps pointing out that it is clear for projective curves (take the ratio of two homogeneous coordinates.) – David E Speyer Oct 26 '16 at 13:58 • Continuing to read, "everything" also does not include Serre duality (last sentence of Prop 4.6), which is the second hardest thing. I agree that this paper is a good guide to what might fit in a 1 hour talk; just pointing out why the other references are so much longer. – David E Speyer Oct 26 '16 at 14:00 • The paper also doesn't show $\dim H^0(\Omega^1) = g$, although this is wouldn't be too hard to fit in. Sorry, I think I've turned into a grumpy old man. – David E Speyer Oct 26 '16 at 14:02 • @DavidSpeyer At least you are more grumpy than you are old :) – Igor Rivin Oct 26 '16 at 14:26 • The proof of Talovikova is far from being self-contained: it refers for Serre's duality to some book. – Alexandre Eremenko Oct 26 '16 at 17:16 Here is one that is not elementary. Joe Polchinski mentions a derivation of Riemann-Roch via Feynman Path integrals. Unfortunately most people don't know what "ghosts" are and try to do String Theory without them. https://physics.stackexchange.com/questions/110322/number-of-zero-modes-on-the-sphere It is worked out in Chapter 5 of Polchinski's String Theory Vol 1 - he is trying to talk about the Moduli space of Riemann Surfaces	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8787396550178528, "perplexity": 404.09421780591214}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250624328.55/warc/CC-MAIN-20200124161014-20200124190014-00099.warc.gz"}
https://www.physicsforums.com/threads/laplace-transform-where-am-i-messing-up.21016/	# Laplace transform: where am I messing up? 1. Apr 16, 2004 ### faust9 Ok, using the definition of Laplace transforms to find $\L\{f(t)\}$ Given: $$f(t)=\{^{\sin{t}, 0\le{t}<{\pi}}_{0, t\ge{\pi}}$$ So, this is what I did: $$\L\{\sin t\}=\int^{\pi}_{0} e^{-st}\sin t dt+\int^{\infty}_{\pi} e^{-st}(0)dt$$ $$=\int^{\pi}_{0} e^{-st}\sin t dt$$ $$=\frac{-e^{-st}\sin{t}}{s}]^{\pi}_{0}+\frac{1}{s}\int^{\pi}_{0} e^{-st}\cos t dt$$ $$=\frac{-e^{-st}\sin{t}}{s}]^{\pi}_{0}+\frac{1}{s}(\frac{-e^{-st}\cos{t}}{s}]^{\pi}_{0}-\frac{1}{s}\int^{\pi}_{0} e^{-st}\sin t dt)$$ $$=\frac{-se^{-s\pi}}{s^2}+\frac{1}{s}(\frac{-1}{s}-\frac{1}{s}\L\{\sin t\})$$ $$\L\{\sin t\}(\frac {s^2+1}{s^2})=\frac{-se^{-s\pi}}{s^2}-\frac{1}{s^2}$$ $$\L\{\sin t\}=\frac {-se^{-s\pi}-1}{s^2+1}$$ Which I know is wrong because the Laplace for sin t should be: $$\L\{\sin t\}=\frac {1}{s^2+1}$$ I know my limits of integration will affect the problem but the restricted limits should only add a term to the numerator $e^{-s\pi}$ I believe. Where did I mess up? Thanks a lot. 2. Apr 16, 2004 ### arildno Your mistake is in the 5.line, in the evaluation of cos(t) at the limits indicated. Last edited: Apr 16, 2004 3. Apr 16, 2004 ### arildno Also, the sin(t) evaluation in the 5.line should be zero. 4. Apr 16, 2004 ### faust9 Got it. Thanks. How silly of me. Similar Discussions: Laplace transform: where am I messing up?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9919208884239197, "perplexity": 3995.499449700472}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121121.5/warc/CC-MAIN-20170423031201-00015-ip-10-145-167-34.ec2.internal.warc.gz"}
https://www.hepdata.net/search/?q=cmenergies%3A%5B1.3+TO+1.4%7D&author=Tisserand%2C+V.	Showing 10 of 77 results #### rivet Analysis Cross sections for the reactions $e^+ e^-\to K_S^0 K_L^0$, $K_S^0 K_L^0 \pi^+\pi^-$, $K_S^0 K_S^0 \pi^+\pi^-$, and $K_S^0 K_S^0 K^+K^-$ from events with initial-state radiation The collaboration Lees, J.P. ; Poireau, V. ; Tisserand, V. ; et al. Phys.Rev.D 89 (2014) 092002, 2014. Inspire Record 1287920 We study the processes $e^+ e^-\to K_S^0 K_L^0 \gamma$, $K_S^0 K_L^0 \pi^+\pi^-\gamma$, $K_S^0 K_S^0 \pi^+\pi^-\gamma$, and $K_S^0 K_S^0 K^+K^-\gamma$, where the photon is radiated from the initial state, providing cross section measurements for the hadronic states over a continuum of center-of-mass energies. The results are based on 469 fb$^{-1}$ of data collected with the BaBar detector at SLAC. We observe the $\phi(1020)$ resonance in the $K_S^0 K_L^0$ final state and measure the product of its electronic width and branching fraction with about 3% uncertainty. We present a measurement of the $e^+ e^-\to K_S^0 K_L^0$ cross section in the energy range from 1.06 to 2.2 GeV and observe the production of a resonance at 1.67 GeV. We present the first measurements of the $e^+ e^-\to K_S^0 K_L^0 \pi^+\pi^-$, $K_S^0 K_S^0 \pi^+\pi^-$, and $K_S^0 K_S^0 K^+K^-$ cross sections, and study the intermediate resonance structures. We obtain the first observations of \jpsi decay to the $K_S^0 K_L^0 \pi^+\pi^-$, $K_S^0 K_S^0 \pi^+\pi^-$, and $K_S^0 K_S^0 K^+K^-$ final states. 8 data tables match query Cross section measurement for PHI(1020). Mass measurement for PHI(1020). Measurement of the PHI(1020) width. More… #### rivet Analysis Cross Sections for the Reactions e+e- --> K+ K- pi+pi-, K+ K- pi0pi0, and K+ K- K+ K- Measured Using Initial-State Radiation Events The collaboration Lees, J.P. ; Poireau, V. ; Prencipe, E. ; et al. Phys.Rev.D 86 (2012) 012008, 2012. Inspire Record 892684 We study the processes e+e- --> K+ K- pi+pi-gamma, K+ K- pi0pi0gamma, and K+ K- K+ K-gamma, where the photon is radiated from the initial state. About 84000, 8000, and 4200 fully reconstructed events, respectively, are selected from 454 fb-1 of BaBar data. The invariant mass of the hadronic final state defines the \epem center-of-mass energy, so that the K+ K- pi+pi- data can be compared with direct measurements of the e+e- --> K+ K- pi+pi- reaction. No direct measurements exist for the e+e- --> K+ K-pi0pi0 or e+e- --> K+ K-K+ K- reactions, and we present an update of our previous result with doubled statistics. Studying the structure of these events, we find contributions from a number of intermediate states, and extract their cross sections. In particular, we perform a more detailed study of the e+e- --> phi(1020)pipigamma reaction, and confirm the presence of the Y(2175) resonance in the phi(1020) f0(980) and K+K-f0(980) modes. In the charmonium region, we observe the J/psi in all three final states and in several intermediate states, as well as the psi(2S) in some modes, and measure the corresponding product of branching fraction and electron width. 1 data table match query Cross section measurements for the reaction E+ E- --> PHI F0(600). Statistical errors only. #### rivet Analysis Measurements of $e^{+} e^{-} \to K^{+} K^{-} \eta$, $K^{+} K^{-} \pi^0$ and $K^0_{s} K^\pm \pi^\mp$ cross- sections using initial state radiation events The collaboration Aubert, Bernard ; Bona, M. ; Boutigny, D. ; et al. Phys.Rev.D 77 (2008) 092002, 2008. Inspire Record 765258 This paper reports measurements of processes: e+e- -> gamma KsK+pi-, e+e- -> gamma K+K-pi0, e+e- -> gamma phi eta, and e+e- -> gamma phi pi0. The initial state radiated photon allows to cover the hadronic final state in the energy range from thresholds up to ~4.6 GeV. The overall size of the data sample analyzed is 232 fb-1, collected by the BaBar detector running at the PEP-II e+e- storage ring. From the Dalitz plot analysis of the KsK+pi- final state, moduli and relative phase of the isoscalar and the isovector components of the e+e- -> K K(892) cross section are determined. Parameters of phi and rho recurrences are also measured, using a global fitting procedure which exploits the interconnection among amplitudes, moduli and phases of the e+e- -> KsK+pi-, K+K-pi0, phi eta final states. The cross section for the OZI-forbidden process e+e- -> phi pi0, and the J/psi branching fractions to KK(892) and K+K-eta are also measured. 3 data tables match query The cross section for E+ E- --> K0S K+ PI- + CC with statistical errors only. The cross section for E+ E- --> K+ K- PI0 with statistical errors only. The cross section for E+ E- --> PHI PI0 with statistical errors only. #### rivet Analysis Inclusive Lambda(c)+ Production in e+ e- Annihilations at s*(1/2) = 10.54-GeV and in Upsilon(4S) Decays The collaboration Aubert, Bernard ; Bona, M. ; Boutigny, D. ; et al. Phys.Rev.D 75 (2007) 012003, 2007. Inspire Record 725377 We present measurements of the total production rates and momentum distributions of the charmed baryon $\Lambda_c^+$ in $e^+e^- \to$ hadrons at a center-of-mass energy of 10.54 GeV and in $\Upsilon(4S)$ decays. In hadronic events at 10.54 GeV, charmed hadrons are almost exclusively leading particles in $e^+e^- \to c\bar{c}$ events, allowing direct studies of $c$-quark fragmentation. We measure a momentum distribution for $\Lambda_c^+$ baryons that differs significantly from those measured previously for charmed mesons. Comparing with a number of models, we find none that can describe the distribution completely. We measure an average scaled momentum of $\left< x_p \right> = 0.574\pm$0.009 and a total rate of $N_{\Lambda c}^{q\bar{q}} = 0.057\pm$0.002(exp.)$\pm$0.015(BF) $\Lambda_c^+$ per hadronic event, where the experimental error is much smaller than that due to the branching fraction into the reconstructed decay mode, $pK^-\pi^+$. In $\Upsilon (4S)$ decays we measure a total rate of $N_{\Lambda c}^{\Upsilon} = 0.091\pm$0.006(exp.)$\pm$0.024(BF) per $\Upsilon(4S)$ decay, and find a much softer momentum distribution than expected from B decays into a $\Lambda_c^+$ plus an antinucleon and one to three pions. 1 data table match query The integrated number of LAMBDA/C+'s per hadronic event for the continuum at cm energy 10.54 GeV. #### rivet Analysis The $e^+e^- \to 3(\pi^+ \pi^-), 2(\pi^+ \pi^- \pi^0)$ and $K^+ K^- 2(\pi^+ \pi^-)$ cross sections at center-of-mass energies from production threshold to 4.5-GeV measured with initial-state radiation The collaboration Aubert, Bernard ; Barate, R. ; Boutigny, D. ; et al. Phys.Rev.D 73 (2006) 052003, 2006. Inspire Record 709730 We study the processes e+ e- --> 3(pi+pi-)gamma, 2(pi+pi-pi0)gamma and K+ K- 2(pi+pi-)gamma, with the photon radiated from the initial state. About 20,000, 33,000 and 4,000 fully reconstructed events, respectively, have been selected from 232 fb-1 of BaBar data. The invariant mass of the hadronic final state defines the effective e+e- center-of-mass energy, so that these data can be compared with the corresponding direct e+e- measurements. From the 3(pi+pi-), 2(pi+pi-pi0) and K+ K- 2(pi+pi-) mass spectra, the cross sections for the processes e+ e- --> 3(pi+pi-), e+ e- --> 2(pi+pi-pi0) and e+ e- --> K+ K- 2(pi+pi-) are measured for center-of-mass energies from production threshold to 4.5 GeV. The uncertainty in the cross section measurement is typically 6-15%. We observe the J/psi in all these final states and measure the corresponding branching fractions. 2 data tables match query The cross section for E+ E- --> 3PI+ 3PI- as measured with the ISR data. Errors are statistical only. The cross section for E+ E- --> 2PI+ 2PI- 2PI0 as measured with the ISR data. Errors are statistical only. #### rivet Analysis The $e^+e^- \to \pi^+ \pi^- \pi^+ \pi^-$, $K^+ K^- \pi^+ \pi^-$, and $K^+ K^- K^+ K^-$ cross sections at center-of-mass energies 0.5-GeV - 4.5-GeV measured with initial-state radiation The collaboration Aubert, Bernard ; Barate, R. ; Boutigny, D. ; et al. Phys.Rev.D 71 (2005) 052001, 2005. Inspire Record 676691 We study the process $e^+e^-\to\pi^+\pi^-\pi^+\pi^-\gamma$, with a hard photon radiated from the initial state. About 60,000 fully reconstructed events have been selected from 89 $fb^{-1}$ of BaBar data. The invariant mass of the hadronic final state defines the effective \epem center-of-mass energy, so that these data can be compared with the corresponding direct $e^+e^-$ measurements. From the $4\pi$-mass spectrum, the cross section for the process $e^+e^-\to\pi^+\pi^-\pi^+\pi^-$ is measured for center-of-mass energies from 0.6 to 4.5 $GeV/c^2$. The uncertainty in the cross section measurement is typically 5%. We also measure the cross sections for the final states $K^+ K^- \pi^+\pi^-$ and $K^+ K^- K^+ K^-$. We observe the $J/\psi$ in all three final states and measure the corresponding branching fractions. We search for X(3872) in $J/\psi (\to\mu^+\mu^-) \pi^+\pi^-$ and obtain an upper limit on the product of the $e^+e^-$ width of the X(3872) and the branching fraction for $X(3872) \to J/\psi\pi^+\pi^-$. 1 data table match query Measured PI+ PI- PI+ PI- cross sections. The errors are statistical only. #### rivet Analysis The e+ e- ---> 2(pi+ pi-) pi0, 2(pi+ pi-) eta, K+ K- pi+ pi- pi0 and K+ K- pi+ pi- eta Cross Sections Measured with Initial-State Radiation The collaboration Aubert, Bernard ; Bona, M. ; Boutigny, D. ; et al. Phys.Rev.D 76 (2007) 092005, 2007. Inspire Record 758568 We study the processes $e^+ e^-\to 2(\pi^+\pi^-)\pi^0\gamma$, $2(\pi^+\pi^-)\eta\gamma$, $K^+ K^-\pi^+\pi^-\pi^0\gamma$ and $K^+ K^-\pi^+\pi^-\eta\gamma$ with the hard photon radiated from the initial state. About 20000, 4300, 5500 and 375 fully reconstructed events, respectively, are selected from 232 fb$^{-1}$ of BaBar data. The invariant mass of the hadronic final state defines the effective $e^+ e^-$ center-of-mass energy, so that the obtained cross sections from the threshold to about 5 GeV can be compared with corresponding direct \epem measurements, currently available only for the $\eta\pi^+\pi^-$ and $\omega\pi^+\pi^-$ submodes of the $e^+ e^-\to 2(\pi^+\pi^-)\pi^0$ channel. Studying the structure of these events, we find contributions from a number of intermediate states, and we extract their cross sections where possible. In particular, we isolate the contribution from $e^+ e^-\to\omega(782)\pi^+\pi^-$ and study the $\omega(1420)$ and $\omega(1650)$ resonances. In the charmonium region, we observe the $J/\psi$ in all these final states and several intermediate states, as well as the $\psi(2S)$ in some modes, and we measure the corresponding branching fractions. 4 data tables match query Measured cross section for E+ E- --> 2(PI+ PI-) PI0 with statistical errorsonly. Measured cross section for E+ E- --> ETA PI+ PI- with statistical errors only. Measured cross section for E+ E- --> OMEGA PI+ PI- with statistical errors only. More… #### Measurement of the anti-Lambda polarization in muon-neutrino charged current interactions in the NOMAD experiment The collaboration Astier, P. ; Autiero, D. ; Baldisseri, A. ; et al. Nucl.Phys.B 605 (2001) 3-14, 2001. Inspire Record 554759 We present a measurement of the polarization of Antilambda hyperons produced in nu_mu charged current interactions. The full data sample from the NOMAD experiment has been analyzed using the same V0 identification procedure and analysis method reported in a previous paper for the case of Lambda hyperons. The Antilambda polarization has been measured for the first time in a neutrino experiment. The polarization vector is found to be compatible with zero. 1 data table match query Lambdabar polarization in regions of the Bjorken scaling variable X. #### Analysis of the pi+ pi- pi+ pi- and pi+ pi0 pi- pi0 final states in quasi-real two-photon collisions at LEP The collaboration Achard, P. ; Adriani, O. ; Aguilar-Benitez, M. ; et al. Phys.Lett.B 638 (2006) 128-139, 2006. Inspire Record 705125 The reactions gamma gamma -> pi^+pi^-pi^+pi^- and gamma gamma -> pi^+pi^0pi^-pi^0 are studied with the L3 detector at LEP in a data sample collected at centre-of-mass energies from 161GeV to 209GeV with a total integrated luminosity of 698/pb. A spin-parity-helicity analysis of the rho^0 rho^0 and rho^+ rho^- systems for two-photon centre-of-mass energies between 1GeV and 3GeV shows the dominance of the spin-parity state 2+ with helicity 2. The contribution of 0+ and 0- spin-parity states is also observed, whereas contributions of 2- states and of a state with spin-parity 2+ and zero helicity are found to be negligible. 4 data tables match query Cross section for 4PI and (RHO0 RHO0) production. Cross section for 4PI and (RHO+ RHO-) production. Spin parity analysis fits for RHO0 RHO0. More… #### High-statistics measurement of neutral pion-pair production in two-photon collisions The collaboration Uehara, S. ; Watanabe, Y. ; Adachi, I. ; et al. Phys.Rev.D 78 (2008) 052004, 2008. Inspire Record 786406 We report a high-statistics measurement of differential cross sections for the process gamma gamma -> pi^0 pi^0 in the kinematic range 0.6 GeV <= W <= 4.0 GeV and \|cos theta\| <= 0.8, where W and theta* are the energy and pion scattering angle, respectively, in the gamma gamma center-of-mass system. Differential cross sections are fitted to obtain information on S, D_0, D_2, G_0 and G_2 waves. The G waves are important above W ~= 1.6 GeV. For W <= 1.6 GeV the D_2 wave is dominated by the f_2(1270) resonance while the S wave requires at least one additional resonance besides the f_0(980), which may be the f_0(1370) or f_0(1500). The differential cross sections are fitted with a simple parameterization to determine the parameters (the mass, total width and Gamma_{gamma gamma}B(f_0 -> pi^0 pi^0)) of this scalar meson as well as the f_0(980). The helicity 0 fraction of the f_2(1270) meson, taking into account interference for the first time, is also obtained. 4 data tables match query Differential cross section for W = 1.27, 1.29 and 1.31 GeV. Differential cross section for W = 1.33, 1.35 and 1.37 GeV. Differential cross section for W = 1.39, 1.41 and 1.43 GeV. 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http://www.perimeterinstitute.ca/video-library/collection/particle-physics?page=17&qt-seminar_series=0	# Particle Physics This series consists of talks in the areas of Particle Physics, High Energy Physics & Quantum Field Theory. ## Seminar Series Events/Videos Currently there are no upcoming talks in this series. ## Channeling and Directional Features in Direct Dark Matter Detection Tuesday Dec 06, 2011 Speaker(s): The channeling of the ion recoiling after a collision with a WIMP produces a larger ionization/scintillation signal in direct dark matter detection experiments than otherwise expected. I will present estimates of the channeling fractions and their impact on data fits. I will also discuss the possibility of having a daily modulation of the signal due to channeling. Since this modulation depends on the recoil directions and thus on the orientation of the detector with respect to the galaxy, it would be a background free signature. Collection/Series: Scientific Areas: ## Scale Without Conformal Invariance Tuesday Nov 29, 2011 We investigate the theoretical implications of scale without conformal invariance in quantum field theory. We argue that the RG flows of such theories correspond to recurrent behaviors, i.e. limit cycles or ergodicity. We discuss the implications for the a-theorem and show how dilatation generators do generate dilatations. Finally, we discuss possible well-behaved non-conformal scale-invariant examples. Collection/Series: Scientific Areas: ## Magnetic Properties of (Holographic) Superconductors Monday Nov 28, 2011 Speaker(s): I will discuss magnetic properties of superconductors, first in a model independent way and then by using holographic models. This approach has the advantage of highlighting the generic features of superconducting materials and, at the same time, the predictions of specific models. I will start with the Meissner effect and the vortices. Given the importance of the magnetic field dynamics in these phenomena, I will describe how to introduce a dynamical gauge field in holography. Collection/Series: Scientific Areas: ## New CP violating observables for the LHC Friday Nov 25, 2011 Speaker(s): I discuss new types of CP violating observables that arise in three body decays that are dominated by an intermediate resonance. If two interfering diagrams with different orderings of the final state particles exist, the required CP even phase arises due to the different virtualities of the resonance in each of the two diagrams. Using momentum asymmetries, I demonstrate that CP violation can be seen in this way at the LHC and future colliders. Collection/Series: Scientific Areas: ## Monojet Events: a Journey Into the Standard Model and Beyond Tuesday Nov 22, 2011 Speaker(s): The Standard Model is currently the theory which describes the most fundamental constituents of matter and the forces which govern their interactions. Since the start-up of the LHC accelerator, the ATLAS detector has collected sufficient data to allow tests of this theory at the smallest distance scales ever probed. The objective is to find significant deviations between the observed data and the Standard Model predictions, revealing the existence of new phenomena. Collection/Series: Scientific Areas: ## A WIMPy Baryogenesis Miracle Tuesday Nov 15, 2011 Speaker(s): We propose models of symmetric WIMP dark matter in which dark matter annihilations generate the baryon asymmetry. We call this mechanism "WIMPy baryogenesis". This provides a dynamical connection between the late-time abundances of both dark matter and baryons. We construct explicit models of leptogenesis and baryogenesis at the weak scale, and find the "miraculous" result that, for order one couplings and weak scale masses for any new fields, the baryon asymmetry and dark matter relic density from WIMPy baryogenesis match the observed values. Collection/Series: Scientific Areas: ## Results on Searches from the CMS Experiment at the LHC Friday Nov 11, 2011 Speaker(s): The LHC has just concluded this year's proton-proton run at 7 TeV CM energy, producing more than 5fb-1of data. While the full data sample collected by the CMS experiment will be analyzed over the winter, many of the present searches for new physics have been completed with 1-2 fb-1. In this talk we will present the most recent updates on the search analyses in CMS, including the Higgs search, searches for supersymmetry, and a plethora of other BSM models, such as extra dimensions, Z's, W_R, leptoquarks, and more. Collection/Series: Scientific Areas: ## First EXO Results: Observation of Two-Neutrino Double-Beta Decay in 136Xe Tuesday Oct 25, 2011 Speaker(s): The Enriched Xenon Observatory (EXO) collaboration has observed the two-neutrino double beta decay of 136Xe with EXO-200, a prototype to the full EXO detector in development. This second order process, predicted by the Standard Model, has been observed for several nuclei but not for 136Xe. The observed decay rate provides new input to matrix element calculations and to the search for the more interesting neutrino-less double-beta decay, the most sensitive probe for the existence of Majorana particles and the measurement of the neutrino mass scale. Collection/Series: Scientific Areas: ## Constraining Dark Matter Tuesday Oct 18, 2011 Speaker(s): In this talk, I will discuss constraints on dark matter (DM) from Collection/Series: Scientific Areas: ## Lattice Study of a Technicolor Dark Matter Candidate Tuesday Oct 11, 2011 Speaker(s): The simplest technicolor model contains would-be Goldstone bosons to provide masses for the observed W and Z particles, replacing the standard Higgs mechanism. Perhaps surprisingly, it also contains an additional Goldstone boson that is a natural dark matter candidate. A recent lattice simulation has confirmed the symmetry-breaking pattern, explored the mass spectrum of the lightest technihadrons, and established an effective field theory. Collection/Series: Scientific Areas: ## RECENT PUBLIC LECTURE ### Molly Shoichet: Engineering Change in Medicine Speaker: Molly Shoichet	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9460597634315491, "perplexity": 2050.4429115738876}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560282140.72/warc/CC-MAIN-20170116095122-00013-ip-10-171-10-70.ec2.internal.warc.gz"}
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1459243/?tool=pubmed	PLoS Biol. 2006 May; 4(5): e151. Published online 2006 May 16. PMCID: PMC1459243 Model Selection and the Molecular Clock There are no mathematical equations in On the Origin of Species. A good thing too, you might think, and it is undoubtedly true that Darwin's clear and flowing narrative style helped ensure the popularity of his writings. Modern research in evolutionary biology can make for less easy reading. Much of it concerns the development of an expanding arsenal of mathematical and statistical techniques, necessary to do battle with the relentless onslaught of gene and genome sequences. Of course, the discrete, ordered nature of genetic information and the stochastic character of Mendelian inheritance have naturally lent themselves to numerical analysis. Consequently, the mathematical foundations of evolutionary genetics have, somewhat unusually for biology, tended to precede the data to which they are applied. The Genetical Theory of Natural Selection by R. A. Fisher, published only fifty years after Darwin's death, is full of equations [ 1]. The simplest weapon in the armoury of evolutionary genetics is genetic distance, a measure of the number of evolutionary changes between sequences from different organisms. Genetic distances can be calculated for a pair of sequences by simply counting the number of nucleotides or amino acids that differ between them. Unfortunately, this approach underestimates the amount of evolutionary change because it does not account for the fact that each site may change more than once during evolutionary history. Statistical tools, called nucleotide or amino acid substitution models, are therefore used to estimate genetic distances between sequences. There is a bewildering hierarchy of substitution models available, each making a different and specific set of assumptions about the evolutionary process of sequence change [ 2]. The simplest models assume that all types of mutation are equivalent and that all sites in a sequence change at the same rate. More complex models loosen these assumptions, allowing heterogeneity in the process of sequence change, but they can be reliably applied to larger datasets only. The task of deciding amongst these competing models is known as statistical model selection and can be thought of as a trade-off between model accuracy and model complexity. The degree to which a model fits the data at hand (accuracy) is always improved by adding more parameters (complexity), but since the amount of data remains constant the statistical uncertainty about each parameter increases. In addition, the biological meaning of each parameter becomes harder to decipher so the explanatory power of the model decreases ( Figure 1). Thus the chosen model should have enough parameters to adequately explain the data—but no more. Once an appropriate model is chosen, genetic distances are combined using other statistical techniques to generate a phylogenetic tree of the sequences being studied [ 2]. The lengths of the branches in the phylogeny thus represent estimated numbers of sequence changes ( Figure 2A). An Illustration of the General Properties of Model Selection Example Phylogenies, Each Representing the Shared Ancestry of Five Organisms However, genetic distances are rather crude indicators of evolutionary history. A small genetic distance between two sequences may suggest a recent common ancestor, but is also consistent with a slower rate of sequence change and a more ancient common ancestor (i.e., genetic distance = evolutionary rate × time). Genetic distances alone are therefore of little use if, for example, we wish to know the age of the common ancestor of mammals, or the rate at which bacterial antibiotic resistance genes evolve. Such questions can be answered only if independent information about rates or divergence times is found. Often paleontology or biogeography can provide a date for one or more points in a phylogeny, which are then used to “calibrate” the timescale for the rest of the phylogeny [ 3, 4]. Less commonly, sequences sampled at different times can provide an estimated rate of evolution; this requires either a very fast evolutionary rate (e.g., rapidly evolving RNA viruses [ 5]) or widely spaced sampling times (e.g., ancient DNA from sub-fossil samples [ 6]). Whatever the source of the independent information, it is usual to calibrate a phylogeny by assuming that all its branches evolve at the same rate—i.e., there is a constant but stochastic “molecular clock” of sequence change. The concept of the molecular clock originated in the early 1960s and has since been used widely, more as a result of its downright usefulness than its biological accuracy, as it is clear that rates of evolution can and do vary considerably among species [ 4, 7]. Evolutionary rates depend on a combination of factors: generation time, population size, metabolic rate, the efficacy of DNA repair, and the degree to which mutations are beneficial or deleterious, all of which may vary among species. As the geneticist Steve Jones recently remarked, evolutionary biologists seem to use the molecular clock “with our fingers crossed” [ 8]. The article by Alexei Drummond, Andrew Rambaut, and colleagues in this issue of PLoS Biology [ 9] gives us reason to uncross our fingers a little. The paper describes a new “relaxed” approach to the estimation of phylogeny divergence times. A relaxed molecular clock is a phylogenetic technique that allows the rate of sequence evolution to vary among groups of organisms, or more generally, among different parts of a phylogeny ( Figure 2B). The use of a single rate across the whole phylogeny is termed a “strict” clock ( Figure 2C). Such methods have developed steadily in the past ten years (e.g., [ 10, 11]) and can now be applied to large datasets due to the continued increase in computer processing speed. A common aspect of previous relaxed-clock approaches is that they considered closely related organisms to have similar rates of evolution. On a phylogeny this means that neighbouring branches have more similar rates than distant branches, a property termed “autocorrelation”. The idea that rates of sequence evolution can be “inherited” in this way played an important role in the history and development of evolutionary theory [ 7, 12], and it is well known that viruses, bacteria, and animals evolve at hugely different rates, but the assumption has never been comprehensively tested. Drummond et al.'s new method allows phylogeny branches to vary in rate, but it does not assume these rates are correlated among adjacent branches ( Figure 2). Thus their relaxed clock is slightly more laid-back than its predecessors, and crucially it can estimate the level of autocorrelation in each dataset. A further advantage of their approach is that it simultaneously estimates both phylogeny shape and rate variation among phylogeny branches, two tasks that previously had to be performed separately. We should note that Drummond et al's paper emphasises the fact that molecular clocks exist as a family of statistical models, analogous to the hierarchy of substitution models discussed earlier, among which the most appropriate model should be chosen. When constructing a phylogeny, many researchers opt not to “enforce” a molecular clock, perhaps believing that they are avoiding having to make any possibly unrealistic assumptions about evolutionary rates. In truth, this “no-clock” approach is equivalent to using an evolutionary model that assumes no limit to the variation in evolutionary rate among branches. In fact, it has a separate evolutionary rate parameter for each branch in the phylogeny. If, as is often the case, rate variation among organisms is not great, then the no-clock model will have an unnecessarily large number of parameters, leading to an increase in statistical uncertainty and, in some circumstances, poorer estimates of phylogeny shape. Drummond et al. analysed five large datasets, containing sequences from bacteria, yeast, plants, animals, and primates, and found that in every case their relaxed-clock model identified the “true” phylogeny slightly more often than the no-clock model. Importantly, the relaxed-clock estimates were more certain than those of the no-clock model, as expected given the greater number of parameters in the latter model [ 9]. A key area of future research will be to investigate these results using statistical model selection theory. It is perhaps surprising that gene sequences contain sufficient information to estimate as complex a process as evolutionary rate variation among organisms. But it is well known that if phylogenies are constructed using the no-clock model, then the genetic distances of sequences to a shared common ancestor are unequal ( Figure 2A). Since sequences are sampled at the same time (on an evolutionary scale), the times to the common ancestor will be identical for each; hence the variation in genetic distance directly reflects the variation in evolutionary rate since the common ancestor. This valuable information about the evolutionary process is ignored whenever the no-clock model is used, despite it being used for many years in the relative rates test, a statistical test used to detect evolutionary rate variation [ 7]. It is likely that the widespread adoption of relaxed-clock models in phylogenetics will act as a stepping-stone to even more intricate models of sequence change. Work has already begun on combining evolutionary rate variation among organisms with rate variation among genomic sites, so that particular sets of sites are able to evolve quicker or slower on different sets of branches [ 13]. This could be important if certain parts of a gene are under selection in some species but not others. This complex situation, known as heterotachy, is currently the subject of debate amongst phylogeneticists, as it is unclear whether model-based statistical approaches are better than “model-free” parsimony methods that appear not to make assumptions about the evolutionary process [ 13, 14]. In many ways, this debate echoes the relaxed-clock and no-clock comparison discussed above. It is quite possible that in this case, too, the model-free parsimony methods are making implicit assumptions about the nature of rate variation among sites and lineages, but the underlying process is so complicated that it will take time for these assumptions to be fully understood. The complexity of heterotachy will also require larger datasets than are currently used in phylogenetics. But in the midst of a revolution in high-speed genomics, it is not sequence data we are short of, but tools for statistical analysis—and the equations on which they are based. Acknowledgments Funding. OGP was funded by the Royal Society. Competing interests. The author has declared that no competing interests exist. Footnotes Citation: Pybus OG (2006) Model selection and the molecular clock. PLoS Biol 4(5): e151. DOI: 10.1371/journal.pbio.0040151 Oliver G. Pybus is in the Department of Zoology, University of Oxford, Oxford, United Kingdom. E-mail: [email protected] References • Fisher RA. The genetical theory of natural selection. A complete variorum edition. Oxford: Oxford University Press; 1999. 354 pp. • Felsenstein J. Inferring phylogenies. Sunderland (Massachusetts): Sinauer Associates; 2004. 664 pp. • Zuckerkandl E, Pauling L. Molecular disease, evolution and genic heterogeneity. In: Kasha M, Pullman B, editors. Horizons in biochemistry. New York: Academic Press; 1962. 604 pp. • Bromham L, Penny D. The modern molecular clock. Nat Rev Genet. 2003;4:216–224. [PubMed] • Buonagurio DA, Nakada S, Parvin JD, Krystal M, Palese P, et al. Evolution of human influenza A viruses over 50 years: Rapid, uniform rate of change in NS gene. Science. 1986;232:980–982. [PubMed] • Lambert DM, Ritchie PA, Millar CD, Holland B, Drummond AJ, et al. Rates of evolution in ancient DNA from Adelie penguins. Science. 2002;295:2270–2273. [PubMed] • Kumar S. Molecular clocks: Four decades of evolution. Nat Rev Genet. 2005;6:654–662. [PubMed] • Jones S. In our time: Human evolution. BBC Radio 4. First broadcast 16 February 2006. 2006 Available: http://www.bbc.co.uk/radio4/history/inourtime/inourtime_20060216.shtml. Accessed 20 March 2006 . • Drummond AJ, Ho SYW, Phillips MJ, Rambaut A. Relaxed phylogenetics and dating with confidence. PLoS Biol. 2006;4:e88. doi: 10.1371/journal.pbio.0040088. [PubMed] • Sanderson MJ. A nonparametric approach to estimating divergence times in the absence of rate constancy. Mol Biol Evol. 1997;14:1218–1231. • Thorn JL, Kishino H, Painter IS. Estimating the rate of evolution of the rate of evolution. Mol Biol Evol. 1998;15:1647–1657. [PubMed] • Gillespie JH. The causes of molecular evolution. New York: Oxford University Press; 1991. 352 pp. • Kolaczkowski B, Thorton JW. Performance of maximum parsimony and likelihood phylogenetics when evolution is heterogeneous. Nature. 2004;431:980–984. [PubMed] • Steel M. Should phylogenetics be trying to “fit an elephant”? Trend Genet. 2005;21:307–309. [PubMed] Articles from PLoS Biology are provided here courtesy of Public Library of Science Formats: Related citations in PubMed See reviews...See all... Cited by other articles in PMC See all... • PubMed PubMed PubMed citations for these articles	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8259138464927673, "perplexity": 2140.040530768104}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131298228.32/warc/CC-MAIN-20150323172138-00274-ip-10-168-14-71.ec2.internal.warc.gz"}
http://repository.bilkent.edu.tr/browse?type=subject&value=Optimization%20techniques	Now showing items 1-5 of 5 • #### Effects of additional independent noise in binary composite hypothesis-testing problems (IEEE, 2009-09) Performance of some suboptimal detectors can be improved by adding independent noise to their observations. In this paper, the effects of adding independent noise to observations of a detector are investigated for binary ... • #### Examining the annealing schedules for RNA design algorithm (IEEE, 2016-07) RNA structures are important for many biological processes in the cell. One important function of RNA are as catalytic elements. Ribozymes are RNA sequences that fold to form active structures that catalyze important ... • #### G-network modelling based abnormal pathway detection in gene regulatory networks (Springer, London, 2012) Gene expression centered gene regulatory networks studies can provide insight into the dynamics of pathway activities that depend on changes in their environmental conditions. Thus we propose a new pathway analysis approach ... • #### Low-order controller design for haptic systems under delayed feedback (2012) In this paper, we consider PD controller design for haptic systems under delayed feedback. More precisely, we present a complete stability analysis of a haptic system where local dynamics are described by some second-order ... • #### Projections onto convex sets (POCS) based optimization by lifting (IEEE, 2013) A new optimization technique based on the projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by ...	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8052582144737244, "perplexity": 2552.556053691364}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499634.11/warc/CC-MAIN-20230128121809-20230128151809-00872.warc.gz"}
http://sifaka.cs.uiuc.edu/jiang4/domain_adaptation/survey/node8.html	Next: 3.3 Change of Functional Up: 3 Instance Weighting Previous: 3.1 Class Imbalance Contents ## 3.2 Covariate Shift Another assumption one can make about the connection between the source and the target domains is that given the same observation , the conditional distributions of are the same in the two domains. However, the marginal distributions of may be different in the source and the target domains. Formally, we assume that for all , but . This difference between the two domains is called covariate shift (Shimodaira, 2000). At first glance, it may appear that covariate shift is not a problem. For classification, we are only interested in . If , why would the classifier learned from the source domain not perform well on the target domain even if ? Shimodaira (2000) showed that this covariate shift becomes a problem when misspecified models are used. Suppose we consider a parametric model family from which a model is selected to minimize the expected classification error. If none of the models in the model family can exactly match the true relation between and , that is, there does not exist any such that for all , then we say that we have a misspecified model family. The intuition of why covariate shift under model misspecification becomes a problem is as follows. With a misspecified model family, the optimal model we select depends on , and if , then the optimal model for the target domain will differ from that for the source domain. The intuitive is that the optimal model performs better in dense regions of than in sparse regions of , because the dense regions dominate the average classification error, which is what we want to minimize. If the dense regions of are different in the source and the target domains, the optimal model for the source domain will no longer be optimal for the target domain. Under covariate shift, the ratio that we derived in Equation () can be rewritten as follows: We therefore want to weight each training instance with . Shimodaira (2000) first proposed to re-weight the log likelihood of each training instance using in maximum likelihood estimation for covariate shift. It can be shown theoretically that if the support of (the set of 's for which ) is contained in the support of , then the optimal model that maximizes this re-weighted log likelihood function asymptotically converges to the optimal model for the target domain. A major challenge is how to estimate the ratio for each in the training set. In some work, a principled method of using non-parametric kernel density estimation is explored (Sugiyama and Müller, 2005; Shimodaira, 2000). In some other work, it is proposed to transform this density ratio estimation into a problem of predicting whether an instance is from the source domain or from the target domain (Zadrozny, 2004; Bickel and Scheffer, 2007). Huang et al. (2007) transformed the problem into a kernel mean matching problem in a reproducing kernel Hilbert space. Bickel et al. (2007) proposed to learn this ratio together with the classification model parameters. Next: 3.3 Change of Functional Up: 3 Instance Weighting Previous: 3.1 Class Imbalance Contents Jing Jiang 2008-03-06	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8767504692077637, "perplexity": 474.28967019575094}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368710115542/warc/CC-MAIN-20130516131515-00058-ip-10-60-113-184.ec2.internal.warc.gz"}
https://online.stat.psu.edu/stat501/book/export/html/967	# 10.3 - Best Subsets Regression, Adjusted R-Sq, Mallows Cp 10.3 - Best Subsets Regression, Adjusted R-Sq, Mallows Cp In this section, we learn about the best subsets regression procedure (or the all possible subsets regression procedure). While we will soon learn the finer details, the general idea behind best subsets regression is that we select the subset of predictors that do the best at meeting some well-defined objective criterion, such as having the largest $$R^{2} \text{-value}$$ or the smallest MSE. Again, our hope is that we end up with a reasonable and useful regression model. There is one sure way of ending up with a model that is certain to be underspecified — and that's if the set of candidate predictor variables doesn't include all of the variables that actually predict the response. Therefore, just as is the case for the stepwise regression procedure, a fundamental rule of the best subsets regression procedure is that the list of candidate predictor variables must include all of the variables that actually predict the response. Otherwise, we are sure to end up with a regression model that is underspecified and therefore misleading. ### The procedure A regression analysis utilizing the best subsets regression procedure involves the following steps: 1. Step #1 First, identify all of the possible regression models derived from all of the possible combinations of the candidate predictors. Unfortunately, this can be a huge number of possible models. For the sake of example, suppose we have three (3) candidate predictors — $$x_{1}$$, $$x_{2}$$, and $$x_{3}$$— for our final regression model. Then, there are eight (8) possible regression models we can consider: • the one (1) model with no predictors • the three (3) models with only one predictor each — the model with $$x_{1}$$ alone; the model with $$x_{2}$$ alone; and the model with $$x_{3}$$ alone • the three (3) models with two predictors each — the model with $$x_{1}$$ and $$x_{2}$$; the model with $$x_{1}$$ and $$x_{3}$$; and the model with $$x_{2}$$ and $$x_{3}$$ • and the one (1) model with all three predictors — that is, the model with $$x_{1}$$, $$x_{2}$$ and $$x_{3}$$ That's 1 + 3 + 3 + 1 = 8 possible models to consider. It can be shown that when there are four candidate predictors — $$x_{1}$$, $$x_{2}$$, $$x_{3}$$ and $$x_{4}$$ — there are 16 possible regression models to consider. In general, if there are p-1 possible candidate predictors, then there are $$2^{p-1}$$ possible regression models containing the predictors. For example, 10 predictors yield $$2^{10} = 1024$$ possible regression models. That's a heck of a lot of models to consider! The good news is that statistical software, such as Minitab, does all of the dirty work for us. 2. Step #2 From the possible models identified in the first step, determine the one-predictor models that do the "best" at meeting some well-defined criteria, the two-predictor models that do the "best," the three-predictor models that do the "best," and so on. For example, suppose we have three candidate predictors — $$x_{1}$$, $$x_{2}$$, and $$x_{3}$$ — for our final regression model. Of the three possible models with one predictor, identify the one or two that does "best." Of the three possible two-predictor models, identify the one or two that does "best." By doing this, it cuts down considerably the number of possible regression models to consider! But, have you noticed that we have not yet even defined what we mean by "best"? What do you think "best" means? Of course, you'll probably define it differently than me or than your neighbor. Therein lies the rub — we might not be able to agree on what's best! In thinking about what "best" means, you might have thought of any of the following: • the model with the largest $$R^{2}$$ • the model with the largest adjusted $$R^{2}$$ • the model with the smallest MSE (or S = square root of MSE) There are other criteria you probably didn't think of, but we could consider, too, for example, Mallows' $$C_{p}$$-statistic, the PRESS statistic, and Predicted $$R^{2}$$ (which is calculated from the PRESS statistic). We'll learn about Mallows' $$C_{p}$$-statistic in this section and about the PRESS statistic and Predicted $$R^{2}$$ in a Section 10.5. To make matters even worse — the different criteria quantify different aspects of the regression model, and therefore often yield different choices for the best set of predictors. That's okay — as long as we don't misuse best subsets regression by claiming that it yields the best model. Rather, we should use best subsets regression as a screening tool — that is, as a way to reduce the large number of possible regression models to just a handful of models that we can evaluate further before arriving at one final model. 3. Step #3 Further evaluate and refine the handful of models identified in the last step. This might entail performing residual analyses, transforming the predictors and/or response, adding interaction terms, and so on. Do this until you are satisfied that you have found a model that meets the model conditions, does a good job of summarizing the trend in the data, and most importantly allows you to answer your research question. ## Example 10-3: Cement Data For the remainder of this section, we discuss how the criteria identified above can help us reduce the large number of possible regression models to just a handful of models suitable for further evaluation. For the sake of example, we will use the cement data to illustrate use of the criteria. Therefore, let's quickly review — the researchers measured and recorded the following data (Cement data) on 13 batches of cement: • Response y: heat evolved in calories during hardening of cement on a per gram basis • Predictor $$x_{1}$$: % of tricalcium aluminate • Predictor $$x_{2}$$: % of tricalcium silicate • Predictor $$x_{3}$$: % of tetracalcium alumino ferrite • Predictor $$x_{4}$$: % of dicalcium silicate And, the matrix plot of the data looks like: ### The $$R^{2} \text{-values}$$ As you may recall, the $$R^{2} \text{-value}$$, which is defined as: $$R^2=\dfrac{SSR}{SSTO}=1-\dfrac{SSE}{SSTO}$$ can only increase as more variables are added. Therefore, it makes no sense to define the "best" model as the model with the largest $$R^{2} \text{-value}$$. After all, if we did, the model with the largest number of predictors would always win. All is not lost, however. We can instead use the $$R^{2} \text{-values}$$ to find the point where adding more predictors is not worthwhile, because it yields a very small increase in the $$R^{2}$$-value. In other words, we look at the size of the increase in $$R^{2}$$, not just its magnitude alone. Because this is such a "wishy-washy" criteria, it is used most often in combination with the other criteria. Let's see how this criterion works on the cement data example. In doing so, you get your first glimpse of Minitab's best subsets regression output. For Minitab, select Stat > Regression > Regression > Best Subsets to do a best subsets regression. ##### Response is y R-Sq R-Sq Mallows x x x x Vars R-Sq (adj) (pred) Cp S 1 2 3 4 1 67.5 64.5 56.0 138.7 8.9639 X 1 66.6 63.6 55.7 142.5 9.0771 X 2 97.9 97.4 96.5 2.7 2.4063 X X 2 97.2 96.7 95.5 5.5 2.7343 X X 3 98.2 97.6 96.9 3.0 2.3087 X X X 3 98.2 97.6 96.7 3.0 2.3232 X X X 4 98.2 97.4 95.9 5.0 2.4460 X X X X Each row in the table represents information about one of the possible regression models. The first column — labeled Vars — tells us how many predictors are in the model. The last four columns — labeled downward x1, x2, x3, and x4 — tell us which predictors are in the model. If an "X" is present in the column, then that predictor is in the model. Otherwise, it is not. For example, the first row in the table contains information about the model in which $$x_{4}$$ is the only predictor, whereas the fourth row contains information about the model in which $$x_{1}$$ and $$x_{4}$$ are the two predictors in the model. The other five columns — labeled R-sq, R-sq(adj), R-sq(pred), Cp and S — pertain to the criteria that we use in deciding which models are "best." As you can see, by default Minitab reports only the two best models for each number of predictors based on the size of the $$R^{2} \text{-value}$$ that is, Minitab reports the two one-predictor models with the largest $$R^{2} \text{-values}$$, followed by the two two-predictor models with the largest $$R^{2} \text{-values}$$, and so on. So, using the $$R^{2} \text{-value}$$ criterion, which model (or models) should we consider for further evaluation? Hmmm — going from the "best" one-predictor model to the "best" two-predictor model, the $$R^{2} \text{-value}$$ jumps from 67.5 to 97.9. That is a jump worth making! That is, with such a substantial increase in the $$R^{2} \text{-value}$$, one could probably not justify — with a straight face at least — using the one-predictor model over the two-predictor model. Now, should we instead consider the "best" three-predictor model? Probably not! The increase in the $$R^{2} \text{-value}$$ is very small — from 97.9 to 98.2 — and therefore, we probably can't justify using the larger three-predictor model over the simpler, smaller two-predictor model. Get it? Based on the $$R^{2} \text{-value}$$ criterion, the "best" model is the model with the two predictors $$x_{1}$$ and $$x_{2}$$. ### The adjusted $$R^{2} \text{-value}$$ and MSE The adjusted $$R^{2} \text{-value}$$, which is defined as: \begin{align} R_{a}^{2}&=1-\left(\dfrac{n-1}{n-p}\right)\left(\dfrac{SSE}{SSTO}\right)\\&=1-\left(\dfrac{n-1}{SSTO}\right)MSE\\&=\dfrac{\dfrac{SSTO}{n-1}-\frac{SSE}{n-p}}{\dfrac{SSTO}{n-1}}\end{align} makes us pay a penalty for adding more predictors to the model. Therefore, we can just use the adjusted $$R^{2} \text{-value}$$ outright. That is, according to the adjusted $$R^{2} \text{-value}$$ criterion, the best regression model is the one with the largest adjusted $$R^{2}$$-value. Now, you might have noticed that the adjusted $$R^{2} \text{-value}$$ is a function of the mean square error (MSE). And, you may — or may not — recall that MSE is defined as: $$MSE=\dfrac{SSE}{n-p}=\dfrac{\sum(y_i-\hat{y}_i)^2}{n-p}$$ That is, MSE quantifies how far away our predicted responses are from our observed responses. Naturally, we want this distance to be small. Therefore, according to the MSE criterion, the best regression model is the one with the smallest MSE. But, aha — the two criteria are equivalent! If you look at the formula again for the adjusted $$R^{2} \text{-value}$$: $$R_{a}^{2}=1-\left(\dfrac{n-1}{SSTO}\right)MSE$$ you can see that the adjusted $$R^{2} \text{-value}$$ increases only if MSE decreases. That is, the adjusted $$R^{2} \text{-value}$$ and MSE criteria always yield the same "best" models. Back to the cement data example! One thing to note is that S is the square root of MSE. Therefore, finding the model with the smallest MSE is equivalent to finding the model with the smallest S: ##### Response is y R-Sq R-Sq Mallows x x x x Vars R-Sq (adj) (pred) Cp S 1 2 3 4 1 67.5 64.5 56.0 138.7 8.9639 X 1 66.6 63.6 55.7 142.5 9.0771 X 2 97.9 97.4 96.5 2.7 2.4063 X X 2 97.2 96.7 95.5 5.5 2.7343 X X 3 98.2 97.6 96.9 3.0 2.3087 X X X 3 98.2 97.6 96.7 3.0 2.3232 X X X 4 98.2 97.4 95.9 5.0 2.4460 X X X X The model with the largest adjusted $$R^{2} \text{-value}$$ (97.6) and the smallest S (2.3087) is the model with the three predictors $$x_{1}$$, $$x_{2}$$, and $$x_{4}$$. See?! Different criteria can indeed lead us to different "best" models. Based on the $$R^{2} \text{-value}$$ criterion, the "best" model is the model with the two predictors $$x_{1}$$ and $$x_{2}$$. But, based on the adjusted $$R^{2} \text{-value}$$ and the smallest MSE criteria, the "best" model is the model with the three predictors $$x_{1}$$, $$x_{2}$$, and $$x_{4}$$. ### Mallows' $$C_{p}$$-statistic Recall that an underspecified model is a model in which important predictors are missing. And, an underspecified model yields biased regression coefficients and biased predictions of the response. Well, in short, Mallows' $$C_{p}$$-statistic estimates the size of the bias that is introduced into the predicted responses by having an underspecified model. Now, we could just jump right in and be told how to use Mallows' $$C_{p}$$-statistic as a way of choosing a "best" model. But, then it wouldn't make any sense to you — and therefore it wouldn't stick to your craw. So, we'll start by justifying the use of the Mallows' $$C_{p}$$-statistic. The problem is it's kind of complicated. So, be patient, don't be frightened by the scary looking formulas, and before you know it, we'll get to the moral of the story. Oh, and by the way, in case you're wondering — it's called Mallows' $$C_{p}$$-statistic, because a guy named Mallows thought of it! Here goes! At issue in any regression model are two things, namely: • The bias in the predicted responses. • The variation in the predicted responses. #### Bias in predicted responses Recall that, in fitting a regression model to data, we attempt to estimate the average — or expected value — of the observed responses $$E \left( y_i \right)$$ at any given predictor value x. That is, $$E \left( y_i \right)$$ is the population regression function. Because the average of the observed responses depends on the value of x, we might also denote this population average or population regression function as $$\mu_{Y\|x}$$. Now, if there is no bias in the predicted responses, then the average of the observed responses $$E \left( y_i \right)$$ and the average of the predicted responses E($$\hat{y}_i$$) both equal the thing we are trying to estimate, namely the average of the responses in the population $$\mu_{Y\|x}$$. On the other hand, if there is bias in the predicted responses, then $$E \left( y_i \right)$$ = $$\mu_{Y\|x}$$ and E($$\hat{y}_i$$) do not equal each other. The difference between $$E \left( y_i \right)$$ and E($$\hat{y}_i$$) is the bias $$B_i$$ in the predicted response. That is, the bias: $$B_i=E(\hat{y}_i) - E(y_i)$$ We can picture this bias as follows: The quantity $$E \left( y_i \right)$$ is the value of the population regression line at a given x. Recall that we assume that the error terms $$\epsilon_i$$ are normally distributed. That's why there is a normal curve — in blue — drawn around the population regression line $$E \left( y_i \right)$$. You can think of the quantity E($$\hat{y}_i$$) as being the predicted regression line — well, technically, it's the average of all of the predicted regression lines you could obtain based on your formulated regression model. Again, since we always assume the error terms $$\epsilon_i$$ are normally distributed, we've drawn a normal curve — in red — around the average predicted regression line E($$\hat{y}_i$$). The difference between the population regression line $$E \left( y_i \right)$$ and the average predicted regression line E($$\hat{y}_i$$) is the bias $$B_i=E(\hat{y}_i)-E(y_i)$$ . Earlier in this lesson, we saw an example in which bias was likely introduced into the predicted responses because of an underspecifed model. The data concerned the heights and weights of martians. The Martian data set — don't laugh — contains the weights (in g), heights (in cm), and amount of daily water consumption (0, 10 or 20 cups per day) of 12 martians. If we regress y = weight on the predictors $$x_{1}$$ = height and $$x_{2}$$ = water, we obtain the following estimated regression equation: ##### Regression Equation weight = -1.220 + -.28344 height + 0.11121 water But, if we regress y = weight on only the one predictor $$x_{1}$$ = height, we obtain the following estimated regression equation: ##### Regression Equation weight = -4.14 + 0.2889 height A plot of the data containing the two estimated regression equations looks like: The three black lines represent the estimated regression equation when the amount of water consumption is taken into account — the first line for 0 cups per day, the second line for 10 cups per day, and the third line for 20 cups per day. The dashed blue line represents the estimated regression equation when we leave the amount of water consumed out of the regression model. As you can see, if we use the blue line to predict the weight of a randomly selected martian, we would consistently overestimate the weight of martians who drink 0 cups of water a day, and we would consistently understimate the weight of martians who drink 20 cups of water a day. That is, our predicted responses would be biased. #### Variation in predicted responses When a bias exists in the predicted responses, the variance in the predicted responses for a data point i is due to two things: • the ever-present random sampling variation, that is $$(\sigma_{\hat{y}_i}^{2})$$ • the variance associated with the bias, that is $$(B_{i}^{2})$$ Now, if our regression model is biased, it doesn't make sense to consider the bias at just one data point i. We need to consider the bias that exists for all n data points. Looking at the plot of the two estimated regression equations for the martian data, we see that the predictions for the underspecified model are more biased for certain data points than for others. And, we can't just consider the variation in the predicted responses at one data point i. We need to consider the total variation in the predicted responses. To quantify the total variation in the predicted responses, we just sum the two variance components — $$(\sigma_{\hat{y}_i}^{2})$$ and $$(B_{i}^{2})$$ — over all n data points to obtain a (standardized) measure of the total variation in the predicted responses $$\Gamma_p$$ (that's the greek letter "gamma"): $$\Gamma_p=\dfrac{1}{\sigma^2} \left\{ \sum_{i=1}^{n}\sigma_{\hat{y}_i}^{2}+\sum_{i=1}^{n}\left( E(\hat{y}_i)-E(y_i) \right) ^2 \right\}$$ I warned you about not being overwhelmed by scary looking formulas! The first term in the brackets quantifies the random sampling variation summed over all n data points, while the second term in the brackets quantifies the amount of bias (squared) summed over all n data points. Because the size of the bias depends on the measurement units used, we divide by $$\sigma^{2}$$ to get a standardized unitless measure. Now, we don't have the tools to prove it, but it can be shown that if there is no bias in the predicted responses — that is, if the bias = 0 — then $$\Gamma_p$$ achieves its smallest possible value, namely p, the number of parameters: $$\Gamma_p=\dfrac{1}{\sigma^2} \left\{ \sum_{i=1}^{n}\sigma_{\hat{y}_i}^{2}+0 \right\} =p$$ Now, because it quantifies the amount of bias and variance in the predicted responses, $$\Gamma_p$$ seems to be a good measure of an underspecified model: $$\Gamma_p=\dfrac{1}{\sigma^2} \left\{ \sum_{i=1}^{n}\sigma_{\hat{y}_i}^{2}+\sum_{i=1}^{n} \left( E(\hat{y}_i)-E(y_i) \right) ^2 \right\}$$ The best model is simply the model with the smallest value of $$\Gamma_p$$. We even know that the theoretical minimum of $$\Gamma_p$$ is the number of parameters p. Well, it's not quite that simple — we still have a problem. Did you notice all of those greek parameters — $$\sigma^{2}$$, $$(\sigma_{\hat{y}_i}^{2})$$, and $$\gamma_p$$? As you know, greek parameters are generally used to denote unknown population quantities. That is, we don't or can't know the value of $$\Gamma_p$$ — we must estimate it. That's where Mallows' $$C_{p}$$-statistic comes into play! #### $$C_{p}$$ as an estimate of $$\Gamma_p$$ If we know the population variance $$\sigma^{2}$$, we can estimate $$\Gamma_{p}$$: $$C_p=p+\dfrac{(MSE_p-\sigma^2)(n-p)}{\sigma^2}$$ where $$MSE_{p}$$ is the mean squared error from fitting the model containing the subset of p-1 predictors (which with the intercept contains p parameters). But we don't know $$\sigma^{2}$$. So, we estimate it using $$MSE_{all}$$, the mean squared error obtained from fitting the model containing all of the candidate predictors. That is: $$C_p=p+\dfrac{(MSE_p-MSE_{all})(n-p)}{MSE_{all}}=\dfrac{SSE_p}{MSE_{all}}-(n-2p)$$ A couple of things to note though. Estimating $$\sigma^{2}$$ using $$MSE_{all}$$: • assumes that there are no biases in the full model with all of the predictors, an assumption that may or may not be valid, but can't be tested without additional information (at the very least you have to have all of the important predictors involved) • guarantees that $$C_{p}$$ = p for the full model because in that case $$MSE_{p}$$ - $$MSE_{all}$$ = 0. #### Using the $$C_{p}$$ criterion to identify "best" models Finally — we're getting to the moral of the story! Just a few final facts about Mallows' $$C_{p}$$-statistic will get us on our way. Recalling that p denotes the number of parameters in the model: • Subset models with small $$C_{p}$$ values have a small total (standardized) variance of prediction. • When the $$C_{p}$$ value is ... • ... near p, the bias is small (next to none) • ... much greater than p, the bias is substantial • ... below p, it is due to sampling error; interpret as no bias • For the largest model containing all of the candidate predictors, $$C_{p}$$ = p (always). Therefore, you shouldn't use $$C_{p}$$ to evaluate the fullest model. That all said, here's a reasonable strategy for using $$C_{p}$$ to identify "best" models: • Identify subsets of predictors for which the $$C_{p}$$ value is near p (if possible). • The full model always yields $$C_{p}$$= p, so don't select the full model based on $$C_{p}$$. • If all models, except the full model, yield a large $$C_{p}$$ not near p, it suggests some important predictor(s) are missing from the analysis. In this case, we are well-advised to identify the predictors that are missing! • If a number of models have $$C_{p}$$ near p, choose the model with the smallest $$C_{p}$$ value, thereby insuring that the combination of the bias and the variance is at a minimum. • When more than one model has a small value of $$C_{p}$$ value near p, in general, choose the simpler model or the model that meets your research needs. ## Example 10-3: Cement Data Continued Ahhh—an example! Let's see what model the $$C_{p}$$ criterion leads us to for the cement data: ##### Response is y R-Sq R-Sq Mallows x x x x Vars R-Sq (adj) (pred) Cp S 1 2 3 4 1 67.5 64.5 56.0 138.7 8.9639 X 1 66.6 63.6 55.7 142.5 9.0771 X 2 97.9 97.4 96.5 2.7 2.4063 X X 2 97.2 96.7 95.5 5.5 2.7343 X X 3 98.2 97.6 96.9 3.0 2.3087 X X X 3 98.2 97.6 96.7 3.0 2.3232 X X X 4 98.2 97.4 95.9 5.0 2.4460 X X X X The first thing you might want to do here is "pencil in" a column to the left of the Vars column. Recall that this column tells us the number of predictors (p-1) that are in the model. But, we need to compare $$C_{p}$$ to the number of parameters (p). There is always one more parameter—the intercept parameter—than predictors. So, you might want to add—at least mentally—a column containing the number of parameters—here, 2, 2, 3, 3, 4, 4, and 5. Here, the model in the third row (containing predictors $$x_{1}$$ and $$x_{2}$$), the model in the fifth row (containing predictors $$x_{1}$$, $$x_{2}$$ and $$x_{4}$$), and the model in the sixth row (containing predictors $$x_{1}$$, $$x_{2}$$ and $$x_{3}$$) are all unbiased models, because their $$C_{p}$$ values equal (or are below) the number of parameters p. For example: • the model containing the predictors $$x_{1}$$ and $$x_{2}$$ contains 3 parameters and its $$C_{p}$$ value is 2.7. When $$C_{p}$$ is less than p, it suggests the model is unbiased; • the model containing the predictors $$x_{1}$$, $$x_{2}$$ and $$x_{4}$$ contains 4 parameters and its $$C_{p}$$ value is 3.0. When $$C_{p}$$ is less than p, it suggests the model is unbiased; • the model containing the predictors $$x_{1}$$, $$x_{2}$$ and $$x_{3}$$ contains 4 parameters and its $$C_{p}$$ value is 3.0. When $$C_{p}$$ is less than p, it suggests the model is unbiased. So, in this case, based on the $$C_{p}$$ criterion, the researcher has three legitimate models from which to choose with respect to bias. Of these three, the model containing the predictors $$x_{1}$$ and $$x_{2}$$ has the smallest $$C_{p}$$ value, but the $$C_{p}$$ values for the other two models are similar and so there is little to separate these models based on this criterion. Incidentally, you might also want to conclude that the last model — the model containing all four predictors — is a legitimate contender because $$C_{p}$$ = 5.0 equals p = 5. Don't forget that the model with all of the predictors is assumed to be unbiased. Therefore, you should not use the $$C_{p}$$ criterion as a way of evaluating the fullest model with all of the predictors. Incidentally, how did Minitab detemine that the $$C_{p}$$ value for the third model is 2.7, while for the fourth model the $$C_{p}$$ value is 5.5? We can verify these calculated $$C_{p}$$ values! The following output obtained by first regressing y on the predictors $$x_{1}$$, $$x_{2}$$, $$x_{3}$$ and $$x_{4}$$ and then by regressing y on the predictors $$x_{1}$$ and $$x_{2}$$: ##### Regression Equation y = 62.4 + 1.55 x1 + 0.51 x2 + 0.102 x3 - 0.144 x4 Source DF SS MS F P Regression 4 2667.90 666.97 111.48 0.000 Residual Error 8 47.86 5.98 Total 12 2715.76 ##### Regression Equation y = 52.6 + 1.47 x1 + 0.662 x2 Source DF SS MS F P Regression 2 2657.9 1328.9 229.50 0.000 Residual Error 10 57.9 5.8 Total 12 2715.8 tells us that, here, $$MSE_{all}$$ = 5.98 and $$MSE_{p}$$ = 5.8. Therefore, just as Minitab claims: $$C_p=p+\dfrac{(MSE_p-MSE_{all})(n-p)}{MSE_{all}}=3+\dfrac{(5.8-5.98)(13-3)}{5.98}=2.7$$ the $$C_{p}$$-statistic equals 2.7 for the model containing the predictors $$x_{1}$$ and $$x_{2}$$. And, the following output obtained by first regressing y on the predictors $$x_{1}$$, $$x_{2}$$, $$x_{3}$$ and $$x_{4}$$ and then by regressing y on the predictors $$x_{1}$$ and $$x_{4}$$: ##### Regression Equation y = 62.4 + 1.55 x1 + 0.51 x2 + 0.102 x3 - 0.144 x4 Source DF SS MS F P Regression 4 2667.90 666.97 111.48 0.000 Residual Error 8 47.86 5.98 Total 12 2715.76 ##### Regression Equation y = 103 + 1.44 x1 - 0.614 x4 Source DF SS MS F P Regression 2 2641.0 1320.5 176.63 0.000 Residual Error 10 74.8 7.5 Total 12 2715.8 tells us that, here, $$MSE_{all}$$ = 5.98 and $$MSE_{p}$$ = 7.5. Therefore, just as Minitab claims: $$C_p=p+\dfrac{(MSE_p-MSE_{all})(n-p)}{MSE_{all}}=3+\dfrac{(7.5-5.98)(13-3)}{5.98}=5.5$$ the $$C_{p}$$-statistic equals 5.5 for the model containing the predictors $$x_{1}$$ and $$x_{4}$$. ## Try it! ### Best subsets regression When there are four candidate predictors — $$x_{1}$$, $$x_{2}$$, $$x_{3}$$ and $$x_{4}$$ — there are 16 possible regression models to consider. Identify the 16 possible models. When there are four candidate predictors — $$x_1$$, $$x_2$$, $$x_3$$ and $$x_4$$ — there are 16 possible regression models to consider. Identify the 16 possible models. The possible predictor sets and the corresponding models are given below: Predictor Set model None of $$x_1, x_2, x_3, x_4$$ $$E(Y)=\beta_0$$ $$x_1$$ $$E(Y)=\beta_0+\beta_1 x_1$$ $$x_2$$ $$E(Y)=\beta_0+\beta_2 x_2$$ $$x_3$$ $$E(Y)=\beta_0+\beta_3 x_3$$ $$x_4$$ $$E(Y)=\beta_0+\beta_4 x_4$$ $$x_1, x_2$$ $$E(Y)=\beta_0+\beta_1 x_1+\beta_2 x_2$$ $$x_1, x_3$$ $$E(Y)=\beta_0+\beta_1 x_1+\beta_3 x_3$$ $$x_1, x_4$$ $$E(Y)=\beta_0+\beta_1 x_1+\beta_4 x_4$$ $$x_2, x_3$$ $$E(Y)=\beta_0+\beta_2 x_2+\beta_3 x_3$$ $$x_2, x_4$$ $$E(Y)=\beta_0+\beta_2 x_2+\beta_4 x_4$$ $$x_3, x_4$$ $$E(Y)=\beta_0+\beta_3 x_3+\beta_4 x_4$$ $$x_1, x_2,x_3$$ $$E(Y)=\beta_0+\beta_1 x_1+\beta_2 x_2+\beta_3 x_3$$ $$x_1, x_2,x_4$$ $$E(Y)=\beta_0+\beta_1 x_1+\beta_2 x_2+\beta_4 x_4$$ $$x_1, x_3,x_4$$ $$E(Y)=\beta_0+\beta_1 x_1+\beta_3 x_3+\beta_4 x_4$$ $$x_2, x_3,x_4$$ $$E(Y)=\beta_0+\beta_2 x_2+\beta_3 x_3+\beta_4 x_4$$ $$x_1, x_2,x_3,x_4$$ $$E(Y)=\beta_0+\beta_1 x_1+\beta_2 x_2+\beta_3 x_3+\beta_4 x_4$$ [1] Link ↥ Has Tooltip/Popover Toggleable Visibility	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8483927249908447, "perplexity": 649.9410725663439}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572163.61/warc/CC-MAIN-20220815085006-20220815115006-00668.warc.gz"}
https://www.arxiv-vanity.com/papers/1709.07572/	# Gravitational Waves from Hidden QCD Phase Transition Mayumi Aoki Institute for Theoretical Physics, Kanazawa University, Kanazawa 920-1192, Japan Hiromitsu Goto Institute for Theoretical Physics, Kanazawa University, Kanazawa 920-1192, Japan Jisuke Kubo Institute for Theoretical Physics, Kanazawa University, Kanazawa 920-1192, Japan ###### Abstract Drastic changes in the early Universe such as first-order phase transition can produce a stochastic gravitational wave (GW) background. We investigate the testability of a scale invariant extension of the standard model (SM) using the GW background produced by the chiral phase transition in a strongly interacting QCD-like hidden sector, which, via a SM singlet real scalar mediator, triggers the electroweak phase transition. Using the Nambu–Jona-Lasinio method in a mean field approximation we estimate the GW signal and find that it can be tested by future space-based detectors. preprint: KANAZAWA-17-08 ## I Introduction It is a challenge for physics beyond the standard model (SM) to answer a long-standing question—what is the origin of mass? The same question applies to dark matter (DM), which, if it is a particle, is absent in the SM. Though various suggestions about how to go beyond the SM exist, there is so far no sign for that from the Large Hadron Collider (LHC) experiments ATLAS ; CMS and no sign from the current DM detection experiments either Akerib:2016vxi ; Aprile:2017iyp . In contrast to this situation, the first observation of the gravitational wave (GW) signal at LIGO Abbott:2016blz has opened up a new way to study astrophysical phenomena and has awakened the hope in particle cosmology that phenomena in the early Universe can also be probed by the GW. It has indeed been known that phenomena in the early Universe such as inflation Starobinsky:1979ty , topological defects Vilenkin:2000jqa , and first-order phase transition Witten:1984rs generate a nonlocalized stochastic GW background. In particular, phase transitions in particle physics are associated with symmetry breaking, and therefore the GW signals produced by these phase transitions can be an alternative approach to investigate the structure of symmetries in the early Universe. Unfortunately, because of not being first order, the phase transition associated with the electroweak (EW) symmetry breaking in the SM cannot produce the GW background Kajantie:1995kf ; Kajantie:1996mn ; Rummukainen:1998as . However, if the SM is extended, observable GW signals associated with a symmetry breaking may be produced and tested in future experiments such as LISA Caprini:2015zlo ; Audley:2017drz and DECIGO Seto:2001qf ; Kawamura:2006up ; Kawamura:2011zz as discussed in Apreda:2001us ; Grojean:2006bp ; Espinosa:2008kw ; Ashoorioon:2009nf ; Das:2009ue ; Schwaller:2015tja ; Kakizaki:2015wua ; Jinno:2016knw ; Hashino:2016rvx ; Kubo:2016kpb ; Vaskonen:2016yiu ; Beniwal:2017eik ; Marzola:2017jzl ; Chao:2017vrq ; Bian:2017wfv ; Chao:2017ilw ; Dev:2016feu . As lattice simulations in QCD have shown Aoki:2006we ; Petreczky:2012rq ; Bhattacharya:2014ara , the chiral phase transition in QCD is, due to a relatively large current mass of the strange quark, a crossover type. This does not prevent the possibility that the chiral phase transition in a QCD-like hidden sector is of first order.111 Other possibilities of a first order phase transition in a QCD-like theory are the deconfinment/confinement phase transition in the quenched QCD Petreczky:2012rq and the chiral phase transition in QCD with a large baryon chemical potential Fodor:2004nz ; Schwarz:2009ii . They may produce the observable GW signal as discussed in Ahmadvand:2017xrw ; Caprini:2010xv ; Ahmadvand:2017tue . In fact, such a possibility with a critical temperature of TeV has been recently found Holthausen:2013ota ; Ametani:2015jla in a scale invariant extension of the SM Hur:2007uz ; Hur:2011sv ; Holthausen:2013ota ; Heikinheimo:2013fta ; Kubo:2014ida ; Ametani:2015jla ; Hatanaka:2016rek , in which dynamical chiral symmetry breaking (DSB) in a QCD-like hidden sector triggers the EW symmetry breaking. In the present paper we focus on this model. In this model, moreover, the EW energy scale and the DM mass have the same origin. In most of the parameter space, the DM mass is created before the EW phase transition and, in a certain region of the parameter space, it takes place during a strong first-order chiral phase transition. By choosing various benchmark points in the parameter space we study the testability of the GW background produced by this phase transition. The paper is organized as follows. In Sec. II we briefly review the scale invariant extension of the SM with a QCD-like hidden sector and describe how we use the Nambu–Jona-Lasinio (NJL) model Nambu:1960xd ; Nambu:1961tp ; Nambu:1961fr as an effective low-energy theory in a mean field approximation Kunihiro:1983ej ; Hatsuda:1994pi . We fix the number of the hidden color and flavor both at , because we can simply rescale the values of the NJL parameters for the real hadrons. In this way we can avoid increasing the number of independent parameters when going from the high-energy theory to the low-energy effective theory. We pick up a set of four benchmark parameters, for which the chiral phase transition in the hidden QCD sector is of first order. For these points we calculate the GW signals. Note that the chiral phase transition in our model occurs in a two-dimensional parameter space, the chiral condensate and the vacuum expectation value (VEV) of the SM singlet real scalar (which is the mediator of the energy scale from the hidden sector to the SM sector). Furthermore, the mean field corresponding to the chiral condensate is a nonpropagating field at the zeroth order in the mean field approximation: It becomes a quantum field at the one-loop level, so that its wave function renormalization constant is far from and depends on the mean fields as well as on the temperature. In Sec. III we discuss how to manage the complications mentioned above to compute the rate of the bubble nucleation that occurs during the cosmological tunneling in the hidden QCD sector. In Sec. IV we discuss the detectability of the GW signals produced by the chiral phase transition for the benchmark points in the parameter space. We summarize and conclude in Sec. V. ## Ii The Model We consider a classically scale invariant extension of the SM studied in Hur:2007uz ; Hur:2011sv ; Holthausen:2013ota ; Heikinheimo:2013fta ; Ametani:2015jla , which consists of a hidden gauge sector coupled via a real singlet scalar field to the SM. The Lagrangian of the hidden sector is written as (1) where the hidden vectorlike fermions transform as a fundamental representation of . The part of the total Lagrangian contains the SM gauge and Yukawa interactions along with the scalar potential VSM+S=λH(H†H)2+14λSS4−12λHSS2(H†H), (2) where is the SM Higgs doublet field with and as the would-be Nambu-Goldstone (NG) fields. The scalar couplings at the tree level have to satisfy the stability condition for the scalar potential λH>0, λS>0 and 2√λHλS−λHS >0. (3) Here and are assumed to be positive. This model explains the origin of the mass of the Higgs boson and the DM in the following sense. • First, due to the DSB in the hidden sector, a nonzero chiral condensate forms and generates a mass scale above the EW scale. Consequently, NG bosons, which are mesons in the hidden sector, appear. • At the same time of the hidden DSB, the singlet scalar field acquires a nonzero VEV because of the Yukawa interaction . Note that the Yukawa interaction breaks the chiral symmetry explicitly, and plays the role of a current mass. Therefore, the mass of the hidden mesons depends crucially on . • These hidden mesons (or a part of them) can become DM candidates, because they are stable due to the vectorlike flavor symmetry that is left unbroken after the DSB. • The EW symmetry breaking is triggered by the Higgs mass term that is nothing but the scalar coupling with the nonzero . In this work we consider the case with and assume that the singlet scalar equally couples to the hidden fermions. Then the hidden chiral symmetry is dynamically broken down to , and thanks to this unbroken symmetry, eight hidden pions become a DM candidate. The DM physics and the impact of the hidden chiral phase transition to the EW phase transition have been investigated in Holthausen:2013ota by using the NJL theory Nambu:1960xd ; Nambu:1961tp ; Nambu:1961fr in the self-consistent mean field (SCMF) approximation Hatsuda:1994pi ; Kunihiro:1983ej . It has been found that a strong first-order chiral phase transition can occur if the Yukawa coupling is small enough, i.e., Ametani:2015jla . Within the framework of the NJL theory we will calculate the GW spectrum produced by the hidden chiral phase transition later on. The same model has been analyzed by using a linear Hur:2007uz and nonlinear Hur:2011sv sigma model and also AdS/QCD approach Hatanaka:2016rek . In Tsumura:2017knk , the GW spectrum from the hidden chiral phase transition has been calculated within the framework of a linear sigma model. ### ii.1 Nambu–Jona-Lasinio Lagrangian in a Mean Field Approximation Following Holthausen:2013ota we approximate the high-energy Lagrangian (1) by the NJL Lagrangian (4) where and are dimensional parameters and (Φ)ij =¯ψi(1−γ5)ψj=12λajiTr ¯ψλa(1−γ5)ψ, (Φ†)ij =¯ψi(1+γ5)ψj=12λajiTr ¯ψλa(1+γ5)ψ. Here are the Gell-Mann matrices with . To deal with the NJL Lagrangian (4), which is nonrenormalizable, we work in the SCMF approximation Hatsuda:1994pi ; Kunihiro:1983ej . The mean fields and are defined in the Bardeen-Cooper-Schrieffer vacuum as ⟨Φ⟩=−14G(diag(σ,σ,σ)+i(λa)Tϕa). (5) After splitting up the NJL Lagrangian into the sum , where contains at most bilinear terms of and is normal ordered with respect to the BCS vacuum, we find the Lagrangian in the SCMF approximation: LMFA= +GD8G2(−Tr ¯ψϕ2ψ+8∑a=1ϕaϕaTr ¯ψψ+iσTr ¯ψγ5ϕψ+σ32G+σ2G8∑a=1(ϕa)2), (6) where , we have suppressed here, and is given by M=σ+yS−GD8G2σ2. (7) Through integrating out the hidden fermions, a nontrivial correction to the tree-level potential for is generated, such that the position of the potential minimum can be shifted from zero to a finite value of . From the definition (5) we see that this is nothing but the chiral condensate in the SCMF approximation. By self-consistency it is meant that the actual value of is computed afterward at the loop level, and then we consider the mean field Lagrangian (6) around this mean field vacuum. At the tree level of (6), the mean fields and are nonpropagating classical fields. Through integrating out the hidden fermions at the one-loop level, their kinetic terms are also generated. At this stage we reinterpret them as propagating quantum fields. ### ii.2 Mass Spectrum The chiral condensation in the hidden sector can be studied by using the one-loop effective potential obtained from the mean field Lagrangian (6): Veff=VSM+S+VNJL, (8) where VNJL(σ,S;ΛH)=38Gσ2−GD16G3σ3−3ncI0(M;ΛH), (9) and is given by I0(M;Λ)=116π2[Λ4ln(1+M2Λ2)−M4ln(1+Λ2M2)+Λ2M2]. (10) Here we have used the four-dimensional cutoff, and is the corresponding cutoff parameter. The NJL parameters for the hidden QCD are obtained by scaling up the values of , and for the real hadrons. That is, we assume that the dimensionless combinations G1/2Λ=1.82, (−GD)1/5Λ=2.29, (11) which are satisfied for the real hadrons, remain unchanged for a higher scale of . For a given set of the free parameters of the model , and , the VEV of and can be determined through the minimization of the scalar potential , where the hidden QCD scale is so chosen to satisfy . The mass spectrum of the particles can be computed from the corresponding two-point functions, which are obtained by integrating out the hidden fermions. Note that the -even scalars , and mix with one another. The flavor eigenstates and the mass eigenstates are related by . Their masses are determined by the zeros of the two-point functions at the one-loop level, i.e., , where Γhh(p2) =p2−3λH⟨h⟩2+12λHS⟨S⟩2, ΓhS=λHS⟨h⟩⟨S⟩, Γhσ=0, ΓSS(p2) =p2−3λS⟨S⟩2+12λHS⟨h⟩2−y23ncIφ2(p2,M;ΛH), ΓSσ(p2) =−y(1−GD⟨σ⟩4G2)3ncIφ2(p2,M;ΛH), Γσσ(p2) =−34G+3GD⟨σ⟩8G3−(1−GD⟨σ⟩4G2)23ncIφ2(p2,M;ΛH) (12) +GDG23ncIV(M;ΛH), and the loop functions are defined as Iφ2(p2,M;Λ) (13) IV(M;Λ) =∫Λd4ki(2π)4M(k2−M2)=−116π2M[Λ2−M2ln(1+Λ2M2)]. (14) We identify the SM Higgs with the mass eigenstate corresponding to , which is supposed to be closest to , and its mass is Olive:2016xmw . Similarly we use and . The DM candidate is the hidden pion and its mass is also generated at the one-loop level. Its two-point function is ΓDM(p2) =−12G+GD⟨σ⟩8G3+(1−GD⟨σ⟩8G2)22ncIϕ2(p2,M;ΛH)+GDG2ncIV(M;ΛH), (15) where the loop function is given by Iϕ2(p2,M;Λ) (16) Then we can calculate the DM mass from . Once the set of the parameters is given, the mass spectrum of the hidden sector particles is fixed. Figure 1 shows the Yukawa coupling dependence of the masses (left) and of the hidden QCD scale (right) for , with two different values of ; (solid lines) and (dashed lines). As shown in Fig. 1 (left), the DM mass is proportional to the Yukawa coupling . This is because the Yukawa interaction breaks the chiral symmetry explicitly. The scale of the DSB in the hidden sector, which is the hidden QCD scale , depends on how the mediator transfers the mass scale to the SM sector. The larger the couplings and are, the closer to the EW scale the hidden QCD scale is located as seen in Fig. 1 (right). Moreover the annihilation processes of the DM also depend on the mass spectrum and the Yukawa coupling . Note that the one-loop effective couplings are given by and . In the small area with , the mass spectrum should satisfy the resonance condition to obtain a realistic DM relic abundance and, in this parameter space, the spin-independent cross section of DM off the nucleon becomes so small Holthausen:2013ota that it will be very difficult to detect DM at direct DM detection experiments such as XENON1T Aprile:2017iyp . On the other hand, the GW signal might be observed since a strong first-order chiral phase transition can appear for a small area Ametani:2015jla . ### ii.3 Chiral Phase Transitions The phase transition at finite temperature can be studied using a one-loop effective potential. Since the EW phase transition occurs well below the critical temperature of the chiral phase transition in the hidden sector, we may assume in investigating the chiral phase transition. Accordingly, the scalar potential to be analyzed is VEFF(S,σ,T)=Vh→0SM+S(S)+VNJL(S,σ)+VCW(S)+VFT(S,σ,T)+V% RING(S,T), (17) where and are given, respectively, in (2) and (9), VCW(S) =−94λ2S32π2(S4−⟨S⟩4)+m4S(S)64π2ln[m2S(S)m2S(⟨S⟩)], (18) VFT(S,σ,T) =T42π2JB(m2S(S)/T2)−6ncT4π2JF(M2(S,σ)/T2), (19) VRING(S,T) =−T12π[(M2S(S,T))3/2−(m2S(S))3/2], (20) and is the field-dependent mass for with its thermal mass M2S=m2S(S)+(λS4−λHS6)T2. (21) The thermal function is JB,F(r2) =∫∞0dxx2ln(1∓e−√x2+r2), (22) for which we use the approximate expression JB,F(r2) =e−r240∑n=0cB,Fnr2n. (23) ### ii.4 Benchmark Points As discussed in Ametani:2015jla , the chiral phase transition in the hidden sector becomes first order for small . We require the perturbativity and stability condition (3) of the scalar potential for to be satisfied up to the Planck scale at the one-loop level.222 According to Bardeen:1995kv , the hierarchy problem can be avoided in this way at least at the one-loop level. We find that 0.13≲λH≲0.14, 0<λHS<0.12, 4λ2HS/λH<λS≲0.23 (24) should be satisfied to meet the requirements. The inequality is our assumption (see (3)), and the interval of is due to the observed Higgs mass. The upper limit of comes from perturbativity, while the lower limit comes from the stability condition with finite and . Note that there is no lower limit on and . We however consider only the case for , which implies that TeV.333A large , which is realized by the small couplings and , does not necessarily mean a heavy as shown in Fig. 1. Therefore, even if is large, the correction to the Higgs mass coming from the internal loop can be small. In Fig. 2 we show the area in the - plane, in which we obtain the VEV of the Higgs field , the correct Higgs mass Olive:2016xmw , - mixing Olive:2016xmw , and the resonance condition (to realize the correct DM relic abundance). Note that the mass of the mediator is bounded, because is bounded as discussed above. Consequently, because of the resonance condition , the DM mass is bounded, too. Similarly, is bounded, because is bounded from above (24) and from below due to our parameter choice . The colored points A, B, C and D in Fig. 2 are our benchmark points. The chosen four benchmark points are named Case A, B, C, and D: the set of the input parameter values , along with the output values of , , and for each benchmark case is given in Table 1. Under and (24), Cases A and B are located as close to the EW scale as possible and for C and D in an opposite way.444There exists the Higgs threshold between Cases A and B, which means the decay channel of the mediator to two Higgs particles is forbidden only for the Case A. This might become a benchmark point for a future collider search. We regard the normalized current quark mass as the characterization for the explicit chiral symmetry breaking. Their values should be compared with that of QCD, i.e. (in the NJL model). In Fig. 3 we show the temperature dependence of and near the critical temperature for each benchmark point. It can be seen that a first-order phase transition appears in all the cases. We also see that and undergo the phase transition at the same time. Moreover, the phase transition in Case C appears for a slightly lower temperature compared with D even though . The reason is that the explicit chiral symmetry breaking, whose strength is expressed by , influences not only the mass of DM but also the critical temperature. Since the chiral phase transition in the hidden sector occurs in the two-dimensional space , we need to deal with quantum tunneling in the two-dimensional space to calculate the GW spectrum. ## Iii Bubbles from Hidden QCD Tunneling Cosmological tunneling has been studied in Coleman:1977py ; Callan:1977pt ; Linde:1981zj . The probability of the bubble nucleation per unit volume per unit time is given by Γ=A(t)exp[−SE(t)], (25) where is the Euclidean action. At a high temperature, the Euclidean action can be replaced by because of the periodicity of in the Euclidean time, where is the corresponding three-dimensional Euclidean action Linde:1981zj . The bubbles can percolate when the probability of the bubble nucleation per unit volume and time is of order one. Since the prefactor in (25) is Linde:1981zj , we can translate this condition as ΓH4∣∣∣t=tt≃1 ⇄ S3(Tt)Tt=4ln(TtHt), (26) where is the Hubble parameter at the transition temperature . The bubble dynamics can be characterized by two parameters, namely, and at Grojean:2006bp : expresses how much energy the phase transition releases, while expresses how long its phase transition takes. These parameters are essential for computing the GW signal from the cosmological phase transition Grojean:2006bp . The parameter is defined as which is the ratio of the latent heat liberated at the phase transition to the thermal energy density in the symmetric phase. The latent heat can be computed from the effective potential at finite temperature as ϵ(T) ≡−ΔVEFF(T)+T∂ΔV% EFF(T)∂T, (28) where is the difference of the effective potential between the true and false vacuum. The parameter is defined as β (29) Using , we can redefine a dimensionless parameter as ~β ≡βHt=TtddT(S3(T)T)∣∣ ∣∣T=Tt. (30) In the following subsections we apply above the general formula (26)–(30) to compute the parameters for our concrete problem, and we estimate the corresponding GW signal. ### iii.1 Bubble Nucleation and Tunneling Parameters In order to discuss the bubble nucleation which stems from the first-order chiral phase transition, we need to calculate . For this purpose we use the effective Lagrangian for the mean field . However, the mean field cannot describe tunneling at a tree level, because its kinetic term is absent at the tree level. Hence we compute its kinetic term from the two-point function at the one-loop level, which is given in (12). First we discuss the zero-temperature case and define the field renormalization constant for the field as Γσσ(p2)=Γσσ(0)+Z−1σ(S,σ)p2+O(p4), where Z−1σ(S,σ) =−(1−GD4G2σ)23ncddp2Iφ2(p2,M;ΛH)∣∣∣p2=0. Thus the effective Lagrangian for the field at zero temperature is Lσ =Z−1σ(S,σ)2∂μσ∂μσ−Veff(S,σ), (31) where [ is given in (9)]. Note that the field renormalization constant at the symmetric phase () diverges (see the Appendix). This is expected, because the composite state disappears in the symmetric phase. As mentioned in the previous section, hidden QCD tunneling should occur in the two-dimensional field space and could be described by the three-dimensional Euclidean action S3(T)=∫d3x[Z−1σ(S,σ,T)2(∂iσ)2+12(∂iS)2+VEFF(S,σ,T)]. (32) The field renormalization constant at finite temperature is computed in the Appendix and found to be Z−1σ(S,σ,T) =3nc8π2(1−GD4G2σ)2[ln(1+Λ2HM2)+Λ2HM2(Λ2H+M2)2−32π2(AF(u2)−BF(u2))], (33) where , and , , and are given in Eqs. (7), (64), and (65), respectively. In Fig. 4 we show the field dependency of the field renormalization constant for and , which corresponds to the black, red, blue, and purple line, respectively. As shown in Fig. 4, the field renormalization constant vanishes in the symmetric phase. The symmetric bounce solution can be obtained by solving the equations of motion d2σdr2+2rdσdr+12∂lnZσ(S,σ,T)∂σ(dσdr)2 =Zσ(S,σ,T)∂VEFF(S,σ,T)∂σ, (34) d2Sdr2+2rdSdr−12∂Z−1σ(S,σ,T)∂S(dσdr)2 =∂VEFF(S,σ,T)∂S, (35) where . The boundary conditions are dσdr∣∣∣r=0=0, dSdr∣∣∣r=0=0, limr→∞σ(r)=0, limr→∞S(r)=0, (36) where the coordinate of the symmetric minimum (false vacuum) of the potential is chosen at the origin of the - space. Note that the field renormalization constant does not depend explicitly on but also depends on the fields. ### iii.2 Computation of Multi-dimensional Bounce Solution In the one-dimensional case we can obtain a bounce solution by using the so-called overshooting/undershooting method Apreda:2001us . However, this is a cumbersome method in the multidimensional case, because two initial conditions have to be simultaneously fine-tuned. Instead, we here employ an approach similar to the path deformation method Wainwright:2011kj . The bounce solution is unique. That is, and , which satisfy the differential equations (34) and (35) with the boundary conditions (36), are a unique function of . If we assume that is an invertible function for , then there exists a unique inverse of , which we denote by . That is, is the identity function, or . Because of this assumption, can be regarded as a function of , i.e., .555We use the same symbol for the functions of and . Therefore, (34) and (35) can be written as, respectively, d2σdr2+2rdσdr+12∂lnZσ(S(σ),σ,T)∂σ(dσdr)2 =Fσ(S(σ),σ), (37) d2Sdσ2(dσdr)2+(dSdσ)(d2σdr2+2rdσdr)−12∂Z−1σ(S(σ),σ,T)∂S(dσdr)2 =FS(S(σ),σ), (38) where and are the rhs of (34) and (35), respectively, and we have suppressed the dependence of and . The point is that if is given, then (37) is a one-dimensional differential equation and hence can be solved by applying the overshooting/undershooting method. If is the true solution of the problem, it should satisfy (38) with obtained from (37) as well, which means that N(r) = 0 (39) is also satisfied, where N(r) =d2Sdσ2(r)(dσdr(r))2+dSdσ(r)Fσ(S,σ)(r)−FS(S,σ)(r) −12(dσdr(r))2(∂Z−1σ(S,σ,T)∂S(r)+dSdσ(r)∂lnZσ(S,σ,T)∂σ(r)). (40) Since the one-dimensional differential equation (37) for a given path can be simply solved, our task is to find which satisfies (39). We do this in an iterative way. We start with a linear function , which connects the true and false vacuum: S0(σ)=SB−SSσB−σS(σ−σS)+SS, (41) where (with ) are the positions of the true and false vacuum, respectively. Then we solve (37) with the path and denote the bounce solution by . Note that is no longer , so that the end point of on the true vacuum side is no longer , i.e. . Next we compute the rhs of (40) using and for and , respectively, and we denote it by . Since is not the true solution of the problem, does not vanish. Knowing , we have to define the next step of the iteration: S1(σ) = S0(σ)+ΔS0(σ). (42) To proceed we assume that not only the true solution but also is an invertible function, so that can be written as a function of , i.e., ^N0(σ) ≡ N0(r=σ−10(σ)). (43) Note that because of the and dependence of (partly shown in Fig. 4) and also of , vanishes at the false vacuum, i.e., at ( also vanishes at ). Further, if vanishes at some nonzero values of , the deformation should also vanish at these values of . This brings us to assume that is proportional to . Therefore, the path in the th step can be defined as Si+1(σ) = Si(σ)+k^Ni(σ), (44) where is the step size, and . Note that satisfies the boundary condition . To obtain , the initial value of has to be fine-tuned in such away that and are satisfied. If is satisfied, is automatically satisfied. Since is different from , the end point of on the true vacuum side is also moved to . Since the assumptions we made above cannot be rigorously justified, there is no guarantee that the steps converge to the true solution of the problem. In fact, if we choose the wrong sign for , steps diverge or do not converge. We have checked our method for a number of examples and found that once we use an appropriate sign and size for , the steps can converge, where we approximate the path (which is obtained numerically) with a fifth-degree polynomial in as in Beniwal:2017eik . In Fig. 5, we present the numerical solution (black solid line) with obtained from (black dashed line) in the two-dimensional field space at TeV [below the critical temperature TeV as shown in Fig. 3 (top left)] for Case A.666 is not satisfied for . The corresponding bounce solution as a function of is shown in Fig. 6. The Euclidean action (32) obtained from the bounce solution is , where the difference of between the 14th and 15th steps is less than a few percent. Computing for each temperature as in the above method, we can find the transition temperature from the condition (26), which is used for the determination of tunneling parameters and given in Eqs. (27) and (30). ### iii.3 Tunneling Parameters for the Benchmark Points The GW spectrum produced by a first-order phase transition can be characterized by the released energy and its duration time, and it is known that they can be parametrized by the set of the parameters . The results for the benchmark points are given in Table 2. We see from Table 2 that and for Cases A and C are larger than those for Cases B and D. Recalling the parameter values for the benchmark points (Table 1), we can infer that the smaller the explicit chiral symmetry breaking (the smaller ) is, the larger and are. This suggests that the parameters of the model can be constrained if the GW is measured with a certain accuracy. ## Iv Signal From the Hidden Sector QCD Finally we come to our main purpose: to check the testability of the GW background produced by the first-order phase transitions in the hidden sector. There coexist three processes contributing to the stochastic GW background spectrum: h2ΩGW=h2Ωφ+h2Ωsw+h2Ωturb, (45) where is the dimensionless Hubble parameter, stands for the scalar field contribution from collisions of bubble walls Kosowsky:1991ua ; Kosowsky:1992rz ; Kosowsky:1992vn ; Kamionkowski:1993fg ; Caprini:2007xq ; Huber:2008hg , for the contribution from sound waves in plasma after the bubble collisions Hindmarsh:2013xza ; Giblin:2013kea ; Giblin:2014qia ; Hindmarsh:2015qta , and for the contribution from magnetohydrodynamic (MHD) turbulence in plasma Caprini:2006jb ; Kahniashvili:2008pf ; Kahniashvili:2008pe ; Kahniashvili:2009mf . Following Caprini:2015zlo , each contribution is given for a given set of the parameters with the velocity of bubble wall and the , and which are the fraction of vacuum energy, respectively, converted into gradient energy of scalar field, bulk motion of the fluid, and MHD turbulence. • Scalar field contribution : h2Ωφ(f)=1.67×10−5~β−2(	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9788027405738831, "perplexity": 709.1573698914443}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057524.58/warc/CC-MAIN-20210924110455-20210924140455-00638.warc.gz"}
https://answers.yahoo.com/question/index?qid=20080106193050AAEM03G	# how do you find the volume of a certain quantities at STP ? gasses at STP ex. 60 g of CO2 Relevance • Anonymous STP means 273.15 K 1 bar. Use ideal gas law PV=nRT P is the pressure in bar V is the volume in L n is the number of moles of gas R is the ideal gas constant = 0.08314 bar L / mol K T is the temperature in K n=m/M Hence for your 60 grams of CO2 (M=44g/mol) V=60/44 mol * 0.08314 bar L/mol K * 273.15 K /1 bar = 31 L 1 mole ( Gram molecular weight) of a compound or element is the atomic mass expressed in grams. The atomic mass can be found on a Perodic Chart of the elements. 1 mole of a gas at STP occupies 22.4 liters of space. Atomic mass of Carbon is 12 grams/mole. Atomic mass of Oxygen is 16 grams/mole. Therefore the atomic mass of CO2 is (2x16) + 12 = 44. 60 grams of CO2 = 60 / 44 = 1.36 moles. 1.36 moles x 22.4 Liters = 30.46 Liters • Anonymous	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8462527394294739, "perplexity": 2736.535665357557}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737883.59/warc/CC-MAIN-20200808135620-20200808165620-00453.warc.gz"}
http://mathhelpforum.com/differential-geometry/130090-lipschitz-continuity.html	1. ## Lipschitz Continuity Hey guys, I need to do the following. Let $c > 0$ and let $f(x) = e^x$. Show that $f(x)$ is Lipschitz continuous for $x \in [-c,c]$. My idea is to set $L = e^c$, but it is hard to prove that this is a valid Lipschitz constant. 2. Originally Posted by EinStone Hey guys, I need to do the following. Let $c > 0$ and let $f(x) = e^x$. Show that $f(x)$ is Lipschitz continuous for $x \in [-c,c]$. My idea is to set $L = e^c$, but it is hard to prove that this is a valid Lipschitz constant. Mean value theorem: $f(y) - f(x) = (y-x)f'(z)$, for some z lying between x and y. So you can take the Lipschitz constant to be the maximum value of \|f'(z)\| in the given interval (which in this case is $e^c$, as you suspected). 3. Originally Posted by EinStone Hey guys, I need to do the following. Let $c > 0$ and let $f(x) = e^x$. Show that $f(x)$ is Lipschitz continuous for $x \in [-c,c]$. My idea is to set $L = e^c$, but it is hard to prove that this is a valid Lipschitz constant. What Opalg is just a consequence of a much broader theorem, namely that if $f:E\mapsto\mathbb{R}$ is differentiable and $f'$ is bounded then $f$ is Lipschitz. (this is, in fact, an iff statement) And thus, if $E$ is compact and if $f$ is continuously differentiable we must have that $f'$ necessarily bounded and thus $f$ is Lipschitz.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 24, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9961303472518921, "perplexity": 88.44560986214422}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368699186520/warc/CC-MAIN-20130516101306-00066-ip-10-60-113-184.ec2.internal.warc.gz"}
https://tex.stackexchange.com/questions/500633/adding-line-numbers-without-lineno-package/501489	Adding line numbers without lineno package I've had several persistent issues with the lineno package and journal article templates (e.g., not numbering certain paragraphs). Is it possible to just add an "unaligned" column of line numbers on the side of the page? • This solution works on the PDF itself. Add page and line numbers to a pdf Jul 19 '19 at 14:44 • Please try with vruler.sty package... Jul 19 '19 at 14:58 • @AlanMunn Please if I have a PdF file. Is it possible to add numbers to all the lines? Unfortunaletly, this template in this answer tex.stackexchange.com/questions/18760/… does not work. Jul 19 '19 at 17:17 • @Student "does not work" is a very vague description, and this question is not the place to have a discussion about it. The solution has quite a few components, including a shell script that calls ImageMagick which you need to run on the file before using the LaTeX code. If you've done all that, ask a new question showing exactly what you did and linking to the original question. Jul 19 '19 at 17:21 • @AlanMunn Thank you very much. Please just how can I add ImageMagick ? Jul 19 '19 at 17:25 The following example uses eso-pic to place a list of numbers (contained within a single-column tabular) on the left and/or right of the text block: \documentclass{article} \usepackage{lipsum,eso-pic,xcolor} % Specify a verbatim list of numbers (or items) to be on the side of the text block \newcommand{\numberlist}[1][r]{% \begin{tabular}{#1} \strut 1 \\ 2 \\ 3 \\ 4 \\ 5 \\ 6 \\ 7 \\ 8 \\ 9 \\ 10 \\ 11 \\ 12 \\ 13 \\ 14 \\ 15 \\ 16 \\ 17 \\ 18 \\ 19 \\ 20 \\ 21 \\ 22 \\ 23 \\ 24 \\ 25 \\ 26 \\ 27 \\ 28 \\ 29 \\ 20 \\ 31 \\ 32 \\ 33 \\ 34 \\ 35 \\ 36 \\ 37 \\ 38 \\ 39 \\ 30 \\ 41 \\ 42 \\ 43 \\ 44 \\ 45 \\ 46 \end{tabular}% } \newcommand{\numberlistfont}{% \ttfamily\color{black!50}% Font/colour used for number list } % Add number list to the ForeGround of every page % Start at the top left of the text block \AtTextUpperLeft{% \numberlistfont % Numbers on left \makebox[0pt][r]{\raisebox{-\height}{% \numberlist[r]% Print numbers, right-aligned }% \hspace{50pt}% Space between left numbers and text block }% \hspace*{\textwidth}% Just to right side of text block \hspace{3em}% Space between right numbers and text block \makebox[0pt][l]{\raisebox{-\height}{% \numberlist[l]% Print numbers, left-aligned }}% }% } \begin{document} \sloppy\lipsum[1-50]\lipsum[1-50] \end{document} You can adjust the lengths and definitions based on the commented code.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000100135803223, "perplexity": 552.6601321147973}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057131.88/warc/CC-MAIN-20210921011047-20210921041047-00119.warc.gz"}
https://arxiv.org/abs/1706.04582	cs.AI (what is this?) # Title: The Opacity of Backbones and Backdoors Under a Weak Assumption Abstract: Backdoors and backbones of Boolean formulas are hidden structural properties that are relevant to the analysis of the hardness of instances of the SAT problem. The development and analysis of algorithms to find and make use of these properties is thus useful to improve the performance of modern solvers and our general understanding of SAT. In this work we show that, under the assumption that P$\neq$NP, there are easily-recognizable sets of Boolean formulas for which it is hard to determine whether they have a backbone. We also show that, under the same assumption, there are easily-recognizable families of Boolean formulas with strong backdoors that are easy to find, for which it is hard to determine whether they are satisfiable or not. Subjects: Artificial Intelligence (cs.AI); Computational Complexity (cs.CC); Logic in Computer Science (cs.LO) ACM classes: F.4.1; F.1.3 Cite as: arXiv:1706.04582 [cs.AI] (or arXiv:1706.04582v1 [cs.AI] for this version) ## Submission history From: Lane A. Hemaspaandra [view email] [v1] Wed, 14 Jun 2017 16:46:01 GMT (9kb)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8141328692436218, "perplexity": 1267.7825867838985}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323889.3/warc/CC-MAIN-20170629070237-20170629090237-00155.warc.gz"}
https://casualcalculations.wordpress.com/2013/04/20/my-infinity-is-bigger-than-yours/	Warning: Attempt at explaining some real mathematics here! 🙂 A common exchange between young children: Child 1: My blank is better than yours! Child 2: Nuh uh! Mine’s twice as good!! Child 1: Mine’s 100 times as good as yours! Child 2: Well mine’s infinity times better! Child 1: Oh yeah?! Well mine’s infinity plus one better than yours!! Now, I hope the average reader is already aware that “infinity plus one” is not a number. Infinity is not a number either; not in any usual sense of numbers anyway. Let’s think of infinity as simply a concept, of sorts. Mathematicians refer to the regular counting numbers, 1, 2, 3, 4… as natural numbers and we use the symbol $\mathbb{N}$ to denote them. So if I were to ask you how many natural numbers there were, then you’d obviously say there are infinitely many; however steer clear of saying you have infinity of them. For argument’s sake, let’s see what happens if we do take infinity to be a number; specifically, we’ll take it to be the total number of natural numbers that there are. If there are “infinity” natural numbers, then there we’ll just exclude the number one and then we’ll have one less number: 2, 3, 4… etc. But surely this isn’t satisfying to say this new set of numbers starting at two, has any less than infinity numbers! Equivalently, we could pair up every single number in the new set with a unique natural number simply by subtracting one from it. So two in the new set gets paired with one in the old; three in the new set get paired with two in the old one, and so on. There is exactly one number in the top set for every number in the bottom one. This means that infinity minus one would still be equal to infinity – hardly makes sense as a number! After all, if $\infty -1=\infty$ then we could subtract infinity from both sides and be left with $-1=0$. Congratulations, you broke math. I hope I’ve convinced you that infinity can’t be a number (in the usual sense of the word), and that the collection of counting numbers starting from 2, 3, 4… has just as many numbers in it as if we had started from 1, 2, 3… Now I want to tell you about “bigger numbers” than this notion of infinity; this is where it may start messing with your head. A mathematician will call a collection of things, a set; think of a set as being any old bag of… stuff. If I have a set, or a bag containing three things, I’ll say the cardinality of this set is three. Cardinality is just a mathematician’s notion of the size of a collection – just the number of things in the collection (at least if there are only finitely many things in it). So what if our “bag” has all of the natural numbers (1, 2, 3…), so there are infinitely many things in the set? I’ve already said we want to talk about bigger infinities than this one, so let’s not use the symbol $\infty$ for the size (or cardinality) of the natural numbers. Instead, mathematicians say the cardinality of the natural numbers is $\aleph_0$, pronounced “aleph naught” or “aleph null”. So to recap: the cardinality (size) of a finite set (collection) is just the number of elements (things) in it, and the cardinality (size) of the natural numbers (1, 2, 3… etc.) is something we call $\aleph_0$, “the smallest infinity”. Now obviously there are far more numbers than just the natural numbers that I keep talking about. What about -2, 0.5, $\pi$ and $\sqrt{2}$? Well it turns out that if we include all of the things that you would regularly consider numbers in one big set (collection), then the cardinality (size) of this set is actually bigger! This larger set of numbers is called the real numbers and is usually denoted by $\mathbb{R}$. I won’t bore you with the proof here but any good real analysis book will have one; even Wiki’s page for Cantor’s diagonalisation argument proves it, although reading it makes me want to edit the page to something more understandable (warning, link contains math). Let’s call the cardinality(size) of the real numbers C, for now. But you may have expected the set of real numbers to be larger than the set of natural numbers; it does intuitively seem like there are more real numbers. The real kicker, is thinking about something in between! What about the set of numbers that can be written as fractions? Like a half, or negative three quarters or $\frac{23234268}{423768923}$? We call these numbers rational numbers (they’re written as a ratio of two integers) and mathematicians use the symbol $\mathbb{Q}$ for them. How big is the set of rational numbers? We can actually list the rational numbers in some order, $0,1,-1,\frac{1}{2},2,-\frac{1}{2},-2,\frac{1}{3},\frac{2}{3},3,\frac{3}{2},-\frac{1}{3},-\frac{2}{3}...$, so there is a first, second, third etc. Since we can write it like this, then we can pair up each of the natural numbers with this list of rational numbers; the first in our list gets paired with the number one, the second is paired with the number two and so forth. This is exactly like the picture above. Since we can do this, there must be just as many rational numbers as there are natural numbers, so we say the cardinality (size) of the rational numbers is also $\aleph_0$ – a little bizarre, hey?! Just to kick your intuition square in the nuts, between any two real numbers there are infinitely many rational numbers! Even though there are way more real numbers than rational ones… Now for the really amazing part! We use the notation $\aleph_0$, because it’s the “smallest infinity”, and we can say $\aleph_1$ is the next smallest, $\aleph_2$ is the next smallest after that, and so on. It is unknown if the cardinality of the real numbers (which we’ve denoted by as C) is equal to $\aleph_1$. But worse than that! It is impossible to ever prove or disprove this using the standard axioms of mathematics! (See Continuum hypothesis) For the mathematically curious, check out the following Wikipedia articles: Natural number, rational number, irrational number, real number, ordinal number, cardinal number.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 17, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8979189395904541, "perplexity": 359.5233144532709}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794863410.22/warc/CC-MAIN-20180520112233-20180520132233-00568.warc.gz"}
https://linearalgebras.com/solution-mira-exercise-2a6.html	If you find any mistakes, please make a comment! Thank you. ## Measure of open intervals and half-open half-closed intervals Solution to Measure, Integration & Real Analysis by Axler Section 2A Exercise 2A6 Prove that if $a,b\in\mathbf R$ and $a<b$, then $$\|(a,b)\|=\|(a,b]\|=\|[a,b)\|=b-a.$$ Solution 1: Since $(a,b)\subset [a,b]$, by 2.5 and 2.14, we have $$\|(a,b)\|\leqslant \|[a,b]\|=b-a.$$Hence to show $\|(a,b)\|=b-a$, it suffices to show that $\|(a,b)\|\geqslant b-a$. Let $\varepsilon>0$ be any positive number which is sufficiently small, for example provided $$2\varepsilon < b-a.$$ Note that $[a+\varepsilon,b-\varepsilon]\subset (a,b)$. Therefore we obtain from 2.5 and 2.14 that $$\|(a,b)\|\geqslant \|[a+\varepsilon,b-\varepsilon]\|=b-a-2\varepsilon.$$Because $\varepsilon$ is arbitrary, we conclude that $\|(a,b)\|\geqslant b-a$. So we have $\|(a,b)\|=b-a$. To show $\|(a,b]\|=b-a$. Notice that $(a,b)\subset (a,b]\subset [a,b]$. It follows from 2.5, 2.14, and $\|(a,b)\|=b-a$ that $$b-a=\|(a,b)\|\leqslant \|(a,b]\|\leqslant \|[a,b]\|=b-a.$$Therefore $\|(a,b]\|=b-a$. The part $\|[a,,b)\|=b-a$ is similar. Solution 2: By 2.4, we know that $$\|\{a,b\}\|=\|\{a\}\|=\|\{b\}\|=0.$$Hence the part $\|(a,b)\|=b-a$ follows from Exercise 2A1 by setting $A$ to be $(a,b)$ and $B=\{a,b\}$. The other two can be obtained in a similar way. Of course, it is also possible to use Exercise 2A3.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9939631819725037, "perplexity": 140.18846033970996}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334992.20/warc/CC-MAIN-20220927064738-20220927094738-00317.warc.gz"}
https://www.physicsforums.com/threads/group-theory-question.198217/	# Group theory question 1. Nov 14, 2007 ### titaniumx3 1. The problem statement, all variables and given/known data If p is a prime and G is group of order p^2, then show that G is abelian. 2. Relevant equations n/a 3. The attempt at a solution I first consider Z(G), the centre of G. Since it is a normal subgroup of G, then by Lagrange's Theorem, \|Z(G)\| divides \|G\|. Hence \|Z(G)\| = 1, p or p^2. We know that Z(G) not the trivial subgroup (proof already given) hence it must be of order p^2 or p. If \|Z(G)\| = p^2, then Z(G) = G and hence by definition it is abelian. If \|Z(G)\| = p, then .... well this is where I am stuck! :( 2. Nov 14, 2007 ### Dick Consider an element q that is not in Z(G). How big is the subgroup generated by q and Z(G)? 3. Nov 14, 2007 ### Kreizhn In the case of your argument, if $\|Z(G)\| = p$ then we have that $\frac{\|G\|}{\|Z(G)\|} = p$ which we can't have. So on the other hand, we know that if $\exists a \in G$ such that $o(a) = p^2$ where $o(a)$ is the order of a, then $G = C_{p^2}$. Thus we can assume that every non-identity element has order p, since the order of the elements must divide the order of the group. Thus consider a non-identity element of G, say a, and the subgroup it generates. Furthemore, consider another non-identity element, say b, that is not in $<a>$. Such an element is guaranteed to exist since $o(a) = p \Rightarrow \|<a>\|\neq\|G\|$. Consider the subgroup generated by $b$. What can we say about the order of $<a>$ and the order of $<b>$ ?. What can we say about their intersection? What can we say about the order of their product? 4. Nov 14, 2007 ### titaniumx3 If we assume that every non-identity element has order p, then <a>, <b> would have order p also. Wouldn't their intersection be the empty set if b is defined as an element not in <a>? Sorry I'm not sure where I'm supposed to go with this. 5. Nov 14, 2007 ### Kreizhn That's precisely correct. They're intersection is empty, and so $$\|<a> \times <b>\| = \frac{\|<a>\|\|<b>\|}{\|<a>\cap<b>\|} = \|<a>\|\|<b>\| = p^2$$ Thus, since $a \in G, \; b\in G, \; \text{ and } \|<a> \times <b>\|=\|G\|$ then $$<a> \times <b> = G$$ Now the question is, what is $<a> \times <b>$ isomorphic to? 6. Nov 14, 2007 ### ircdan for any group G, if G/Z(G) has prime order, then G/Z(G) is cyclic, hence G is abelian 7. Nov 14, 2007 ### titaniumx3 Cyclic group of order p^2? 8. Nov 14, 2007 ### JasonRox Assume G is non-abelian and go by contradiction. And you'll need ircdan's statement. It's a nice question. 9. Nov 14, 2007 ### Kreizhn $$C_p \times C_p$$ 10. Nov 14, 2007 ### Kreizhn Via this method we've actually proved something stronger than the actual question. Namely that every group of order $$p^2$$ is isomorphic to either $C_{p^2} \text{ or } C_p \times C_p$ 11. Nov 14, 2007 ### JasonRox This question pretty much does that. 12. Nov 14, 2007 ### titaniumx3 Is $$C_p \times C_p$$ also cyclic? How do you know it is abelian? 13. Nov 14, 2007 ### ircdan C_p x C_p is not cyclic but it is abelian since each factor is 14. Nov 14, 2007 ### JasonRox This question tells us that all groups of order p^2 are abelian. What kind of abelian groups are there of order p^2? Well, it can be cyclic if it has an element of order p^2 if not, then all the elements must be of order p (Lagrange's Theorem). And you work from there. 15. Nov 14, 2007 ### titaniumx3 Thanks for all the help! I've written the proof both ways and they seem to be pretty much equivalent. I'm not sure if I should open a new thread for this but I would appreciate some help on another related question: "If G is a group of order 48 then show that it is not simple" Now \|G\| = 2^4 * 3. I'm thinking it would be a similiar argument to how you show groups of order (p^2 * q) are not simple, but in all honesty I don't even understand the proof for that very well. I guess if you apply Sylow's theorem, then clearly there are Sylow p-subgroups of order 2^4. Are these p-subgroups normal? If so, how would you go about showing this? 16. Nov 14, 2007 ### Kummer A theorem by Burnside states that the center of a finite p-group is non-trivial. So if \|G\|=p^2 and Z(G)!=G choose x in G so that x not in Z(G). We know by divisibility that Z(G) >= p (Burnside). But that means the centralizer C(x) must be G a contradiction. So Z(G)=G. 17. Nov 15, 2007 ### ircdan you can produce a counting arguement 18. Nov 15, 2007 ### titaniumx3 Can you elaborate on that? (I assume you are talking about \|G\| = 48 not being simple) 19. Nov 15, 2007 ### Kreizhn I imagine you should exploit the class equation 20. Nov 15, 2007 ### morphism How many of these can we have? Let n be the number of Sylow-2's. Then n=1(mod2) and n\|3. This leaves us with n=1 or n=3. If n=1, we're done, because this implies the unique Sylow-2 is normal in G (why?). So suppose n=3. One possible way you can proceed from here is via group actions. Let G act on the set X of 3 Sylow-2's by conjugation. This induces a nontrivial homomorphism from G into Sym(X). What is its kernel? (Don't think too hard about what the kernel actually is; think about what kernels are, and how they could be relevant to proving the non-simplicity of G.) 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https://coldfusionblog.net/2014/05/06/widom-larsen-part-1-overview/	# Widom-Larsen part 1: Overview The Widom-Larson theory of cold fusion started with this paper: “Ultra Low Momentum Neutron Catalyzed Nuclear Reactions on Metallic Hydride Surfaces” by A. Widom, L. Larsen, 2005. A follow-up paper with more mathematical details is here, while a follow-up with slightly more qualitative discussion is here. This is apparently the most popular theoretical explanation of cold fusion. For example, it was the theoretical justification supporting NASA’s cold-fusion program. Apparently, lots of reasonable people are convinced by it. On the other hand, we have things like Ron Maimon’s post railing against the theory (“…a bunch of words strung together with no coherent relation to known weak interaction theory, or to energy conservation, or to surface theory of metals, or to known nuclear physics of neutrons…”), a critical paper by Tennfors (with a 4-sentence reply here at newenergytimes), and this paper by Hagelstein that suggested that the Widom-Larsen calculation is wrong by 17 orders of magnitude, which then solicited this angry and sarcastic response by Widom et al., and this critical paper by Vysotskii, and another critical paper by Hagelstein… (Lots more papers related to Widom Larsen theory, both for and against it, are listed here at newenergytimes.com.) I want to get to the bottom of this. If Widom-Larsen theory is right, I want to clearly explain and justify every detail. If it’s wrong, I want to understand all the mistakes, what the authors were thinking, and how they got led astray. There is a lot of ground to cover. It will take many blog posts. Let’s get started! Very quick summary: The paper makes two claims: • The electron-capture process $e^- + p^+ \rightarrow n + \nu_e$ (electron plus proton turns into neutron plus electron neutrino) can and does happen on the palladium hydride surface. (Discussed in Sections 1-3 of the paper.) • The neutrons can enable a variety of nuclear reactions which indirectly turns deuteriums into helium-4: $D+D + \cdots \rightarrow \cdots \rightarrow \text{He}^4 + \cdots$. (Discussed in Section 4 of the paper.)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 2, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9158834218978882, "perplexity": 2541.3397539597595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703519843.24/warc/CC-MAIN-20210119232006-20210120022006-00298.warc.gz"}
http://mathhelpforum.com/advanced-statistics/224181-lebesgue-measurable.html	# Math Help - Lebesgue measurable 1. ## Lebesgue measurable Prove that if f:R->([0,∞]) and f^(-1)((r,∞]) ∈ M for each r∈ M,then f is Lebesgue measurable. (M is the σ-algebra of Lebesgue measurable sets) 2. ## Re: Lebesgue measurable Originally Posted by Sonifa Prove that if f:R->([0,∞]) and f^(-1)((r,∞]) ∈ M for each r∈ M,then f is Lebesgue measurable. (M is the σ-algebra of Lebesgue measurable sets) I think you mean: Prove that if $f:\mathbb{R} \to [0,\infty]$ and $f^{-1}((r,\infty])\in \mathcal{M}$ for each $r \in \mathbb{R}_{\ge 0}$, then $f$ is Lebesgue measurable. I am rewriting to verify what you are trying to prove because if $r\in \mathcal{M}$, then $(r,\infty]$ does not make sense. Anyway, use subadditivity. $(r_1,r_2] = (r_1,\infty]\setminus (r_2,\infty]$. So, given any subset of $[0,\infty]$, you can cover it with a countable union of sets of the form $(r_1,r_2]$. Then, think about the definition of the Lebesgue measure.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.991437554359436, "perplexity": 1068.9935816239895}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701160918.28/warc/CC-MAIN-20160205193920-00082-ip-10-236-182-209.ec2.internal.warc.gz"}
https://mathmaine.com/2010/11/18/algebra-part-9/	# Algebra Intro 9: Fractions, Reciprocals, and Properties of Division Now that fractions and rational numbers have been introduced, let’s explore what they do for us a bit ### Fractions And Rational Numbers A rational number is one that can be represented by the ratio of two integers. A fraction is a number that is written as the ratio of two quantities. This means that the number 5 is a rational number because it can be represented as $\dfrac{10}{2}$ which is a ratio of two integers – and one of many such possible ratios. 5 is not a fraction because, while it can be written as the ratio of two quantities, it is not written that way in this case. $\dfrac{10}{2}$ is a fraction because it is written as a ratio of two quantities. Based on the above definitions, all rational numbers can be represented using fractions, however not all fractions will represent rational numbers. For example, $\dfrac{\sqrt{3}}{2}$ is a fraction, but it is not a rational number because it cannot be represented by the ratio of two integers. ### Interpreting Fractions A fraction is a ratio of two quantities. But what does it mean? There are several ways to interpret fractions. The simplest is as a division problem: $\dfrac{6}{2}$ means “divide six into two equal portions: how big will each portion be?” Or “what quantity must I multiply by two to obtain six”? The answer will be three: Or you may interpret a fraction as a grouping situation. The above fraction represents 6 items arranged in groups of 2. How many such groups are there? Three: A similar approach is to interpret a fraction as parts of a whole. The fraction above, as well as the diagram immediately above, represent six parts (the numerator) of a type where two parts make up a “whole” (the denominator). If two parts make up a “whole”, then I can create three “wholes” from the six parts I have, and the fraction therefore represents the quantity three. ### “Proper” And “Improper” Fractions A “proper” fraction has a numerator that is closer to zero than its denominator. Since this means that there are fewer parts than needed to make “a whole”, the decimal value of such a fraction will be between negative one and one. An “improper” fraction has a numerator that is further from zero than its denominator, so it represents a number that is further away from zero than negative one or positive one. Why do we bother distinguishing between proper and improper fractions? One reason is that an “improper” fraction can always be simplified by rewriting it as the sum of a whole number and a “proper” fraction: $\dfrac{14}{3}=4\frac{2}{3}$ whereas a “proper” fraction does not contain a whole number that can be pulled out of it: $\dfrac{2}{3}=\frac{2}{3}$ A second reason is that “proper” and “improper” fractions will have opposite effects when used as factors. When a number is multiplied by an “improper” fraction (whose absolute value is greater than one), the result will be larger than the original number: $2\cdot\dfrac{6}{3}=4$ When a number is multiplied by a “proper” fraction (whose absolute value is between zero and one), the result will be smaller (closer to zero) than the original number: $2\cdot\dfrac{3}{6}=1$ When an “improper” fraction is used as a factor in a multiplication problem, it grows the result. When a “proper” fraction is used as a factor, it shrinks the result… which leads us to realize that there is more than one way to shrink a value: divide it by a number with an absolute value greater than one, or multiply it by a number with an absolute value between zero and one. ### Undoing Multiplication The discussion of proper and improper fractions may have led you to wonder if there is a way of undoing multiplication without resorting to division. If a number has been multiplied by three, can the result be multiplied by some proper fraction to produce the original number? If so, what fraction will accomplish the goal? $5\cdot 3=15\\15\cdot\frac{1}{3}=5$ $5\cdot 4=20\\20\cdot\frac{1}{4}=5$ The results above hopefully make sense intuitively, as our words describe what we are doing well. Multiplying by one third undoes multiplying by three, as we are dividing the tripled quantity into three parts, then taking one of them… which will be the same quantity we started with. Multiplying by one fourth undoes multiplying by four, as we are dividing the quadrupled quantity into four parts, then taking one of them, which will be the same quantity we had before multiplying by four. Notice the relationship between three and one third, or four and one fourth. This relationship is so useful in mathematics that it has been given a name: a reciprocal. To create the reciprocal of a number, divide one by the number. The reciprocal of 5 is $\frac{1}{5}$, and the reciprocal of $\frac{1}{5}$ is 5: $\dfrac{1}{\frac{1}{5}}=1\cdot\frac{5}{1}=5$ ### Division As Multiplication By The Reciprocal Based on the examples of undoing multiplication given above, you can see that there are two ways of undoing multiplication by a factor: divide by the same factor, or multiply by the reciprocal of the factor. Division is equivalent to multiplying by the reciprocal of the divisor: $\dfrac{15}{3}=15\cdot\dfrac{1}{3}$ This is a very useful property, as you will see in a minute. ### Properties Of Division Like subtraction, division is not associative: $\dfrac{\left(\dfrac{5}{10}\right)}{2}\neq\dfrac{5}{\left(\dfrac{10}{2}\right)}$ and is not commutative: $\dfrac{2}{10}\neq\dfrac{10}{2}$ so problems that involve division cannot be rearranged without changing the result. To get around this problem, we rewrite division problems as multiplication by the reciprocal, just was we rewrote subtraction problems as addition of the negative. The problem shown above becomes: $\dfrac{2}{10}\;\;=\;\;2\cdot\dfrac{1}{10}$ so that it can now be rearranged and/or regrouped easily using the commutative and/or associative properties of multiplication: $\dfrac{2}{10}\;\;=\;\;2\cdot\dfrac{1}{10}\;\;=\;\;\dfrac{1}{10}\cdot 2$ A more complex division problem is usually much easier to work with when converted to multiplication by the reciprocal: $\dfrac{\left(\dfrac{5}{10}\right)}{2}\;\;=\;\;\dfrac{5}{10}\cdot\dfrac{1}{2}\;\;=\;\;5\cdot\dfrac{1}{10}\cdot\dfrac{1}{2}\;\;=\;\;\left[\dfrac{1}{2}\cdot\dfrac{1}{10}\right]\cdot 5\;\;=\;\;\dfrac{1}{2}\cdot\left [\dfrac{1}{10}\cdot5\right]$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 19, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.95359867811203, "perplexity": 571.5466092588932}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315750.62/warc/CC-MAIN-20190821022901-20190821044901-00040.warc.gz"}
http://nrich.maths.org/6253/solution?nomenu=1	$UK$ means $10U + K$ and $SMC$ means $100S + 10M + C$, so we have $$10U+K+4=100S+10M+C$$ The left hand side is at most $$10 \times 9 + 8 + 4 = 102$$ so $$100S+10M+C \leq 102$$ Therefore $S \leq 1$, so $S=1$ (since it can't be zero). So $$10M+C \leq2$$ So $M=0$ $M$ has the lowest value.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9830053448677063, "perplexity": 45.2010220863845}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931007301.29/warc/CC-MAIN-20141125155647-00100-ip-10-235-23-156.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/applications-of-derivatives-of-trig-functions.139179/	# Homework Help: Applications of Derivatives of Trig. Functions 1. Oct 19, 2006 ### Jacobpm64 The voltage, V, in volts, in an electrical outlet is given as a function of time, t, in seconds, by the function $$V = 156\cos(120 \pi t)$$. (a) Give an expression for the rate of change of voltage with respect to time. (b) Is the rate of change ever zero? Explain. (c) What is the maximum value of the rate of change? Here's my attempts: (a) This one is easy. $$\frac{dV}{dt} = 156(-\sin(120 \pi t))(120\pi)$$ $$\frac{dV}{dt} = -18720\pi\sin(120 \pi t)$$ (b) This one is more tough. The rate of change is zero at some times. (I don't know how to explain.).. I could probably just say that since the original function is a cosine function, at every peak and trough, the rate of change will be zero because the derivative at that point is zero. (c) I'm not sure about this one. Wouldn't the maximum rate of change be the point of inflection? So, we can just think of the graph of the original function, and since it has a period of 1/60, and a cosine function starts at (0,1) and goes downwards, we should be able to divide the period by 4 to get the point of inflection with negative slope. So, the point of inflection with positive slope would be the period times 3/4. So, one of the points of inflection is at x = 1/80. Now we just need to find the rate of change at that point because it will be the maximum rate of change. So, I suppose we could plug x = 1/80 into the derivative equation. $$\frac{dV}{dt} = -18720\pi\sin{120\pi(\frac{1}{80})} = 18720\pi$$ or $$58810.6145$$ volts/second Are these correct? I'm not sure about my approach to them. Last edited: Oct 19, 2006 2. Oct 19, 2006 I am assuming that this is $$V = 156\cos{120 \pi t}$$ (b) Solve $$\frac{dV}{dt} = 0$$ (c) Set $$\frac{d^{2} V}{dt^{2}} = 0$$ to find critical points. Last edited: Oct 19, 2006 3. Oct 19, 2006 ### Jacobpm64 All right.. so assuming part a is correct: (b) $$-18720 \pi \sin(120 \pi t) = 0$$ $$\sin(120 \pi t) = 0$$ I forgot how to solve this (using the inverse sine but i forget exactly). (c) $$\frac{d^2 V}{dt^2} = -18720 \pi \cos(120 \pi t) * 120 \pi$$ $$\frac{d^2 V}{dt^2} = -18720(120) \pi ^2 \cos(120 \pi t)$$ $$-18720(120) \pi ^2 \cos(120 \pi t) = 0$$ $$\cos(120 \pi t) = 0$$ Again, I forgot how to solve this. Thanks for the help in advance. 4. Oct 19, 2006 $$\sin(120 \pi t) = 0$$ $$\arcsin(\sin(120\pi t) = \arcsin(0)$$ $$120\pi t = 0 + n\pi$$ $$\arccos(\cos(120\pi t) = \arccos(0)$$ $$120\pi t = \frac{\pi}{2} + n\pi$$ 5. Oct 19, 2006 ### Jacobpm64 All right, I'll continue.. (b) $$\sin(120 \pi t) = 0$$ $$\arcsin (\sin (120 \pi t) = \arcsin (0)$$ $$120 \pi t = 0 = n \pi$$ $$t = \frac{n \pi }{120 \pi } = \frac{n}{120}$$ Yes, it is zero at all times $$t = \frac{n}{120}$$. The rate of change is zero at these points because the derivative at the points is zero. (c) $$\arccos(\cos(120\pi t) = \arccos(0)$$ $$120\pi t = \frac{\pi}{2} + n\pi$$ $$t = \frac{1}{240} + \frac{n}{120}$$ So, the rate of change is max at all these points. But, they are asking for the maximum rate of change, so i'll try 2 values, since one will be the minimum rate of change, and the next will be the maximum rate of change. $$V'(0) = -18720\pi \sin(120 \pi * (\frac{1}{240} + \frac{0}{120})) = -18720 \pi \approx -58810.6145$$ <---- this is the minimum rate of change So, I'll try the next number to get the maximum rate of change. $$V'(1) = -18720\pi \sin(120 \pi * (\frac{1}{240} + \frac{1}{120})) = 18720 \pi \approx 58810.6145$$ <---- this is the maximum rate of change Looks good now? Same answers as before lol, just a lot more work	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9625502228736877, "perplexity": 404.07863287137883}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589573.27/warc/CC-MAIN-20180717051134-20180717071134-00232.warc.gz"}
http://davidruescas.com/category/philosophy-of-science/page/2/	## Simplicity and meta-theoretic induction During my discussion of induction and occams razor, I have said The key is that our intuition, in fact our intelligence in general, has a built-in simplicity bias. We strongly favor the odd number theory because it is the simplest theory that fits the facts. Hence induction, including our everyday intuitions and the scientific method, is founded upon Occam’s razor as a way to discriminate between equally supported theories. Note that I have described Occam as a simplicity bias. I deliberately chose this word in order to convey that simplicity is a guideline that we use prior and independent of experience. In the language of probability, Occam takes the form of a prior probability distribution that favors simpler theories before any updating has occured, and is unaffected by posterior evidence. This state of affairs does not seem satisfactory; as described above, Occam seems like an unjustified and arbitrary principle, in effect, an unsupported bias. Surely, there should be some way to anchor this widely applicable principle on something other than arbitrary choice[1]. The obvious course would be to say something like this: Simpler theories are more likely to be true because they have been so in the past thus grounding the principle on experience, just like any other case of inductive inference and scientific knowledge. But let’s go back to the source of the problem that this principle is trying to fix. We have two theories, S and C, which make identical, correct predictions with respect to all observations made to date. These two theories only differ in their future predictions. And yet, in practice, we consider the predictions made by S much more likely than those made by C. Because by definition these two theories share likelihoods for observed evidence, it is only through their priors that we can assign them different probabilities. Here’s where the simplicity principle comes in. We favour theory S because it is simple, hence granting it a greater prior probability and consequently a greater posterior despite its shared likelihood with C. When asking ourselves how we justify the simplcity principle, we answer Because simple theories have been true in the past. So the simplicity principle acts like a meta-theory and can accrue probability through experience just like any other theory. Until now, everything seems to work, but here’s the problem. Let’s say we have two guiding principles: Occam: Simpler theories are more likely to be true Occam(t): Simpler theories are more likely to be true until time t Whatever the mechanism by which the simplicity meta-theory accumulates posterior probability, so shall its peculiar brother, and in the same exact amount. When going back to our two theories, S and C, Occam will favour S while Occam(t) will favour C. Because both Occam and Occam(t) are supported by the same amount of evidence, equal priors will be assigned to S and C. The only way out of this is for Occam and Occam(t) to have different priors themselves. But this leaves us back where we started! So in conclusion, if we try to solve the problem with Simpler theories are more likely to be true because they have been so in the past we are just recasting the original problem at the meta level, we end up begging the question[2] or in an infinite regress. Which should not really come as a surprise, there is no way to justify knowledge absolutely, there must be unjustified assumptions somewhere. In my point of view, Occam is such a bedrock The way I see it, the foundations of scientific knowledge are the postulates of probability theory (as derived for example by Bernardo-Smith or Cox) together with Occam’s razor. Please see my next post where I formalize meta-theoretic induction [1] In essence, this is the problem of induction, which dates back to Hume who first posed it in its original form. [2] The future is like the past because in the past, the future was like the past ## Epistemological dive Note: I wrote this piece before the two posts presenting simple model of learning using bayesian inference. There is significant overlap, and conclusions are stated without complete explanations. I attended an informal talk on climate change recently, after which I had several discussion regarding the scientific process and the foundations of knowledge (in science). One question was Is scientific knowledge is inductive or deductive? Well, the scientific method requires deductive inference to establish the logical consequences of a theory in order to make predictions. But the justification of theories, the method by which a theory is temporarily accepted or discarded is inductive. In the language of Bayes, theory confirmation/invalidation occurs by updating theory posteriors inductively (P(H\|E)), whereas evidence conditioning on theories (P(E\|H)) is derived deductively. So, although deduction plays a part in establishing the logical consequences of theories in the form of testable predictions, the nature of the knowledge, or rather, the process by which that knowledge is gained, is fundamentally inductive. What does this say about the foundations of knowledge in science? If scientific knowledge were deductive, we could simply say that its foundations are axiomatic. We could also talk about incompleteness and other interesting things. But if as we have stated this knowledge is inductive, what are its foundations? Is induction a valid procedure, and what are its endpoints? This is a very deep subject, trying to go all the way to the bottom is what I have titled this post as an epistemological dive. I’m not going to give this a thorough treatment here, but I’ll briefly state what my position is and what I argued in discussion that day. The way I see it, the foundations of scientific knowledge are the postulates of probability theory (as derived for example by Bernardo-Smith or Cox) together with Occam’s razor. In fact, given that most people are aware of probability theory I would say that the best single answer to the foundation of knowledge, in the sense that it is something we are less aware of, is Occam’s razor. I will give a brief example of this, borrowed from a talk by Shane Legg on machine super intelligence. Let’s consider a minimal example of a scientific process. An agent is placed in an environment and must form theories whose predictions correctly match the agent’s observations. Although minimal, this description accounts for the fundamental elements of science. There is one missing element, and that is a specification of how the agent forms theories, but for now we will use our own intuition, as if we were the agent. For this minimal example we will say that the agent observes a sequence of numbers which its environment produces. Thus, the agent’s observations are the sequence, and it must form a theory which correctly describes past observations and predicts future ones. Let’s imagine this is what happens a time goes forward, beginning with 1 For the moment there is only one data point, so it seems impossible to form a theory in a principled way. 1,3 Among others, two theories could be proposed here, odd numbers, and powers of 3, with corresponding predictions of 5 and 9: f(n) = 2n – 1 f(n) = 3^n the observations continue: 1,3,5 The powers of three theory is ruled out due to the incorrect prediction 9, while odd number theory was correct. 1,3,5,7 The odd number theory has described all observations and made correct predictions. At this point our agent would be pretty confident that the next observation will be 9. 1,3,5,7,57 What?! That really threw the agent off, it was very confident that the next item would be 9. But it turned out to be 57. As the builder of this small universe I’ll let you know the correct theory, call it theory_57: f(n) = 2n – 1 + 2(n-1)(n-2)(n-3)(n-4) which if you check correctly describes all the numbers in the sequence of observations. If the 5th observation had instead been 9, our odd number theory would have been correct again, and we would have stayed with it. So depending on this 5th observation: 9 => f(n) = 2n-1 57 => f(n) = 2n – 1 + 2(n-1)(n-2)(n-3)(n-4) Although we only list two items, the list is actually infinite because there are an infinite number of theories that correctly predict the observations up until the 4th result. In fact, and here is the key, there are an infinite number of theories that correctly predict any number of observations! But let us restrict the discussion to only the two seen above. What our intuition tells us is that no reasonable agent would believe in theory_57 after the fourth observation, even though it is just as compatible with the odd number theory. Our intuition strongly asserts that the odd number theory is the correct theory for that data. But how can we justify that on the basis of induction, if they make the same predictions (ie they have the same P(E\|H))? The key is that our intuition, in fact our intelligence in general, has a built-in simplicity bias. We strongly favor the odd number theory because it is the simplest theory that fits the facts. Hence induction, including our everyday intuitions and the scientific method, is founded upon Occam’s razor as a way to discriminate between equally supported theories. Without this or some more specific bias (in machine learning we would call this inductive bias), induction would be impossible, as there would be too many theories to entertain. Occam’s razor is the most generally applicable bias; it is a prerequisite for any kind of induction, in science or anywhere else. ## Learning and the subject-object distinction Previously I presented a model where learning is impossible. In this post I want to emphasize ..not only must the phenomenon be learnable, but additionally the learning agent must incorporate a bias to exploit existing regularity. Without such a bias, the learner cannot penalize complex “noisy” hypotheses that fit the data. In the model, the environment (phenomenon) that gives rise to observations in the form of the binary sequence of ‘0’ and ‘1’ is left unspecified. Nothing is said about how the environment evolves, whether it is deterministic or stochastic, or whether it follows a certain rule or not. The model I presented is thus completely orthogonal to the nature of the environment. And yet Whatever the sequence of events, the learning agent does not gain any knowledge about the future from the past, learning is impossible. So a property of the learning agent, the subject, makes learning impossible irrespective of the environment, the object. This property of the subject is the belief that all sequences of observations are equally likely, that is, the lack of a-priori bias favoring any of the outcomes[1]. Even if the object was completely predictable, the subject would be unable to learn. Learning imposes constraints on both, hence the subject-object distinction; To drive this point home, we could specify any environment and note how the conclusions regarding the model would not change. I hinted at this by presenting an example of the environment’s evolution that began with 111. Now assume the environment is such that it produces ‘1’ indefinitely in a completely deterministic and predictable way. You could interpret this as the classical example in philosophical treatments of induction: ‘1’ means that the sun rises the next day[2], and ‘0’ means that the sun does not rise. But again, this would make no difference, the learner would never catch on to this regularity. Conversely, specifying an unlearnable environment will not do the learner any good either, of course. In fact, the astute reader will have realized that the learning agent’s prior corresponds exactly to the belief that the sequence of ‘0’ and ‘1’ are the results of a series of coin flips, where the coin is fair. And of course, given the assumption describing the coin, previous coin flips do not yield any information that serve to make predictions about future coin flips; the environment has no structure to be learned. Most problems of bayesian inference include, in the problem statement, a description of the environment that is automatically used as the agent’s prior knowledge or at least a starting point, as in the typical case of drawing balls from an urn. This prior knowledge is incomplete of course, as no inference would be necessary otherwise. But in these cases the subject-object distinction is not so apparent; analysis about the agent’s learning performance assumes the problem definition is of course true! However, the subject-object distinction is more important when asking what model of inference applies to the scientific investigation of nature and the problem of induction. This is because in these models, there is no problem definition, prior knowledge is genuinely prior to any experience. Pending questions: What problem definition applies to inductive inference in science? What happens when extending our model to cases with infinite observations/theories? Does learning logically require bias, and if so, what bias is appropriate universally and intuitively acceptable?[3] [1] In fact, not only must there be bias, but it must be a bias that exploits structure. Altering the distribution such that it favors more ‘1’ in the sequence irrespective of previous observations is a bias, but does not allow learning. This is another important distinction, the entropy-learnability distinction. [2] Or after 24 hours if you want to be picky about tautologies [3] Another more technical question is, can prior knowledge in inference problems always be recast as a bias over theories that are deterministic predictions over entire sequences of possible events? (as we saw when noting that the binary sequence model is equivalent to a repeated coin flip scenario) If so, what property of these distributions allows learning? ## When learning is impossible I’ve defined learning as the extraction of generally applicable knowledge from specific examples. In that post I remarked An agent may have the ability to learn, but that is not enough to guarantee that learning does in fact take place [1]. The extra necessary ingredient is that the target of learning must be learnable. Today I’m going to a present a model where learning is impossible in the context of bayesian inference. We will see in this case that not only must the phenomenon be learnable, but also that the learning agent must incorporate a bias to exploit existing regularity. Without such a bias, the learner cannot penalize complex “noisy” hypotheses that fit the data. As components of the model we have an agent, an environment from which observations are made, and theories the agent probabilistically reasons about as the object of its learning. For observations we use a binary sequence, S = {0, 1}^n, like for example S = 1010111010 The learning agent sees a number of elements and must try to predict subsequent ones according to different theories, which are of the form H = {0,1}^n. An important aspect of the model is that the agent will consider all possible theories that can explain and predict observations. The number of theories is therefore equal to the number of possible observations, which are both 2^n. If the agent considered a smaller number of theories it could be that the true theory describing the environment would be left out. Furthermore, let’s say that a-priori, the agent has no reason to consider any theory more likely than the rest. So it will assign an a-priori equal probability to each theory: P(H) = 1 / 2^n Define the total observations up to a given time as Si, where i <= n, and that a given theory is Hk, where k <= n. We can apply bayes theorem to obtain the probability that a given theory is true given the observations (feel free to skip the math down to the conclusion): P(Hk\|Si) = P(Si\|Hk)P(Hk) / P(Si) and the probability of a given sequence of observations P(Si) is obtained by summing[1] over all theories that yield such a prediction: P(Hk\|Si) = P(Si\|Hk)P(Hk) / Sum(k) P(Si\|Hk)P(Hk) in other words, summing over all theories that begin with Si. To see exactly whats happening let’s restrict the example to n = 4. This gives us a total of 2^4 = 16 possible observations and theories. Say the agent has observed three elements ‘111’ and call the sequence S3: S3 = 111 Let’s calculate the posterior probability on theories for this case. First for theories that do not predict 111: P(Hk\|Si) = P(Si\|Hk)P(Hk) / Sum(k) P(Si\|Hk)P(Hk) but since P(Si\|Hk) = 0, then P(Hk\|Si) = 0 ie theories that do not predict 111 are ruled out as should be the case. There are two theories that do predict 111: H1 = {1110} H2 = {1111} the denominator of the posterior is Sum(k) P(S3\|Hk)P(Hk) there are two theories that predict the sequence, therefore Sum(k) P(S3\|Hk)P(Hk) = P(H1) + P(H2) plugin this in, the posterior is therefore P(H1\|S3) = P(S3\|H1)P(H1) / [P(H1) + P(H2)] P(H2\|S3) = P(S3\|H2)P(H2) / [P(H1) + P(H2)] since both H1 and H2 predict S3 (P(S3\|H) = 1), this reduces to P(H1\|S3) = P(H1) / [P(H1) + P(H2)] P(H2\|S3) = P(H2) / [P(H1) + P(H2)] but because all theories are equally likely a priori P(H1) = P(H2) = 1/16 so P(H1\|S3) = 1/16/ [1/16 + 1/16] = 1/2 and similarly P(H2\|S3) = 1/16/ [1/16 + 1/16] = 1/2 So H1 and H2 are assigned equal probabilities, 1/2. Because no other theories are possible and 1/2 + 1/2 = 1, it all works out. Now, the agent will use these two theories to predict the next observation: P(1110\|S3) = 1 1/2 + 0 * 1/2 = 1/2 P(1111\|S3) = 0 * 1/2 + 1 * 1/2 = 1/2 Thus, the agent considers that it is equally likely for the next element to be 1 or 0. But there is nothing special about the example we chose with n = 4 and S3 = 111. In fact, you could carry out the exact same calculations for any n, and S. Here’s the key point, the learning agent makes the exact same predictions as to what will happen no matter how many observations it has made, and no matter what those observations are. Whatever the sequence of events, it does not gain any knowledge about the future from the past, learning is impossible. I’m going to leave the discussion for later posts, but here are some relevant questions that will come up: Does learning logically require bias? Can one meaningfully speak of theories when there is no compression of observations? What happens when the model is extended to an infinite number of observations/theories? Is this an adequate (though simplistic) model of scientific investigation/knowledge? Notes/references [1] I’m using the notation Sum(n) as the equivalent of the Sigma sum over elements with subscript n ## The most incomprehensible thing about the universe is that it is comprehensible It’s a quote by Albert Einstein, which is where we left off last time. Comprehensible translates to, for example, mathematically intelligible, regular or lawful. These are different ways to say that it is possible to arrive at descriptions of the world that allow us to understand it and make predictions. Einstein’s point was that there is no particular reason to expect the universe to be the way it is, i.e. following elegant mathematical laws. It could have just as well been a chaotic mess impossible to make sense out of. It’s hard to tell whether it’s even meaningful to speak of the way the universe could have been without speaking of how the universe and its characteristics arise. Indeed, one of the deepest questions in physics is, why does the universe have the laws it has? (Second only to why is there something rather than nothing?) But imagine for the moment that the universe was in fact a messy chaos. Well, one thing seems clear, that kind of universe would not contain life, because life is one of the most obvious examples of order and regularity (or if you like, life requires order and regularity to exist), and intelligent life is precisely the kind of life that requires most order. The point is that our very existence screens off the possibility of a non-regular universe, it is impossible for us to observe anything different because we would not have existed under those circumstances. This point is known as the anthropic principle. Does it answer the question? Not really; the anthropic principle has been labeled as unscientific and metaphysical by critics. You have to be careful to not take the point too far. In this case I’m just saying that life implies a selection effect to the universe it inhabits. But again, that does not answer the question. However, if we additionally postulate that there isn’t one universe, but many, the situation makes some sense: Alice: Why is the universe comprehensible? Bob: The thing is, there isn’t just one, there are many, so it turns out that some of them are comprehensible, just like in a lottery someone must end up winning. Alice: But what about the coincidence that we landed precisely on a comprehensible one? Bob: That’s not a coincidence, our very existence implies that the universe we are in must be orderly. We couldn’t have landed in any other one. Alice: So it’s a combination of those two things that answers the question, the anthropic principle is not enough.. Bob: Yes Although in fact the question is still not answered because we had to postulate the existence of many universes, and we could in turn ask ourselves why that is the case. Oh well.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8643657565116882, "perplexity": 644.7923190391978}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591596.64/warc/CC-MAIN-20180720115631-20180720135631-00002.warc.gz"}
https://math.stackexchange.com/questions/22522/extending-morphisms-with-zorns-lemma/99764	# Extending morphisms with Zorn's lemma I have stumbled upon a remarkable similarity between the proof of Baer's criterion and an extension theorem in field theory. Here are the statements: Baer's criterion: Let $R$ be a ring. A left $R$-module $E$ is injective iff every $R$-map $f:I \to E$, where $I$ is a left ideal of $R$, can be extended to a map $R\to E$. Extension theorem: let $F\subset K$ be an algebraic field extension, and $L$ an algebraically closed field. Then every field homomorphism $\sigma: F \to L$ can be extended to a field homomorphism $K\to L$. Now, these two theorems don't seem to have anything to do with each other, but the proofs are strikingly similar. Here's how they go: For Baer's criterion (the non-trivial statement, i.e. the sufficiency of the ideal condition): to prove injectivity, we let $A\subset B$ be a submodule and $f:A\to E$ an $R$-map, and define $X=\{(A',g'): A\subset A'\subset B,\, g': A' \to E,\, g'\|_A=f\}$. Let $\leq$ be the partial order in $X$ given by $(A',g')\leq (A'',g'') \iff A'\subset A'' \text{ and } g''\|_{A'}=g'$. By Zorn's lemma there's $(A_0,g_0)$ a maximal element. If $A_0=B$ we're done, if not, let $b\in B\setminus A_0$, define $I=\{r\in R: rb\in A_0\}$ and $h:I\to E$, $r \mapsto g_0(rb)$. Apply the hypothesis to find an extension $\tilde{h}$ of $h$ to $R$. Let $A_1=A_0 + Rb$ and $g_1:A_1 \to E$, $a_0+rb \mapsto g_0(a_0)+r\tilde{h}(1)$, and $(A_1,g_1)$ contradict the maximality of $(A_0,g_0)$. For the extension theorem: define $M=\{(A,\tau):F\subset A \subset K,\, \tau:A\to L,\, \tau\|_F=\sigma\}$. Let $\leq$ be the partial order on $M$ given by $(A,\tau)\leq (A',\tau') \iff A\subset A' \text{ and } \tau'\|_A=\tau$. By Zorn's lemma there's $(A,\tau)$ a maximal element. If $A=K$ we're done, if not let $\alpha \in K\setminus A$, I claim $\tau$ extends to $A(\alpha)\to L$, contradiction. Let $p$ be the minimal polynomial for $\alpha$ over $A$. The polynomial $\tau p\in L[X]$ has a root $r\in L$ by hypothesis. Since $A(\alpha)= \frac{A[X]}{\langle p \rangle}$, define $\tilde{\tau}: \frac{A[X]}{\langle p \rangle} \to L$ as $\tilde{\tau}\|_A=\tau$, $\tilde{\tau}(X)=r$, and $(A(\alpha),\tilde{\tau})$ contradicts the maximality of $(A,\tau)$. The resemblance of both proofs shouldn't come as such a surprise since both are about extending morphisms, so maybe the only observation to make is "it's a useful technique, remember it's useful for extending morphisms". If that's it, then this question is useless. But I'm intrigued. Is this technique used to prove other extending theorems? Is it possible to generalize it and write a single categorical proof for situations of this kind? Any other observations are appreciated (or perhaps it's just a dumb observation that doesn't serve any purpose). • It is a very common pattern. – Mariano Suárez-Álvarez Feb 17 '11 at 16:37 • It is the very standard application of Zorn's Lemma. I used it in a paper to construct amalgams of nilpotent groups, by constructing "partial amalgams" and then applying Zorn's Lemma to extend them. The general idea is that if you can do a "single-step extension", then you can do an arbitrary extension by transfinite induction "one-step-at-a-time". Don't know if it can be categorified, but I doubt it since it fails in many situations when you try to go from the finite to the infinite case. – Arturo Magidin Feb 17 '11 at 16:48 • Every proof using Zorn's lemma looks the same. (Imre Leader said in a lecture once something like "once you've seen one application of Zorn's lemma, you've seen them all," but he gave three anyway.) – Qiaochu Yuan Feb 17 '11 at 16:53 • If you want to crystallize a strategy out of this similarity, here it is: If you want to define a map from some arbitrarily-infinite space (like $R$ in Baer's criterion, or $K$ in the extension theorem), but you can only do it on small finite parts of it (such as finitely generated submodules of $R$ in Baer's criterion, or finite extensions of $F$ in the extension theorem), then you can use the Zorn lemma. Here, "arbitrarily-infinite" means that it MAY be very large (infinite, not finitely generated, etc.), although it needs not be - we just don't know how large it is. – darij grinberg Feb 17 '11 at 19:07 I do see some nontrivial commonality here, but it is not precisely between the two theorems you suggest. Namely, just as the injective modules are (obviously!) the injective objects in the category of $R$-modules, the algebraically closed fields are the injective objects in the category of fields. Indeed, the latter statement is precisely your Extension Theorem. Thus your Extension Theorem doesn't strike me as a "Baer criterion" per se. Perhaps it is better the other way around: if we define an injective field as being a field which satisfies the conclusion of the Extension Theorem, then maybe "Baer's Criterion" is that a field is injective iff it is algebraically closed? (To be clear, this is definitely a true fact; it's not clear whether it is worthy of this name.) Let me try this: to check whether a field $K$ is injective, it suffices to check that for every maximal ideal $I$ of $K[t]$ there exists a $K$-algebra map $K[t]/I \rightarrow K$. This is perhaps "Baeresque"? Note that I came to the analogy here by trying to understand why the injective envelope $M \rightarrow E(M)$ is not a natural [in the categorical sense] construction: it is unique up to nonunique isomorphism over $M$. This is just the same situation as the algebraic closure of a field. And then I found this paper by Adamek, Herrlich, Rosicky and Tholen exploring this issue in a more general categorical context. • On the other hand, this makes me think one can define the "absolute Galois group" (well-defined up to an inner automorphism!) of an $R$-module as the group of automorphisms of "the" extension $M \hookrightarrow E(M)$. Anyone know anything about the Inverse Galois Problem in this context? – Pete L. Clark Feb 18 '11 at 6:09 • your answer is great food for thought. Thank you. – Bruno Stonek Feb 20 '11 at 22:07 I suspect you'll find highly interesting the following paper on related topics, which I mentioned in some prior answers that you may find of interest. Below is the introduction of said paper. • Somewhat related is Schmidt, J: "Uber die Rolle der transfiniten Schlussweisen in einer allgemeinen Idealtheorie." Math. Nachr. 7 (1952) 165--182. – Willie Wong Jan 17 '12 at 10:23 • I've just read this introduction. It's really interesting. Thank you very much! I think I see the link between Theorem 1 and the proof of the characterization of semisimple modules: "a module is direct sum of simple modules iff every submodule has a complement". I will download & print the paper, and I'll try to read and think it through when I have more time. Thank you again, your intuition was right, I do find this highly interesting! – Bruno Stonek Jan 17 '12 at 13:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.950660228729248, "perplexity": 215.7428824862722}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572516.46/warc/CC-MAIN-20190916080044-20190916102044-00137.warc.gz"}
https://www.transtutors.com/questions/understanding-the-effects-of-operating-leverage-hightech-inc-and-oldtime-co-compete--1361426.htm	# Understanding the effects of operating leverage HighTech, Inc., and OldTime Co. compete within... Understanding the effects of operating leverage HighTech, Inc., and OldTime Co. compete within the same industry and had the following operating results in 2012: HighTech, Inc. OldTime Co. Sales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $2,100,000$2,100,000 Variable expenses . . . . . . . . . . . . . . . . . . . . . . 420,000 1,260,000 Contribution margin . . . . . . . . . . . . . . . . . . . . . $1,680,000$ 840,000 Fixed expenses . . . . . . . . . . . . . . . . . . . . . . . . 1,470,000 630,000 Operating income . . . . . . . . . . . . . . . . . . . . . . $210,000$ 210,000 Required: a. Calculate the break-even point for each firm in terms of revenue. b. What observations can you draw by examining the break-even point of each firm given that they earned an equal amount of operating income on identical sales volumes in 2012? c. Calculate the amount of operating income (or loss) that you would expect each firm to report in 2013 if sales were to 1. Increase by 20%. 2. Decrease by 20%. d. Using the amounts computed in requirement c, calculate the increase or decrease in the amount of operating income expected in 2013 from the amount reported in 2012. e. Explain why an equal percentage increase (or decrease) in sales for each firm would have such differing effects on operating income. f. Calculate the ratio of contribution margin to operating income for each firm in 2012. (Hint: Divide contribution margin by operating income.) g. Multiply the expected increase in sales of 20% for 2013 by the ratio of contribution margin to operating income for 2012 computed in requirement f for each firm. (Hint: Multiply your answer in requirement f by 0.2.) h. Multiply your answer in requirement g by the operating income of \$210,000 reported in 2012 for each firm. i. Compare your answer in requirement h with your answer in requirement d. What conclusions can you draw about the effects of operating leverage from the steps you performed in requirements f, g, and h?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9662392735481262, "perplexity": 419.64368320522595}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267159160.59/warc/CC-MAIN-20180923055928-20180923080328-00059.warc.gz"}
https://www.vedantu.com/question-answer/find-the-value-of-11th-term-of-an-ap-4914-class-10-maths-cbse-5edf56f8d6b8da423c12028c	Question Find the value of 11th term of an A.P.: 4,9,14,... Given series: $4,9,14,...$ Difference between the first and the second term is $5$, and the second and third term is also $5$. Therefore, common difference in this series is $5$, ${t_n} = 4 + \left( {n - 1} \right)5 = 5n - 1$ For $n = 11,{t_n} = 5\left( {11} \right) - 1 = 54$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8520251512527466, "perplexity": 315.1039468363574}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988802.93/warc/CC-MAIN-20210507181103-20210507211103-00116.warc.gz"}
http://fpish.net/blog/CKoenig/id/2125/http~3a~2f~2fgettingsharper.de~2f~3fp~3d270	0 comment on 12/5/2011 4:00 PM Finally we will produce some output. And after the work we did so far it will be rather easy. The last “hard” part will be the shading: First (very) simple shading The idea is very simple. A object will reflect … Weiterlesen →	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9678308963775635, "perplexity": 1851.818248503284}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891485.97/warc/CC-MAIN-20180122153557-20180122173557-00395.warc.gz"}
https://www.physicsforums.com/threads/another-practice-question-nortons-theorem.162679/	# Another practice question: nortons theorem 1. Mar 26, 2007 ### amy_a hi guys, sorry to be a bothersome newbie but i have another electrical query. this time its nortons theorem. i need to determine the current through RL, the voltage across RL and the power developed in RL using the theorem. any pointers on where to start would be really appreciated :!!) #### Attached Files: • ###### 22.bmp File size: 21.3 KB Views: 105 2. Mar 26, 2007 ### Nacer R(Norton) = R (Thevenin). I(Norton) = [E/(R1+(R2//R3))][(R2//R3)/R3] Regards, Nacer. 3. Mar 27, 2007 ### amy_a thanks nacer, i'd best get to work :) 4. Mar 27, 2007 ### amy_a ok forgive my naivety but what do the double backslashes indicate? // like that? i know the single one is divide. i feel really retarded now. 5. Mar 27, 2007 ### antoker I think he is referring to a parallel combination, i.e R1//R2 = (R1R2)/(R1+R2) Norton equivalent is no different from Thevenin. Norton equi. = Current Source with a resistor in parallel and Thevenin has voltage source and resistor in series. So, basically you can apply your knowledge of Thevenin equivalents from antoher thread and then just replace a thevenin equ that you'll get with Nortons 6. Mar 28, 2007 ### amy_a thanks guys :) i appreciate it! can anyone tell me why r4 is not considered when calculating the current (using the equation given by nacer) would i just have to apply that formula to the diagram above to find the norton current? 7. Mar 28, 2007 ### antoker Every resistor excluding Rl&R4 has to be considered, because you're looking for so-called short-circuit current, so when you have a direct connection between the RL terminals, where does the current go? Since the current is looking for the easiest path, the path with least resistance, it will go just via a direct connection, rather then going via R4. http://en.wikipedia.org/wiki/Norton's_theorem I suggest that you read up on the Nortons procedure. 1. Calculate the short-circuit current by applying the direct connection between output terminals 2. Calculate output resistance by replacing the voltage source with a short-circuit 3. Norton-source = short-circuit current & Output resistance = resistance from step 2. Similar Discussions: Another practice question: nortons theorem	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8129287362098694, "perplexity": 3127.4645204222493}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122629.72/warc/CC-MAIN-20170423031202-00042-ip-10-145-167-34.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/hollow-sphere-with-uniform-surface-charge.855990/	Hollow Sphere with Uniform Surface charge 1. Feb 6, 2016 woprxcpe1704tks 1. The problem statement, all variables and given/known data 2. Relevant equations Poynting's Theorem S = 1/μ0 (E x B) Momentum = p = μ0ε0 ∫ S dτ 3. The attempt at a solution My strategy was to treat the hollow sphere as a point charge (by Gauss' Law), so E = 1/4πε0 Q/a2. I believe the magnetic field would be B = 2/3μ0M (where M is the magnetic dipole moment per unit volume). For part A, would this be the correct total electromagnetic momentum if I used the formula stated above and the relevant E and B fields. Also, do I have the E and B field formula's correct? 2. Feb 7, 2016 woprxcpe1704tks The attachment is my current attempt at part A Attached Files: • Doc Feb 07, 2016, 11_23.pdf File size: 447.3 KB Views: 34 Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook Have something to add? Draft saved Draft deleted Similar Discussions: Hollow Sphere with Uniform Surface charge	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9398061633110046, "perplexity": 2017.3923835702549}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187828134.97/warc/CC-MAIN-20171024033919-20171024053919-00647.warc.gz"}
https://learn.saylor.org/mod/page/view.php?id=31628	## What is Entropy? The second law of thermodynamics involves a thermodynamic quantity we call entropy (S). Entropy is a measure of the disorder of a system, measured in joules (J). The second law of thermodynamics states that the entropy of the universe is always increasing. One consequence of the second law of thermodynamics is that in any engine there will be some energy lost as heat that cannot be harnessed to do work. We observe this in our everyday lives. If you touch the hood of your car while the engine is running, the hood of the car will feel hot. This is because some of the energy from your car engine is lost as heat. Because of this, the second law of thermodynamics explains why a perpetual motion machine can never exist. Read this text. The first section explains the difference between reversible and irreversible processes. A reversible process can be modeled as a series of tiny steps, while an irreversible process must be modeled as a single large change. The second section discusses the meaning of entropy, and what disorder means on a microscopic level. Entropy is a state function, which means we can apply Hess' Law to it. Absolute entropies of most common substances are tabulated, allowing us to calculate the entropy of a reaction in the same way we can calculate enthalpy of reaction from standard enthalpies of formation. Entropy is one of the most fundamental concepts of physical science, with far-reaching consequences ranging from cosmology to chemistry. It is also widely misrepresented as a measure of disorder, as we discuss below. The German physicist Rudolf Clausius originated the concept as energy gone to waste in the early 1850s, and its definition went through a number of more precise definitions over the next 15 years. We have explored how the tendency of thermal energy to disperse as widely as possible is what drives all spontaneous processes, including chemical reactions. Now we need to understand how the direction and extent of the spreading and sharing of energy can be related to measurable thermodynamic properties of substances – that is, of reactants and products. You will recall that when a quantity of heat q flows from a warmer body to a cooler one, permitting the available thermal energy to spread into and populate more microstates, that the ratio q/T measures the extent of this energy spreading. It turns out that we can generalize this to other processes as well, but there is a difficulty with using q because it is not a state function; that is, its value is dependent on the pathway or manner in which a process is carried out. This means, of course, that the quotient q/T cannot be a state function either, so we are unable to use it to get differences between reactants and products as we do with the other state functions. The way around this is to restrict our consideration to a special class of pathways that are described as reversible. ### Reversible and Irreversible Changes A change is said to occur reversibly when it can be carried out in a series of infinitesimal steps, each one of which can be undone by making a similarly minute change to the conditions that bring the change about. For example, the reversible expansion of a gas can be achieved by reducing the external pressure in a series of infinitesimal steps; reversing any step will restore the system and the surroundings to their previous state. Similarly, heat can be transferred reversibly between two bodies by changing the temperature difference between them in infinitesimal steps each of which can be undone by reversing the temperature difference. The most widely cited example of an irreversible change is the free expansion of a gas into a vacuum. Although the system can always be restored to its original state by recompressing the gas, this would require that the surroundings perform work on the gas. Since the gas does no work on the surrounding in a free expansion (the external pressure is zero, so PΔV = 0,) there will be a permanent change in the surroundings. Another example of irreversible change is the conversion of mechanical work into frictional heat; there is no way, by reversing the motion of a weight along a surface, that the heat released due to friction can be restored to the system. #### Reversible and Irreversible Gas Expansion and Compression These diagrams show the same expansion and compression ±ΔV carried out in different numbers of steps ranging from a single step at the top to an infinite number of steps at the bottom. As the number of steps increases, the processes become less irreversible; that is, the difference between the work done in expansion and that required to re-compress the gas diminishes. In the limit of an infinite number of steps (bottom), these work terms are identical, and both the system and surroundings (the world) are unchanged by the expansion-compression cycle. In all other cases the system (the gas) is restored to its initial state, but the surroundings are forever changed. A reversible change is one carried out in such as way that, when undone, both the system and surroundings (that is, the world) remain unchanged. #### Reversible = Impossible: So Why Bother? It should go without saying, of course, that any process that proceeds in infinitesimal steps would take infinitely long to occur, so thermodynamic reversibility is an idealization that is never achieved in real processes, except when the system is already at equilibrium, in which case no change will occur anyway! So why is the concept of a reversible process so important? The answer can be seen by recalling that the change in the internal energy that characterizes any process can be distributed in an infinity of ways between heat flow across the boundaries of the system and work done on or by the system, as expressed by the First Law ΔU = q + w. Each combination of q and w represents a different pathway between the initial and final states. It can be shown that as a process such as the expansion of a gas is carried out in successively longer series of smaller steps, the absolute value of q approaches a minimum, and that of w approaches a maximum that is characteristic of the particular process. Thus when a process is carried out reversibly, the w-term in the First Law expression has its greatest possible value, and the q-term is at its smallest. These special quantities wmax and qmin (which we denote as qrev and pronounce q-reversible) have unique values for any given process and are therefore state functions. #### Work and Reversibility Note that the reversible condition implies wmax and qmin. The impossibility of extracting all of the internal energy as work is essentially a statement of the Second Law. For a process that reversibly exchanges a quantity of heat qrev with the surroundings, the entropy change is defined as: $\Delta S=\frac{q_{rev}}{T}$ This is the basic way of evaluating ΔS for constant-temperature processes such as phase changes, or the isothermal expansion of a gas. For processes in which the temperature is not constant such as heating or cooling of a substance, the equation must be integrated over the required temperature range, as in the equation $S=k\: In\: \Omega$. ...but if no real process can take place reversibly, what use is an expression involving qrev? This is a rather fine point that you should understand: although transfer of heat between the system and surroundings is impossible to achieve in a truly reversible manner, this idealized pathway is only crucial for the definition of ΔS; by virtue of its being a state function, the same value of ΔS will apply when the system undergoes the same net change via any pathway. For example, the entropy change a gas undergoes when its volume is doubled at constant temperature will be the same regardless of whether the expansion is carried out in 1,000 tiny steps (as reversible as patience is likely to allow) or by a single-step (as irreversible a pathway as you can get!) expansion into a vacuum. ### The Physical Meaning of Entropy Entropy is a measure of the degree of spreading and sharing of thermal energy within a system. This spreading and sharing can be spreading of the thermal energy into a larger volume of space or its sharing amongst previously inaccessible microstates of the system. The following table shows how this concept applies to a number of common processes. #### Source of Entropy Increase of System A deck of cards is shuffled, or 100 coins, initially heads up, are randomly tossed. This has nothing to do with entropy because macro objects are unable to exchange thermal energy with the surroundings within the time scale of the process Two identical blocks of copper, one at 20°C and the other at 40°C, are placed in contact. The cooler block contains more unoccupied microstates, so heat flows from the warmer block until equal numbers of microstates are populated in the two blocks. A gas expands isothermally to twice its initial volume. A constant amount of thermal energy spreads over a larger volume of space 1 mole of water is heated by 1C°. The increased thermal energy makes additional microstates accessible. (The increase is by a factor of about 1020,000,000,000,000, 000,000,000.) Equal volumes of two gases are allowed to mix. The effect is the same as allowing each gas to expand to twice its volume; the thermal energy in each is now spread over a larger volume. One mole of dihydrogen, H2, is placed in a container and heated to 3000K. Some of the H2 dissociates to H because at this temperature there are more thermally accessible microstates in the 2 moles of H. The above reaction mixture is cooled to 300K. The composition shifts back to virtually all H2 because this molecule contains more thermally accessible microstates at low temperatures. Entropy is an extensive quantity; that is, it is proportional to the quantity of matter in a system; thus 100 g of metallic copper has twice the entropy of 50 g at the same temperature. This makes sense because the larger piece of copper contains twice as many quantized energy levels able to contain the thermal energy. #### Entropy and Disorder The late Frank Lambert contributed greatly to debunking the entropy = disorder myth in chemistry education. Entropy is still described, particularly in older textbooks, as a measure of disorder. In a narrow technical sense this is correct, since the spreading and sharing of thermal energy does have the effect of randomizing the disposition of thermal energy within a system. But to simply equate entropy with disorder without further qualification is extremely misleading because it is far too easy to forget that entropy (and thermodynamics in general) applies only to molecular-level systems capable of exchanging thermal energy with the surroundings. Carrying these concepts over to macro systems may yield compelling analogies, but it is no longer science. it is far better to avoid the term disorder altogether in discussing entropy. Fig. 2-1 Source: Charles Mallery, University of Miami) ### Standard Entropies of Substances The standard entropy of a substance is its entropy at 1 atm pressure. The values found in tables are normally those for 298K, and are expressed in units of J K–1 mol–1. The table below shows some typical values for gaseous substances. He 126 H2 131 CH4 186 Ne 146 N2 192 H2O(g) 187 Ar 155 CO 197 CO2 213 Kr 164 F2 203 C2H6 229 Xe 170 O2 205 n -C3H8 270 Cl2 223 n -C4H10 310 Table 1: Standard entropies of some gases at 298K, J K –1 mol –1 Note especially how the values given in this table illustrate these important points: • Although the standard internal energies and enthalpies of these substances would be zero, the entropies are not. This is because there is no absolute scale of energy, so we conventionally set the energies of formation of elements in their standard states to zero. Entropy, however, measures not energy itself, but its dispersal amongst the various quantum states available to accept it, and these exist even in pure elements. • It is apparent that entropies generally increase with molecular weight. For the noble gases, this is of course a direct reflection of the principle that translational quantum states are more closely packed in heavier molecules, allowing of them to be occupied. • The entropies of the diatomic and polyatomic molecules show the additional effects of rotational quantum levels. C (diamond) C (graphite) Fe Pb Na S (rhombic) Si W 2.5 5.7 27.1 51.0 64.9 32.0 18.9 33.5 Table 2: Entropies of some solid elements at 298 K, J K–1 mol–1 The entropies of the solid elements are strongly influenced by the manner in which the atoms are bound to one another. The contrast between diamond and graphite is particularly striking; graphite, which is built up of loosely-bound stacks of hexagonal sheets, appears to be more than twice as good at soaking up thermal energy as diamond, in which the carbon atoms are tightly locked into a three-dimensional lattice, thus affording them less opportunity to vibrate around their equilibrium positions. Looking at all the examples in the above table, you will note a general inverse correlation between the hardness of a solid and its entropy. Thus sodium, which can be cut with a knife, has almost twice the entropy of iron; the much greater entropy of lead reflects both its high atomic weight and the relative softness of this metal. These trends are consistent with the oft-expressed principle that the more disordered a substance, the greater its entropy. Solid Liquid Gas 41 70 186 Table 3: Entropy of water at 298K, J K–1 mol–1 Gases , which serve as efficient vehicles for spreading thermal energy over a large volume of space, have much higher entropies than condensed phases. 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https://www.jkcs.or.kr/journal/view.php?doi=10.4191/kcers.2019.56.3.01	J. Korean Ceram. Soc. > Volume 56(3); 2019 > Article Moradkhani, Baharvandi, and Naserifar: Effect of Sintering Temperature on the Grain Size and Mechanical Properties of Al2O3-SiC Nanocomposites ### Abstract In this research, some mechanical properties of Al2O3-based composites containing nanoSiC and nanoMgO additives, including elasticity modulus, hardness, and fracture toughness, have been evaluated. Micron-sized Al2O3 powders containing 0.08 wt.% nanoMgO particles have been mixed with different volume fractions of nanoSiC particles (2.5 to 15 vol.%). Untreated samples have been sintered by using hot-press technique at temperatures of 1600 to 1750°C. The results show significant increases in the mechanical characteristics with increases in the sintering temperature and amount of nanoSiC particles, with the result that the elasticity modulus, hardness, and fracture toughness were obtained as 426 GPa, 21 GPa, and 4.5 MPa.m1/2, respectively. ### 1. Introduction Alumina (Al2O3) is an abundant and relatively inexpensive ceramic material that has unique physical and chemical properties. Alumina is one of the oldest types of industrial ceramics that is still prevalent as an industrial material.1) It exhibits two main phases, namely α and γ. The α phase consists of colorless crystals and crystallizes in hexagonal structure, whereas the γ phase is composed of very tiny colourless crystals that exhibit cubic structure and a specific weight of 3.6 g/cm3. The latter phase transforms to the former phase at high temperatures. The stable phase of alumina is corundum, which exhibits a hexagonal close-packed structure composed of oxygen atoms, in which aluminum atoms occupy two-thirds of the octahedral spaces.2,3) Alumina has significant industrial and commercial importance owing to a wide variety of applications in high-strength materials, bioceramics, microelectronics, coatings, abrasive materials, refractory and reinforcing materials, and catalysts.3,4) In order to enhance the mechanical characteristics of alumina, different additives, including ZrO2,5) MgO,6) Nb2O5,7) and SiC,8) can be added to it. Adding SiC to Al2O3 in the optimum proportion and the mechanisms involving crack deflection, crack bridging, and phase transformation decrease the grain growth rate and increase the grain boundary strength, resulting in the mechanical properties being improved in comparison with those of pure alumina.9,10) This composite can be fabricated through common methods, including pressure-off and cold isostatic press or hot press method. Hot press method generally affords the most favorable properties among all the techniques.9,11) Adding only 5 vol.% nanoSiC to alumina leads to its fracture strength and toughness increasing by 3 and 3.5 times, respectively. Within the sintered and polycrystallized alumina structure, some tensile stress remains at the grain boundaries and in the grains owing to anisotropy in the thermal expansion coefficient and elasticity modulus across different crystallographic directions. In this situation, a crack forms along the grain boundary, with dimensions comparable to that of a grain, owing to the existence of residual stress and defects during the manufacturing process.10,12-14) By sintering alumina at 1500°C, it is quite possible to achieve a density that is close to the theoretical density. However, after adding 5 vol.% nanoSiC particles, condensation of the composite becomes more difficult and it is necessary to increase the sintering temperature up to 1700°C to achieve full density. If the volume fraction of the particles is increased to 10 vol.%, the sintering temperature of the composite should be increased to more than 1750°C to realize full density. Since SiC particles do not have sufficient mobility and do not react with Al2O3 at the sintering temperature, they reduce the mobility of the grain boundaries and, as a result, inhibit the condensation of Al2O3. Hence, after the addition of SiC nanopowders, the sintering temperature should increase.10) Scientists have figured out that adding low amounts of MgO can lead to increased compressibility of Al2O3, corresponding to the range of the theoretical density. The prevalent theory is that MgO prevents grain growth by decreasing the grain boundary mobility, which is a result of the formation of a solid solution. Another theory includes accelerated condensation of Al2O3 upon adding MgO, in which increases in the network permeation coefficients and a decrease in the surface permeation rate are known to be responsible for this phenomenon.15) In addition, adding MgO to alumina enhances its sintering capability and leads to the fabrication of alumina with a controlled microstructure. 16) In Al2O3-SiC nanocomposites, with regard to the presence of SiC nanoparticles, which reduce the grain boundary mobility, the activated mechanisms that are attributed to the addition of MgO are more complicated, in contrast to those in pure alumina.17) With respect to the fact that some ceramic characteristics such as ballistic performance depend on a number of parameters, including density, porosity, hardness, fracture toughness, elasticity modulus, sonic velocity, mechanical strength, sintering temperature, and microstructural properties, in this study, nanoSiC powders in volume fractions of 0 to 15 vol.% have been sintered along with micron-sized Al2O3 powders containing 0.08 wt.% nanoMgO at temperatures of 1600, 1650, 1700, and 1750°C. The effects of sintering temperature and different combinations of nanoparticle substances on the mechanical characteristics of the fabricated samples, including the density, flexural strength, elasticity modulus, hardness, and fracture toughness, have been investigated, and phase and microstructural analyses of the samples have been performed. ### 2.1. Materials The raw materials used for preparing the nanocomposite samples include micronized powder of alumina, silicon carbide nanopowder (nanoSiC), magnesium oxide nanopowder (nanoMgO), isopropanol solution, and argon gas. The alumina powder used had a purity of 99.6% and its chemical composition is as listed in Table 1; its average size was less than 5 μm, with the main phase being γ-Al2O3. Figure 1 reveals the X-ray diffraction (XRD) pattern of the alumina powder, which indicates the presence of γ-Al2O3 phase. The microstructural images of the alumina, nanoSiC, and nanoMgO powders obtained by SEM or TEM are shown in Fig. 2, which reveals the existence of particles with the maximum size of roughly 5 μm in the Al2O3 powder. The SiC nanopowder used in this experiment contains α-SiC phase with an average size of 70 nm. The MgO nanopowder used was obtained by thermal decomposition of ammonium oxalate and magnesium sulfate with particle sizes less than 100 nm, and is a result of the research work of Ahmadzadeh et al..18) The XRD patterns of nanoSiC and nanoMgO are displayed in Fig. 3. Isopropanol with the chemical formulation of C3H7OH and purity 99.6% was used in a ball-mill environment. The argon gas employed was 99.99% pure, and the results of its chemical analysis are as follows. O2<2ppmH2O<3ppmN2<0.1ppmCnHm<0.1ppm The chamber used for the ball-milling is made of stainless steel, with the inner wall composed of 17 tungsten carbide (WC) balls having the diameter of 17 cm. In order to dry out the samples and expedite the evaporation of alcohol over them, a laboratory drier machine manufactured by Elektro-Warme-Aachen Co. (model FTK) was used. In order to polish the samples, diamond pastes of variety 30, 6, and 1 μm were used. The samples were mounted with a Struers Primopress machine, and Stypex materials were manufactured by Ampco Company at the temperature of 155°C by applying a force of 27 KN on the samples. To determine the flexural strengths of the samples, a five-ton machine manufactured by Zwick Company was used at the loading rate of 0.7 mm/min. To apply Vickers impressions on the samples, the hardness machine UV1 model manufactured by Koopa Company was utilized. To measure and observe the impressions made by the Vickers indenter on the samples, the hardness machine FM-700 model manufactured by Future Tech Company was employed. To study the microstructure of the samples and perform calculations based on the Vickers impressions, a SEM manufactured by Philips Company (model XL30) was used at the voltage of 20 KV and wavelength of λ = 1.54 Å. For phase analysis of the materials, the XRD equipment model 3003TT manufactured by Seifert Company was used. ### 2.2. Procedure The samples were fabricated by using hot press method with simultaneous application of heat and pressure on the mixture of primary nanopowders. The value of the nano-MgO was 800 ppm in proportion to the weight of the solid sample, whereas the values of the nanoSiC were 0, 2.5, 5, 7.5, 10, and 15 vol.%. After weighing the primary nanopowders, a suspension of their mixture was prepared in isopropanol and placed inside the ball-mill enclosure for homogenization for 3 h. The ball-to-powder ratio was 14:1. Afterwards, the resulting mixture was placed in an oven at the temperature of 90°C for 24 h. A mass of 330 g of the resulting powder then formed by using a press machine at a pressure of 2 MPa for 30 s. The resulting samples were placed in a hot-press machine for synthesis at the heating rate of 10°C/min in argon atmosphere with a graphite mold at temperatures of 1600, 1650, 1700, and 1750°C by simultaneously applying a pressure of 35 MPa for three hours. Then, the furnace was turned off to allow the samples to lose their heat and cool naturally to the room temperature. By heating the samples at 1000°C inside a heat-treatment furnace for three hours, the graphite attached to the samples in the sintering phase was removed. Meanwhile, thermal etching of the samples was performed for the purpose of examination of their microstructures. Five pieces of samples were prepared and their densities and porosities measured through Archimedes method based on ASTM B311 standard.19) The theoretical density of the composite sample can be obtained from Eq. (1), in which the alumina density (dA) is equal to 3.986 g/cm3, SiC density (dSiC) is equal to 3.217 g/cm3,20) and MgO density is 3.58 g/cm3.21) ##### (1) dcom.=WA.dA+WSiC.DMgO+WSiC.DMgO where WA is the weight fraction of the alumina powder, WSiC is the weight fraction of the nanoSiC, and WMgo is the weight fraction of the nanoMgO in the composite. The exterior volume (V) of the experimental samples can be obtained by Eq. (2) as the difference between the immersion weight and the saturation weight. ##### (2) V=M-S Assume that water weighs 1 g. This assumption for water at room temperature would correspond to a volume of 1 cm3 with the approximation of one-thousandths, which can be calculated as the percentage of the open porosity volume with respect to its total volume. The apparent porosity is calculated by Eq. (3). ##### (3) P=[(M-D)/V]×100 Water absorption (A) can be quantified as the percentage of the weight of absorbed water relative to the dry sample weight (Eq. (4)): ##### (4) A=[(W-D)/D]×100 The apparent density (T) refers to a portion of the sample that is water proof and is obtained by Eq. (5). ##### (5) T=D/(D-S) The relative fraction of the apparent density of the sample to its theoretical density is calculated according to Eq. (6). ##### (6) %R.D.=T/dcom.×100 where T is the nominal (apparent) density and dcom. is the theoretical density of the composite. The flexural strength or modulus of rupture (MOR) of the samples was obtained based on ASTM C1161 standard22) by using the three-point method and Eq. (7) with three repetitions of the measurement per sample. ##### (7) MOR=3Fl2bd2 where F is the break force, l is the support span, b is the width of the sample, and d is the thickness of the sample. The elasticity moduli of the samples can be obtained based on ASTM C769 standard23) by considering the changes in sonic velocity in the sample material. In this method, an ultrasonic pulse with the frequency of 4 MHz that is generated by the energy converter machine Echometer1070 manufactured by Karl Deutsch Wuppertal and equipped with DSE Lemo probe, which converts electrical energy to sonic waves, is transmitted through each sample four times and the reflected wave measured. By recording the reversal time and measuring the sample thickness, the sonic velocity in the sample is determined. By using Eq. (8), the elasticity modulus (E) is obtained.23) ##### (8) E=ρv2 where ρ is the density of the sample and ν is the sonic velocity of the sample. The hardness values of the samples were calculated by Vickers method based on ASTM C1327 standard. 24) By applying 49 N (5 kgf) load through a hardness machine for 30 s, seven impressions of the Vickers indenter were created on each sample and, by using Eq. (9), the Vickers hardness (H) was calculated. ##### (9) H=(1.8544)Pd2 where P is the load applied for producing the Vickers impressions and d is the average diameter of the Vickers impressions. The average resulting from the seven measurements of the hardness was reported as the sample hardness. By using Eqs. (10) to (12), the fracture toughness (KIC) values of the samples can be calculated.25-27) ##### (10) KIC=0.00366(EHv)1/2tAve3/2PA3/2 ##### (11) KIC=0.0889(Hv.Pi=14Ci)1/2 ##### (12) KIC=0.0089(EHv)2/5(Pa.C1/2) where E is Young’s modulus, Hv is Vickers hardness, P is the load applied for creating the Vickers impressions, tave is the average thickness of the microcracks formed around the indented section, A is the surface area corresponding to the effect of the whole microcracks formed around the indented section of the sample, C is the crack length of the median/radial, and a is one-half of the diameter of the indented section on the sample that is created by the application of the Vickers diamond. The average resulting from the seven measurements was reported as the fracture toughness of the sample. The surface morphologies of the samples and the dimensions and shapes of the nanoparticles were investigated by SEM in the secondary electron (SE) and back scattered electron (BSE) modes. Furthermore, the grain size of the matrix phase was calculated by using a Philips-FEGC200 transmission electron microscope. ### 3.1. Relative density Figure 4 shows the relative densities of the samples as functions of the sintering temperature for different volume fractions of nanoSiC. As observed, with the increase in the sintering temperature for all volume fractions of nanoSiC, the relative density increased. The increase in temperature causes the mobility of the grain boundaries and, as a result, alumina condensation is promoted. Wang et al.10) showed that with the increase in the sintering temperature of an alumina nanocomposite containing 10 vol.% nanoSiC up to 1700°C, a density close to the theoretical density can be possibly realized. The results of this research also verify this finding. The increase in the temperature for different nanoSiC volume fractions eventually leads to an increase in the density up to the theoretical density. On the other hand, addition of SiC nanoparticles decreases the density. It seems that at lower temperatures, this reduction in density has a greater effect due to the lower sintering capacities of the samples. The effect of increased temperature on the increase in the density would be different for different nanoSiC volume fractions, such that it is enormously increased upon increasing the nanoSiC volume fraction in the range of sintering temperatures 1600 to 1700°C. Moreover, at all temperatures, the relative density decreases. Since nanoSiC particles contribute to the immobility of the grain boundaries and prevent Al2O3 condensation, the addition of nanoSiC leads to the relative density being decreased. In addition, it is revealed that the relative density of the alumina sample containing no nanoSiC additive increases up to 99.9%. The achievement of such a high density can be ascribed to the existence of MgO. It is assumed that MgO forms a solid solution that reduces the volume of grain boundaries. Similarly, excessive grain growth is minimized. On the other hand, the increase in the surface permeability and mobility of the pores causes the porosity of the sample to be reduced. Therefore, the sample density is increased during sintering.16,17,28-30) ### 3.2. Phase analysis, microstructure, and variations in the grain sizes of samples Figure 5 shows the XRD pattern of Al2O3-nanoSiC sample sintered at 1750°C with 15 vol.% nanoSiC, in which the existence of α-Al2O3 and α-SiC without any reaction occurring between them at the experimental temperature and pressure has been illustrated. Figure 6 presents the microstructures of some of the sintered samples obtained by SEM at different temperatures. As observed, with the increase in the sintering temperature, the alumina grains become larger; on the other hand, an increase in the volume fraction of nanoSiC prevents extreme growth of the alumina grains. Wang et al.17) proved that monophase Al2O3 grains are large and heterogeneous and that some of the grains grow extraordinarily. However, the addition of nanoSiC particles inhibits the extraordinary growth of the grains and maintains a small grain size. In addition, the grains get homogenized in the composite. Based on Fig. 6, with the increase in the nanoSiC volume fraction in the samples, the grain size decreases at all the temperatures, which can be attributed to the lack of reaction between the nanoSiC particles and the alumina matrix at the sintering temperatures and to the effect of the nanoSiC particles in reducing the mobility of the grain boundaries.10,31-34) Furthermore, it has been demonstrated that based on Zener model, the secondary phase refrains from the growth of matrix grains, the size of which (G) can be obtained from Eq. (13).17) ##### (13) G=4r/3f where r is the radius of the grains of the secondary phase and f is the volume fraction of the secondary phase. This equation shows that with the increase in the volume fraction of the secondary phase, the grain size of the matrix is decreased. Fig. 7 shows a TEM image of the microstructure of a nonadditive sample that was sintered at 1600°C. Based on the figure, the average size of the sample seed is about 6 μm. In Fig. 8, the average grain sizes of the samples have been shown as functions of the sintering temperature for different nanoSiC volume fractions. This figure reveals that with the increase in temperature, the grain size increases for all the cases. With the addition of nanoSiC particles, the rate of increase in the grain size is reduced, so that the maximum increase in the grain size is for the nonadditive sample, about 61%, and the minimum value is for the sample containing 15 vol.% nanoSiC, roughly 24%. Moreover, the alumina grain size of the samples increases from the maximum initial size of 5 μm to about 6-14 μm. Figures 9(a) and 9(b) show the microstructural SEM images of the sample containing 2.5 vol.% nanoSiC and sintered at 1600°C and the sample containing 7.5 vol.% nanoSiC and sintered at 1700°C, respectively, which were obtained by using a BSE detector. As is evident, the nanoSiC particles are located at the grain boundaries and inside the alumina grains. With the increase in the nanoSiC volume fraction, its effect in preventing grain growth does not increase linearly. The reason is that, for example, when the SiC volume fraction is duplicated, a substantial fraction of the particles will occupy the interior of the alumina grains, which implies that the nanoSiC particles existing at the grain boundaries and preventing their growth have not been duplicated. Moreover, owing to the increase in the sintering temperature, the effect of the added nanoSiC particles in inhibiting grain growth will be somewhat decreased.10) Alumina grain overgrowth often occurs owing to the extremely high energy. Controlling the grain growth in terms of its size and morphology is highly important, as it plays an important role in determining the quality of the produced material; in addition, realizing a high density that is required to stop the growth during sintering is crucial. Therefore, the inhibition of grain growth is utilized as part of the solid solution mechanism in the production of alumina. The important effects of adding MgO include a reduction in the mobility of the grain boundaries, an increase in the surface permeation, and, as a result, an increase in the mobility of the pores, an increase in the condensation with increases in the grain boundaries and network permeation, and reductions in the surface energy and nonuniformity of the grains. Moreover, as the SiC particles do not have enough mobility and do not react with Al2O3 at the sintering temperature, they reduce the mobility of the grain boundaries and, as a result, prevent the Al2O3 condensation. Therefore, after the addition of SiC nanopowder, this issue is addressed by increasing the sintering temperature. ### 4.1. Elasticity modulus The elasticity moduli of the samples have been shown as functions of the sintering temperature for different volume fractions of nanoSiC in Fig. 10. As seen, with the increase in temperature, the elasticity modulus increases for all the samples, which can be due to the completely sintered particles. With complete sintering, the porosity of samples is reduced and the sonic velocity is increased throughout the sample, which causes the elasticity modulus to be enhanced.31) The elasticity moduli of the sintered samples follow increasing trends up to 7.5 vol.% of nanoSiC at 1700 and 1750°C, before decreasing. The increased elasticity modulus upon adding nanoSiC can be ascribed to the relatively high elasticity modulus of SiC compared to that of Al2O3.31) The elasticity modulus of monocomponent alumina has been reported to be roughly 340-400 GPa in the literature2,32) which suggests that the elasticity moduli of the nonadditive samples, which are in the range 401-426 GPa, exceed that of monocomponent alumina. Anya et al.31) achieved the maximum elasticity modulus of 409.5 GPa for a sample with a relative density of 99.6% that was obtained through pressure-off synthesis and sintering of Al2O3-SiC nanocomposites. Moreover, Moradkhani et al.33) obtained an elasticity modulus of 402 GPa for hot press sintered alumina samples containing 15 vol.% 800 nm SiC particles at 1700°C. The results indicate an increase in the elasticity modulus of the composite. According to the combination law for a particle (powder) composite with a random phase distribution, the elasticity modulus of the composite can be calculated by using Eq. (14), based on the elasticity modulus of the components. ##### (14) E=ΣEi.Vi Where Ei and Vi are the elasticity modulus and volume ratios, respectively, of the components of a composite. Therefore, Eq. (15) is obtained for Al2O3-SiC composite. ##### (15) Ecomp=EA.VA+ES.VS where Ecomp is the elasticity modulus of the composite, EA is the elasticity modulus of Al2O3, equal to 380 GPa, and ES is the elasticity modulus of SiC, equal to 414 GPa.34) Therefore, it is expected that with the increase in the amount of SiC, the elasticity modulus of the composite will increase. In contrast, the increase in SiC volume fraction leads to a decreased density and the creation of pores that contributes to a reduction in the sonic velocity in the sample and, hence, the elasticity modulus is decreased.31) ### 4.2. Hardness Figure 11 illustrates the Vickers impressions produced on a few samples for the determination of their hardness. In Fig. 12, the hardness values of the samples have been presented in terms of the sintering temperature for different volume fractions of nanoSiC. It is revealed that with the increase in the sintering temperature up to 1650°C, the hardness is increased for all the samples, which can be caused by the completely sintered particles, whereas after that, the hardness decreases owing to grain growth.35,36) The hardness of the alumina sample without nanoSiC added is 12 GPa (which is the least) at 1600°C, which is increased to nearly 17 GPa at 1700°C. The hardness of monocomponent alumina was reported to be about 12-18 GPa.3) In addition, the hardness of the sintered samples increases upon increasing the nanoSiC volume fraction up to 7.5 vol.% at all the temperatures, which can be attributed to the finer grains existing in the structure with the increase in the nanoSiC volume fraction.31) The hardness of Al2O3-SiC nanocomposite containing 20 vol.% 200 nm SiC particles prepared by hot press method at 1740°C reaches 19.7 GPa maximum, which is approved based on the current findings. 12) It seems that with the increase in the nanoSiC volume fraction beyond 10 vol.%, the porosity is increased, while the density is decreased, which cause a reduction in the hardness. On the other hand, agglomeration of the nanoSiC particles increases and their distribution homogeneity in the alumina matrix decreases, and hence, the hardness declines. In addition, with the increase in the nanoSiC volume fraction of the composite, the residual stress resulting from the discrepancy in thermal expansion between SiC? and Al2O3 increases, until it is released, which leads to the formation of microcracks in nanoSiC; as a result, the hardness is reduced.36) ### 4.3. Fracture toughness Figure 13 displays the changes in the fracture toughness of the samples resulting from Eqs. (10) to (12) as functions of the sintering temperature. Through careful attention and comparison of the results, it can be learned that the findings from Eq. (10), which have been recently presented and used for a few brittle materials,33,37-40) exhibit a high accuracy. As it turned out from the comparison of the results, the difference between the findings from Eq. (10) and all the other findings is less than 13% for all the cases. As observed, with the increase in the sintering temperature up to 1650°C, the fracture toughness is increased, owing to the samples being completely sintered. Further increases in temperature lead to minor changes in the fracture toughness of the samples. The reduction in the fracture toughness with the increase in temperature can be ascribed to increased grain size; on the other hand, the increase in the fracture toughness caused by an increase in temperature can be attributed to a reduction in the defects and pores, which are sources of cracks.31,35) The increase in the fracture toughness at 1750°C can be attributed to the formation of combined phases such as mullite (3Al2O3.2SiO2), which results from the reaction of SiO2, available at the SiC particle surfaces, with alumina, and also to the partial formation of the spinel phase MgO. Al2O3 at high temperatures. The resulting phases can be observed at the grain boundaries and pores, and resist crack growth, thus increasing the fracture toughness.11) Moreover, the fracture toughness of the samples is increased by adding nanoSiC up to 5 vol.% and, in some cases, up to 7.5 vol.%. The mechanisms of enhancement in fracture toughness that include crack deflection and microcrack toughening have been proposed for the improvement in the toughness upon increasing the nanoSiC volume fraction.30) Other studies also verify the increase in the fracture toughness of alumina samples, from almost 1.2 to 4.5 MPa.m1/2.33) The fracture toughness of alumina nanocomposites containing SiC additive has been reported to be in the range 2-4.5 MPa.m1/2, which is in agreement with the current findings.2,12) With the increase in the nanoSiC volume fraction, the agglomeration of the nanoSiC particles is increased and their distribution homogeneity in the alumina matrix is decreased. On the other hand, the residual stress resulting from the discrepancy in thermal expansion between SiC? and Al2O3 is increased, which is eventually released, causing the grain boundaries to get clinched. As a result, with the decrease in the resistance to crack formation, the fracture toughness is also reduced.36,41) ### 4.4. Flexural strength Figure 14 shows the flexural strengths of the samples as functions of the sintering temperature for different nanoSiC volume fractions. As is evident, the flexural strength continuously decreases with the increase in the sintering temperature for the nonadditive sample and the sample with 2.5 vol.% nanoSiC. This can be attributed to the increase in the grain size during the rise in temperature, which decreases the flexural strengths of the samples. In the samples with 5 vol.% or more nanoSiC, the temperature required for complete sintering of the samples is increased, owing to the existence of SiC particles and the high melting temperature of SiC (nearly 2670°C), compared to that of Al2O3 (roughly 2050°C).2) Consequently, the increase in the temperature up to 1650°C contributes to the increase in the sintering capacity of the sample being more than the increase in the grain size. Thus, the flexural strength of the sample is increased. However, the increase in the sintering temperature to 1700°C results in a notable increase in the grain growth. This increase in the grain growth has a more significant impact on the flexural strength in comparison to the increase in the sintering temperature from 1650 to 1700°C, which causes the strengths to be decreased.35) In the samples containing more than 2.5 vol.% nanoSiC, the increase in the temperature up to 1750°C leads to an increase in the strength. This can be described by the formation of combined phases such as mullite (3Al2O3·2SiO2), which results from the reaction of SiO2, available at the SiC particle surfaces, with alumina, and also to the partial formation of the spinel phase MgO·Al2O3 at high temperatures. The resulting phases can be observed at the pores and grain boundaries, and resist the crack growth caused by stress, thus increasing the strength.11,41,42) The flexural strengths of the samples increase upon adding nanoSiC up to 10 vol.%. A portion of this increase can be attributed to the finer grains existing in the structure upon the addition of the SiC nanoparticles.36) That is because the nanoSiC particles lack sufficient mobility, and also because they do not react with alumina, which reduce the mobility of the grain boundaries. Therefore, a structure with smaller grain dimensions can be obtained. It seems that with the increase in the amount of nanoSiC, in addition to increasing the porosity and decreasing the density, the agglomeration of the nanoSiC particles is increased and their distribution homogeneity in the alumina matrix is decreased. Thus, the flexural strength is decreased. On the other hand, with the increase in the nanoSiC volume fraction of the composite, the residual stress resulting from the discrepancy in thermal expansion coefficient between SiC and Al2O3 is increased, until it is released, which produces microcracks in nanoSiC; as a result, the strength is decreased.36) The flexural strength of monocomponent alumina has been reported to be about 270-370 MPa in the literature;3) the current findings reveal higher flexural strengths of monocomponent alumina in some cases. The highest strength is obtained for the sample containing 10 vol.% nanoSiC at the sintering temperature of 1650°C or higher; this reflects the increase in the flexural strength of alumina from 251 MPa in the nonadditive nanoSiC sample to 396 MPa in a sintered sample at 1750°C, which correspond to an increase of 57%. Figure 15 shows the changes in the flexural strengths of the samples as functions of the grain size at different sintering temperatures. As observed, with the decrease in the grain size, the strength is increased. However, in the sample with 15 vol.% nanoSiC, the strength decreases, which can be ascribed to the increase in porosity and release of the residual stress developed inside the grains.36) Adding SiC particles leads to homogeneity of the structure, in addition to preventing extraordinary growth of the grains and maintaining their dimensions small, which heavily impacts their mechanical properties, including the increase in the flexural strength. On the other side, because the residual stress originating from the discrepancy in the thermal expansion coefficient between SiC and Al2O3, strengthens the grain boundaries, the flexural strength increases.42) The relation between the yield stress (σy) and the grain diameter (d), called Hall-Petch equation, has been expressed in Eq. (16).43) ##### (16) σy=σ0+kd Here, σ0 is a material constant denoting the initial stress in the dislocation direction and k is an inherent constant of the material. The Hall-Petch equation verifies the increased strength of the material with the decrease in the grain size. The thermal expansion coefficient of alumina in the temperature range 0-1727°C is increased to be roughly 8.58 × 10−6/°C, whereas the thermal expansion coefficient of SiC is nearly 4.70 × 10−6/°C in the temperature range 0-1700°C.42) As a consequence, when cooling a Al2O3/SiC composite sample in a hot press furnace after heat treatment, the Al2O3 particles tend to shrink more than the SiC particles, which produces a compressive stress on the nanoSiC particles present at the grain boundaries, which ultimately increases the resistance of the grain boundaries to slippage. Thus, the strength of a sample is increased upon adding nanoSiC particles. 44) ### 5. Conclusions This study investigated the effect of sintering temperature on the mechanical characteristics of alumina-based nanocomposites containing nanoMgO and nanoSiC additives and analyzed their microstructures. The results obtained can be summarized as follow. With the increase in the sintering temperature, the relative density is increased for all nanoSiC volume fractions, so that the relative density is increased from about 96.5% for 15 vol.% nanoSiC sample sintered at 1600°C to 99.5% for the sample sintered at 1750°C. Furthermore, the relative density of the alumina sample containing nanoMgO without any nanoSiC additive increases to 99.9%, which decreases with the increase in nanoSiC volume fraction at all the sintering temperatures. The realization of such a high density can be ascribed to the existence of MgO. The XRD pattern of the Al2O3-5 vol.% nanoSiC sample containing α-Al2O3 and α-SiC shows that no considerable reaction takes place between Al2O3 and nanoSiC at the experimental pressure and temperature. The alumina grain size varies from 6.06 μm for the sample containing 15 vol.% nanoSiC sintered at 1600°C to 13.25 μm for the nonadditive sample sintered at 1750°C. With the decrease in the sintering temperature and increase in the nanoSiC volume fraction, the alumina grain size increases. The elasticity moduli of the samples are in the range 401- 426 GPa, which follows an increasing trend up to 7.5 vol.% nanoSiC, before decreasing, for the samples sintered at 1700 and 1750°C and containing nanoSiC additive. The increased elasticity modulus upon adding nanoSiC can be ascribed to the relatively high elasticity modulus of SiC compared to that of Al2O3. In contrast, the increase in SiC volume fraction leads to decreased density and formation of pores, which contributes to the reduction in the sonic velocity in the sample and, thus, the elasticity modulus is decreased. The minimum hardness value of nearly 12 GPa corresponds to the nonadditive alumina sample sintered at 1600°C, and reaches the maximum of 21 GPa upon increasing the sintering temperature to 1650°C and adding 7.5 vol.% nanoSiC, which suggests an increase of 63%. The hardness of the sintered samples is increased by increasing the nanoSiC vol.% up to 7.5 vol.% at all the temperatures, which can be attributed to the finer grains existing in the structure upon increasing the nanoSiC volume fraction. Upon adding nanoSiC up to 7.5 vol.%, the fracture toughness of the samples is increased; at higher values of nanoSiC addition, the fracture toughness decreases. The increase in the fracture toughness caused by the increase in temperature can be attributed to a reduction in the defects and pores, which are sources of cracks. On the other hand, the reduction in the fracture toughness observed with increasing temperature can be ascribed to the increased grain size. Further, the results obtained from Eq. (10) differ by less than 13% from the results obtained by using other equations pertaining to fracture toughness. The flexural strengths of the samples sintered at 1750°C increase from 251 MPa for the nonadditive sample to 396 MPa for the sample containing 10 vol.% nanoSiC, which corresponds to an increase of 57%. Moreover, the increase in temperature up to 1650°C contributes to the increase in the sintering capacity of the sample being more than the increase in the grain size. Therefore, the flexural strength of the sample is increased. However, with the increase in temperature up to 1700°C, grain growth leads to a reduction in the flexural strength of the sample. ##### Fig. 1 XRD pattern of the alumina powder. ##### Fig. 2 Microstructural images: (a) SEM image of the alumina powder, (b) TEM image of the nanoSiC powder, and (c) SEM image of the nanoMgO powder.18) ##### Fig. 3 (a) XRD pattern of nanoSiC; (b) XRD pattern of nanoMgO.18) ##### Fig. 4 Relative densities of the samples versus the sintering temperature for different nanoSiC volume fractions. ##### Fig. 5 XRD pattern of Al2O3-nanoSiC sample sintered at 1750°C with 15 vol.% nanoSiC (A: α-Al2O3 and S: α-SiC) ##### Fig. 6 Microstructures of the sintered samples corresponding to the conditions of (a) 1600°C and 0 vol.% nanoSiC; (b) 1600°C and 7.5 vol.% nanoSiC; (c) 1750°C and 0 vol.% nanoSiC; and (d) 1750°C and 7.5 vol.% nanoSiC. ##### Fig. 7 TEM image of the microstructure of the sample sintered at 1600°C with 0 vol.% nanoSiC. ##### Fig. 8 Average grain sizes of the samples as functions of sintering temperature for different nanoSiC volume fractions. ##### Fig. 9 SEM images of the microstructures of the samples sintered at (a) 1600°C with 2.5 vol.% nanoSiC, and (b) 1700°C with 7.5 vol.% nanoSiC. (The spots indicated by white circles show a portion of the SiC particles). ##### Fig. 10 Elasticity moduli of the samples as functions of sintering temperature for different volume fractions of nanoSiC. ##### Fig. 11 Microstructural SEM images of the Vickers impressions created on the samples. (a) with 2.5 vol.% nanoSiC and sintered at 1600°C; (b) with 5 vol.% nanoSiC and sintered at 1700°C for the determination of hardness. ##### Fig. 12 Hardness of the samples as functions of sintering temperature for different nanoSiC volume fractions. ##### Fig. 13 Fracture toughness of the samples as functions of sintering temperature for different nanoSiC volume fractions, obtained by using Eqs. (a) (10), (b) (11), and (c) (12) ##### Fig. 14 Flexural strengths of the samples as functions of sintering temperature for different nanoSiC volume fractions. ##### Fig. 15 Flexural strengths of the samples as functions of their grain size at different sintering temperatures (the numbers beside the signs indicate the volume fractions of nanoSiC). ##### Table 1 Chemical Analysis of Micronized Powder of Primary Alumina Material Weight percent Al2O3 > 99.6 Na2O < 0.1 Fe2O3 < 0.03 SiO2 < 0.05 TiO2 < 0.005 CaO < 0.05 MgO < 0.1 ### REFERENCES 1. DW. Richerson, Modern Ceramic Engineering; 2nd Edition. Marcel Dekker Inc., NewYork Basel, 1992. 2. CA. Harper, Handbook of Materials for Product Materials for Product Design; 3rd Edition. McGraw-Hill, London, 2001. 3. S. Sömiya, Handbook of Advanced Ceramics; Elsevier Academic Press, Oxford, 2003. 4. C. Kalkandelen, M. Suleymanoglu, SE. Kuruca, A. Akan, FN. Oktar, and O. Gunduz, “Part 2: Biocompatibility Evaluation of Hydroxyapatite-based Clinoptilolite and Al2O3 Composites,” J Aust Ceram Soc, 53 [1] 217-23 (2017). 5. CH. Huang, and Y. Chen, “Effect of Mechanical Properties on the Ballistic Resistance Capability of Al2O3-ZrO2 Functionally Graded Materials,” Ceram Int, 42 [11] 12946-55 (2016). 6. Z. Aslanoglu, and A. Sesver, “The Postmortem Study of Used Refractory Brick in EAF Dust Recovery Kiln,” J Aust Ceram Soc, 53 [2] 933-38 (2017). 7. SN. Monteiro, LHL. Louro, AV. Gomes, CFM. Chagas, AB. Caldeira, and EP. Lima, “How Effective is a Convex Al2O3-Nb2O5 Ceramic Armor,” Ceram Int, 42 [6] 7844-47 (2016). 8. H. Setiawan, R. Khairani, MA. Rahman, R. Septawendar, RR. Mukti, HK. Dipojono, and BS. Purwasasmita, “Synthesis of Zeolite and γ-Alumina Nanoparticles as Ceramic Membranes for Desalination Applications,” J Aust Ceram Soc, 53 [2] 531-38 (2017). 9. NJ. Welham, and N. Setoudeh, “Formation of an Alumina-Silicon Carbide Nanocomposite,” J Mater Sci, 40 [12] 3271-73 (2005). 10. HZ. Wang, L. Gao, and JK. Guo, “The Effect of Nanoscale SiC Particles on the Microstructure of Al2O3 Ceramics,” Ceram Int, 26 [4] 391-96 (2000). 11. A. Gadalla, M. Elmasry, and P. Kongkachuichay, “High Temperature Reactions within SiC-Al2O3 Composites,” J Mater Res, 7 [9] 2585-92 (1992). 12. M. Parchovianský, J. Balko, P. Švančárek, J. Sedláček, J. Dusza, F. Lofaj, and D. Galusek, “Mechanical Properties and Sliding Wear Behaviour of Al2O3-SiC Nanocomposites with 3-20 vol% SiC,” J Eur Ceram Soc, 37 [14] 4297-306 (2017). 13. C. Greskovich, and BJ. Anthony, “Solubility of Magnesia in Polycrystalline Alumina at High Temperatures,” J Am Ceram Soc, 84 [2] 420-25 (2004). 14. RS. Mishra, and AK. Mukherjee, “Processing of High Hardness-High Toughness Alumina Matrix Nanocomposites,” Mater Sci Eng A, 301 [1] 97-101 (2001). 15. RD. Bagley, and DL. Johnson, “Effect of Magnesia on Grain Growth in Alumina,” Adv Ceram, 10 666-78 (1984). 16. CA. Duan, “Effects of Chemical in Homogeneities on Grain Growth and Microstructure in Al2O3 ,” J Am Ceram Soc, 72 [1] 130-36 (1989). 17. J. Wang, SY. Lim, SC. Ng, CH. Chew, and LM. Gan, “Dramatic Effect of a Small Amount of MgO Addition on the Sintering of Al2O3-5 vol% SiC Nanocomposite,” Mater Lett, 33 [5-6] 273-77 (1998). 18. M. Ahmadzadeh, H. Baharvandi, H. Abdizadeh, and AM. Hadian, “Synthesis of Nano-Size MgO Powder by Chemical Deposition of Low Cost Raw Materials,” Int J Mod Phys B, 22 [18] 3185-92 (2008). 20. D. Galusek, J. Sedláček, P. Švančárek, R. Riedel, R. Satet, and M. Hoffmann, “The Influence of Post-Sintering HIP on the Microstructure, Hardness, and Indentation Fracture Toughness of Polymer-Derived Al2O3-SiC Nanocomposites,” J Eur Ceram Soc, 27 [2-3] 1237-45 (2007). 21. S. Sinhamahapatra, M. Shamim, HS. Tripathi, A. Ghosh, and K. Dana, “Kinetic Modeling of Solid State Magnesium Aluminum at Espinel Formation and its Validation,” Ceram Int, 42 [7] 9204-13 (2016). 25. A. Moradkhani, H. Baharvandi, M. Tajdari, H. Latifi, and J. Martikainen, “Determination of Fracture Toughness Using the Areas of Microcrack Tracks Left in Brittle Materials by Vickers Indentation Test,” J Adv Ceram, 2 [1] 87-102 (2013). 26. KA. Nihhara, R. Morena, and DPH. Hasselman, “Evaluation of KIC of Brittle Solids by the Indentation Method with Low Crack-to-Indent Ratios,” J Mater Sci Lett, 1 [1] 13-6 (1982). 27. DK. Shetty, IG. Wright, PN. Mincer, and AH. Cluar, “Indentation Fracture of WC-Co Cermets,” J Mater Sci, 20 [5] 1873-82 (1985). 28. R. Gao, H. Wang, Q. Zhu, Q. Yang, X. Sun, B. Li, S. Xu, and X. Zhang, “The Forming Region and Mechanical Properties of SiO2-Al2O3-MgO Glasses,” J Non-Cryst Solids, 470 132-37 (2017). 29. R. Mohammad-Rahimi, HR. Rezaie, and A. Nemati, “Sintering of Al2O3-SiC Composite from Sol-Gel Method with MgO, TiO2 and Y2O3 Addition,” Ceram Int, 37 [5] 1681-88 (2011). 30. AR. Yazdi, H. Baharvandi, H. Abdizadeh, J. Purasad, A. Fathi, and H. Ahmadi, “Effect of Sintering Temperature and Siliconcarbide Fraction on Density, Mechanical Properties and Fracture mode of Alumina-Silicon Carbide Micro/Nanocomposites,” Mater Des, 37 251-55 (2012). 31. CC. Anya, and SG. Roberts, “Pressureless Sintering and Elastic Constants of A12O3-SiC Nanocomposites,” J Eur Ceram Soc, 17 [4] 565-73 (1997). 32. E. Medvedovski, “Alumina-Mullite Ceramics for Structural Applications,” Ceram Int, 32 [4] 369-75 (2006). 33. A. Moradkhani, and H. Baharvandi, “Microstructural Analysis of Fracture Surfaces and Determination of Mechanical Properties of Al2O3-SiC-MgO Nanocomposites,” Int J Refract Met Hard Mater, 67 40-55 (2017). 34. M. Sternitzke, “Review: Structural Ceramic Nanocomposites,” J Eur Ceram Soc, 17 [9] 1061-82 (1997). 35. L. Xuefei, L. Hanlian, H. Chuanzhen, Z. Bin, and Z. Longwei, “High Temperature Mechanical Properties of Al2O3-based Ceramic Tool Material Toughened by SiC Whiskers and Nanoparticles,” Ceram Int, 43 [1] 1160-65 (2017). 36. JF. Shackelford, and W. Alexander, CRC Materials Science and Engineering Handbook; 3rd Edition. CRC Press, Florida, 2001. 37. A. Moradkhani, H. Baharvandi, and MMM. Samani, “Mechanical Properties and Microstructure of B4C-Nano-TiB2-Fe/Ni Composites under Different Sintering Temperatures,” Mater Sci Eng A, 665 141-53 (2016). 38. A. Moradkhani, and H. Baharvandi, “Analyzing the Microstructures of W-ZrC Composites Fabricated through Reaction Sintering and Determining their Fracture Toughness Values by Using the SENB and VIF Methods,” Eng Fract Mech, 189 501-13 (2018). 39. A. Moradkhani, and H. Baharvandi, “Effects of Additive Amount, Testing Method, Fabrication Process and Sintering Temperature on the Mechanical Properties of Al2O3/3Y-TZP Composites,” Eng Fract Mech, 191 446-60 (2017). 40. A. Moradkhani, H. Baharvandi, and A. Naserifar, “Fracture Toughness of 3Y-TZP Dental Ceramics by Using Vickers Indentation Fracture and SELNB Methods,” J Korean Ceram Soc, 56 [1] 37-48 (2019). 41. BK. Jang, M. Enoki, T. Kishi, and HK. Oh, “Effect of Second Phase on Mechanical Properties and Toughening of Al2O3 based Ceramic Composites,” Comps Eng, 5 [10-11] 1275-86 (1995). 42. J. Zhao, LC. Stearns, MP. Harmer, HM. Chan, GA. Miller, and RF. Cook, “Mechanical Behavior of Alumina-Silicon Carbide Nanocomposites,” J Am Ceram Soc, 76 [2] 503-10 (1993). 43. T. Ohji, YK. Jeong, YH. Choa, and K. Niihara, “Strengthening and Toughening Mechanisms of Ceramic Nanocomposites,” J Am Ceram Soc, 81 [6] 1453-60 (1998). 44. I. Levin, WD. Kaplan, DG. Brandon, and AA. Layyous, “Effect of SiC Submicrometer Particle Size and Content on Fracture Toughness of Alumina-SiC Nanocomposites,” J Am Ceram Soc, 78 [1] 254-56 (1995). TOOLS Full text via DOI CrossRef TDM E-Mail Print Share: METRICS 6 Crossref 7 Scopus 6,836 View	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8473626375198364, "perplexity": 3558.499152904295}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662572800.59/warc/CC-MAIN-20220524110236-20220524140236-00720.warc.gz"}
http://math.stackexchange.com/questions/46606/simplifying-imaginary-term-of-jt-in-fourier?answertab=active	# Simplifying imaginary term of jt in Fourier I can't figure this out. Don't blame me, but please answer this question. I want to simplify this term: $3(e^{5it} + e^{-5it})$ It would be nice to see a detailed workout. I know the answer is $2\sin{3t}$, but how to get to this is what I want to know. Thanks. - Hint: $\mathrm e^{\mathrm i t} \equiv \cos t + \mathrm i \sin t$. P.S. The answer is wrong. See if you can correct it! - HINT Two things you need to know: First, use Euler's formula, $e^{it}=cos(t)+isin(t)$ $\therefore$ $$3(e^{5it}+e^{-5it})$$ $$3(cos(5t)+isin(5t))~+~(cos(-5t)+isin(-5t))$$ Second, since cosine is an even function, $cos(t)=cos(-t)$ And since sine is an odd function, $-sin(t)=sin(-t)$ Second hint, the answer is not what you claim it is. - Use Euler's formula. Also, the answer is not $2\sin 3t$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9622504115104675, "perplexity": 169.8397114629252}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1387345765796/warc/CC-MAIN-20131218054925-00050-ip-10-33-133-15.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/294150/motivation-behind-the-definition-of-ideal-class-group	# Motivation behind the definition of ideal class group Let $O$ be a Dedekind domain and $K$ its field of fractions. The set of all fractional ideals of $K$ form a group, the ideal group $J_K$ of K. The fractional principal ideals $(a) = aO, a \in K^$, form a subgroup of the group of ideals $J_K$, which will be denoted $P_K$. The quotient group $$CL_K=J_K/P_K$$ is called the ideal class group of $K$. This definition looks completely arbitary, I fail to see why the class group or the ideal class group is worth studying. So, why is the class group or ideal class group interesting? I've read that ideal class group "measures" how much unique factorization fails in a domain, but I don't understand how it does so. This from Algebraic Number Theory by Neukirch. The class group $C_K$ measures the expansion that takes place when we pass from numbers to ideals, whereas the unit group $O^$ measures the contraction in the same process. This immediately raises the problem of understanding these groups $O^$ and $C_K$ more thoroughly. I don't understand the above paragraph. What does it mean by "the expansion that takes place when we pass from numbers to ideals"? And why should we even bother about such "expansion"? - Very shorty: the ideal group gives you an idea of how "far" is some ring (a Dedekind domain) from being principal (and, thus, a unique factorization domain, say). If you put yourself within the frame of finite algebraic extension of the rationals and their rings of integers, these rings are always Dedekind and etc. – DonAntonio Feb 4 '13 at 2:41 Some ideals are not principal, so the group of ideals could be said to "expand" the numbers. How large does this become then? Well, we simply take a quotient, the ideal class-group. Moreover, different numbers could generate the same ideal, and they differ by units, thus the group of units is said to measure how they contract in this process. – awllower Feb 5 '13 at 16:27 As to why we should bother about this expansion, consider the quadratic form $x²+5 y²$. To determine which integers could be represented by this form (a Diophantine equation in fact), we are led to consider the ideals in the ring $Z[\sqrt{-5}]$. Namely, arithmetic question oft leads us to consider similar expansions; that is exactly why we should look at such measurements of the expansions and contractions during the process. Only a brief view. Hope it helps. – awllower Feb 5 '13 at 16:32 @Mohan Maybe if you say Matthew Emerton's name three times in a mirror he will come. – Alex Youcis Feb 6 '13 at 6:37 @Mohan, ideals were invented to "fix" the failing of unique factorization: if you study the proof that ideals have unique factorization it will shed light on the definition of the ideal class group. See here – user58512 Feb 6 '13 at 14:00 Let $K$ be an algebraic number field and $\mathcal{O}_K$ the integral closure of $\Bbb{Z}$ in $K$. Let us recall that a Dedekind domain is a UFD iff it is a PID. Classically, I think that the questions concerning whether or not a certain Dedekind domain was a UFD were very important, see e.g. this thread here. Perhaps from the point of view of algebra asking if something is a PID is easier to approach: we know how to factor ideals in Dedekind domains and thus there should at least be a tool to measure how far does a Dedekind domain differ from being a principal ideal domain. Let me now give you an alternative definition of the ideal class group. We will put an equivalence relation on the set of all ideals defined as follows. We say that an ideal $I$ of $\mathcal{O}_K$ is equivalent to $J$ iff there is $\alpha,\beta \in \mathcal{O}_K$ so that $$\alpha I = \beta J.$$ One easily checks that this is an equivalence relation. With a little bit more work, one can show that the set of all equivalence classes has a well defined multiplication law and is actually a group. The identity element being the class of all principal ideals. Now for some exercises. Exercise 1: Check that the "class" of all principal ideals is actually a class. Namely if $I$ is an ideal such that $\alpha I = (\beta)$ then show that $I$ is actually principal. Hint: $\mathcal{O}_K$ is an integral domain. Exercise 2: Show that this definition of an ideal class group is actually equivalent to the one given in Neukirch. Hint: Use the first isomorphism theorem. Now do you see how the definition I have given you of an ideal class group actually measures nicely whether or not $\mathcal{O}_K$ is a PID? We see that $\mathcal{O}_K$ is a PID iff its ideal class group is trivial. Now on to more interesting material. In advanced subjects such as Class Field Theory one can construct something know as the Hilbert Class Field of $K$. I don't know all the details of this construction as my algebraic number theory is not so advanced, but in the Hilbert class field every ideal of $\mathcal{O}_K$ becomes principal!! One can now ask the question: can we avoid talking of the Hilbert class field and find such an extension? The answer is: Of course we can! This is where the ideal class group comes in. Firstly from Minkowski's bound we get that $Cl_K$ is actually a finite group. Using this, here are now two exercises which you can do: Exercise 3: Let $I$ be an ideal of $\mathcal{O}_K$ show that there is a finite extension $L/K$ so that $I\mathcal{O}_L$ is principal. Hint: By finiteness of the class group there is an $n$ so that $I^n = \alpha$ for some $\alpha \in \mathcal{O}_K$. Now consider $L = K(\sqrt[n]{\alpha})$. Exercise 4: Show that there is a finite extension of $L$ in which every ideal of $\mathcal{O}_K$ becomes principal. Wowowowowow! Hint: Use exercise 3 and the definition of the ideal class group given in the beginning of my answer, not the one in Neukirch. If you are stuck with any of these exercises I can post their solutions for you to view here. Solution to Exercise 1 (As requested by user Andrew): Suppose that $\alpha I = (\beta)$. Then in particular there is $x \in I$ so that $\alpha x = \beta$. We claim that $I = (x)$. Now it is clear that $(x) \subseteq I$. For the reverse inclusion take any $y \in I$. Then $\alpha y = \beta \gamma$ for some $\gamma \in R$. Since $\beta = \alpha x$ we get that $$\alpha y = \alpha x \gamma.$$ But now $\mathcal{O}_K$ is an integral domain and so $y = x\gamma$, so that $I \subseteq (x)$. Hence $I = (x)$ and so $I$ is principal. - Dear BenjaLim I have been self-studying some notes that somewhat follow "Ireland & Rosen" which use your definition of an ideal class group, but doesn't go much further. in fact I had posted a question regarding a presentation in those notes: math.stackexchange.com/questions/290839/… which got a nice answer but didn't specifically address my question. I had some further questions, e.g., I&R says the identity element is the ring of integers itself, so is that the same as all principal ideals? Plus I have some – Andrew Feb 9 '13 at 12:40 (cont) others. I would very much appreciate you thoughts on them. I could post them as a question which I hope you would be kind enough to consider or any other mechanism of communication as appropriate. Also, since I am such a beginner and never sure of my own thinking, if it is not too much trouble, I would appreciate your elaboration on the identity element remark and Ex. 1. Thanks best regards, Andrew – Andrew Feb 9 '13 at 12:45 @Andrew: just as a not-so-side remark about your last comment note that all principal ideals $\alpha{\cal O}_K$ are isomorphic to ${\cal O}_K$ as ${\cal O}_K$-modules. In fact the class group parametrizes isomorphism classes of ${\cal O}_K$-modules which are locally free of rank 1. This opens up a parallelism with the geometric situation of line bundles over a curve. – Andrea Mori Feb 10 '13 at 23:21 @Andrew It is true that the class of all principal ideals is the identity class. However how does this stop the class group from being non-trivial? There are of course ideals that are non-principal in some rings of integers. – fpqc Feb 11 '13 at 1:50 @Andrew Let me just say that by exercise 1 of my answer above, a non-principal ideal cannot possibly be equivalent to a principal one. By the word "equivalent", I mean "equivalent with respect to the equivalence relation defined above". – fpqc Feb 16 '13 at 22:43 At a crucial point in the proof that the equation $y^2=x^3-31$ has no solutions in the integers, one has an equation relating ideals, $$((y+\sqrt{-31})/2)=(2,(3+\sqrt{-31})/2)A^3$$ for a certain ideal $A$ in the ring of integers in ${\bf Q}(\sqrt{-31})$. But it turns out that the class number of that ring of integers is $3$, so $A^3$ is a principal ideal, and you get a contradiction, since you can prove that $(2,(3+\sqrt{-31})/2)$ is not a principal ideal. Needless to say, this is just one example among many where class group properties help solve Diophantine equations. - We have the short exact sequence of groups $$1\to k^\times\to J_k\to \text{cl}(k)\to 1$$ The issue with this is that we have been forced to go to "group land" because we don't want to deal with monoids (e.g. the monoid of $\mathcal{O}_k$ under multiplication). So, let's forget that we have taken monoids at each step and done some kind of fractional process to get groups. What we end up with is $$1\to \mathcal{O}_k\to \left\{\text{ideals of }\mathcal{O}_k\right\}\to \text{cl}(k)\to 1$$ So, we see that the class group can be roughly though about as the ratio of $\{\text{ideals of }\mathcal{O}_k\}$ to $\mathcal{O}_k$ itself. In other words, in our quest for unique factorization we have passed from elements of $\mathcal{O}_k$ (which may not be a UFD) to ideals of $\mathcal{O}_k$ (which always do have unique factorization). In a perfect world of sunshine and lollipops the ideals of $\mathcal{O}_k$ would be the same as $\mathcal{O}_k$ because $\mathcal{O}_k$ would be a PID. Alas, we live in no such sweet world and in general we are going to have to "add in extra" to get the unique factorization we need. The ratio of $\left\{\text{ideals of }\mathcal{O}_k\right\}$ to $\mathcal{O}_k$ (i.e the class group) measures just how much extra we had to add in. - The concept of ideal entered the world of mathematics somewhere in the 19th century, I believe in the context of the ring of cyclotomic integers $\Bbb Z[\zeta_n]$, where $\zeta_n=e^{2\pi i/n}$, in the attempt to attack Fermat's last theorem. An ideal is a generalization of a number--or more generally speaking of an element of a ring--because if $x\in{\cal O}_K$ the subset $(x)=x{\cal O}_K$ is indeed an ideal. The concept became soon useful in other contexts, e.g. in geometry where the set of polynomial functions vanishing on an algebraic set in affine space is actually an ideal, and so on. The motivation behind the introduction of ideals, at least in an arithmetic context, is that a ring of algebraic integers ${\cal O}_K$ is a Unique Factorization Domain (and in particular the notions of irreducible and prime elements coincide) if and only if every ideal $I$ is actually principal, i.e. $I$ is one of those ideal generated by, or "coming from" a single number as before: $I=(x)$. Actually, a less strict requirement on the ideals of $\Bbb Z[\zeta_p]$ for $p$ prime was devised by Kummer to show the unsolvability, when the requirement is met, of Fermat's equation with exponent $p$. These are obvious clues that the set of ideals is worth studying. So, a first natural question is: "How much do we enlarge the set of elements when we generalize from elements to ideals"? Basically, the idea is that the more the set of ideals is relatively bigger, the more "complicated" the arithmetic of ${\cal O}_K$ is. Since both sets are infinite, the answer to this question cannot be too straightforward. The key observation is that the ordinary multiplication in $K$ induces a multiplication between ideals which in fact "extends" the obvious multiplication $(x)\cdot(y)=(xy)$ between principal ideals. It is remarkable that under this extended multiplication the uniqueness of factorization is recovered: ideals can be uniquely decomposed as aproduct of prime ideals, and a prime principal ideals are exactly those generated by prime elements. Moreover, if we further generalize our picture introducing fractional ideals, these multiplications actually define a structure of abelian group on the set $J_K$ of fractional ideals for which the subset $P_K$ of principal fractional ideals is a subgroup. But now that we have groups there's a very natural way to compare sizes: just take the quotient $C_K=J_K/{\cal O}_K$. So the fundamental result that $C_K$ is finite means that when we generalize from elements to ideals we do deal with a bigger set, but not that relatively bigger. Or, in other words, that for a generic number field $K$ the arithmetic of ${\cal O}_K$ may be essentially more complicated than that of $\Bbb Z$ but after all not that more complicated (warning: this last interpretation may be read too optimistically and lead to false expectations; :-) ) - The group $K^$ is interesting. However, it is hard to study. The group $J_K$ is relatively easy to study. There is a homomorphism $f:K^* \to J_K$ connecting the two, that sends a non-zero element of $K$ to the principal fractional ideal it generates. Therefore, we can learn a lot of information about $K^$ by studying $J_K$ instead. The drawback is, of course, that $J_K$ is not actually $K^$. And sometimes, that difference matters. The difference is quantified by two other groups: $\mathcal{O}^$ is the kernel of $f$, and $CL_K$ is the cokernel of $f$. If we can obtain knowledge about these two additional groups, that helps us understand the difference between $K^$ and $J_K$. That said, sometimes $CL_K$ is interesting in its own right, and sometimes $J_K$ is the group we're actually interested in. We might even be specifically interested in the map $f$! Even in those cases, knowledge of the other groups can still help. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8657941222190857, "perplexity": 164.24682023788785}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394011098060/warc/CC-MAIN-20140305091818-00098-ip-10-183-142-35.ec2.internal.warc.gz"}
https://cs.stackexchange.com/questions/55281/if-l-is-a-regular-language-then-the-language-replacel-%CF%83-%CF%84-is-also-regular	# If L is a regular language then the language replace(L,σ,τ) is also regular I am stuck at the following problem: Prove that if $L$ is a regular language over some alphabet $\Sigma$ and that $\sigma, \tau \in \Sigma$, Then the language $replace(L,\sigma,\tau)$ is regular. Where $replace(L,\sigma,\tau)$ is defined as: $replace(L,\sigma,\tau) = \{x\tau y\in \Sigma^\| x\sigma y\in L\}$. My try: Since $L$ is a regular language there exists a deterministic finite automaton $A=(\Sigma, Q, q_0, F, \delta_A)$ such that $L(A)=L$. Now for each state $s\in Q$ we will define a non deterministic finite automaton $B_s=(\Sigma\cup\{\gamma\}, Q\times \{1,2\}, q_s, F\times \{2\}, \delta_{B_s})$ where $\gamma\notin \Sigma$ such that: $\forall p\in Q,\mu\in\Sigma, \delta_{B_s}((p,1),\mu)=\{(\delta_A(p, \mu),1)\}$ $\forall p\in Q-\{s\}, \delta_{B_s}((p,1),\gamma)=\emptyset$ $\delta_{B_s}((s,1),\gamma)=\{(\delta_A(s,\sigma),2)\}$ $\forall p\in Q,\mu\in\Sigma, \delta_{B_s}((p,2),\mu)=\{(\delta_A(p, \mu),2)\}$ $\forall p\in Q, \delta_{B_s}((p,2),\gamma)=\emptyset$ Now we'all define a new non deterministic finite automaton with $\epsilon$ moves $B$ by linking he starting state of this automaton to all of the starting states of the automatons $B_{s}$ for every state $s$, And we will also link the final states of all of the $B_{s}$ automatons to the final state of the automaton $B$. The automaton $B$ will satisfy the property $L(B)=\{x\gamma y\|x\sigma y\in L\}$ ( This is probably incorrect!!!) Now we will define an homomorphism $h:\Sigma\cup\{\gamma\}\longrightarrow\Sigma$ such that: $\forall \mu\in\Sigma,h(\mu)=\mu$ $h(\gamma)=\tau$ Since regular languages are closed under homomorphisms we can conclude that $h(L(B))$ is regular, But $h(L(B))=h(\{x\gamma y\|x\sigma y\in L\})=\{x\tau y\|x\sigma y\in L\}$ and so $replace(L,\sigma,\tau)$ is regular over $\Sigma$. Thanks for any hint or help. • Which kind of other closure properties can you exploit? That against (finite-state) transduction would help, for instance. – Raphael Apr 1 '16 at 5:48 • What is your question? We don't do homework checking. – Raphael Apr 1 '16 at 5:49 Let $A$ be the alphabet and let $a$, $b$, $c$, ... be the letters (this is easier to type). Hint. Consider the (non-deterministic) transducer $A^ \to A^*$ defined by $1 \xrightarrow{c \mid c}1\xrightarrow{a \mid b} 2 \xrightarrow{c \mid c} 2$ (more precisely, there are transitions $1 \xrightarrow{c \mid c} 1$ and $2 \xrightarrow{c \mid c} 2$ for any letter $c$ of $A$, including $a$ and $b$, but there is a single transition form $1$ to $2$). For each transition, the left hand part of the label is the input letter, the vertical bar is a separator and the right hand part is the output letter.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9747815728187561, "perplexity": 262.70360043686713}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573331.86/warc/CC-MAIN-20190918193432-20190918215432-00303.warc.gz"}
http://strata.opengamma.io/apidocs/com/opengamma/strata/market/curve/class-use/RatesCurveGroupDefinitionBuilder.html	Uses of Classcom.opengamma.strata.market.curve.RatesCurveGroupDefinitionBuilder • Packages that use RatesCurveGroupDefinitionBuilder Package Description com.opengamma.strata.market.curve Definitions of curves. • Uses of RatesCurveGroupDefinitionBuilder in com.opengamma.strata.market.curve Methods in com.opengamma.strata.market.curve that return RatesCurveGroupDefinitionBuilder Modifier and Type Method Description RatesCurveGroupDefinitionBuilder RatesCurveGroupDefinitionBuilder.addCurve(CurveDefinition curveDefinition, Currency currency, RateIndex index, RateIndex... otherIndices) Adds the definition of a curve to the curve group definition which is used to provide discount rates and forward rates. RatesCurveGroupDefinitionBuilder RatesCurveGroupDefinitionBuilder.addCurve(CurveName curveName, Currency currency, RateIndex index, RateIndex... otherIndices) Adds a curve to the curve group definition which is used to provide discount rates and forward rates. RatesCurveGroupDefinitionBuilder RatesCurveGroupDefinitionBuilder.addDiscountCurve(CurveDefinition curveDefinition, Currency currency, Currency... otherCurrencies) Adds the definition of a discount curve to the curve group definition. RatesCurveGroupDefinitionBuilder RatesCurveGroupDefinitionBuilder.addDiscountCurve(CurveName curveName, Currency currency, Currency... otherCurrencies) Adds the definition of a discount curve to the curve group definition. RatesCurveGroupDefinitionBuilder RatesCurveGroupDefinitionBuilder.addForwardCurve(CurveDefinition curveDefinition, Index index, Index... otherIndices) Adds the definition of a forward curve to the curve group definition. RatesCurveGroupDefinitionBuilder RatesCurveGroupDefinitionBuilder.addForwardCurve(CurveName curveName, Index index, Index... otherIndices) Adds the definition of a forward curve to the curve group definition. RatesCurveGroupDefinitionBuilder RatesCurveGroupDefinitionBuilder.addSeasonality(CurveName curveName, SeasonalityDefinition seasonalityDefinition) Adds a seasonality to the curve group definition. static RatesCurveGroupDefinitionBuilder RatesCurveGroupDefinition.builder() Returns a mutable builder for building the definition for a curve group. RatesCurveGroupDefinitionBuilder RatesCurveGroupDefinitionBuilder.computeJacobian(boolean computeJacobian) Sets the 'compute Jacobian' flag of the curve group definition. RatesCurveGroupDefinitionBuilder RatesCurveGroupDefinitionBuilder.computePvSensitivityToMarketQuote(boolean computePvSensitivityToMarketQuote) Sets the 'compute PV sensitivity to market quote' flag of the curve group definition. RatesCurveGroupDefinitionBuilder RatesCurveGroupDefinitionBuilder.name(CurveGroupName name) Sets the name of the curve group definition. RatesCurveGroupDefinitionBuilder RatesCurveGroupDefinition.toBuilder() Converts to builder.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8675524592399597, "perplexity": 4169.394211566864}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583897417.81/warc/CC-MAIN-20190123044447-20190123070447-00420.warc.gz"}
https://www.physicsforums.com/threads/what-caused-the-supercontinent-to-break-up.153753/	# What caused the supercontinent to break up 1. Jan 30, 2007 ### verdigris When the Earth first formed there was a single supercontinent. Why did the ocean ridges appear and break up this continent into smaller units? 2. Jan 30, 2007 ### HallsofIvy Staff Emeritus That's not true. Plates of the earth's crust have been in motion ever since the formation of the earth. The "supercontinent" you are referring to, Pangea, was a fairly recent (compared to the age of the earth) incident in which a number of areas happened to come together. It was necessarily unstable, just like todays continent formations. 3. Jan 30, 2007 ### verdigris HALLSOFIVY said: "a number of areas happened to come together" Did these areas contain all the land mass on Earth? 4. Jan 30, 2007 ### billiards The fact that the earth is differentiated suggests that either it accreted that way (unlikely, and pretty much a dead theory), or that it has gradually evolved. Therefore plates weren't always there, geochemistry tells us that the mantle (sampled in its bastardized MORB (Mid-Ocean Ridge Basalt) form) is depleted in 'incompatible' elements, and that the crust is enriched in them, suggesting that at some point the crust and mantle separated and the crust took more than its fair share of these elements. The formation of ocean ridges cannot be fully explained, they are necessary for preserving a mass balance, this is where mantle material is upwelled; matter is downwelled at subduction zones. Essentially your question -which is one that troubles many eartn scientists - is why do we have plate tectonics? Why do we not have a stagnant lid like Venus? Most people think it has something to do with the moon forming impact early on in Earth's history, there is currently no mechanism proposed that I am aware of, but watch this space... 5. Jan 30, 2007 ### Andre There are ideas that Venus is not about stagnant lids, which is only a hypothesis. It might be that the thermal gradient of Venus is too low to require plate tectonics in the first place. There are also ideas that the generated heat inside the planet is related to friction heat due to mantle core friction caused by the orbital perbutations on which inner core and mantle react differently. Since the rotation of Venus is negliglible, it could be that Venus is no longer generating significant amounts of heat. The total lack of internal magnetic field, thought to be caused by outer core convection cells appears to support that idea. Most of Venus heat is already outside. 6. Jan 31, 2007 ### verdigris A lot of the water in the oceans came from comets.Maybe a big impact from a comet played a part in the fracturing of the Earth's surface. 7. Jan 31, 2007 ### billiards A big impact (with an object the size of mars) would have melted the surface... 8. Feb 1, 2007 ### verdigris The surface of the Earth may have been intially smooth.But if J Marvin Herndon is right about there being a nuclear fission reactor at the Earth's core,then perhaps there was an explosion in the core at one time ( Wigner energy caused the fire at Windscale nuclear reactor because pressure built up in the moderating material) that sent S and P waves to the Earth's surface and cracked the crust.The heat released and pressure waves would have pumped magma through the cracks and formed the continental land mass.The explosion must have been on one side of the core or else continents could have formed elsewhere.So,in this scenario,at one time the core of the Earth must have had an inhomogenous chemical composition. Perhaps shear wave anisotropy in the Lehman discontinuity - which happens under the continents but not under the oceans - has something to do with energy coming from an explosion at the Earth's core. 9. Feb 1, 2007 ### Andre or would have caused another asteroid belt. I think we could do better than that. Suppose that we put a planet identical to Earth but about 90% size in Venus orbit but without moon. What if we mix the geophysical thoughts of Jim Vanyo about core-mantle coupling and orbital pertubations http://www.me.ucsb.edu/dept_site/vanyo.htm [Broken] and stir it with some ordinary basic physcis like gyroscopic effects, and then let it simmer for a couple of billion years, what would be cooking? Last edited by a moderator: May 2, 2017 10. Feb 1, 2007 ### billiards First, there is no evidence that suggests that he is right, that paper is old (1993) if I remember correctly, deep earth geophysics has advanced A LOT since then. The most recent work seems to suggest that the inner core is composed of iron with perhaps some light element alloys, there is nothing to suggest that there is a sufficient composition of uranium/thorium down there to do the things suggested in that paper. Second, I think you might be overplaying the capacity of S and P waves to crack the crust - they are elastic waves. Then again it is not entirely impossible (as far as I am aware) that the rarefaction which follows a shock wave might be capable of cracking the crust (see: shatter cones), however the explosion would have to have been MASSIVE (think millions to billions of nukes all at the same time) because shock waves cannot travel that far. No, it simply doesn't work like that. How exactly are you proposing the continents formed? EDIT: I just reread your pumping magma through cracks idea so I guess that answers my question! Let me ask you this instead: where exactly did the cracks you propose actually happen? I fail to see your point here. The anisotropy occurs under the oceans and not under the continents because there is difference between oceanic and continental crust. Shear wave anisotropy will result in so-called shear wave splitting: normally this involves the horizontally polarized s wave arriving a little before the vertically polarized s wave (depending on the nature of the anisotropy). This is just a property of the material down there, and it enables us to constrain (work out within limits) what that material might be; as far as I am aware it has nothing to do with energy coming from the core. Last edited: Feb 1, 2007 11. Feb 1, 2007 ### verdigris BILLIARDS said: "there is no evidence that suggests that he is right" Evidence could be hard to come by because he says that there is only a five mile radius core of uranium - would that resolve as a detail in a s - wave,p - wave analysis done at the surface? But the fact that venus and other planets radiate more heat than they receive from the sun could be supporting evidence,although some people attribute this heat excess to stored gravitational energy. "the explosion would have to have been MASSIVE (think millions to billions of nukes all at the same time)" I agree - the explosion would have been massive but an atomic bomb needs less than 1 kg of uranium 235 and a five mile radius could have at least 10 to the power of 12 kg given that u235/u238 ratio in nature is 1%.And there is also the possibility that a fission reaction involving hydrogen started a fusion reaction which is more energetic and created helium.This link shows that there is up to 1 % by mass of hydrogen in the Earth's core:http://www.nature.com/nature/journal/v268/n5616/abs/268130a0.html. and this link that helium can come from the lower mantle(perhaps the core?) to the upper mantle: http://camb.demonhosting.co.uk/JConfAbs/5/768.pdf[/URL] There may not have been an explosion just a rapid and uneven release of a large amount of heat - it depends on what the full chemical core composition was at the time. "I fail to see your point here. The anisotropy occurs under the oceans and not under the continents because there is difference between oceanic and continental crust. Shear wave anisotropy will result in so-called shear wave splitting: normally this involves the horizontally polarized s wave arriving a little before the vertically polarized s wave (depending on the nature of the anisotropy). This is just a property of the material down there," But did the material get that property from the pressure of an explosion - whatever the property is. Last edited by a moderator: May 2, 2017 12. Feb 1, 2007 ### Andre Verdigris, When we were doing that puzzle, thinking itwas a nuclear reactor, pieces did not fit pretty soon. you can have individual nuclear molecules decaying and producing heat but there is not the beginning of a ghost of a chance that there is a near critical mass of fission material that sustains a nuclear chain reaction. Everything about that is a very long shot and two long shots together is about the same change that you hit the jackpot of two lotteries on the same day. 13. Feb 2, 2007 ### verdigris I looked at the thread from 2004 on a nuclear reactor at the Earth's core. If I was asked to bet on the cause of heating in the Earth I would say that it was down to residual heat from Earth's formation and radioactivity in the mantle.Then movement of large masses of mantle material affecting Earth's axis tilt through gravitational effects and climate sometimes through volcanic effects. Last edited: Feb 2, 2007 Similar Discussions: What caused the supercontinent to break up	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8277597427368164, "perplexity": 1438.9721373141829}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934804680.40/warc/CC-MAIN-20171118075712-20171118095712-00759.warc.gz"}
https://www.physicsforums.com/threads/evaluating-limit-as-h-0-of-e-h-1-h.623092/	# Evaluating limit as h->0 of (e^h-1)/h 1. Jul 24, 2012 ### autodidude I'm trying to differentiate e^x from first principles but I can't find a way to manipulate this expression $$\frac{e^h-1}{h}$$ so I can evaluate the limit without getting 0/0 2. Jul 24, 2012 ### eumyang Use the definition of e: $lim_{h \rightarrow 0} \left( 1 + h \right)^{1/h} = e$ So for small values of h, $e \approx \left( 1 + h \right)^{1/h}$, or $e^h \approx 1 + h$. Replace eh in $\frac{e^h-1}{h}$ with 1 + h and go on from there. 3. Jul 24, 2012 ### Diffy 4. Jul 24, 2012 ### Mute In order to use L'Hopital's rule, you need to know the derivative of ex, but that's what the OP is trying to prove. To use L'Hopital's rule in this case would be circular logic. 5. Jul 24, 2012 ### eumyang I'm not sure how. The OP is trying to "differentiate ex from first principles," which I assume means that he/she want to find the derivative of ex by using the limit definition: $$\frac{d}{dx}e^x = lim_{h \rightarrow 0} \frac{e^{x+h} - e^x}{h} = ...$$ I don't think you can use L'Hopitals' Rule when we "don't know" the derivative of ex yet. EDIT: Beaten to it by Mute. 6. Jul 24, 2012 ### Diffy 7. Jul 25, 2012 ### autodidude Don't we get 0/0 again? Limit h->0 $$\frac{1+h-1}{h}$$ 8. Jul 25, 2012 ### eumyang Um, you need to simplify the expression. $$lim_{h \rightarrow 0}\frac{1+h-1}{h} = lim_{h \rightarrow 0} \frac{h}{h} = ...$$ 9. Jul 25, 2012 ### autodidude ^ Ah, thanks a lot...must've had a brain meltdown :p Similar Discussions: Evaluating limit as h->0 of (e^h-1)/h	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9778929948806763, "perplexity": 2608.268016500827}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105304.35/warc/CC-MAIN-20170819051034-20170819071034-00060.warc.gz"}
https://ergodicity.net/2012/07/18/a-comment-about-maximal-versus-average-error/	# A comment about maximal versus average error In my previous post I made some vague comments about maximal and average error which I think are not complicated but don’t often arise when we think about plain vanilla information theory problems. These come up in arbitrarily varying channels, but also help motivate some interesting alternative models. We most often think of error criteria as being about the desiderata for communication — asking for the maximal error over messages to be small is more stringent than asking for the average error. However, if we have a code which has small average error we can expurgate bad codewords to get a code which has small maximal error. With that meta-argument in hand, at a first pass we’re done : average error and maximal error are pretty much the same. However, choosing an error criterion can also be a choice about the communication model. If the noise can somehow depend on what is being transmitted, then this distinction can come up. If the error criterion is maximal error and the interference is arbitrary, then for each message and each interference signal, I need to guarantee that probability of error is small. Implicitly, this allows the interference to be chosen as a function of the message. Under average error, the interference cannot be a function of the message. If we allow for common randomness, the transmitter can mask the dependence of the codeword on the message. Suppose we have a deterministic code with $N$ codewords which has small average error. Then we can create a randomized code by choosing a random permutation $\pi$ of $N$ and encoding message $m$ with the $\pi(m)$-th codeword of the original code. In this way we get the maximal error to be small, since the maximal error is averaged over the common randomness. From this it’s clear that the choice of error criterion is also a modeling choice, especially when there is no common randomness allowed. However, this is all looking at the case where the interference can depend on the message. The trickier situation is when the interference can depend on the transmitted codeword, which is what I discussed in the previous post. In that setting using common randomness to mask the message-codeword dependence doesn’t buy that much. What I was working on recently was how much it buys you when the dependence is weakened. As a final note, this model of interference depending on the transmitted codeword appears in a stochastic form under the name “correlated jamming” and has been worked on by several researchers, including Muriel Médard, Shabnam Shafiee, and Sennur Ulukus. My goal was to get an AVC and geometric perspective on these kinds of communication models. This site uses Akismet to reduce spam. Learn how your comment data is processed.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 5, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.878433346748352, "perplexity": 443.49705894051476}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337287.87/warc/CC-MAIN-20221002052710-20221002082710-00157.warc.gz"}
https://worldwidescience.org/topicpages/l/left-right+supersymmetric+models.html	#### Sample records for left-right supersymmetric models 1. A constrained supersymmetric left-right model Energy Technology Data Exchange (ETDEWEB) Hirsch, Martin [AHEP Group, Instituto de Física Corpuscular - C.S.I.C./Universitat de València, Edificio de Institutos de Paterna, Apartado 22085, E-46071 València (Spain); Krauss, Manuel E. [Bethe Center for Theoretical Physics & Physikalisches Institut der Universität Bonn, Nussallee 12, 53115 Bonn (Germany); Institut für Theoretische Physik und Astronomie, Universität Würzburg,Emil-Hilb-Weg 22, 97074 Wuerzburg (Germany); Opferkuch, Toby [Bethe Center for Theoretical Physics & Physikalisches Institut der Universität Bonn, Nussallee 12, 53115 Bonn (Germany); Porod, Werner [Institut für Theoretische Physik und Astronomie, Universität Würzburg,Emil-Hilb-Weg 22, 97074 Wuerzburg (Germany); Staub, Florian [Theory Division, CERN,1211 Geneva 23 (Switzerland) 2016-03-02 We present a supersymmetric left-right model which predicts gauge coupling unification close to the string scale and extra vector bosons at the TeV scale. The subtleties in constructing a model which is in agreement with the measured quark masses and mixing for such a low left-right breaking scale are discussed. It is shown that in the constrained version of this model radiative breaking of the gauge symmetries is possible and a SM-like Higgs is obtained. Additional CP-even scalars of a similar mass or even much lighter are possible. The expected mass hierarchies for the supersymmetric states differ clearly from those of the constrained MSSM. In particular, the lightest down-type squark, which is a mixture of the sbottom and extra vector-like states, is always lighter than the stop. We also comment on the model’s capability to explain current anomalies observed at the LHC. 2. Leptogenesis in the left-right supersymmetric model International Nuclear Information System (INIS) Frank, M. 2004-01-01 We analyze the effects of the current neutrino data on thermal leptogenesis and 0νββ decay in a fully left-right extension of the minimal supersymmetric model. The model has several additional phases compared to the minimal supersymmetric model. These phases appear from both the heavy and light neutrino sectors: two CKM-type phases and four Majorana phases which give new contributions to CP-violating parameters and leptogenesis. We study observable effects of these phases on leptogenesis in most general neutrino mixing scenarios, with either hierarchical, inverse hierarchical, or quasidegenerate light and heavy neutrinos. We comment on the effects of these scenarios on the 0νββ decay. The CP-violating phases in both the heavy and light neutrino sectors of the left-right supersymmetric model have unique features, resulting in bounds on heavy neutrino masses different from the minimal scenario in leptogenesis, and which may distinguish the model from other supersymmetric scenarios 3. Chargino and neutralino production at the Large Hadron Collider in left-right supersymmetric models CERN Document Server Alloul, Adam; Fuks, Benjamin; Rausch de Traubenberg, Michel 2013-10-04 We present a complete and extensive analysis of associated chargino and neutralino production in the framework of a supersymmetric theory augmented by left-right symmetry. This model provides additional gaugino and higgsino states in both the neutral and charged sectors, thus potentially enhancing new physics signals at the LHC. For a choice of benchmark scenarios, we calculate cross sections for 7, 8 and 14 TeV. We then simulate events expected to be produced at the LHC, and classify them according to the number of leptons in the final state. We devise methods to reduce the background and compare the signals with consistently simulated events for the Minimal Supersymmetric Standard Model. We pinpoint promising scenarios where left-right symmetric supersymmetric signals can be distinguished both from background and from the Minimal Supersymmetric Standard Model events. 4. The electric dipole moment of the neutron in the left-right supersymmetric model International Nuclear Information System (INIS) Frank, M. 1999-01-01 We calculate the neutron electric dipole moment (EDM) in the left-right supersymmetric model, including one-loop contributions from the chargino, the neutralino and the gluino diagrams. We discuss the dependence of the EDM on the phases of the model, as well as on the mass parameters in the left and right sectors. The neutron EDM imposes different conditions on the supersymmetric spectrum from either the electron EDM, or the neutron EDM in the minimal supersymmetric standard model. The neutron EDM may be a clue to an extended gauge structure in supersymmetry. (author) 5. Introduction to left-right symmetric models International Nuclear Information System (INIS) Grimus, W. 1993-01-01 We motivate left-right symmetric models by the possibility of spontaneous parity breaking. Then we describe the multiplets and the Lagrangian of such models. Finally we discuss lower bounds on the right-handed scale. (author) 6. Roadmap of left-right models based on GUTs Science.gov (United States) Chakrabortty, Joydeep; Maji, Rinku; Patra, Sunando Kumar; Srivastava, Tripurari; Mohanty, Subhendra 2018-05-01 We perform a detailed study of the grand unified theories S O (10 ) and E (6 ) with left-right intermediate gauge symmetries of the form S U (N )L⊗S U (N )R⊗G . Proton decay lifetime constrains the unification scale to be ≳1016 GeV and, as discussed in this paper, unwanted cosmological relics can be evaded if the intermediate symmetry scale is ≳1012 GeV . With these conditions, we study the renormalization group evolution of the gauge couplings and do a comparative analysis of all possible left-right models where unification can occur. Both the D-parity conserved and broken scenarios as well as the supersymmetric (SUSY) and nonsupersymmetric (non-SUSY) versions are considered. In addition to the fermion and scalar representations at each stage of the symmetry breaking, contributing to the β functions, we list the intermediate left-right groups that successfully meet these requirements. We make use of the dimension-5 kinetic mixing effective operators for achieving unification and large intermediate scale. A significant result in the supersymmetric case is that to achieve successful unification for some breaking patterns, the scale of SUSY breaking needs to be at least a few TeV. In some of these cases, the intermediate scale can be as low as ˜1012 GeV , for the SUSY scale to be ˜30 TeV . This has important consequences in the collider searches for SUSY particles and phenomenology of the lightest neutralino as dark matter. 7. Weak interaction models with spontaneously broken left-right symmetry International Nuclear Information System (INIS) Mohapatra, R.H. 1978-01-01 The present status of weak interaction models with spontaneously broken left-right symmetry is reviewed. The theoretical basis for asymptotic parity conservation, manifest left-right symmetry in charged current weak interactions, natural parity conservation in neutral currents and CP-violation in the context of SU(2)/sub L/ circled x SU (2)/sub R/ circled x U(1) models are outlined in detail. Various directions for further research in the theoretical and experimental side are indicated 8. Flat directions in left-right symmetric string derived models International Nuclear Information System (INIS) Cleaver, Gerald B.; Clements, David J.; Faraggi, Alon E. 2002-01-01 The only string models known to reproduce the minimal supersymmetric standard model in the low energy effective field theory are those constructed in the free fermionic formulation. We demonstrate the existence of quasirealistic free fermionic heterotic string models in which supersymmetric singlet flat directions do not exist. This raises the possibility that supersymmetry is broken perturbatively in such models by the one-loop Fayet-Iliopoulos term. We show, however, that supersymmetric flat directions that utilize vacuum expectation values of some non-Abelian fields in the massless string spectrum do exist in the model. We argue that hidden sector condensates lift the flat directions and break supersymmetry hierarchically 9. Continuons left-right symmetrical model of electroweak interactions International Nuclear Information System (INIS) Boyarkin, O.M. 1993-01-01 The left-right model (LR) is suggested which is characterized by the orientation angle of the SU(2) R generator in the group space. This model reproduces all the known LR models. The production processes of gauge bosons at electron-positron and hardon colliders are investigated 10. Exotic fermions in the left-right symmetric model International Nuclear Information System (INIS) Choi, J.; Volkas, R.R. 1992-01-01 A systematic study is made of non-standard fermion multiplets in left-right symmetric models with gauge group SU(3) x SU(2) L x SU(2) R x U(1) BL . Constraints from gauge anomaly cancellation and invariance of Yukawa coupling terms are used to define interesting classes of exotic fermions. The standard quark lepton spectrum of left-right symmetric models was identified as the simplest member of an infinite class. Phenomenological implications of the next simplest member of this class are then studied. Classes of exotic fermions which may couple to the standard fermions through doublet Higgs bosons were also considered, then shown that some of these exotics may be used to induce a generalised universal see-saw mechanism. 12 refs., 1 tab 11. Mixed dark matter in left-right symmetric models Energy Technology Data Exchange (ETDEWEB) Berlin, Asher [Department of Physics, University of Chicago,Chicago, Illinois 60637 (United States); Fox, Patrick J. [Theoretical Physics Department, Fermilab,Batavia, Illinois 60510 (United States); Hooper, Dan [Center for Particle Astrophysics, Fermi National Accelerator Laboratory,Batavia, Illinois 60510 (United States); Department of Astronomy and Astrophysics, University of Chicago,Chicago, Illinois 60637 (United States); Mohlabeng, Gopolang [Center for Particle Astrophysics, Fermi National Accelerator Laboratory,Batavia, Illinois 60510 (United States); Department of Physics and Astronomy, University of Kansas,Lawrence, Kansas 66045 (United States) 2016-06-08 Motivated by the recently reported diboson and dijet excesses in Run 1 data at ATLAS and CMS, we explore models of mixed dark matter in left-right symmetric theories. In this study, we calculate the relic abundance and the elastic scattering cross section with nuclei for a number of dark matter candidates that appear within the fermionic multiplets of left-right symmetric models. In contrast to the case of pure multiplets, WIMP-nucleon scattering proceeds at tree-level, and hence the projected reach of future direct detection experiments such as LUX-ZEPLIN and XENON1T will cover large regions of parameter space for TeV-scale thermal dark matter. Decays of the heavy charged W{sup ′} boson to particles in the dark sector can potentially shift the right-handed gauge coupling to larger values when fixed to the rate of the Run 1 excesses, moving towards the theoretically attractive scenario, g{sub R}=g{sub L}. This region of parameter space may be probed by future collider searches for new Higgs bosons or electroweak fermions. 12. Naturally light Dirac neutrino in Left-Right Symmetric Model Energy Technology Data Exchange (ETDEWEB) Borah, Debasish [Department of Physics, Indian Institute of Technology Guwahati, Assam-781039 (India); Dasgupta, Arnab, E-mail: [email protected], E-mail: [email protected] [Institute of Physics, HBNI, Sachivalaya Marg, Bhubaneshwar-751005 (India) 2017-06-01 We study the possibility of generating tiny Dirac masses of neutrinos in Left-Right Symmetric Model (LRSM) without requiring the existence of any additional symmetries. The charged fermions acquire masses through a universal seesaw mechanism due to the presence of additional vector like fermions. The neutrinos acquire a one-loop Dirac mass from the same additional vector like charged leptons without requiring any additional discrete symmetries. The model can also be extended by an additional Z {sub 2} symmetry in order to have a scotogenic version of this scenario predicting a stable dark matter candidate. We show that the latest Planck upper bound on the effective number of relativistic degrees of freedom N {sub eff}=3.15 ± 0.23 tightly constrains the right sector gauge boson masses to be heavier than 3.548 TeV . This bound on gauge boson mass also affects the allowed values of right scalar doublet dark matter mass from the requirement of satisfying the Planck bound on dark matter relic abundance. We also discuss the possible implications of such a scenario in charged lepton flavour violation and generating observable electric dipole moment of leptons. 13. Higgs bosons in the left-right model International Nuclear Information System (INIS) Boyarkina, G.G.; Boyarkin, O.M. 2000-01-01 The model with the SU(2) L x SU(2) R x U(1) B-L gauge group, containing one bidoublet and two triplets in the Higgs sector, is considered. The link between the constants determining the physical Higgs boson interactions and the neutrino oscillation parameters is found. It is shown that the observation of the ultrahigh-energy neutrinos with the help of the processes e - ν e →W - Z, e - ν e →μ - ν μ , gives us information on the singly charged Higgs bosons. The processes of the doubly charged Higgs boson production, e - μ - →Δ (--) 1 γ, e - μ - →Δ (--) 1 Z, are investigated. From the point of view of detecting the neutral Higgs bosons the process of the electron-muon recharge e - μ + →e + μ - is studied. (orig.) 14. Higgs bosons and sleptons in an alternative left-right model International Nuclear Information System (INIS) Roszkowski, L. 1990-01-01 The phenomenological structure of the combined Higgs-boson--slepton sector of the alternative left-right-supersymmetric model introduced by Ma is explored. Constraints upon and relations between Higgs-boson and slepton masses are derived and a tightly constrained mass spectrum is found. In general, one neutral Higgs boson is never heavier than 98 GeV, one neutral Higgs boson is always nearly degenerate in mass with the extra neutral gauge boson Z 2 0 , and the charged Higgs boson can in principle be as light as 22 GeV. Further constraints require large ratios of Higgs vacuum expectation values, strongly favor the W R mass above ∼423 GeV, predict one Higgs-boson mass to be always very close to 98 GeV, and masses of the other Higgs bosons and the sleptons to be bounded from above and preferably not much above the Z mass. In addition, the possibility of detecting light Higgs bosons at CERN LEP and the SLAC Linear Collider is briefly discussed 15. Cancellation of leading divergences in left-right electroweak model and heavy particles International Nuclear Information System (INIS) Andrianov, A.A.; Romanenko, N.V. 1997-01-01 The fine-tuning principles are analyzed in search for estimation of heavy-particle masses in the left-right symmetric model. The modification of Veltman condition based on the hypothesis of the compression between fermion and boson energies within the left-right model multiples is proposed. The hypothesis is supplied with the requirement of the stability under rescaling. With regard to these requirements the necessity of existence of right-handed Majorana neutrinos with masses of order of right-handed gauge bosons is shown and estimations on the top-quark which are in a good agreement with the experimental value are obtained 16. Supersymmetric sigma models International Nuclear Information System (INIS) Bagger, J.A. 1984-09-01 We begin to construct the most general supersymmetric Lagrangians in one, two and four dimensions. We find that the matter couplings have a natural interpretation in the language of the nonlinear sigma model 17. Supersymmetric sigma models Energy Technology Data Exchange (ETDEWEB) Bagger, J.A. 1984-09-01 We begin to construct the most general supersymmetric Lagrangians in one, two and four dimensions. We find that the matter couplings have a natural interpretation in the language of the nonlinear sigma model. 18. Neutrinoless double-beta decay in left-right symmetric models International Nuclear Information System (INIS) Picciotto, C.E.; Zahir, M.S. 1982-06-01 Neutrinoless double-beta decay is calculated via doubly charged Higgs, which occur naturally in left-right symmetric models. We find that the comparison with known half-lives yields values of phenomenological parameters which are compatible with earlier analyses of neutral current data. In particular, we obtain a right-handed gauge-boson mass lower bound of the order of 240 GeV. Using this result and expressions for neutrino masses derived in a parity non-conserving left-right symmetric model, we obtain msub(νsub(e)) < 1.5 eV, msub(νsub(μ)) < 0.05 MeV and msub(νsub(tau)) < 18 MeV 19. Mechanisms of Left-Right Coordination in Mammalian Locomotor Pattern Generation Circuits: A Mathematical Modeling View Science.gov (United States) Talpalar, Adolfo E.; Rybak, Ilya A. 2015-01-01 The locomotor gait in limbed animals is defined by the left-right leg coordination and locomotor speed. Coordination between left and right neural activities in the spinal cord controlling left and right legs is provided by commissural interneurons (CINs). Several CIN types have been genetically identified, including the excitatory V3 and excitatory and inhibitory V0 types. Recent studies demonstrated that genetic elimination of all V0 CINs caused switching from a normal left-right alternating activity to a left-right synchronized “hopping” pattern. Furthermore, ablation of only the inhibitory V0 CINs (V0D subtype) resulted in a lack of left-right alternation at low locomotor frequencies and retaining this alternation at high frequencies, whereas selective ablation of the excitatory V0 neurons (V0V subtype) maintained the left–right alternation at low frequencies and switched to a hopping pattern at high frequencies. To analyze these findings, we developed a simplified mathematical model of neural circuits consisting of four pacemaker neurons representing left and right, flexor and extensor rhythm-generating centers interacting via commissural pathways representing V3, V0D, and V0V CINs. The locomotor frequency was controlled by a parameter defining the excitation of neurons and commissural pathways mimicking the effects of N-methyl-D-aspartate on locomotor frequency in isolated rodent spinal cord preparations. The model demonstrated a typical left-right alternating pattern under control conditions, switching to a hopping activity at any frequency after removing both V0 connections, a synchronized pattern at low frequencies with alternation at high frequencies after removing only V0D connections, and an alternating pattern at low frequencies with hopping at high frequencies after removing only V0V connections. We used bifurcation theory and fast-slow decomposition methods to analyze network behavior in the above regimes and transitions between them. The model 20. Dark Gauge U(1) symmetry for an alternative left-right model Science.gov (United States) Kownacki, Corey; Ma, Ernest; Pollard, Nicholas; Popov, Oleg; Zakeri, Mohammadreza 2018-02-01 An alternative left-right model of quarks and leptons, where the SU(2)_R lepton doublet (ν ,l)_R is replaced with (n,l)_R so that n_R is not the Dirac mass partner of ν _L, has been known since 1987. Previous versions assumed a global U(1)_S symmetry to allow n to be identified as a dark-matter fermion. We propose here a gauge extension by the addition of extra fermions to render the model free of gauge anomalies, and just one singlet scalar to break U(1)_S. This results in two layers of dark matter, one hidden behind the other. 1. Connecting Dirac and Majorana neutrino mass matrices in the minimal left-right symmetric model. Science.gov (United States) Nemevšek, Miha; Senjanović, Goran; Tello, Vladimir 2013-04-12 Probing the origin of neutrino mass by disentangling the seesaw mechanism is one of the central issues of particle physics. We address it in the minimal left-right symmetric model and show how the knowledge of light and heavy neutrino masses and mixings suffices to determine their Dirac Yukawa couplings. This in turn allows one to make predictions for a number of high and low energy phenomena, such as decays of heavy neutrinos, neutrinoless double beta decay, electric dipole moments of charged leptons, and neutrino transition moments. We also discuss a way of reconstructing the neutrino Dirac Yukawa couplings at colliders such as the LHC. 2. Single top partner production at lepton colliders in the left-right twin Higgs model Science.gov (United States) Jiang, Xingyu; Han, Jinzhong; Hou, Biaofeng; Yu, Chunxu 2018-04-01 In the framework of the left-right twin Higgs (LRTH) model, we investigate the single top partner production at lepton colliders. We calculate the production cross-sections of the processes e‑γ → ν ebT¯, e‑e+ → W‑b¯T (W+bT¯) and γγ → W‑b¯T (W+bT¯) at s = 2.0 TeV, and display some typical differential distributions of the final state particles. 3. Right-handed quark mixings in minimal left-right symmetric model with general CP violation International Nuclear Information System (INIS) Zhang Yue; Ji Xiangdong; An Haipeng; Mohapatra, R. N. 2007-01-01 We solve systematically for the right-handed quark mixings in the minimal left-right symmetric model which generally has both explicit and spontaneous CP violations. The leading-order result has the same hierarchical structure as the left-handed Cabibbo-Kobayashi-Maskawa mixing, but with additional CP phases originating from a spontaneous CP-violating phase in the Higgs vacuum expectation values. We explore the phenomenology entailed by the new right-handed mixing matrix, particularly the bounds on the mass of W R and the CP phase of the Higgs vacuum expectation values 4. Supersymmetric models without R parity International Nuclear Information System (INIS) Ross, G.G.; Valle, J.W.F. 1985-01-01 We show that many supersymmetric models may spontaneously break R parity through scalar neutrinos acquiring a vacuum expectation value (vev). These models allow supersymmetric particles to be produced singly and to decay to nonsupersymmetric states. This leads to a new pattern of supersymmetric phenomenology. We discuss the lepton number violation to be expected in this class of models. (orig.) 5. Neutrino masses and leptogenesis in left-right symmetric models: a review from a model building perspective Science.gov (United States) Hati, Chandan; Patra, Sudhanwa; Pritimita, Prativa; Sarkar, Utpal 2018-03-01 In this review, we present several variants of left-right symmetric models in the context of neutrino masses and leptogenesis. In particular, we discuss various low scale seesaw mechanisms like linear seesaw, inverse seesaw, extended seesaw and their implications to lepton number violating process like neutrinoless double beta decay. We also visit an alternative framework of left-right models with the inclusion of vector-like fermions to analyze the aspects of universal seesaw. The symmetry breaking of left-right symmetric model around few TeV scale predicts the existence of massive right-handed gauge bosons W_R and Z_R which might be detected at the LHC in near future. If such signals are detected at the LHC that can have severe implications for leptogenesis, a mechanism to explain the observed baryon asymmetry of the Universe. We review the implications of TeV scale left-right symmetry breaking for leptogenesis. 6. Perspectives for detecting lepton flavour violation in left-right symmetric models Energy Technology Data Exchange (ETDEWEB) Bonilla, Cesar [AHEP Group, Instituto de Física Corpuscular - C.S.I.C./Universitat de València,Edificio de Institutos de Paterna, C/Catedratico José Beltrán 2,E-46980 Paterna (València) (Spain); Krauss, Manuel E.; Opferkuch, Toby [Bethe Center for Theoretical Physics & Physikalisches Institut der Universität Bonn,Nussallee 12, 53115 Bonn (Germany); Porod, Werner [Institut für Theoretische Physik und Astronomie, Universität Würzburg,Am Hubland, 97074 Würzburg (Germany) 2017-03-06 We investigate lepton flavour violation in a class of minimal left-right symmetric models where the left-right symmetry is broken by triplet scalars. In this context we present a method to consistently calculate the triplet-Yukawa couplings which takes into account the experimental data while simultaneously respecting the underlying symmetries. Analysing various scenarios, we then calculate the full set of tree-level and one-loop contributions to all radiative and three-body flavour-violating fully leptonic decays as well as μ−e conversion in nuclei. Our method illustrates how these processes depend on the underlying parameters of the theory. To that end we observe that, for many choices of the model parameters, there is a strong complementarity between the different observables. For instance, in a large part of the parameter space, lepton flavour violating τ-decays have a large enough branching ratio to be measured in upcoming experiments. Our results further show that experiments coming online in the immediate future, like Mu3e and BELLE II, or longer-term, such as PRISM/PRIME, will probe significant portions of the currently allowed parameter space. 7. Perspectives for detecting lepton flavour violation in left-right symmetric models International Nuclear Information System (INIS) Bonilla, Cesar; Krauss, Manuel E.; Opferkuch, Toby; Porod, Werner 2017-01-01 We investigate lepton flavour violation in a class of minimal left-right symmetric models where the left-right symmetry is broken by triplet scalars. In this context we present a method to consistently calculate the triplet-Yukawa couplings which takes into account the experimental data while simultaneously respecting the underlying symmetries. Analysing various scenarios, we then calculate the full set of tree-level and one-loop contributions to all radiative and three-body flavour-violating fully leptonic decays as well as μ−e conversion in nuclei. Our method illustrates how these processes depend on the underlying parameters of the theory. To that end we observe that, for many choices of the model parameters, there is a strong complementarity between the different observables. For instance, in a large part of the parameter space, lepton flavour violating τ-decays have a large enough branching ratio to be measured in upcoming experiments. Our results further show that experiments coming online in the immediate future, like Mu3e and BELLE II, or longer-term, such as PRISM/PRIME, will probe significant portions of the currently allowed parameter space. 8. Dark gauge U(1) symmetry for an alternative left-right model Energy Technology Data Exchange (ETDEWEB) Kownacki, Corey; Ma, Ernest; Pollard, Nicholas; Popov, Oleg; Zakeri, Mohammadreza [University of California, Department of Physics and Astronomy, Riverside, CA (United States) 2018-02-15 An alternative left-right model of quarks and leptons, where the SU(2){sub R} lepton doublet (ν, l){sub R} is replaced with (n, l){sub R} so that n{sub R} is not the Dirac mass partner of ν{sub L}, has been known since 1987. Previous versions assumed a global U(1){sub S} symmetry to allow n to be identified as a dark-matter fermion. We propose here a gauge extension by the addition of extra fermions to render the model free of gauge anomalies, and just one singlet scalar to break U(1){sub S}. This results in two layers of dark matter, one hidden behind the other. (orig.) 9. (g-2)μ anomaly and neutrino oscillations within the left-right model International Nuclear Information System (INIS) Boyarkin, O.M.; Bakanova, T.I. 2003-12-01 The Higgs sector structure of the left right model is investigated. The coupling constants of the physical Higgs bosons are expressed in terms of the oscillation parameters of the heavy neutrinos. The electroweak corrections to the value of the anomalous magnetic moment of the muon coming from the Higgs bosons axe found. It is shown that in the LRM the motion of the light neutrino flux in matter is described within the hybrid three-neutrino scheme, namely, the neutrino oscillations and the non standard neutrino interactions, caused by the Higgs sector. These non standard contributions may considerably change the matter potential compared with the SM prediction. Therefore, the analysis of the (g-2)μ, anomaly and the oscillations of the light neutrinos in matter could be used to constrain the parameters of the heavy neutrinos. (author) 10. A supersymmetric Skyrme model International Nuclear Information System (INIS) Gudnason, Sven Bjarke; Nitta, Muneto; Sasaki, Shin 2016-01-01 Construction of a supersymmetric extension of the Skyrme term was a long-standing problem because of the auxiliary field problem; that is, the auxiliary field may propagate and cannot be eliminated, and the problem of having fourth-order time derivative terms. In this paper, we construct for the first time a supersymmetric extension of the Skyrme term in four spacetime dimensions, in the manifestly supersymmetric superfield formalism that does not suffer from the auxiliary field problem. Chiral symmetry breaking in supersymmetric theories results not only in Nambu-Goldstone (NG) bosons (pions) but also in the same number of quasi-NG bosons so that the low-energy theory is described by an SL(N,ℂ)-valued matrix field instead of SU(N) for NG bosons. The solution of auxiliary fields is trivial on the canonical branch of the auxiliary field equation, in which case our model results in a fourth-order derivative term that is not the Skyrme term. For the case of SL(2,ℂ), we find explicitly a nontrivial solution to the algebraic auxiliary field equations that we call a non-canonical branch, which when substituted back into the Lagrangian gives a Skyrme-like model. If we restrict to a submanifold, where quasi-NG bosons are turned off, which is tantamount to restricting the Skyrme field to SU(2), then the fourth-order derivative term reduces exactly to the standard Skyrme term. Our model is the first example of a nontrivial auxiliary field solution in a multi-component model. 11. Universal seesaw and 0νββ in new 3331 left-right symmetric model Directory of Open Access Journals (Sweden) Debasish Borah 2017-08-01 Full Text Available We consider a class of left-right symmetric model with enlarged gauge group SU(3c×SU(3L×SU(3R×U(1X without having scalar bitriplet. In the absence of scalar bitriplet, there is no Dirac mass term for fermions including usual quarks and leptons. We introduce new isosinglet vector-like fermions so that all the fermions get their masses through a universal seesaw mechanism. We extend our discussion to neutrino mass and its implications in neutrinoless double beta decay (0νββ. We show that for TeV scale SU(3R gauge bosons, the heavy-light neutrino mixing contributes dominantly to 0νββ that can be observed at ongoing experiments. The new physics contributions arising from purely left-handed currents via exchange of keV scale right-handed neutrinos and the so called mixed helicity λ-diagram can saturate the KamLANDZen bound. We show that the right handed neutrinos in this model can have mass in the sub keV range and can be long lived compared to the age of the Universe. The contributions of these right handed neutrinos to flavour physics observables like μ→eγ and muon g−2 is also discussed. Towards the end we also comment on different possible symmetry breaking patterns of this enlarged gauge symmetry to that of the standard model. 12. Searching for dark matter signals in the left-right symmetric gauge model with CP symmetry International Nuclear Information System (INIS) Guo Wanlei; Wu Yueliang; Zhou Yufeng 2010-01-01 We investigate the singlet scalar dark matter (DM) candidate in a left-right symmetric gauge model with two Higgs bidoublets in which the stabilization of the DM particle is induced by the discrete symmetries P and CP. According to the observed DM abundance, we predict the DM direct and indirect detection cross sections for the DM mass range from 10 to 500 GeV. We show that the DM indirect detection cross section is not sensitive to the light Higgs mixing and Yukawa couplings except for the resonance regions. The predicted spin-independent DM-nucleon elastic scattering cross section is found to be significantly dependent on the above two factors. Our results show that the future DM direct search experiments can cover the most parts of the allowed parameter space. The PAMELA antiproton data can only exclude two very narrow regions in the two Higgs bidoublets model. It is very difficult to detect the DM direct or indirect signals in the resonance regions due to the Breit-Wigner resonance effect. 13. Low energy restrictions for a flipped left-right symmetric model Energy Technology Data Exchange (ETDEWEB) Eeg, J.O. (Oslo Univ. (Norway). Fysisk Inst.) 1990-05-01 I consider some low energy restrictions for a 'flipped' left-right symmetric model containing exotic fermions of E{sub 6} and a right-handed W-boson, all with odd R-parity. The new interactions due to W{sub R}-exchange have no significant impact on rare kaon decays, because the W{sub R} does not couple to d, s, b quarks. On the other hand, W{sub R} exchanges might induce rare processes like D-anti D mixing, D{sup 0}{yields}{mu}anti {mu}, D{sup 0}{yields}{mu}anti e, {mu}{yields}e{gamma}, {mu}{yields}3e, and {mu}N{yields}eN. It turns out that the strongest bound is obtained from D-anti D mixing. With reasonable extra assumptions, it is found that the exotic right-handed W-boson is likely to be heavier than 500 to 1500 GeV. (orig.). 14. Detection of heavy neutrinos and right-handed bosons of the left-right symmetric model CERN Document Server Kirsanov, M 2008-01-01 The left-right symmetric model can explain the origin of parity violation in weak interactions and predicts the existence of additional $W_R$ and $Z'$ gauge bosons and heavy right-handed neutrino states $N_l$. $N_l$ can be partners of light neutrino states ($l=e,\\mu,\\tau$), related to their non-zero masses through the see-saw mechanism. This makes the searches of $W_R$, $Z'$ and $N_l$ interesting and important. We studied the potential of the CMS experiment to observe signals from the $N_l$ and $W_R$ production at the LHC. It is shown that their decay signals can be identified over a small background. The mass region up to $M_{W_R} = 2100$ GeV and $M_{N_l} = 1200$ GeV can be explored with an expected Gaussian significance of 5$\\sigma$ with an integrated luminosity $\\mathcal{L}_{int} = 100$ pb$^{-1}$ (at the collision energy $\\sqrt{s}=14$ TeV). 15. Modelling genetic reorganization in the mouse spinal cord affecting left-right coordination during locomotion DEFF Research Database (Denmark) Rybak, Ilya A.; Shevtsova, Natalia A.; Kiehn, Ole 2013-01-01 glutamatergic interneurons, whose axon guidance involves the EphA4 receptor. In EphA4 knockout (KO) and Netrin-1 KO mice, the normal left-right alternating pattern is replaced with a synchronized hopping gait, and the cord of DCC KO mice exhibits uncoordinated left and right oscillations. To investigate... 16. Scalar dark matter explanation of the DAMPE data in the minimal left-right symmetric model Science.gov (United States) Cao, Junjie; Guo, Xiaofei; Shang, Liangliang; Wang, Fei; Wu, Peiwen; Zu, Lei 2018-03-01 The left-right symmetric model (LRSM) is an attractive extension of the Standard Model (SM) that can address the origin of parity violation in the SM electroweak interactions, generate tiny neutrino masses, accommodate dark matter (DM) candidates, and provide a natural framework for baryogenesis through leptogenesis. In this work, we utilize the minimal LRSM to study the recently reported DAMPE results of the cosmic e+e- spectrum, which exhibits a tentative peak around 1.4 TeV, while satisfying the current neutrino data. We propose to explain the DAMPE peak with a complex scalar DM χ in two scenarios: (1) χ χ→H1++H1-→ℓi+ℓi+ℓj-ℓj- , and (2) χ χ→Hk++Hk-→ℓi+ℓi+ℓj-ℓj- accompanied by χ χ→H1+H1-→ℓi+νℓiℓj-νℓj , with ℓi,j=e , μ , τ and k =1 , 2. We fit the theoretical prediction of the e+e- spectrum to relevant experimental data to determine the scalar mass spectrum favored by the DAMPE excess. We also consider various constraints from theoretical principles and collider experiments, as well as DM relic density and direct search experiments. We find that there is ample parameter space to interpret the DAMPE data while also passing the constraints. On the other hand, our explanations usually imply the existence of other new physics at an energy scale ranging from 107 to 1011 GeV . Collider tests of our explanations are also discussed. 17. Decoupling of parity- and SU(2)/sub R/-breaking scales: A new approach to left-right symmetric models International Nuclear Information System (INIS) Chang, D.; Mohapatra, R.N.; Parida, M.K. 1984-01-01 A new approach to left-right symmetric models is proposed, where the left-right discrete-symmetry- and SU(2)/sub R/-breaking scales are decoupled from each other. This changes the spectrum of physical Higgs bosons which leads to different patterns for gauge hierarchies in SU(2)/sub L/xSU(2)/sub R/xSU(4)/sub C/ and SO(10) models. Most interesting are two SO(10) symmetry-breaking chains with an intermediate U(1)/sub R/ symmetry. These are such as to provide new motivation to search for ΔB = 2 and right-handed current effects at low energies 18. Multi-component fermionic dark matter and IceCube PeV scale neutrinos in left-right model with gauge unification Science.gov (United States) Borah, Debasish; Dasgupta, Arnab; Dey, Ujjal Kumar; Patra, Sudhanwa; Tomar, Gaurav 2017-09-01 We consider a simple extension of the minimal left-right symmetric model (LRSM) in order to explain the PeV neutrino events seen at the IceCube experiment from a heavy decaying dark matter. The dark matter sector is composed of two fermions: one at PeV scale and the other at TeV scale such that the heavier one can decay into the lighter one and two neutrinos. The gauge annihilation cross sections of PeV dark matter are not large enough to generate its relic abundance within the observed limit. We include a pair of real scalar triplets Ω L,R which can bring the thermally overproduced PeV dark matter abundance into the observed range through late time decay and consequent entropy release thereby providing a consistent way to obtain the correct relic abundance without violating the unitarity bound on dark matter mass. Another scalar field, a bitriplet under left-right gauge group is added to assist the heavier dark matter decay. The presence of an approximate global U(1) X symmetry can naturally explain the origin of tiny couplings required for long-lived nature of these decaying particles. We also show, how such an extended LRSM can be incorporated within a non-supersymmetric SO(10) model where the gauge coupling unification at a very high scale naturally accommodate a PeV scale intermediate symmetry, required to explain the PeV events at IceCube. 19. Supersymmetric models and their phenomenology International Nuclear Information System (INIS) Ross, G.G. 1995-01-01 The prospects for unification of the Standard Model are considered and the need for supersymmetry discussed. The prediction of the gauge couplings, the electroweak breaking scale, the fermion masses and the dark matter abundance are all consistent with simple unification if there is a stage of supersymmetric unification below the TeV scale. The prospects for discovery of the new SUSY states is considered, both in the minimal supersymmetric standard model and in non-minimal extensions. (author) 20. Lepton number violating signals of the top quark partners in the left-right twin Higgs model International Nuclear Information System (INIS) Goh, Hock-Seng; Krenke, Christopher A. 2010-01-01 We study the collider signatures of the left-right twin Higgs model in the case that the right-handed neutrino mass is less than the mass of the right-handed gauge boson. In this scenario, new leptonic decay chains open up, allowing the particles which cancel the one-loop quadratic divergences of the Higgs, the right-handed gauge bosons and top-partners, to be discovered. Half of these events contain same-sign leptons without missing energy, which have no genuine standard model background and for which the backgrounds are purely instrumental. These signals may be used to complement other collider searches and, in certain regions of parameter space, may be the only way to observe the particles responsible for natural electroweak symmetry breaking in the left-right twin Higgs model. 1. Phenomenology of a left-right-symmetric model inspired by the trinification model Energy Technology Data Exchange (ETDEWEB) Hetzel, Jamil 2015-02-04 The trinification model is an interesting extension of the Standard Model based on the gauge group SU(3){sub C} x SU(3){sub L} x SU(3){sub R}. It naturally explains parity violation as a result of spontaneous symmetry breaking, and the observed fermion masses and mixings can be reproduced using only a few parameters. We study the low-energy phenomenology of the trinification model in order to compare its predictions to experiment. To this end, we construct a low-energy effective field theory, thereby reducing the number of particles and free parameters that need to be studied. We constrain the model parameters using limits from new-particle searches as well as precision measurements. The scalar sector of the model allows for various phenomenological scenarios, such as the presence of a light fermiophobic scalar in addition to a Standard-Model-like Higgs, or a degenerate (twin) Higgs state at 126 GeV. We show how a measurement of the Higgs couplings can be used to distinguish such scenarios from the Standard Model. We find that the trinification model predicts that several new scalar particles have masses in the O(100 GeV) range. Moreover, large regions of the parameter space lead to measurable deviations from Standard-Model predictions of the Higgs couplings. Hence the trinification model awaits crucial tests at the Large Hadron Collider in the coming years. 2. An Analysis of $B_{s}$ Decays in the Left-Right-Symmetric Model with Spontaneous CP Violation CERN Document Server Ball, Patricia; Ball, Patricia; Fleischer, Robert 2000-01-01 Non-leptonic B_s decays into CP eigenstates that are caused by \\bar b -> \\bar cc\\bar s quark-level transitions, such as B_s -> D_s^+D^-_s, J/psi eta^(') or J/psi phi, provide a powerful tool to search for new physics'', as the CP-violating effects in these modes are tiny in the Standard Model. We explore these effects for a particular scenario of new physics, the left-right-symmetric model with spontaneous CP violation. In our analysis, we take into account all presently available experimental constraints on the parameters of this model, i.e. those implied by K- and B-decay observables; we find that CP asymmetries as large as O(40%) may arise in the B_s channels, whereas the left-right-symmetric model favours a small CP asymmetry in the gold-plated'' mode B_d -> J/psi K_S. Such a pattern would be in favour of B-physics experiments at hadron machines, where the B_s modes are very accessible. 3. Acoustic and Perceptual Effects of Left-Right Laryngeal Asymmetries Based on Computational Modeling Science.gov (United States) Samlan, Robin A.; Story, Brad H.; Lotto, Andrew J.; Bunton, Kate 2014-01-01 Purpose: Computational modeling was used to examine the consequences of 5 different laryngeal asymmetries on acoustic and perceptual measures of vocal function. Method: A kinematic vocal fold model was used to impose 5 laryngeal asymmetries: adduction, edge bulging, nodal point ratio, amplitude of vibration, and starting phase. Thirty /a/ and /?/… 4. Non-minimal supersymmetric models. LHC phenomenolgy and model discrimination Energy Technology Data Exchange (ETDEWEB) Krauss, Manuel Ernst 2015-12-18 It is generally agreed upon the fact that the Standard Model of particle physics can only be viewed as an effective theory that needs to be extended as it leaves some essential questions unanswered. The exact realization of the necessary extension is subject to discussion. Supersymmetry is among the most promising approaches to physics beyond the Standard Model as it can simultaneously solve the hierarchy problem and provide an explanation for the dark matter abundance in the universe. Despite further virtues like gauge coupling unification and radiative electroweak symmetry breaking, minimal supersymmetric models cannot be the ultimate answer to the open questions of the Standard Model as they still do not incorporate neutrino masses and are besides heavily constrained by LHC data. This does, however, not derogate the beauty of the concept of supersymmetry. It is therefore time to explore non-minimal supersymmetric models which are able to close these gaps, review their consistency, test them against experimental data and provide prospects for future experiments. The goal of this thesis is to contribute to this process by exploring an extraordinarily well motivated class of models which bases upon a left-right symmetric gauge group. While relaxing the tension with LHC data, those models automatically include the ingredients for neutrino masses. We start with a left-right supersymmetric model at the TeV scale in which scalar SU(2){sub R} triplets are responsible for the breaking of left-right symmetry as well as for the generation of neutrino masses. Although a tachyonic doubly-charged scalar is present at tree-level in this kind of models, we show by performing the first complete one-loop evaluation that it gains a real mass at the loop level. The constraints on the predicted additional charged gauge bosons are then evaluated using LHC data, and we find that we can explain small excesses in the data of which the current LHC run will reveal if they are actual new 5. Neutrino mass and oscillation angle phenomena within the asymmetric left-right models International Nuclear Information System (INIS) Boyarkin, O.; Rein, D. 1994-07-01 The light and heavy Majorana neutrinos which appear naturally in SU(2) L x SU(2) R x U(1) B-L model are investigated. The exact solutions are presented for the system of two neutrinos with multipole moments propagating through magnetic and matter fields. The cross section of the reaction e - e - → W - k W - n calculated and its dependence on the mass of the right-handed neutrino and the oscillation angle is investigated. The process e + e - → W + k W - n is also included in our analysis. (author). 26 refs, 9 figs 6. Spontaneous baryogenesis in supersymmetric models International Nuclear Information System (INIS) Abel, S.A.; Cottingham, W.N.; Whittingham, I.B. 1993-01-01 In this paper we extent the results of previous work on spontaneous baryogenesis to general models involving charge-parity (CP) violation in the Higgs sector. We show how to deal with Chern-Simons terms appearing in the effective potential arising from phase changes in the vacuum expectation values of the Higgs fields. In particular, this enables us to apply this mechanism to general supersymmetric models including the minimal supersymmetric standard model, and the extended model with a gauge singlet. A comparison is made between this approach, and that in which one solves the equations of motion for Higgs winding modes. As anticipated in earlier work, the effect of the latter approach is found to be small. (Author) 7. Fermion number in supersymmetric models International Nuclear Information System (INIS) Mainland, G.B.; Tanaka, K. 1975-01-01 The two known methods for introducing a conserved fermion number into supersymmetric models are discussed. While the introduction of a conserved fermion number often requires that the Lagrangian be massless or that bosons carry fermion number, a model is discussed in which masses can be introduced via spontaneous symmetry breaking and fermion number is conserved at all stages without assigning fermion number to bosons. (U.S.) 8. Breaking symmetry: the zebrafish as a model for understanding left-right asymmetry in the developing brain. Science.gov (United States) Roussigne, Myriam; Blader, Patrick; Wilson, Stephen W 2012-03-01 How does left-right asymmetry develop in the brain and how does the resultant asymmetric circuitry impact on brain function and lateralized behaviors? By enabling scientists to address these questions at the levels of genes, neurons, circuitry and behavior,the zebrafish model system provides a route to resolve the complexity of brain lateralization. In this review, we present the progress made towards characterizing the nature of the gene networks and the sequence of morphogenetic events involved in the asymmetric development of zebrafish epithalamus. In an attempt to integrate the recent extensive knowledge into a working model and to identify the future challenges,we discuss how insights gained at a cellular/developmental level can be linked to the data obtained at a molecular/genetic level. Finally, we present some evolutionary thoughts and discuss how significant discoveries made in zebrafish should provide entry points to better understand the evolutionary origins of brain lateralization. 9. Supersymmetric models with light higgsinos International Nuclear Information System (INIS) Bruemmer, F. 2012-05-01 In the Minimal Supersymmetric Standard Model, the higgsinos can have masses around the electroweak scale, while the other supersymmetric particles have TeV-scale masses. This happens in models of gauge-mediated SUSY breaking with a high messenger scale, which are motivated from string theory. For particular choices of the messenger eld content, multi-TeV squark and gluino masses naturally lead to a much lower electroweak scale, somewhat similar to focus point supersymmetry. They also induce Higgs masses of 124-126 GeV, while making the discovery of supersymmetry at the LHC unlikely. The light higgsinos will be di cult to see at the LHC but may eventually be discovered at a linear collider. 10. Testing Left-Right extensions of the standard model of electroweak interactions with double-beta decay and LHC measurements Science.gov (United States) Civitarese, O.; Suhonen, J.; Zuber, K. 2015-07-01 The minimal extension of the standard model of electroweak interactions allows for massive neutrinos, a massive right-handed boson WR, and a left-right mixing angle ζ. While an estimate of the light (electron) neutrino can be extracted from the non-observation of the neutrinoless double beta decay, the limits on the mixing angle and the mass of the righthanded (RH) boson may be extracted from a combined analysis of the double beta decay measurements (GERDA, EXO-200 and KamLAND-Zen collaborations) and ATLAS data on the two-jets two-leptons signals following the excitation of a virtual RH boson mediated by a heavy-mass neutrino. In this work we shall compare results of both types of experiments, and show that the estimates are not in tension. 11. Electroweak breaking in supersymmetric models CERN Document Server Ibáñez, L E 1992-01-01 We discuss the mechanism for electroweak symmetry breaking in supersymmetric versions of the standard model. After briefly reviewing the possible sources of supersymmetry breaking, we show how the required pattern of symmetry breaking can automatically result from the structure of quantum corrections in the theory. We demonstrate that this radiative breaking mechanism works well for a heavy top quark and can be combined in unified versions of the theory with excellent predictions for the running couplings of the model. (To be published in Perspectives in Higgs Physics'', G. Kane editor.) 12. Non-minimal flavored S{sub 3} x Z{sub 2} left-right symmetric model Energy Technology Data Exchange (ETDEWEB) Gomez-Izquierdo, Juan Carlos [Tecnologico de Monterrey, Campus Estado de Mexico, Estado de Mexico, Estado de Mexico (Mexico); Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Mexico, D.F. (Mexico); Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Mexico, D.F. (Mexico) 2017-08-15 We propose a non-minimal left-right symmetric model with parity symmetry where the fermion mixings arise as a result of imposing an S{sub 3} x Z{sub 2} flavor symmetry, and an extra Z{sup e}{sub 2} symmetry is considered in the lepton sector. Then the neutrino mass matrix possesses approximately the μ-τ symmetry. The breaking of the μ-τ symmetry induces sizable non-zero θ{sub 13}, and the deviation of θ{sub 23} from 45 {sup circle} is strongly controlled by an ε free parameter and the neutrino masses. So, an analytic study of the CP parities in the neutrino masses is carried out to constrain the ε parameter and the lightest neutrino mass that accommodate the mixing angles. The results are: (a) the normal hierarchy is ruled out for any values of the Majorana phases; (b) for the inverted hierarchy the values of the reactor and atmospheric angles are compatible up to 2, 3 σ C.L.; (c) the degenerate ordering is the most favorable such that the reactor and atmospheric angle are compatible with the experimental data for a large set of values of the free parameters. The model predicts defined regions for the effective neutrino mass, the neutrino mass scale and the sum of the neutrino masses for the favored cases. Therefore, this model may be testable by the future experiments. (orig.) 13. Supersymmetric and non-supersymmetric models without catastrophic Goldstone bosons Energy Technology Data Exchange (ETDEWEB) Braathen, Johannes; Goodsell, Mark D. [LPTHE, UPMC Univ. Paris 6, Sorbonne Universites, Paris (France); LPTHE, CNRS, Paris (France); Staub, Florian [Karlsruhe Institute of Technology, Institute for Theoretical Physics (ITP), Karlsruhe (Germany); Karlsruhe Institute of Technology, Institute for Nuclear Physics (IKP), Eggenstein-Leopoldshafen (Germany) 2017-11-15 The calculation of the Higgs mass in general renormalisable field theories has been plagued by the so-called ''Goldstone Boson Catastrophe'', where light (would-be) Goldstone bosons give infra-red divergent loop integrals. In supersymmetric models, previous approaches included a workaround that ameliorated the problem for most, but not all, parameter space regions; while giving divergent results everywhere for non-supersymmetric models. We present an implementation of a general solution to the problem in the public code SARAH, along with new calculations of some necessary loop integrals and generic expressions. We discuss the validation of our code in the Standard Model, where we find remarkable agreement with the known results. We then show new applications in Split SUSY, the NMSSM, the Two-Higgs-Doublet Model, and the Georgi-Machacek model. In particular, we take some first steps to exploring where the habit of using tree-level mass relations in non-supersymmetric models breaks down, and show that the loop corrections usually become very large well before naive perturbativity bounds are reached. (orig.) 14. Neutrino jets from high-mass WR gauge bosons in TeV-scale left-right symmetric models Science.gov (United States) Mitra, Manimala; Ruiz, Richard; Scott, Darren J.; Spannowsky, Michael 2016-11-01 We reexamine the discovery potential at hadron colliders of high-mass right-handed (RH) gauge bosons WR—an inherent ingredient of left-right symmetric models (LRSM). We focus on the regime where the WR is very heavy compared to the heavy Majorana neutrino N , and we investigate an alternative signature for WR→N decays. The produced neutrinos are highly boosted in this mass regime. Subsequently, their decays via off-shell WR bosons to jets, i.e., N →ℓ±jj, are highly collimated, forming a single neutrino jet (jN). The final-state collider signature is then ℓ±jN, instead of the widely studied ℓ±ℓ±j j . Present search strategies are not sensitive to this hierarchical mass regime due to the breakdown of the collider signature definition. We take into account QCD corrections beyond next-to-leading order (NLO) that are important for high-mass Drell-Yan processes at the 13 TeV Large Hadron Collider (LHC). For the first time, we evaluate WR production at NLO with threshold resummation at next-to-next-to-leading logarithm (NNLL) matched to the threshold-improved parton distributions. With these improvements, we find that a WR of mass MWR=3 (4 )[5 ] TeV and mass ratio of (mN/MWR)discovered with a 5 - 6 σ statistical significance at 13 TeV after 10 (100 )[2000 ] fb-1 of data. Extending the analysis to the hypothetical 100 TeV Very Large Hadron Collider (VLHC), 5 σ can be obtained for WR masses up to MW R=15 (30 ) with approximately 100 fb-1 (10 ab-1 ). Conversely, with 0.9 (10 )[150 ] fb-1 of 13 TeV data, MWR<3 (4 )[5 ] TeV and (mN/MWR)<0.1 can be excluded at 95% C.L.; with 100 fb-1 (2.5 ab-1 ) of 100 TeV data, MW R<22 (33 ) TeV can be excluded. 15. Patterns of flavor signals in supersymmetric models Energy Technology Data Exchange (ETDEWEB) Goto, T. [KEK National High Energy Physics, Tsukuba (Japan)]\|[Kyoto Univ. (Japan). YITP; Okada, Y. [KEK National High Energy Physics, Tsukuba (Japan)]\|[Graduate Univ. for Advanced Studies, Tsukuba (Japan). Dept. of Particle and Nucelar Physics; Shindou, T. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]\|[International School for Advanced Studies, Trieste (Italy); Tanaka, M. [Osaka Univ., Toyonaka (Japan). Dept. of Physics 2007-11-15 Quark and lepton flavor signals are studied in four supersymmetric models, namely the minimal supergravity model, the minimal supersymmetric standard model with right-handed neutrinos, SU(5) supersymmetric grand unified theory with right-handed neutrinos and the minimal supersymmetric standard model with U(2) flavor symmetry. We calculate b{yields}s(d) transition observables in B{sub d} and B{sub s} decays, taking the constraint from the B{sub s}- anti B{sub s} mixing recently observed at Tevatron into account. We also calculate lepton flavor violating processes {mu} {yields} e{gamma}, {tau} {yields} {mu}{gamma} and {tau} {yields} e{gamma} for the models with right-handed neutrinos. We investigate possibilities to distinguish the flavor structure of the supersymmetry breaking sector with use of patterns of various flavor signals which are expected to be measured in experiments such as MEG, LHCb and a future Super B Factory. (orig.) 16. Patterns of flavor signals in supersymmetric models International Nuclear Information System (INIS) Goto, T.; Tanaka, M. 2007-11-01 Quark and lepton flavor signals are studied in four supersymmetric models, namely the minimal supergravity model, the minimal supersymmetric standard model with right-handed neutrinos, SU(5) supersymmetric grand unified theory with right-handed neutrinos and the minimal supersymmetric standard model with U(2) flavor symmetry. We calculate b→s(d) transition observables in B d and B s decays, taking the constraint from the B s - anti B s mixing recently observed at Tevatron into account. We also calculate lepton flavor violating processes μ → eγ, τ → μγ and τ → eγ for the models with right-handed neutrinos. We investigate possibilities to distinguish the flavor structure of the supersymmetry breaking sector with use of patterns of various flavor signals which are expected to be measured in experiments such as MEG, LHCb and a future Super B Factory. (orig.) 17. Left-right supersymmetry after the Higgs boson discovery Science.gov (United States) Frank, Mariana; Ghosh, Dilip Kumar; Huitu, Katri; Rai, Santosh Kumar; Saha, Ipsita; Waltari, Harri 2014-12-01 We perform a thorough analysis of the parameter space of the minimal left-right supersymmetric model in agreement with the LHC data. The model contains left- and right-handed fermionic doublets, two Higgs bidoublets, two Higgs triplet representations, and one singlet, insuring a charge-conserving vacuum. We impose the condition that the model complies with the experimental constraints on supersymmetric particles masses and on the doubly charged Higgs bosons and require that the parameter space of the model satisfies the LHC data on neutral Higgs signal strengths at 2 σ . We choose benchmark scenarios by fixing some basic parameters and scanning over the rest. The lightest supersymmetric particle in our scenarios is always the lightest neutralino. We find that the signals for H →γ γ and H →V V⋆ are correlated, while H →b b ¯ is anticorrelated with all of the other decay modes, and also that the contribution from singly charged scalars dominates that of the doubly charged scalars in H →γ γ and H →Z γ loops, contrary to type II seesaw models. We also illustrate the range for mass spectrum of the LRSUSY model in light of planned measurements of the branching ratio of H →γ γ to 10% level. 18. Non-supersymmetric orientifolds of Gepner models Energy Technology Data Exchange (ETDEWEB) Gato-Rivera, B. [NIKHEF Theory Group, Kruislaan 409, 1098 SJ Amsterdam (Netherlands); Instituto de Fisica Fundamental, CSIC, Serrano 123, Madrid 28006 (Spain); Schellekens, A.N. [NIKHEF Theory Group, Kruislaan 409, 1098 SJ Amsterdam (Netherlands); Instituto de Fisica Fundamental, CSIC, Serrano 123, Madrid 28006 (Spain); IMAPP, Radboud Universiteit, Nijmegen (Netherlands)], E-mail: [email protected] 2009-01-12 Starting from a previously collected set of tachyon-free closed strings, we search for N=2 minimal model orientifold spectra which contain the standard model and are free of tachyons and tadpoles at lowest order. For each class of tachyon-free closed strings - bulk supersymmetry, automorphism invariants or Klein bottle projection - we do indeed find non-supersymmetric and tachyon free chiral brane configurations that contain the standard model. However, a tadpole-cancelling hidden sector could only be found in the case of bulk supersymmetry. Although about half of the examples we have found make use of branes that break the bulk space-time supersymmetry, the resulting massless open string spectra are nevertheless supersymmetric in all cases. Dropping the requirement that the standard model be contained in the spectrum, we find chiral tachyon and tadpole-free solutions in all three cases, although in the case of bulk supersymmetry all massless spectra are supersymmetric. In the other two cases we find truly non-supersymmetric spectra, but a large fraction of them are nevertheless partly or fully supersymmetric at the massless level. 19. A supersymmetric SYK-like tensor model Energy Technology Data Exchange (ETDEWEB) Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia [Department of Physics, Brown University,Providence, RI, 02912 (United States) 2017-05-11 We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, “quarks” and “mesons”. We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic “melon” diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model. 20. A supersymmetric SYK-like tensor model International Nuclear Information System (INIS) Peng, Cheng; Spradlin, Marcus; Volovich, Anastasia 2017-01-01 We consider a supersymmetric SYK-like model without quenched disorder that is built by coupling two kinds of fermionic N=1 tensor-valued superfields, “quarks” and “mesons”. We prove that the model has a well-defined large-N limit in which the (s)quark 2-point functions are dominated by mesonic “melon” diagrams. We sum these diagrams to obtain the Schwinger-Dyson equations and show that in the IR, the solution agrees with that of the supersymmetric SYK model. 1. Spectral properties in supersymmetric matrix models International Nuclear Information System (INIS) Boulton, Lyonell; Garcia del Moral, Maria Pilar; Restuccia, Alvaro 2012-01-01 We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-supersymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather than just their semiclassical limits. In such a framework we examine spectral properties of various (1+0) matrix models. We consider the BMN model of M-theory compactified on a maximally supersymmetric pp-wave background, different regularizations of the supermembrane with central charges and a non-supersymmetric model comprising a bound state of N D2 with m D0. While the first two examples have a purely discrete spectrum, the latter has a continuous spectrum with a lower end given in terms of the monopole charge. 2. Early universe cosmology. In supersymmetric extensions of the standard model Energy Technology Data Exchange (ETDEWEB) Baumann, Jochen Peter 2012-03-19 In this thesis we investigate possible connections between cosmological inflation and leptogenesis on the one side and particle physics on the other side. We work in supersymmetric extensions of the Standard Model. A key role is played by the right-handed sneutrino, the superpartner of the right-handed neutrino involved in the type I seesaw mechanism. We study a combined model of inflation and non-thermal leptogenesis that is a simple extension of the Minimal Supersymmetric Standard Model (MSSM) with conserved R-parity, where we add three right-handed neutrino super fields. The inflaton direction is given by the imaginary components of the corresponding scalar component fields, which are protected from the supergravity (SUGRA) {eta}-problem by a shift symmetry in the Kaehler potential. We discuss the model first in a globally supersymmetric (SUSY) and then in a supergravity context and compute the inflationary predictions of the model. We also study reheating and non-thermal leptogenesis in this model. A numerical simulation shows that shortly after the waterfall phase transition that ends inflation, the universe is dominated by right-handed sneutrinos and their out-of-equilibrium decay can produce the desired matter-antimatter asymmetry. Using a simplified time-averaged description, we derive analytical expressions for the model predictions. Combining the results from inflation and leptogenesis allows us to constrain the allowed parameter space from two different directions, with implications for low energy neutrino physics. As a second thread of investigation, we discuss a generalisation of the inflationary model discussed above to include gauge non-singlet fields as inflatons. This is motivated by the fact that in left-right symmetric, supersymmetric Grand Unified Theories (SUSY GUTs), like SUSY Pati-Salam unification or SUSY SO(10) GUTs, the righthanded (s)neutrino is an indispensable ingredient and does not have to be put in by hand as in the MSSM. We discuss 3. Early universe cosmology. In supersymmetric extensions of the standard model International Nuclear Information System (INIS) Baumann, Jochen Peter 2012-01-01 In this thesis we investigate possible connections between cosmological inflation and leptogenesis on the one side and particle physics on the other side. We work in supersymmetric extensions of the Standard Model. A key role is played by the right-handed sneutrino, the superpartner of the right-handed neutrino involved in the type I seesaw mechanism. We study a combined model of inflation and non-thermal leptogenesis that is a simple extension of the Minimal Supersymmetric Standard Model (MSSM) with conserved R-parity, where we add three right-handed neutrino super fields. The inflaton direction is given by the imaginary components of the corresponding scalar component fields, which are protected from the supergravity (SUGRA) η-problem by a shift symmetry in the Kaehler potential. We discuss the model first in a globally supersymmetric (SUSY) and then in a supergravity context and compute the inflationary predictions of the model. We also study reheating and non-thermal leptogenesis in this model. A numerical simulation shows that shortly after the waterfall phase transition that ends inflation, the universe is dominated by right-handed sneutrinos and their out-of-equilibrium decay can produce the desired matter-antimatter asymmetry. Using a simplified time-averaged description, we derive analytical expressions for the model predictions. Combining the results from inflation and leptogenesis allows us to constrain the allowed parameter space from two different directions, with implications for low energy neutrino physics. As a second thread of investigation, we discuss a generalisation of the inflationary model discussed above to include gauge non-singlet fields as inflatons. This is motivated by the fact that in left-right symmetric, supersymmetric Grand Unified Theories (SUSY GUTs), like SUSY Pati-Salam unification or SUSY SO(10) GUTs, the righthanded (s)neutrino is an indispensable ingredient and does not have to be put in by hand as in the MSSM. We discuss the 4. The Higgs-strahlung and double Higgs-strahlung production in the left-right twin Higgs model at the ILC International Nuclear Information System (INIS) Yao-Bei, Liu; Hong-Mei, Han; Xue-Lei, Wang 2008-01-01 The Higgs-strahlung process e + e - → ZH and the double Higgs-strahlung process e + e - → ZHH are very important for studying Higgs boson properties and the Higgs self-coupling in the high-energy e + e - collider (ILC). We calculate the contributions of the left-right twin Higgs (LRTH) model to these processes and find that, in the favorable parameter spaces, the LRTH model can generate significant corrections to the production cross-section of these processes. We expect that the possible signals of the LRTH model can be detected via these processes in the future ILC experiments. (authors) 5. N=1 supersymmetric extension of the baby Skyrme model International Nuclear Information System (INIS) Adam, C.; Queiruga, J. M.; Sanchez-Guillen, J.; Wereszczynski, A. 2011-01-01 We construct a method to supersymmetrize higher kinetic terms and apply it to the baby Skyrme model. We find that there exist N=1 supersymmetric extensions for baby Skyrme models with arbitrary potential. 6. The rho-parameter in supersymmetric models International Nuclear Information System (INIS) Lim, C.S.; Inami, T.; Sakai, N. 1983-10-01 The electroweak rho-parameter is examined in a general class of supersymmetric models. Formulae are given for one-loop contributions to Δrho from scalar quarks and leptons, gauge-Higgs fermions and an extra doublet of Higgs scalars. Mass differences between members of isodoublet scalar quarks and leptons are constrained to be less than about 200 GeV. (author) 7. ''Natural'' left-right symmetry International Nuclear Information System (INIS) Mohapatra, R.N.; Pati, J.C. 1975-01-01 It is remarked that left-right symmetry of the starting gauge interactions is retained as a ''natural'' symmetry if it is broken in no way except possibly by mass terms in the Lagrangian. The implications of this result for the unification of coupling constants and for parity nonconservation at low and high energies are stressed 8. Resonant slepton production and right sneutrino dark matter in left-right supersymmetry Science.gov (United States) Frank, Mariana; Fuks, Benjamin; Huitu, Katri; Rai, Santosh Kumar; Waltari, Harri 2017-05-01 Right-handed sneutrinos are natural components of left-right symmetric supersymmetric models where the gauge sector is extended to include right-handed weak interactions. Unlike in other models where right-handed sneutrinos are gauge singlets, here the right sneutrino is part of a doublet and could be a dark matter candidate whose annihilation proceeds via gauge interactions. We investigate this possibility, and find that relic density, low-energy observable and direct supersymmetry search constraints can be satisfied when the lightest supersymmetric particle is a right-handed sneutrino. We introduce benchmarks for left-right supersymmetric realizations where either a sneutrino or a neutralino is the lightest superpartner. We then study the LHC signals arising through resonant right-handed slepton production via a W R gauge-boson exchange that lead to final states enriched in leptons, additionally containing a large amount of missing transverse momentum, and featuring a low jet multiplicity. We find that such a resonant production would boost the chances of discovering these weakly interacting supersymmetric particles for a mass range extending beyond 1 TeV already with a luminosity of 100 fb-1. Finally, we compare sneutrino versus neutralino scenarios, and comment on differences with other sneutrino dark matter models. 9. Resonant slepton production and right sneutrino dark matter in left-right supersymmetry International Nuclear Information System (INIS) Frank, Mariana; Fuks, Benjamin; Huitu, Katri; Rai, Santosh Kumar; Waltari, Harri 2017-01-01 Right-handed sneutrinos are natural components of left-right symmetric supersymmetric models where the gauge sector is extended to include right-handed weak interactions. Unlike in other models where right-handed sneutrinos are gauge singlets, here the right sneutrino is part of a doublet and could be a dark matter candidate whose annihilation proceeds via gauge interactions. We investigate this possibility, and find that relic density, low-energy observable and direct supersymmetry search constraints can be satisfied when the lightest supersymmetric particle is a right-handed sneutrino. We introduce benchmarks for left-right supersymmetric realizations where either a sneutrino or a neutralino is the lightest superpartner. We then study the LHC signals arising through resonant right-handed slepton production via a W R gauge-boson exchange that lead to final states enriched in leptons, additionally containing a large amount of missing transverse momentum, and featuring a low jet multiplicity. We find that such a resonant production would boost the chances of discovering these weakly interacting supersymmetric particles for a mass range extending beyond 1 TeV already with a luminosity of 100 fb −1 . Finally, we compare sneutrino versus neutralino scenarios, and comment on differences with other sneutrino dark matter models. 10. Supersymmetric SO(10) models inspired by deconstruction International Nuclear Information System (INIS) Huang Chaoshang; Jiang Jing; Li Tianjun 2004-01-01 We consider 4-dimensional N=1 supersymmetric SO(10) models inspired by deconstruction of 5-dimensional N=1 supersymmetric orbifold SO(10) models and high-dimensional non-supersymmetric SO(10) models with Wilson line gauge symmetry breaking. We discuss the SO(10)xSO(10) models with bi-fundamental link fields where the gauge symmetry can be broken down to the Pati-Salam, SU(5)xU(1), flipped SU(5)xU(1)' or the Standard Model like gauge symmetry. We also propose an SO(10)xSO(6)xSO(4) model with bi-fundamental link fields where the gauge symmetry is broken down to the Pati-Salam gauge symmetry, and an SO(10)xSO(10) model with bi-spinor link fields where the gauge symmetry is broken down to the flipped SU(5)xU(1)' gauge symmetry. In these two models, the Pati-Salam and flipped SU(5)xU(1)' gauge symmetry can be further broken down to the Standard Model gauge symmetry, the doublet-triplet splittings can be obtained by the missing partner mechanism, and the proton decay problem can be solved. We also study the gauge coupling unification. We briefly comment on the interesting variation models with gauge groups SO(10)xSO(6) and SO(10)xflippedSU(5)xU(1)' in which the proton decay problem can be solved 11. Utilitarian supersymmetric gauge model of particle interactions International Nuclear Information System (INIS) Ma, Ernest 2010-01-01 A remarkabale U(1) gauge extension of the supersymmetric standard model was proposed 8 years ago. It is anomaly free, has no μ term, and conserves baryon and lepton numbers automatically. The phenomenology of a specific version of this model is discussed. In particular, leptoquarks are predicted, with couplings to the heavy singlet neutrinos, the scalar partners of which may be components of dark matter. The Majorana neutrino mass matrix itself may have two zero subdeterminants. 12. Hierarchy generation in compactified supersymmetric models International Nuclear Information System (INIS) Ross, G.G. 1988-01-01 The problem of generating a large hierarchy in compactified supersymmetric models is re-examined. It is shown how, even for the class of models for which Str M 2 is non-vanishing, a combination of non-perturbative effects and radiative corrections may lead to an exponentially large hierarchy. A corollary is that the couplings of the effective field theory in the visible sector should be small, i.e., perturbation theory should be applicable. (orig.) 13. More supersymmetric standardlike models from intersecting D6-branes on type IIA orientifolds International Nuclear Information System (INIS) 2003-01-01 We present new classes of supersymmetric standardlike models from a type IIA T 6 /(Z 2 xZ 2 ) orientifold with intersecting D6-branes. D6-branes can wrap general supersymmetric three-cycles of T 6 =T 2 xT 2 xT 2 , and any T 2 is allowed to be tilted. The models still suffer from additional exotics; however, we obtain solutions with fewer Higgs doublets, as well as models with all three families of left-handed quarks and leptons arising from the same intersecting sector, and examples of a genuine left-right symmetric model with three copies of left-handed and right-handed families of quarks and leptons 14. Topological solitons in the supersymmetric Skyrme model Energy Technology Data Exchange (ETDEWEB) Gudnason, Sven Bjarke [Institute of Modern Physics, Chinese Academy of Sciences,Lanzhou 730000 (China); Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences,Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan); Sasaki, Shin [Department of Physics, Kitasato University,Sagamihara 252-0373 (Japan) 2017-01-04 A supersymmetric extension of the Skyrme model was obtained recently, which consists of only the Skyrme term in the Nambu-Goldstone (pion) sector complemented by the same number of quasi-Nambu-Goldstone bosons. Scherk-Schwarz dimensional reduction yields a kinetic term in three or lower dimensions and a potential term in two dimensions, preserving supersymmetry. Euclidean solitons (instantons) are constructed in the supersymmetric Skyrme model. In four dimensions, the soliton is an instanton first found by Speight. Scherk-Schwarz dimensional reduction is then performed once to get a 3-dimensional theory in which a 3d Skyrmion-instanton is found and then once more to get a 2d theory in which a 2d vortex-instanton is obtained. Although the last one is a global vortex it has finite action in contrast to conventional theory. All of them are non-BPS states breaking all supersymmetries. 15. Higgs bosons in supersymmetric models. Pt. 1 International Nuclear Information System (INIS) Gunion, J.F. 1986-01-01 We describe the properties of Higgs bosons in a class of supersymmetric theories. We consider models in which the low-energy sector contains two weak complex doublets and perhaps one complex gauge-singlet Higgs field. Supersymmetry is assumed to be either softly or spontaneously broken, thereby imposing a number of restrictions on the Higgs boson parameters. We elucidate the Higgs boson masses and present Feynman rules for their couplings to the gauge bosons, fermions and scalars of the theory. We also present Feynman rules for vertices which are related by supersymmetry to the above couplings. Exact analytic expressions are given in two useful limits - one corresponding to the absence of the gauge-singlet Higgs field and the other corresponding to the absence of a supersymmetric Higgs mass term. (orig.) 16. Single vector-like top partner production in the left-right twin Higgs model at TeV energy eγ colliders International Nuclear Information System (INIS) Guo Zhanying; Yang Guang; Yang Bingfang 2013-01-01 The left-right twin Higgs model contains a new vector-like heavy top quark, which mixes with the SM-like top quark. In this work, we studied the single vector-like top partner production via process e - γ → νeT-barb at the International Linear Collider. We calculated the production cross section at tree level and displayed the relevant differential distributions. The result shows that there will be 125 events produced each year with √s=2 TeV and the integrated luminosity Script Lint ≈ 500 fb -1 , and the b-quark tagging and the relevant missing energy cut will be helpful to detect this new effect. (authors) 17. Asymptotically Free Natural Supersymmetric Twin Higgs Model Science.gov (United States) 2018-05-01 Twin Higgs (TH) models explain the absence of new colored particles responsible for natural electroweak symmetry breaking (EWSB). All known ultraviolet completions of TH models require some nonperturbative dynamics below the Planck scale. We propose a supersymmetric model in which the TH mechanism is introduced by a new asymptotically free gauge interaction. The model features natural EWSB for squarks and gluino heavier than 2 TeV even if supersymmetry breaking is mediated around the Planck scale, and has interesting flavor phenomenology including the top quark decay into the Higgs boson and the up quark which may be discovered at the LHC. 18. On the supersymmetric sine-Gordon model International Nuclear Information System (INIS) Hruby, J. 1977-01-01 The sine-Gordon model as the theory of a massless scalar field in one space and one time dimension with interaction Lagrangian density proportional to cosβsub(phi) is generalized for a scalar superfield and it is shown that the solution of the supercovariant sine-Gordon equation is the ''supersoliton'', it is the superfield, which has all ordinary fields in two dimensions as a type of the soliton solution. We also obtain the massive Thirring model and the new equations of motion coupling the Fermi field and the Bose field. The notice about supersymmetric ''SLAC-BAG'' model is done 19. Supersymmetric flavon-chromon models International Nuclear Information System (INIS) Pati, J.C.; Salam, A. 1983-07-01 Using the supersymmetry and R-breaking mechanism induced by N=1 supergravity, we develop the minimal flavon-chromon preonic model where spin 1/2 and spin 0 components of four preonic chiral multiplets correspond to flavons and chromons, from which quarks and leptons are made as composites. The emergence of the concepts of flavour and colour, in this minimal model, is synonymous with R and supersymmetry breaking. This breaking also gives a heavy mass to the gaugino, which is necessary for the implementation of the model. (author) 20. Minimal Left-Right Symmetric Dark Matter. Science.gov (United States) Heeck, Julian; Patra, Sudhanwa 2015-09-18 We show that left-right symmetric models can easily accommodate stable TeV-scale dark matter particles without the need for an ad hoc stabilizing symmetry. The stability of a newly introduced multiplet either arises accidentally as in the minimal dark matter framework or comes courtesy of the remaining unbroken Z_{2} subgroup of B-L. Only one new parameter is introduced: the mass of the new multiplet. As minimal examples, we study left-right fermion triplets and quintuplets and show that they can form viable two-component dark matter. This approach is, in particular, valid for SU(2)×SU(2)×U(1) models that explain the recent diboson excess at ATLAS in terms of a new charged gauge boson of mass 2 TeV. 1. Beyond the supersymmetric standard model Energy Technology Data Exchange (ETDEWEB) Hall, L.J. 1988-02-01 The possibility of baryon number violation at the weak scale and an alternative primordial nucleosynthesis scheme arising from the decay of gravitations are discussed. The minimal low energy supergravity model is defined and a few of its features are described. Renormalization group scaling and flavor physics are mentioned. 2. Beyond the supersymmetric standard model International Nuclear Information System (INIS) Hall, L.J. 1988-02-01 The possibility of baryon number violation at the weak scale and an alternative primordial nucleosynthesis scheme arising from the decay of gravitations are discussed. The minimal low energy supergravity model is defined and a few of its features are described. Renormalization group scaling and flavor physics are mentioned 3. The minimally tuned minimal supersymmetric standard model International Nuclear Information System (INIS) Essig, Rouven; Fortin, Jean-Francois 2008-01-01 The regions in the Minimal Supersymmetric Standard Model with the minimal amount of fine-tuning of electroweak symmetry breaking are presented for general messenger scale. No a priori relations among the soft supersymmetry breaking parameters are assumed and fine-tuning is minimized with respect to all the important parameters which affect electroweak symmetry breaking. The superpartner spectra in the minimally tuned region of parameter space are quite distinctive with large stop mixing at the low scale and negative squark soft masses at the high scale. The minimal amount of tuning increases enormously for a Higgs mass beyond roughly 120 GeV 4. A semi-Markov model for stroke with piecewise-constant hazards in the presence of left, right and interval censoring. Science.gov (United States) Kapetanakis, Venediktos; Matthews, Fiona E; van den Hout, Ardo 2013-02-20 This paper presents a parametric method of fitting semi-Markov models with piecewise-constant hazards in the presence of left, right and interval censoring. We investigate transition intensities in a three-state illness-death model with no recovery. We relax the Markov assumption by adjusting the intensity for the transition from state 2 (illness) to state 3 (death) for the time spent in state 2 through a time-varying covariate. This involves the exact time of the transition from state 1 (healthy) to state 2. When the data are subject to left or interval censoring, this time is unknown. In the estimation of the likelihood, we take into account interval censoring by integrating out all possible times for the transition from state 1 to state 2. For left censoring, we use an Expectation-Maximisation inspired algorithm. A simulation study reflects the performance of the method. The proposed combination of statistical procedures provides great flexibility. We illustrate the method in an application by using data on stroke onset for the older population from the UK Medical Research Council Cognitive Function and Ageing Study. Copyright © 2012 John Wiley & Sons, Ltd. 5. Why PeV scale left-right symmetry is a good thing Science.gov (United States) Yajnik, Urjit A. 2017-10-01 Left-right symmetric gauge theory presents a minimal paradigm to accommodate massive neutrinos with all the known conserved symmetries duly gauged. The work presented here is based on the argument that the see-saw mechanism does not force the new right-handed symmetry scale to be very high, and as such some of the species from the spectrum of the new gauge and Higgs bosons can have masses within a few orders of magnitude of the TeV scale. The scale of the left-right parity breaking in turn can be sequestered from the Planck scale by supersymmetry. We have studied several formulations of such just beyond Standard Model (JBSM) theories for their consistency with cosmology. Specifically, the need to eliminate phenomenologically undesirable domain walls gives many useful clues. The possibility that the exact left-right symmetry breaks in conjunction with supersymmetry has been explored in the context of gauge mediation, placing restrictions on the available parameter space. Finally, we have also studied a left-right symmetric model in the context of metastable supersymmetric vacua and obtained constraints on the mass scale of right-handed symmetry. In all the cases studied, the mass scale of the right-handed neutrino M_R remains bounded from above, and in some of the cases the scale 10^9 GeV favourable for supersymmetric thermal leptogenesis is disallowed. On the other hand, PeV scale remains a viable option, and the results warrant a more detailed study of such models for their observability in collider and astroparticle experiments. 6. Mutations in zebrafish pitx2 model congenital malformations in Axenfeld-Rieger syndrome but do not disrupt left-right placement of visceral organs. Science.gov (United States) Ji, Yongchang; Buel, Sharleen M; Amack, Jeffrey D 2016-08-01 Pitx2 is a conserved homeodomain transcription factor that has multiple functions during embryonic development. Mutations in human PITX2 cause autosomal dominant Axenfeld-Rieger syndrome (ARS), characterized by congenital eye and tooth malformations. Pitx2(-/-) knockout mouse models recapitulate aspects of ARS, but are embryonic lethal. To date, ARS treatments remain limited to managing individual symptoms due to an incomplete understanding of PITX2 function. In addition to regulating eye and tooth development, Pitx2 is a target of a conserved Nodal (TGFβ) signaling pathway that mediates left-right (LR) asymmetry of visceral organs. Based on its highly conserved asymmetric expression domain, the Nodal-Pitx2 axis has long been considered a common denominator of LR development in vertebrate embryos. However, functions of Pitx2 during asymmetric organ morphogenesis are not well understood. To gain new insight into Pitx2 function we used genome editing to create mutations in the zebrafish pitx2 gene. Mutations in the pitx2 homeodomain caused phenotypes reminiscent of ARS, including aberrant development of the cornea and anterior chamber of the eye and reduced or absent teeth. Intriguingly, LR asymmetric looping of the heart and gut was normal in pitx2 mutants. These results suggest conserved roles for Pitx2 in eye and tooth development and indicate Pitx2 is not required for asymmetric looping of zebrafish visceral organs. This work establishes zebrafish pitx2 mutants as a new animal model for investigating mechanisms underlying congenital malformations in ARS and high-throughput drug screening for ARS therapeutics. Additionally, pitx2 mutants present a unique opportunity to identify new genes involved in vertebrate LR patterning. We show Nodal signaling-independent of Pitx2-controls asymmetric expression of the fatty acid elongase elovl6 in zebrafish, pointing to a potential novel pathway during LR organogenesis. Copyright © 2016 Elsevier Inc. All rights reserved. 7. Flavour changing decays of Z0 in supersymmetric models International Nuclear Information System (INIS) Gamberini, G.; Ridolfi, G. 1987-01-01 The possible existence of detectable flavour-changing branching modes of the Z 0 boson is examined in the context of supersymmetric models of currrent interest. An explicit calculation shows that in the so-called minimal version of the supersymmetric standard model the branching ratios for Z 0 →banti s or tanti c are not larger than in the standard model itself and are as such unobservable. On the contrary, we find that in a recently proposed extension of the supersymmetric standard model the mode Z 0 →tanti c may be at the order of being detectable. (orig.) 8. Supersymmetric sigma models and composite Yang-Mills theory International Nuclear Information System (INIS) Lukierski, J. 1980-04-01 We describe two types of supersymmetric sigma models: with field values in supercoset space and with superfields. The notion of Riemannian symmetric pair (H,G/H) is generalized to supergroups. Using the supercoset approach the superconformal-invariant model of composite U(n) Yang-Mills fields in introduced. In the framework of the superfield approach we present with some details two versions of the composite N=1 supersymmetric Yang-Mills theory in four dimensions with U(n) and U(m) x U(n) local invariance. We argue that especially the superfield sigma models can be used for the description of pre-QCD supersymmetric dynamics. (author) 9. Pseudoclassical supersymmetrical model for 2+1 Dirac particle OpenAIRE Gitman, D. M.; Gonçalves, A. E.; Tyutin, I. V. 1996-01-01 A new pseudoclassical supersymmetrical model of a spinning particle in 2+1 dimensions is proposed. Different ways of its quantization are discussed. They all reproduce the minimal quantum theory of the particle. 10. Lepton radiative decays in supersymmetric standard model International Nuclear Information System (INIS) Volkov, G.G.; Liparteliani, A.G. 1988-01-01 Radiative decays of charged leptons l i →l j γ(γ ) have been discussed in the framework of the supersymmetric generalization of the standard model. The most general form of the formfactors for the one-loop vertex function is written. Decay widths of the mentioned radiative decays are calculated. Scalar lepton masses are estimated at the maximal mixing angle in the scalar sector proceeding from the present upper limit for the branching of the decay μ→eγ. In case of the maximal mixing angle and the least mass degeneration of scalar leptons of various generations the following lower limit for the scalar electron mass m e-tilde >1.5 TeV has been obtained. The mass of the scalar neutrino is 0(1) TeV, in case the charged calibrino is lighter than the scalar neutrino. The result obtained sensitive to the choice of the lepton mixing angle in the scalar sector, namely, in decreasing the value sin 2 θ by an order of magnitude, the limitation on the scalar electron mass may decrease more than 3 times. In the latter case the direct observation of electrons at the e + e - -collider (1x1 TeV) becomes available 11. Left-right symmetric superstring supergravitation International Nuclear Information System (INIS) Burova, M.V.; Ter-Martirosyan, K.E. 1988-01-01 A left-right (L-R) symmetric model of four-dimensional supergravitation with a SO(10) gauge group obtained as the low-energy limit is superstring theory is considered. The spectrum of the gauge fields and their interactions are in agreement with the Weinberg-Salam theory. In addition, the model includes heavy W R ± and Z μ ' bosons. Beside the N g =3 generations of the 16-plets the SO(10) model includes the fragments of such generations which play the role of Higgs particles and also scalar chiral filds, the number of which exceeds by one the number of generations. As a result the neutrinos of each generation obtain a stable small Majorana mass. It is shown that the scalar field potential leads to spontaneous violation of the SU(2) R group and L-R symmetry and at low energies the standard Weinberg-Salam theory appears. However, reasonable values of X bosons masses M x and sun 2 Θ W (Θ W is the Weinberg angle) can be obtained in the model only in the case of high mass scale M R ∼10 10 -10 12 GeV of the right group SU(2) R violation 12. Precision calculations in supersymmetric extensions of the Standard Model International Nuclear Information System (INIS) Slavich, P. 2013-01-01 This dissertation is organized as follows: in the next chapter I will summarize the structure of the supersymmetric extensions of the standard model (SM), namely the MSSM (Minimal Supersymmetric Standard Model) and the NMSSM (Next-to-Minimal Supersymmetric Standard Model), I will provide a brief overview of different patterns of SUSY (supersymmetry) breaking and discuss some issues on the renormalization of the input parameters that are common to all calculations of higher-order corrections in SUSY models. In chapter 3 I will review and describe computations on the production of MSSM Higgs bosons in gluon fusion. In chapter 4 I will review results on the radiative corrections to the Higgs boson masses in the NMSSM. In chapter 5 I will review the calculation of BR(B → X s γ in the MSSM with Minimal Flavor Violation (MFV). Finally, in chapter 6 I will briefly summarize the outlook of my future research. (author) 13. Left Right Patterning, Evolution and Cardiac Development Science.gov (United States) Dykes, Iain M. 2018-01-01 Many aspects of heart development are determined by the left right axis and as a result several congenital diseases have their origins in aberrant left-right patterning. Establishment of this axis occurs early in embryogenesis before formation of the linear heart tube yet impacts upon much later morphogenetic events. In this review I discuss the differing mechanisms by which left-right polarity is achieved in the mouse and chick embryos and comment on the evolution of this system. I then discus three major classes of cardiovascular defect associated with aberrant left-right patterning seen in mouse mutants and human disease. I describe phenotypes associated with the determination of atrial identity and venous connections, looping morphogenesis of the heart tube and finally the asymmetric remodelling of the embryonic branchial arch arterial system to form the leftward looped arch of aorta and associated great arteries. Where appropriate, I consider left right patterning defects from an evolutionary perspective, demonstrating how developmental processes have been modified in species over time and illustrating how comparative embryology can aide in our understanding of congenital heart disease. PMID:29755990 14. A Specific N=2 Supersymmetric Quantum Mechanical Model: Supervariable Approach Directory of Open Access Journals (Sweden) 2017-01-01 Full Text Available By exploiting the supersymmetric invariant restrictions on the chiral and antichiral supervariables, we derive the off-shell nilpotent symmetry transformations for a specific (0 + 1-dimensional N=2 supersymmetric quantum mechanical model which is considered on a (1, 2-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables (θ,θ¯. We also provide the geometrical meaning to the symmetry transformations. Finally, we show that this specific N=2 SUSY quantum mechanical model is a model for Hodge theory. 15. Thermal leptogenesis in a supersymmetric neutrinophilic Higgs model International Nuclear Information System (INIS) Haba, Naoyuki; Seto, Osamu 2011-01-01 We investigate thermal leptogenesis in a supersymmetric neutrinophilic Higgs model by taking phenomenological constraints into account, where, in addition to the minimal supersymmetric standard model, we introduce an extra Higgs field with a tiny vacuum expectation value which generates neutrino masses. Thanks to this tiny vacuum expectation value of the neutrinophilic Higgs, our model allows us to reduce the mass of the lightest right-handed (s)neutrino to be O(10 5 ) GeV, keeping sufficiently large CP asymmetry in its decay. Therefore, the reheating temperature after inflation is not necessarily high; hence this scenario is free from the gravitino problem. 16. Exterior calculus and two-dimensional supersymmetric models International Nuclear Information System (INIS) Sciuto, S. 1980-01-01 An important property of the calculus of differential forms on superspace is pointed out, and an economical way to treat the linear problem associated with certain supersymmetric two-dimensional models is discussed. A generalization of the super sine-Gordon model is proposed; its bosonic limit is a new model whose associate linear set has an SU(3) structure. (orig.) 17. Predictions for mt and MW in minimal supersymmetric models International Nuclear Information System (INIS) Buchmueller, O.; Ellis, J.R.; Flaecher, H.; Isidori, G. 2009-12-01 Using a frequentist analysis of experimental constraints within two versions of the minimal supersymmetric extension of the Standard Model, we derive the predictions for the top quark mass, m t , and the W boson mass, m W . We find that the supersymmetric predictions for both m t and m W , obtained by incorporating all the relevant experimental information and state-of-the-art theoretical predictions, are highly compatible with the experimental values with small remaining uncertainties, yielding an improvement compared to the case of the Standard Model. (orig.) 18. Dark matter, constrained minimal supersymmetric standard model, and lattice QCD. Science.gov (United States) Giedt, Joel; Thomas, Anthony W; Young, Ross D 2009-11-13 Recent lattice measurements have given accurate estimates of the quark condensates in the proton. We use these results to significantly improve the dark matter predictions in benchmark models within the constrained minimal supersymmetric standard model. The predicted spin-independent cross sections are at least an order of magnitude smaller than previously suggested and our results have significant consequences for dark matter searches. 19. 90 - GeV Higgs boson in supersymmetric models International Nuclear Information System (INIS) Grzadkowski, B.; Kalinowski, J.; Pokorski, S. 1989-07-01 We discuss supersymmetric models with a hierarchy of vacuum expectation values of Higgs fields. These models predict one of the physical neutral Higgs bosons to have its mass very close to the Z-boson mass. Properties of such a 90-GeV Higgs boson are discussed. (author) 20. Left-right gauge symmetry breaking by radiative corrections in supergravity International Nuclear Information System (INIS) Moxhay, P.; Yamamoto, K. 1984-01-01 A supersymmetric SU(2)sub(L) x SU(2)sub(R) x U(1)sub(B-L) gauge theory coupled to N = 1 supergravity is investigated. The scale of left-right gauge symmetry breaking is determined as Msub(R) proportional Msub(P) esup(-1/α) by radiative corrections through the logarithmic evolution of soft supersymmetry breakings. SU(2)sub(L) x SU(2)sub(R) x U(1)sub(B-L) may be embedded in SO(10) grand unification. Cosmological implications intrinsic to the present model are also discussed, which may give a constraint Msub(R) approx.= 10 9-12 GeV. (orig.) 1. Left-right correlation in coupled F-center defects. Science.gov (United States) Janesko, Benjamin G 2016-08-07 This work explores how left-right correlation, a textbook problem in electronic structure theory, manifests in a textbook example of electrons trapped in crystal defects. I show that adjacent F-center defects in lithium fluoride display symptoms of "strong" left-right correlation, symptoms similar to those seen in stretched H2. Simulations of UV/visible absorption spectra qualitatively fail to reproduce experiment unless left-right correlation is taken into account. This is of interest to both the electronic structure theory and crystal-defect communities. Theorists have a new well-behaved system to test their methods. Crystal-defect groups are cautioned that the approximations that successfully model single F-centers may fail for adjacent F-centers. 2. Left-right correlation in coupled F-center defects International Nuclear Information System (INIS) Janesko, Benjamin G. 2016-01-01 This work explores how left-right correlation, a textbook problem in electronic structure theory, manifests in a textbook example of electrons trapped in crystal defects. I show that adjacent F-center defects in lithium fluoride display symptoms of “strong” left-right correlation, symptoms similar to those seen in stretched H 2 . Simulations of UV/visible absorption spectra qualitatively fail to reproduce experiment unless left-right correlation is taken into account. This is of interest to both the electronic structure theory and crystal-defect communities. Theorists have a new well-behaved system to test their methods. Crystal-defect groups are cautioned that the approximations that successfully model single F-centers may fail for adjacent F-centers. 3. Charged and neutral minimal supersymmetric standard model Higgs ... physics pp. 759–763. Charged and neutral minimal supersymmetric standard model Higgs boson decays and measurement of tan β at the compact linear collider. E CONIAVITIS and A FERRARI∗. Department of Nuclear and Particle Physics, Uppsala University, 75121 Uppsala, Sweden. ∗E-mail: [email protected]. Abstract. 4. Impact of the muon anomalous magnetic moment on supersymmetric models International Nuclear Information System (INIS) Baer, Howard; Balazs, Csaba; Ferrandis, Javier; Tata, Xerxes 2001-01-01 The recent measurement of a μ =(g μ -2)/2 by the E821 Collaboration at Brookhaven deviates from the quoted standard model (SM) central value prediction by 2.6σ. The difference between SM theory and experiment may be easily accounted for in a variety of particle physics models employing weak scale supersymmetry (SUSY). Other supersymmetric models are distinctly disfavored. We evaluate a μ for various supersymmetric models, including minimal supergravity, Yukawa unified SO(10) SUSY GUT's, models with inverted mass hierarchies, models with nonuniversal gaugino masses, gauge mediated SUSY breaking models, anomaly-mediated SUSY breaking models and models with gaugino mediated SUSY breaking. Models with Yukawa coupling unification or multi-TeV first and second generation scalars are disfavored by the a μ measurement 5. Left-right subtraction of brain CT International Nuclear Information System (INIS) 1986-01-01 A new image-processing method to obtain a left-right subtraction image of CT was designed for the automated detection of abnormalities in brain CT. An original CT image was divided in two by a centerline. Then the right half of the image was subtracted from the left half by calculating the absorption value of the pixels on the symmetrical positions against the centerline. The mean and the standard deviation of the absorption value of the pixels in the subtraction image were used as parameters for analysis, and the detectability of abnormal CT findings was evaluated in 100 cases - 50 cases each with normal and abnormal CT. The presence of abnormalities could be diagnosed with a sensitivity of 86 %, a specificity of 90 %, and an overall accuracy of 88 % when the borderline of these parameters between normal and abnormal CT was set at the mean + 2SD in the normal group. As a further analysis, the CT image was subdivided into several areas from a functional or anatomical viewpoint, such as cerebral vascular territories, and the left-right subtraction image of each area was obtained. The possibilities of diagnosing the location of an abnormality and of detecting smaller lesions with this method were shown. Left-right subtraction was considered to be a useful method for the detection of asymmetric abnormalities in the automated diagnosis of brain CT. (author) 6. Complete integrability of the supersymmetric (cos phi)2 model International Nuclear Information System (INIS) Kulish, P.P.; Tsyplyaev, S.A. 1987-01-01 Complete integrability of the supersymmetric two-dimensional sine-Gordon field-theoretical model is proved in the framework of the Hamiltonian interpretation of the inverse problem method. The classical r-matrix of this model is computed and shown to be equivalent to the r-matrix of the Grassmann Thirring model. Creation-annihilation variables are constructed and the elementary excitation spectrum is determined 7. Supersymmetric standard model from the heterotic string (II) International Nuclear Information System (INIS) Buchmueller, W.; Hamaguchi, K.; Tokyo Univ.; Lebedev, O.; Ratz, M. 2006-06-01 We describe in detail a Z 6 orbifold compactification of the heterotic E 8 x E 8 string which leads to the (supersymmetric) standard model gauge group and matter content. The quarks and leptons appear as three 16-plets of SO(10), two of which are localized at fixed points with local SO(10) symmetry. The model has supersymmetric vacua without exotics at low energies and is consistent with gauge coupling unification. Supersymmetry can be broken via gaugino condensation in the hidden sector. The model has large vacuum degeneracy. Certain vacua with approximate B-L symmetry have attractive phenomenological features. The top quark Yukawa coupling arises from gauge interactions and is of the order of the gauge couplings. The other Yukawa couplings are suppressed by powers of standard model singlet fields, similarly to the Froggatt-Nielsen mechanism. (Orig.) 8. SCYNet. Testing supersymmetric models at the LHC with neural networks Energy Technology Data Exchange (ETDEWEB) Bechtle, Philip; Belkner, Sebastian; Hamer, Matthias [Universitaet Bonn, Bonn (Germany); Dercks, Daniel [Universitaet Hamburg, Hamburg (Germany); Keller, Tim; Kraemer, Michael; Sarrazin, Bjoern; Schuette-Engel, Jan; Tattersall, Jamie [RWTH Aachen University, Institute for Theoretical Particle Physics and Cosmology, Aachen (Germany) 2017-10-15 SCYNet (SUSY Calculating Yield Net) is a tool for testing supersymmetric models against LHC data. It uses neural network regression for a fast evaluation of the profile likelihood ratio. Two neural network approaches have been developed: one network has been trained using the parameters of the 11-dimensional phenomenological Minimal Supersymmetric Standard Model (pMSSM-11) as an input and evaluates the corresponding profile likelihood ratio within milliseconds. It can thus be used in global pMSSM-11 fits without time penalty. In the second approach, the neural network has been trained using model-independent signature-related objects, such as energies and particle multiplicities, which were estimated from the parameters of a given new physics model. (orig.) 9. Quasicomplex N=2, d=1 Supersymmetric Sigma Models Directory of Open Access Journals (Sweden) Evgeny A. Ivanov 2013-11-01 Full Text Available We derive and discuss a new type of N=2 supersymmetric quantum mechanical sigma models which appear when the superfield action of the (1,2,1 multiplets is modified by adding an imaginary antisymmetric tensor to the target space metric, thus completing the latter to a non-symmetric Hermitian metric. These models are not equivalent to the standard de Rham sigma models, but are related to them through a certain special similarity transformation of the supercharges. On the other hand, they can be obtained by a Hamiltonian reduction from the complex supersymmetric N=2 sigma models built on the multiplets (2,2,0 and describing the Dolbeault complex on the manifolds with proper isometries. We study in detail the extremal two-dimensional case, when the target space metric is defined solely by the antisymmetric tensor, and show that the corresponding quantum systems reveal a hidden N=4 supersymmetry. 10. Higgs detectability in the extended supersymmetric standard model International Nuclear Information System (INIS) Kamoshita, Jun-ichi 1995-01-01 Higgs detectability at a future linear collider are discussed in the minimal supersymmetric standard model (MSSM) and a supersymmetric standard model with a gauge singlet Higgs field (NMSSM). First, in the MSSM at least one of the neutral scalar Higgs is shown to be detectable irrespective of parameters of the model in a future e + e - linear collider at √s = 300-500 GeV. Next the Higgs sector of the NMSSM is considered, since the lightest Higgs boson can be singlet dominated and therefore decouple from Z 0 boson it is important to consider the production of heavier Higgses. It is shown that also in this case at least one of the neutral scalar Higgs will be detectable in a future linear collider. We extend the analysis and show that the same is true even if three singlets are included. Thus the detectability of these Higgs bosons of these models is guaranteed. (author) 11. Supersymmetric composite models on intersecting D-branes International Nuclear Information System (INIS) Kitazawa, Noriaki 2004-01-01 We construct supersymmetric composite models of quarks and leptons from type IIA T6/(Z2xZ2) orientifold with intersecting D6-branes. In case of T6=T2xT2xT2 with no tilted T2, a composite model of supersymmetric SU(5) grand unified theory with four generations is constructed. In case of that one T2 is tilted, a composite model with SU(3)cxSU(2)LxU(1)Y gauge symmetry with three generations of left-handed quarks and leptons is constructed. These models are not realistic, but contain relatively fewer additional exotic particles and U(1) gauge symmetries due to the introduction of the compositeness of quarks and leptons. The masses of some exotic particles are naturally generated through the Yukawa interactions among 'preons' 12. Supersymmetric U(1)' model with multiple dark matters International Nuclear Information System (INIS) Hur, Taeil; Lee, Hye-Sung; Nasri, Salah 2008-01-01 We consider a scenario where a supersymmetric model has multiple dark matter particles. Adding a U(1) ' gauge symmetry is a well-motivated extension of the minimal supersymmetric standard model (MSSM). It can cure the problems of the MSSM such as the μ problem or the proton decay problem with high-dimensional lepton number and baryon number violating operators which R parity allows. An extra parity (U parity) may arise as a residual discrete symmetry after U(1) ' gauge symmetry is spontaneously broken. The lightest U-parity particle (LUP) is stable under the new parity becoming a new dark matter candidate. Up to three massive particles can be stable in the presence of the R parity and the U parity. We numerically illustrate that multiple stable particles in our model can satisfy both constraints from the relic density and the direct detection, thus providing a specific scenario where a supersymmetric model has well-motivated multiple dark matters consistent with experimental constraints. The scenario provides new possibilities in the present and upcoming dark matter searches in the direct detection and collider experiments 13. Spontaneously broken abelian gauge invariant supersymmetric model International Nuclear Information System (INIS) Mainland, G.B.; Tanaka, K. A model is presented that is invariant under an Abelian gauge transformation and a modified supersymmetry transformation. This model is broken spontaneously, and the interplay between symmetry breaking, Goldstone particles, and mass breaking is studied. In the present model, spontaneously breaking the Abelian symmetry of the vacuum restores the invariance of the vacuum under a modified supersymmetry transformation. (U.S.) 14. Exploring the supersymmetric U(1 ) B -L×U(1 ) R model with dark matter, muon g - 2 , and Z' mass limits Science.gov (United States) Frank, Mariana; Özdal, Özer 2018-01-01 We study the low scale predictions of the supersymmetric standard model extended by U (1 )B -L×U (1 )R symmetry, obtained from S O (10 ) breaking via a left-right supersymmetric model, imposing universal boundary conditions. Two singlet Higgs fields are responsible for the radiative U (1 )B -L×U (1 )R symmetry breaking, and a singlet fermion S is introduced to generate neutrino masses through an inverse seesaw mechanism. The lightest neutralino or sneutrino emerge as dark matter candidates, with different low scale implications. We find that the composition of the neutralino lightest supersymmetric particle (LSP) changes considerably depending on the neutralino LSP mass, from roughly half U (1 )R bino, half minimal supersymmetric model (MSSM) bino, to a singlet higgsino, or completely dominated by the MSSM higgsino. The sneutrino LSP is statistically much less likely, and when it occurs it is a 50-50 mixture of right-handed sneutrino and the scalar S ˜. Most of the solutions consistent with the relic density constraint survive the XENON 1T exclusion curve for both LSP cases. We compare the two scenarios and investigate parameter space points and find consistency with the muon anomalous magnetic moment only at the edge of a 2 σ deviation from the measured value. However, we find that the sneutrino LSP solutions could be ruled out completely by the strict reinforcement of the recent Z' mass bounds. We finally discuss collider prospects for testing the model. 15. Supersymmetric models of weak and electromagnetic interactions International Nuclear Information System (INIS) Egoryan, Eh.; Slavnov, A.A. 1978-01-01 Examples of realistic supergauge lepton models based on the SU(2)xU(1) and SU(2)xSU(2)xU(1) groups are considered. These models do not contradict to up-to-date experimental data, give a natural explanation for the Higgs mechanism and predict the existence of heavy leptons. The first model predicts the conservation of parity, the second one predicts parity breaking in atomic processes 16. Flipped version of the supersymmetric strongly coupled preon model Energy Technology Data Exchange (ETDEWEB) Fajfer, S. (Institut za Fiziku, University of Sarajevo, Sarajevo, (Yugoslavia)); Milekovic, M.; Tadic, D. (Zavod za Teorijsku Fiziku, Prirodoslovno-Matematicki Fakultet, University of Zagreb, Croatia, (Yugoslavia)) 1989-12-01 In the supersymmetric SU(5) (SUSY SU(5)) composite model (which was described in an earlier paper) the fermion mass terms can be easily constructed. The SUSY SU(5){direct product}U(1), i.e., flipped, composite model possesses a completely analogous composite-particle spectrum. However, in that model one cannot construct a renormalizable superpotential which would generate fermion mass terms. This contrasts with the standard noncomposite grand unified theories (GUT's) in which both the Georgi-Glashow electrical charge embedding and its flipped counterpart lead to the renormalizable theories. 17. Required experimental accuracy to select between supersymmetrical models Science.gov (United States) Grellscheid, David 2004-03-01 We will present a method to decide a priori whether various supersymmetrical scenarios can be distinguished based on sparticle mass data alone. For each model, a scan over all free SUSY breaking parameters reveals the extent of that model's physically allowed region of sparticle-mass-space. Based on the geometrical configuration of these regions in mass-space, it is possible to obtain an estimate of the required accuracy of future sparticle mass measurements to distinguish between the models. We will illustrate this algorithm with an example. This talk is based on work done in collaboration with B C Allanach (LAPTH, Annecy) and F Quevedo (DAMTP, Cambridge). 18. ATLAS Z Excess in Minimal Supersymmetric Standard Model International Nuclear Information System (INIS) 2015-06-01 Recently the ATLAS collaboration reported a 3 sigma excess in the search for the events containing a dilepton pair from a Z boson and large missing transverse energy. Although the excess is not sufficiently significant yet, it is quite tempting to explain this excess by a well-motivated model beyond the standard model. In this paper we study a possibility of the minimal supersymmetric standard model (MSSM) for this excess. Especially, we focus on the MSSM spectrum where the sfermions are heavier than the gauginos and Higgsinos. We show that the excess can be explained by the reasonable MSSM mass spectrum. 19. A review of Higgs mass calculations in supersymmetric models DEFF Research Database (Denmark) Draper, P.; Rzehak, H. 2016-01-01 The discovery of the Higgs boson is both a milestone achievement for the Standard Model and an exciting probe of new physics beyond the SM. One of the most important properties of the Higgs is its mass, a number that has proven to be highly constraining for models of new physics, particularly those...... related to the electroweak hierarchy problem. Perhaps the most extensively studied examples are supersymmetric models, which, while capable of producing a 125 GeV Higgs boson with SM-like properties, do so in non-generic parts of their parameter spaces. We review the computation of the Higgs mass... 20. Examining a renormalizable supersymmetric SO(10) model Energy Technology Data Exchange (ETDEWEB) Chen, Zhi-Yong; Zhang, Da-Xin [Peking University, School of Physics and State Key Laboratory of Nuclear Physics and Technology, Beijing (China) 2017-10-15 We examine a renormalizable SUSY SO(10) model without fine-tuning. We show how to construct MSSM doublets and to predict proton decay. We find that in the minimal set of Yukawa couplings the model is consistent with the experiments, while including 120{sub H} to fit the data there are inconsistencies. (orig.) 1. One-scale supersymmetric inflationary models International Nuclear Information System (INIS) Bertolami, O.; Ross, G.G. 1986-01-01 The reheating phase is studied in a class of supergravity inflationary models involving a two-component hidden sector in which the scale of supersymmetry breaking and the scale generating inflation are related. It is shown that these models have an ''entropy crisis'' in which there is a large entropy release after nucleosynthesis leading to unacceptable low nuclear abundances. (orig.) 2. Supersymmetric sigma models and the heterotic string International Nuclear Information System (INIS) Hull, C.M.; Witten, E. 1989-01-01 The authors define the (1 + 1)-dimensional supersymmetry algebra of type (p, q) to be that generated by p right-handed Majorana-Weyl supercharges and q left-handed ones. They construct the non-linear sigma models with supersymmetry of type (1, 0) and (2, 0) and discuss their geometry and their relevance to compactifications of the heterotic superstring. The sigma-model anomalies can be canceled by a mechanism closely related to that used by Green and Schwarz to cancel gravitational and Yang-Mills anomalies for the superstring 3. On radiative gauge symmetry breaking in the minimal supersymmetric model International Nuclear Information System (INIS) Gamberini, G.; Ridolfi, G.; Zwirner, F. 1990-01-01 We present a critical reappraisal of radiative gauge symmetry breaking in the minimal supersymmetric standard model. We show that a naive use of the renormalization group improved tree-level potential can lead to incorrect conclusions. We specify the conditions under which the above method gives reliable results, by performing a comparison with the results obtained from the full one-loop potential. We also point out how the stability constraint and the conditions for the absence of charge- and colour-breaking minima should be applied. Finally, we comment on the uncertainties affecting the model predictions for physical observables, in particular for the top quark mass. (orig.) 4. Constraints on supersymmetric models from the muon anomalous magnetic moment International Nuclear Information System (INIS) Carena, M.; Giudice, G.F.; Wagner, C.E.M. 1996-10-01 We study the impact of present and future (g - 2) μ measurements on supersymmetric models. The corrections to (g - 2) μ become particularly relevant in the presence of light sleptons, charginos and neutralinos, especially in the large tan β regime. For moderate or large values of tan β, it is possible to rule out scenarios in which charginos and sneutrinos are both light, but nevertheless escape detection at the LEP2 collider. Furthermore, models in which supersymmetry breaking is transferred to the observable sector through gauge interactions can be efficiently constrained by the (g - 2) μ measurement. (orig.) 5. Charge and color breaking minima in supersymmetric models International Nuclear Information System (INIS) Brhlik, Michal 2001-01-01 Supersymmetric extensions of the Standard Model include complicated scalar sectors leading to the possible occurrence of non-standard minima along suitable directions in the field space. These minima usually break charge and/or color and their presence in the theory would require an explanation why the universe has settled in the standard electroweak symmetry breaking minimum. In this talk I illustrate the relevance of the charge and color breaking minima in the framework of the minimal supergravity model and a string motivated Horava-Witten scenario 6. Phenomenology of non-minimal supersymmetric models at linear colliders International Nuclear Information System (INIS) Porto, Stefano 2015-06-01 The focus of this thesis is on the phenomenology of several non-minimal supersymmetric models in the context of future linear colliders (LCs). Extensions of the minimal supersymmetric Standard Model (MSSM) may accommodate the observed Higgs boson mass at about 125 GeV in a more natural way than the MSSM, with a richer phenomenology. We consider both F-term extensions of the MSSM, as for instance the non-minimal supersymmetric Standard Model (NMSSM), as well as D-terms extensions arising at low energies from gauge extended supersymmetric models. The NMSSM offers a solution to the μ-problem with an additional gauge singlet supermultiplet. The enlarged neutralino sector of the NMSSM can be accurately studied at a LC and used to distinguish the model from the MSSM. We show that exploiting the power of the polarised beams of a LC can be used to reconstruct the neutralino and chargino sector and eventually distinguish the NMSSM even considering challenging scenarios that resemble the MSSM. Non-decoupling D-terms extensions of the MSSM can raise the tree-level Higgs mass with respect to the MSSM. This is done through additional contributions to the Higgs quartic potential, effectively generated by an extended gauge group. We study how this can happen and we show how these additional non-decoupling D-terms affect the SM-like Higgs boson couplings to fermions and gauge bosons. We estimate how the deviations from the SM couplings can be spotted at the Large Hadron Collider (LHC) and at the International Linear Collider (ILC), showing how the ILC would be suitable for the model identication. Since our results prove that a linear collider is a fundamental machine for studying supersymmetry phenomenology at a high level of precision, we argue that also a thorough comprehension of the physics at the interaction point (IP) of a LC is needed. Therefore, we finally consider the possibility of observing intense electromagnetic field effects and nonlinear quantum electrodynamics 7. Left-right symmetry, mixing and CP violation in B0 - B-bar0 International Nuclear Information System (INIS) Ecker, G.; Grimus, W. 1986-01-01 We discuss B 0 - B-bar 0 mixing and CP violation in the minimal left-right symmetric model. While the amount of mixing is not much changed with respect to the standard model, left-right symmtery can give rise to significantly larger CP violation in the B 0 sub(s) - B-bar 0 sub(s) system. (Author) 8. Electroweak symmetry breaking in supersymmetric gauge-Higgs unification models International Nuclear Information System (INIS) Choi, Kiwoon; Jeong, Kwang-Sik; Okumura, Ken-ichi; Haba, Naoyuki; Shimizu, Yasuhiro; Yamaguchi, Masahiro 2004-01-01 We examine the Higgs mass parameters and electroweak symmetry breaking in supersymmetric orbifold field theories in which the 4-dimensional Higgs fields originate from higher-dimensional gauge supermultiplets. It is noted that such gauge-Higgs unification leads to a specific boundary condition on the Higgs mass parameters at the compactification scale, which is independent of the details of supersymmetry breaking mechanism. With this boundary condition, phenomenologically viable parameter space of the model is severely constrained by the condition of electroweak symmetry breaking for supersymmetry breaking scenarios which can be realized naturally in orbifold field theories. For instance, if it is assumed that the 4-dimensional effective theory is the minimal supersymmetric standard model with supersymmetry breaking parameters induced by the Scherk-Schwarz mechanism, a correct electroweak symmetry breaking can not be achieved for reasonable range of parameters of the model, even when one includes additional contributions to the Higgs mass parameters from the auxiliary component of 4-dimensional conformal compensator. However if there exists a supersymmetry breaking mediated by brane superfields, sizable portion of the parameter space can give a correct electroweak symmetry breaking. (author) 9. Investigating multiple solutions in the constrained minimal supersymmetric standard model Energy Technology Data Exchange (ETDEWEB) Allanach, B.C. [DAMTP, CMS, University of Cambridge,Wilberforce Road, Cambridge, CB3 0HA (United Kingdom); George, Damien P. [DAMTP, CMS, University of Cambridge,Wilberforce Road, Cambridge, CB3 0HA (United Kingdom); Cavendish Laboratory, University of Cambridge,JJ Thomson Avenue, Cambridge, CB3 0HE (United Kingdom); Nachman, Benjamin [SLAC, Stanford University,2575 Sand Hill Rd, Menlo Park, CA 94025 (United States) 2014-02-07 Recent work has shown that the Constrained Minimal Supersymmetric Standard Model (CMSSM) can possess several distinct solutions for certain values of its parameters. The extra solutions were not previously found by public supersymmetric spectrum generators because fixed point iteration (the algorithm used by the generators) is unstable in the neighbourhood of these solutions. The existence of the additional solutions calls into question the robustness of exclusion limits derived from collider experiments and cosmological observations upon the CMSSM, because limits were only placed on one of the solutions. Here, we map the CMSSM by exploring its multi-dimensional parameter space using the shooting method, which is not subject to the stability issues which can plague fixed point iteration. We are able to find multiple solutions where in all previous literature only one was found. The multiple solutions are of two distinct classes. One class, close to the border of bad electroweak symmetry breaking, is disfavoured by LEP2 searches for neutralinos and charginos. The other class has sparticles that are heavy enough to evade the LEP2 bounds. Chargino masses may differ by up to around 10% between the different solutions, whereas other sparticle masses differ at the sub-percent level. The prediction for the dark matter relic density can vary by a hundred percent or more between the different solutions, so analyses employing the dark matter constraint are incomplete without their inclusion. 10. New aspects of flavour model building in supersymmetric grand unification International Nuclear Information System (INIS) Spinrath, Martin 2010-01-01 We derive predictions for Yukawa coupling ratios within Grand Unified Theories generated from operators with mass dimension four and five. These relations are a characteristic property of unified flavour models and can reduce the large number of free parameters related to the flavour sector of the Standard Model. The Yukawa couplings of the down-type quarks and charged leptons are affected within supersymmetric models by tan β-enhanced threshold corrections which can be sizeable if tan β is large. In this case their careful inclusion in the renormalisation group evolution is mandatory. We analyse these corrections and give simple analytic expressions and numerical estimates for them. The threshold corrections sensitively depend on the soft supersymmetry breaking parameters. Especially, they determine the overall sign of the corrections and therefore if the affected Yukawa couplings are enhanced or suppressed. In the minimal supersymmetric extension of the Standard Model many free parameters are introduced by supersymmetry breaking about which we make some plausible assumptions in our first simplified approach. In a second, more sophisticated approach we use three common breaking schemes in which all the soft breaking parameters at the electroweak scale can be calculated from only a handful of parameters. Within the second approach, we apply various phenomenological constraints on the supersymmetric parameters and find in this way new viable Yukawa coupling relations, for example y μ /y s =9/2 or 6 or y τ /y b =3/2 in SU(5). Furthermore, we study a special class of quark mass matrix textures for small tan β where θ u 13 =θ d 13 =0. We derive sum rules for the quark mixing parameters and find a simple relation between the two phases δ u 12 and δ d 12 and the right unitarity triangle angle α which suggests a simple phase structure for the quark mass matrices where one matrix element is purely imaginary and the remaining ones are purely real. To complement 11. New aspects of flavour model building in supersymmetric grand unification Energy Technology Data Exchange (ETDEWEB) Spinrath, Martin 2010-05-19 We derive predictions for Yukawa coupling ratios within Grand Unified Theories generated from operators with mass dimension four and five. These relations are a characteristic property of unified flavour models and can reduce the large number of free parameters related to the flavour sector of the Standard Model. The Yukawa couplings of the down-type quarks and charged leptons are affected within supersymmetric models by tan {beta}-enhanced threshold corrections which can be sizeable if tan {beta} is large. In this case their careful inclusion in the renormalisation group evolution is mandatory. We analyse these corrections and give simple analytic expressions and numerical estimates for them. The threshold corrections sensitively depend on the soft supersymmetry breaking parameters. Especially, they determine the overall sign of the corrections and therefore if the affected Yukawa couplings are enhanced or suppressed. In the minimal supersymmetric extension of the Standard Model many free parameters are introduced by supersymmetry breaking about which we make some plausible assumptions in our first simplified approach. In a second, more sophisticated approach we use three common breaking schemes in which all the soft breaking parameters at the electroweak scale can be calculated from only a handful of parameters. Within the second approach, we apply various phenomenological constraints on the supersymmetric parameters and find in this way new viable Yukawa coupling relations, for example y{sub {mu}}/y{sub s}=9/2 or 6 or y{sub {tau}}/y{sub b}=3/2 in SU(5). Furthermore, we study a special class of quark mass matrix textures for small tan {beta} where {theta}{sup u}{sub 13}={theta}{sup d}{sub 13}=0. We derive sum rules for the quark mixing parameters and find a simple relation between the two phases {delta}{sup u}{sub 12} and {delta}{sup d}{sub 12} and the right unitarity triangle angle {alpha} which suggests a simple phase structure for the quark mass matrices where 12. Nucleon electric dipole moments in high-scale supersymmetric models International Nuclear Information System (INIS) Hisano, Junji; Kobayashi, Daiki; Kuramoto, Wataru; Kuwahara, Takumi 2015-01-01 The electric dipole moments (EDMs) of electron and nucleons are promising probes of the new physics. In generic high-scale supersymmetric (SUSY) scenarios such as models based on mixture of the anomaly and gauge mediations, gluino has an additional contribution to the nucleon EDMs. In this paper, we studied the effect of the CP-violating gluon Weinberg operator induced by the gluino chromoelectric dipole moment in the high-scale SUSY scenarios, and we evaluated the nucleon and electron EDMs in the scenarios. We found that in the generic high-scale SUSY models, the nucleon EDMs may receive the sizable contribution from the Weinberg operator. Thus, it is important to compare the nucleon EDMs with the electron one in order to discriminate among the high-scale SUSY models. 13. Lepton Dipole Moments in Supersymmetric Low-Scale Seesaw Models CERN Document Server Ilakovac, Amon; Popov, Luka 2014-01-01 We study the anomalous magnetic and electric dipole moments of charged leptons in supersymmetric low-scale seesaw models with right-handed neutrino superfields. We consider a minimally extended framework of minimal supergravity, by assuming that CP violation originates from complex soft SUSY-breaking bilinear and trilinear couplings associated with the right-handed sneutrino sector. We present numerical estimates of the muon anomalous magnetic moment and the electron electric dipole moment (EDM), as functions of key model parameters, such as the Majorana mass scale mN and tan(\\beta). In particular, we find that the contributions of the singlet heavy neutrinos and sneutrinos to the electron EDM are naturally small in this model, of order 10^{-27} - 10^{-28} e cm, and can be probed in the present and future experiments. 14. Nucleon electric dipole moments in high-scale supersymmetric models Energy Technology Data Exchange (ETDEWEB) Hisano, Junji [Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI),Nagoya University,Nagoya 464-8602 (Japan); Department of Physics, Nagoya University,Nagoya 464-8602 (Japan); Kavli IPMU (WPI), UTIAS, University of Tokyo,Kashiwa, Chiba 277-8584 (Japan); Kobayashi, Daiki; Kuramoto, Wataru; Kuwahara, Takumi [Department of Physics, Nagoya University,Nagoya 464-8602 (Japan) 2015-11-12 The electric dipole moments (EDMs) of electron and nucleons are promising probes of the new physics. In generic high-scale supersymmetric (SUSY) scenarios such as models based on mixture of the anomaly and gauge mediations, gluino has an additional contribution to the nucleon EDMs. In this paper, we studied the effect of the CP-violating gluon Weinberg operator induced by the gluino chromoelectric dipole moment in the high-scale SUSY scenarios, and we evaluated the nucleon and electron EDMs in the scenarios. We found that in the generic high-scale SUSY models, the nucleon EDMs may receive the sizable contribution from the Weinberg operator. Thus, it is important to compare the nucleon EDMs with the electron one in order to discriminate among the high-scale SUSY models. 15. Neutron electric dipole moment in the minimal supersymmetric standard model International Nuclear Information System (INIS) Inui, T.; Mimura, Y.; Sakai, N.; Sasaki, T. 1995-01-01 The neutron electric dipole moment (EDM) due to the single quark EDM and to the transition EDM is calculated in the minimal supersymmetric standard model. Assuming that the Cabibbo-Kobayashi-Maskawa matrix at the grand unification scale is the only source of CP violation, complex phases are induced in the parameters of soft supersymmetry breaking at low energies. The chargino one-loop diagram is found to give the dominant contribution of the order of 10 -27 similar 10 -29 e.cm for the quark EDM, assuming the light chargino mass and the universal scalar mass to be 50 GeV and 100 GeV, respectively. Therefore the neutron EDM in this class of model is difficult to measure experimentally. The gluino one-loop diagram also contributes due to the flavor changing gluino coupling. The transition EDM is found to give dominant contributions for certain parameter regions. (orig.) 16. Anatomy of Higgs mass in supersymmetric inverse seesaw models Energy Technology Data Exchange (ETDEWEB) Chun, Eung Jin, E-mail: [email protected] [Korea Institute for Advanced Study, Seoul 130-722 (Korea, Republic of); Mummidi, V. Suryanarayana, E-mail: [email protected] [Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012 (India); Vempati, Sudhir K., E-mail: [email protected] [Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012 (India) 2014-09-07 We compute the one loop corrections to the CP-even Higgs mass matrix in the supersymmetric inverse seesaw model to single out the different cases where the radiative corrections from the neutrino sector could become important. It is found that there could be a significant enhancement in the Higgs mass even for Dirac neutrino masses of O(30) GeV if the left-handed sneutrino soft mass is comparable or larger than the right-handed neutrino mass. In the case where right-handed neutrino masses are significantly larger than the supersymmetry breaking scale, the corrections can utmost account to an upward shift of 3 GeV. For very heavy multi TeV sneutrinos, the corrections replicate the stop corrections at 1-loop. We further show that general gauge mediation with inverse seesaw model naturally accommodates a 125 GeV Higgs with TeV scale stops. 17. Electroweak symmetry breaking in supersymmetric models with heavy scalar superpartners International Nuclear Information System (INIS) Chankowski, Piotr H.; Falkowski, Adam; Pokorski, Stefan; Wagner, Jakub 2004-01-01 We propose a novel mechanism of electroweak symmetry breaking in supersymmetric models, as the one recently discussed by Birkedal, Chacko and Gaillard, in which the Standard Model Higgs doublet is a pseudo-Goldstone boson of some global symmetry. The Higgs mass parameter is generated at one-loop level by two different, moderately fine-tuned sources of the global symmetry breaking. The mechanism works for scalar superpartner masses of order 10 TeV, but gauginos can be light. The scale at which supersymmetry breaking is mediated to the visible sector has to be low, of order 100 TeV. Fine-tuning in the scalar potential is at least two orders of magnitude smaller than in the MSSM with similar soft scalar masses. The physical Higgs boson mass is (for tanβ >> 1) in the range 120-135 GeV 18. Supersymmetric quantum mechanics, spinors and the standard model International Nuclear Information System (INIS) Woit, P. 1988-01-01 The quantization of the simplest supersymmetric quantum mechanical theory of a free fermion on a riemannian manifold requires the introduction of a complex structure on the tangent space. In 4 dimensions, the subgroup of the group of frame rotations that preserves the complex structure is SU(2) x U(1), and it is argued that this symmetry can be consistently interpreted to be an internal gauge symmetry for the analytically continued theory in Minkowski space. The states of the theory carry the quantum numbers of a generation of leptons in the Weinberg-Salam model. Examination of the geometry of spinors in four dimensions also provides a natural SU(3) symmetry and very simple construction of a multiplet with the standard model quantum numbers. (orig.) 19. Supersymmetric models with tan β close to unity International Nuclear Information System (INIS) Ananthanarayan, B.; Babu, K.S.; Shafi, Q. 1994-01-01 Within the framework of supersymmetric grand unification, estimates of the b quark mass based on the asymptotic relation m b similar eqm τ single out the region with tan β close to unity, particularly if m t (m t ) < or ∼170 GeV. We explore the radiative breaking of the electroweak symmetry and the associated sparticle and higgs spectroscopy in models with 1 < tan β< or ∼1.6. The lightest scalar higgs is expected to have a mass below 100 GeV, while the remaining four higgs masses exceed 300 GeV. The lower bounds on some of the sparticle masses are within the range of LEP 200. ((orig.)) 20. Gauge hierarchy in an SO(10) supersymmetric grand unified model International Nuclear Information System (INIS) Zhiyong, Z. 1982-01-01 An SO(10) supersymmetric grand unified model is constructed in which the gauge hierarchy problem may be solved. Using Higgs superfields belonging to the SO(10) representations 16, 10 and 54, it is found that if SO(10) is broken down to SU(3)sub(c)xSU(2)sub(L)xU(1) via SO(6)xSO(4)approximately equal to SU(4)sub(c)xSU(2)sub(L)xSU(2)sub(R) at unification mass scales without supersymmetry breaking, the gauge hierarchy puzzle might be carried away. It is also shown that the colour-triplet Higgs, which mediates proton decay, is superheavy by an incredibly accurate, but 'natural' adjustment of parameters in the potential. (author) 1. Renormalization of supersymmetric models without using auxiliary fields International Nuclear Information System (INIS) Urbanek, P. 1986-01-01 Previously a linear representation of supersymmetry (Ss) was used in investigations of renormalizability. There auxiliary fields have been introduced in order that the Ss-algebra closes 'off-shell'. When the auxiliary fields are eliminated by their equations of motion, the Ss representation becomes nonlinear and Ss closes only 'on-shell'. Following O.Piguet and K.Sibold 1984 Ss is expressed through Ward identities which are formulated as functional variations of the generating functional of the Green functions. These functional operators form a closed algebra, a fact essential for the proof of renormalizability, which is given. It is not necessary to use a specific subtraction scheme in the Green functions. The procedure is applied to the Wess-Zumino model and the supersymmetric extension of the quantum electrodynamics. 15 refs. (qui) 2. The GRACE system for the minimal supersymmetric standard model International Nuclear Information System (INIS) Tanaka, H.; Kaneko, T.; Jimbo, M.; Kon, T. 1997-01-01 The algorithm of constructing the Feynman amplitudes for the GRACE system is extended to processes involving supersymmetric particles. New vertex amplitude subroutines needed to compute these processes are now part of the CHANEL library. (orig.) 3. Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory International Nuclear Information System (INIS) Lee, Bum-Hoon; Ro, Daeho; Yang, Hyun Seok 2017-01-01 We study localization of five-dimensional supersymmetric U(1) gauge theory on S 3 ×ℝ θ 2 where ℝ θ 2 is a noncommutative (NC) plane. The theory can be isomorphically mapped to three-dimensional supersymmetric U(N→∞) gauge theory on S 3 using the matrix representation on a separable Hilbert space on which NC fields linearly act. Therefore the NC space ℝ θ 2 allows for a flexible path to derive matrix models via localization from a higher-dimensional supersymmetric NC U(1) gauge theory. The result shows a rich duality between NC U(1) gauge theories and large N matrix models in various dimensions. 4. Phenomenology of left-right symmetric dark matter International Nuclear Information System (INIS) Garcia-Cely, Camilo; Heeck, Julian 2016-01-01 We present a detailed study of dark matter phenomenology in low-scale left-right symmetric models. Stability of new fermion or scalar multiplets is ensured by an accidental matter parity that survives the spontaneous symmetry breaking of the gauge group by scalar triplets. The relic abundance of these particles is set by gauge interactions and gives rise to dark matter candidates with masses above the electroweak scale. Dark matter annihilations are thus modified by the Sommerfeld effect, not only in the early Universe, but also today, for instance, in the Center of the Galaxy. Majorana candidates—triplet, quintuplet, bi-doublet, and bi-triplet—bring only one new parameter to the model, their mass, and are hence highly testable at colliders and through astrophysical observations. Scalar candidates—doublet and 7-plet, the latter being only stable at the renormalizable level—have additional scalar-scalar interactions that give rise to rich phenomenology. The particles under discussion share many features with the well-known candidates wino, Higgsino, inert doublet scalar, sneutrino, and Minimal Dark Matter. In particular, they all predict a large gamma-ray flux from dark matter annihilations, which can be searched for with Cherenkov telescopes. We furthermore discuss models with unequal left-right gauge couplings, g R ≠ g L , taking the recent experimental hints for a charged gauge boson with 2 TeV mass as a benchmark point. In this case, the dark matter mass is determined by the observed relic density 5. Quark mass matrices in left-right symmetric gauge theories International Nuclear Information System (INIS) Ecker, G.; Grimus, W.; Konetschny, W. 1981-01-01 The most general left-right symmetry for SU(2)sub(L) x SU(2)sub(R) x U(1) gauge theories with any number of flavours and with at most two scalar multiplets transforming as anti qq bilinears is analyzed. In order to get additional constraints on the structure of quark mass matrices all possible horizontal groups (continuous or discrete) are investigated. A complete classification of physically inequivalent quark mass matrices is given for four and six flavours. It is argued that the methods and results are also applicable in the case of dynamical symmetry breaking. Parity invariance and horizontal symmetry are shown to imply CP conservation on the Lagrangian level. For all non-trivial three-generation models there is spontaneous CP violation which in most cases turns out to be naturally small. (Auth.) 6. Dark Matter from the Supersymmetric Custodial Triplet Model CERN Document Server Delgado, Antonio; Ostdiek, Bryan; Quiros, Mariano 2015-01-01 The Supersymmetric Custodial Triplet Model (SCTM) adds to the particle content of the MSSM three $SU(2)_L$ triplet chiral superfields with hypercharge $Y=(0,\\pm1)$. At the superpotential level the model respects a global $SU(2)_L \\otimes SU(2)_R$ symmetry only broken by the Yukawa interactions. The pattern of vacuum expectation values of the neutral doublet and triplet scalar fields depends on the symmetry pattern of the Higgs soft breaking masses. We study the cases where this symmetry is maintained in the Higgs sector, and when it is broken only by the two doublets attaining different vacuum expectation values. In the former case, the symmetry is spontaneously broken down to the vectorial subgroup $SU(2)_V$ and the $\\rho$ parameter is protected by the custodial symmetry. However in both situations the $\\rho$ parameter is protected at tree level, allowing for light triplet scalars with large vacuum expectation values. We find that over a large range of parameter space, a light neutralino can supply the corre... 7. Probes of Yukawa unification in supersymmetric SO(10) models Energy Technology Data Exchange (ETDEWEB) Westhoff, Susanne 2009-10-23 This work is composed as follows: In Chapter 1, the disposed reader is made familiar with the foundations of flavourphysics and Grand Unification, including group-theoretical aspects of SO(10). In Chapter 2, we introduce a specific supersymmetric GUT model based on SO(10) and designed to probe down-quark-lepton Yukawa unification. Within this framework we explore the effects of large atmospheric neutrino mixing in bottom-strange transitions on the mass difference and CP phase in B{sub s}- anti B{sub s} meson mixing. Chapter 3 is devoted to corrections to Yukawa unification. We derive constraints on Yukawa corrections for light fermions from K- anti K and B{sub d}- anti B {sub d} mixing. As an application we study implications of neutrino mixing effects in CP-violating K and B{sub d} observables on the unitrity triangle. Finally, in Chapter 4, we discuss effects of large tan {beta} in B{yields}(D){tau}{nu} decays with respect to their potential to discover charged Higgs bosons and to discriminate between different GUT models of flavour. 8. The hyper-Kaehler supersymmetric sigma-model in six dimensions International Nuclear Information System (INIS) Sierra, G.; Townsend, P.K. 1983-01-01 The maximally supersymmetric, hyper-Kaehler, sigma-model is given in six-dimensional superfield form. The hyper-Kaehler condition follows from the requirements that the equations of motion be derivable from an action. (orig.) 9. Chiral Lagrangian calculation of nucleon branching ratios in the supersymmetric SU(5) model International Nuclear Information System (INIS) 1983-12-01 The branching ratios are calculated for the two body nucleon decay modes involving pseudoscalars in the minimal SU(5) supersymmetric model with three generations using the techniques of chiral dynamics. (author) 10. The gauge-invariant N=2 supersymmetric sigma-model with general scalar potential International Nuclear Information System (INIS) Sierra, G.; Townsend, P.K. 1984-01-01 We construct the supersymmetric sigma-model, in six dimensions, for an arbitrary hyper-Kaehler manifold, and its minimal coupling to super-Yang-Mills theory. Non-trivial reduction to five or four dimensions yields the corresponding five- or four-dimensional N=2 supersymmetric model with general scalar potential. We discuss briefly the coupling to supergravity in six dimensions and we give the on-shell supergravity torsion constraints. (orig.) 11. (4,0) supersymmetric sigma-model and t-duality International Nuclear Information System (INIS) Lhallabi, T. 1997-08-01 The conserved supercurrents J ++ and J -- are deduced for the (4,0) supersymmetric sigma model on harmonic superspace with arbitrary background gauge connection. These are introduced in the Lagrangian density of the model by their couplings to the analytic gauge superfields Γ -- and Γ ++ . The T-duality transformations are obtained by integrating out the analytic gauge superfields. Finally the (4,0) supersymmetric anomaly is derived. (author). 20 refs 12. On Newton's law in supersymmetric braneworld models Energy Technology Data Exchange (ETDEWEB) Palma, G.A. 2007-05-15 We study the propagation of gravitons within 5-D supersymmetric braneworld models with a bulk scalar field. The setup considered here consists of a 5-D bulk spacetime bounded by two 4-D branes localized at the fixed points of an S{sup 1}/Z{sub 2} orbifold. There is a scalar field {phi} in the bulk which, provided a superpotential W({phi}), determines the warped geometry of the 5-D spacetime. This type of scenario is common in string theory, where the bulk scalar field {phi} is related to the volume of small compact extra dimensions. We show that, after the moduli are stabilized by supersymmetry breaking terms localized on the branes, the only relevant degrees of freedom in the bulk consist of a 5-D massive spectrum of gravitons. Then we analyze the gravitational interaction between massive bodies localized at the positive tension brane mediated by these bulk gravitons. It is shown that the Newtonian potential describing this interaction picks up a non-trivial contribution at short distances that depends on the shape of the superpotential W({phi}). We compute this contribution for dilatonic braneworld scenarios W({phi})=e{sup {alpha}}{sup {phi}} (where {alpha} is a constant) and discuss the particular case of 5-D Heterotic M-theory: It is argued that a specific footprint at micron scales could be observable in the near future. (orig.) 13. Electroweak precision observables in the minimal supersymmetric standard model International Nuclear Information System (INIS) Heinemeyer, S.; Hollik, W.; Weiglein, G. 2006-01-01 The current status of electroweak precision observables in the Minimal Supersymmetric Standard Model (MSSM) is reviewed. We focus in particular on the W boson mass, M W , the effective leptonic weak mixing angle, sin 2 θ eff , the anomalous magnetic moment of the muon (g-2) μ , and the lightest CP-even MSSM Higgs boson mass, m h . We summarize the current experimental situation and the status of the theoretical evaluations. An estimate of the current theoretical uncertainties from unknown higher-order corrections and from the experimental errors of the input parameters is given. We discuss future prospects for both the experimental accuracies and the precision of the theoretical predictions. Confronting the precision data with the theory predictions within the unconstrained MSSM and within specific SUSY-breaking scenarios, we analyse how well the data are described by the theory. The mSUGRA scenario with cosmological constraints yields a very good fit to the data, showing a clear preference for a relatively light mass scale of the SUSY particles. The constraints on the parameter space from the precision data are discussed, and it is shown that the prospective accuracy at the next generation of colliders will enhance the sensitivity of the precision tests very significantly 14. Bardeen-anomaly and Wess-Zumino term in the supersymmetric standard model CERN Document Server Ferrara, Sergio; Porrati, Massimo; Stora, Raymond Félix 1994-01-01 We construct the Bardeen anomaly and its related Wess-Zumino term in the supersymmetric standard model. In particular we show that it can be written in terms of a composite linear superfield related to supersymmetrized Chern-Simons forms, in very much the same way as the Green-Schwarz term in four-dimensional string theory. Some physical applications, such as the contribution to the g-2 of gauginos when a heavy top is integrated out, are briefly discussed. 15. Low energy supersymmetric models for several generations and proton decay International Nuclear Information System (INIS) Deo, B.B.; Sarkar, U. 1983-08-01 It is found that by invoking additional horizontal gauge symmetries required to explain the generational structure the low energy standard supersymmetric unified theories avoid the renormalizable unsuppressed baryon number violating interactions in a natural way. Theories considered here are anomaly-free by construction. (author) 16. Higgs boson masses in a non-minimal supersymmetric model International Nuclear Information System (INIS) Tiesi, Alessandro 2002-01-01 A study of the neutral Higgs spectrum in a general Z 3 -breaking Next to Minimal Supersymmetric Standard Model (NMSSM) is reported in several significant contexts. Particular attention has been devoted to the upper bound on lightest Higgs boson. In the CP-conserving case we show that the extra terms involved in the general Z 3 -breaking superpotential do not affect the upper bound which remains unchanged: it is ∼ 136 GeV when tan β = 2.7. The Spontaneous CP Violation scenario in the Z 3 -breaking NMSSM can occur at tree-level. When the phases of the fields are small the spectrum shows the lightest Higgs particle to be an almost singlet CP-odd. The second lightest particle, a doublet almost-CP-even state, still manifests the upper bound of the CP-conserving case. When the CP-violating phases are large the lightest particle is a doublet with no definite CP parity and its mass shows the usual upper bound at ∼ 136 GeV. The large number of parameters involved in the effective potential can be significantly reduced in the Infrared Quasi Fixed Point (IRQFP) resulting after solving the Renormalization Group (RG) equations assuming universality for the soft SUSY breaking masses. In the Z 3 -breaking NMSSM, unlike the Z 3 -conserving NMSSM, it is possible to find a Higgs spectrum which is still compatible with both experiment and universality at the unification scale. Because in the IRQFP regime tan β ∼ 1.8 and the stop mixing parameter is reduced then the upper bound on the lightest Higgs boson turns out to be ∼ 121 GeV. This result is compatible with experimental data coming from LEPII and might be one of the next predictions to be tested at hadron collider experiments. (author) 17. Higgs particles in the standard model and supersymmetric theories International Nuclear Information System (INIS) Muehlleitner, M.M. 2000-08-01 This thesis presents a theoretical analysis of the properties of the Higgs bosons in the standard model (SM) and the minimal supersymmetric extension (MSSM), which can be investigated at the LHC and e + e - linear colliders. The final goal is the reconstruction of the Higgs potential and thus the verification of the Higgs mechanism. MSSM Higgs boson production processes at future γγ colliders are calculated in several decay channels. Heavy scalar and pseudoscalar Higgs bosons can be discovered in the bb final state in the investigated mass range 200 to 800 GeV for moderate and large values of tanβ. The τ + τ - channel provides a heavy Higgs boson discovery potential for large values of tanβ. Several mechanisms that can be exploited at e + e - linear colliders for the measurement of the lifetime of a SM Higgs boson in the intermediate mass range are analysed. In the WW mode, the lifetime of Higgs scalars with masses below ∝160 GeV can be determined with an error less than 10%. The reconstruction of the Higgs potential requires the measurement of the Higgs self-couplings. The SM and MSSM trilinear Higgs self-couplings are accessible in double and triple Higgs production. A theoretical analysis is presented in the relevant channels at the LHC and e + e - linear colliders. For high luminosities, the SM trilinear Higgs self-coupling can be measured with an accuracy of 20% at a 500 GeV e + e - linear collider. The MSSM coupling among three light Higgs bosons has to be extracted from continuum production. The other trilinear Higgs couplings are measurable in a restricted range of the MSSM parameter space. At the LHC, the Hhh coupling can be probed in resonant decays. (orig.) 18. Left-right asymmetry in neutrino-produced hadron jets International Nuclear Information System (INIS) Ballagh, H.C.; Bingham, H.H.; Lawry, T.J.; Lys, J.; Lynch, G.R.; Sokoloff, M.D.; Stevenson, M.L.; Huson, F.R.; Schmidt, E.; Smart, W.; Treadwell, E.; Cence, R.J.; Harris, F.A.; Jones, M.D.; Koide, A.; Peters, M.W.; Peterson, V.Z.; Lubatti, H.J.; Moriyasu, K.; Wolin, E. 1989-01-01 In an experiment (E546) to study interactions of left-angle E right-angle=100 GeV and left-angle Q 2 right-angle=17 GeV 2 neutrinos in the Fermilab 15-foot bubble chamber, we have looked for a left-right asymmetry in the azimuthal angle φ of individual hadrons about the direction of the lepton momentum transfer (q vector). Significant asymmetry is found for forward positive hadrons; for x F >0.10, we find left-angle cosφ right-angle=-0.029±0.008, where x F is the Feynman x variable. Negative hadrons with x F >0.10 show no asymmetry, left-angle cosφ right-angle=0.004±0.011. A model which includes parton intrinsic transverse momentum k t reproduces the asymmetry of combined positive and negative hadrons with x F >0.10, left-angle cosφ right-angle=-0.018±0.0065, if left-angle k t 2 right-angle=0.065±0.024 GeV 2 /c 2 . But the model predicts almost equal asymmetries for positive and negative hadrons. The model also agrees poorly with the observed dependence on the kinematic variables x and Q 2 if the k t distribution is assumed to be independent of kinematic variables 19. Left-right symmetry breaking in mice by left-right dynein may occur via a biased chromatid segregation mechanism, without directly involving the Nodal gene Energy Technology Data Exchange (ETDEWEB) Sauer, Stephan; Klar, Amar J. S., E-mail: [email protected], E-mail: [email protected] [Gene Regulation and Chromosome Biology Laboratory, Frederick National Laboratory for Cancer Research, Frederick, MD (United States) 2012-11-16 Ever since cloning the classic iv (inversedviscerum) mutation identified the “left-right dynein” (lrd) gene in mice, most research on body laterality determination has focused on its function in motile cilia at the node embryonic organizer. This model is attractive, as it links chirality of cilia architecture to asymmetry development. However, lrd is also expressed in blastocysts and embryonic stem cells, where it was shown to bias the segregation of recombined sister chromatids away from each other in mitosis. These data suggested that lrd is part of a cellular mechanism that recognizes and selectively segregates sister chromatids based on their replication history: old “Watson” versus old “Crick” strands. We previously proposed that the mouse left-right axis is established via an asymmetric cell division prior to/or during gastrulation. In this model, left-right dynein selectively segregates epigenetically differentiated sister chromatids harboring a hypothetical “left-right axis development 1” (“lra1”) gene during the left-right axis establishing cell division. Here, asymmetry development would be ultimately governed by the chirality of the cytoskeleton and the DNA molecule. Our model predicts that randomization of chromatid segregation in lrd mutants should produce embryos with 25% situs solitus, 25% situs inversus, and 50% embryonic death due to heterotaxia and isomerism. Here we confirmed this prediction by using two distinct lrd mutant alleles. Other than lrd, thus far Nodal gene is the most upstream function implicated in visceral organs laterality determination. We next tested whether the Nodal gene constitutes the lra1 gene hypothesized in the model by testing mutant’s effect on 50% embryonic lethality observed in lrd mutants. Since Nodal mutation did not suppress lethality, we conclude that Nodal is not equivalent to the lra1 gene. In summary, we describe the origin of 50% lethality in lrd mutant mice not yet explained by any other 20. Left-right symmetry breaking in mice by left-right dynein may occur via a biased chromatid segregation mechanism, without directly involving the Nodal gene Directory of Open Access Journals (Sweden) Stephan eSauer 2012-11-01 Full Text Available Ever since cloning the classic iv mutation identified the ‘left-right dynein’ (lrd gene in mice, most research on body laterality determination has focused on its function in motile cilia at the node embryonic organizer. This model is attractive, as it links chirality of cilia architecture to asymmetry development. However, lrd is also expressed in blastocysts and embryonic stem cells, where it was shown to bias the segregation of recombined sister chromatids away from each other in mitosis. These data suggested that lrd is part of a cellular mechanism that recognizes and selectively segregates sister chromatids based on their replication history: old ‘Watson’ vs. old ‘Crick’ strands. We previously proposed that the mouse left-right axis is established via an asymmetric cell division prior to/or during gastrulation. In this model, left-right dynein selectively segregates epigenetically differentiated sister chromatids harboring a hypothetical ‘left-right axis development 1’ (‘lra1’ gene during the left-right axis establishing cell division. Here, asymmetry development would be ultimately governed by the chirality of the cytoskeleton and the DNA molecule. Our model predicts that randomization of chromatid segregation in lrd mutants should produce embryos with 25% situs solitus, 25% situs inversus, and 50% embryonic death due to heterotaxia and isomerism. Here we confirmed this prediction by using two distinct lrd mutant alleles. Other than lrd, thus far Nodal gene is the most upstream function implicated in visceral organs laterality determination. We next tested whether the Nodal gene constitutes the lra1 gene hypothesized in the model by testing mutant’s effect on 50% embryonic lethality observed in lrd mutants. Since Nodal mutation did not suppress lethality, we conclude that Nodal is not equivalent to the lra1 gene. In summary, we describe the origin of 50% lethality in lrd mutant mice not yet explained by any other 1. Left-right symmetry breaking in mice by left-right dynein may occur via a biased chromatid segregation mechanism, without directly involving the Nodal gene International Nuclear Information System (INIS) Sauer, Stephan; Klar, Amar J. S. 2012-01-01 Ever since cloning the classic iv (inversedviscerum) mutation identified the “left-right dynein” (lrd) gene in mice, most research on body laterality determination has focused on its function in motile cilia at the node embryonic organizer. This model is attractive, as it links chirality of cilia architecture to asymmetry development. However, lrd is also expressed in blastocysts and embryonic stem cells, where it was shown to bias the segregation of recombined sister chromatids away from each other in mitosis. These data suggested that lrd is part of a cellular mechanism that recognizes and selectively segregates sister chromatids based on their replication history: old “Watson” versus old “Crick” strands. We previously proposed that the mouse left-right axis is established via an asymmetric cell division prior to/or during gastrulation. In this model, left-right dynein selectively segregates epigenetically differentiated sister chromatids harboring a hypothetical “left-right axis development 1” (“lra1”) gene during the left-right axis establishing cell division. Here, asymmetry development would be ultimately governed by the chirality of the cytoskeleton and the DNA molecule. Our model predicts that randomization of chromatid segregation in lrd mutants should produce embryos with 25% situs solitus, 25% situs inversus, and 50% embryonic death due to heterotaxia and isomerism. Here we confirmed this prediction by using two distinct lrd mutant alleles. Other than lrd, thus far Nodal gene is the most upstream function implicated in visceral organs laterality determination. We next tested whether the Nodal gene constitutes the lra1 gene hypothesized in the model by testing mutant’s effect on 50% embryonic lethality observed in lrd mutants. Since Nodal mutation did not suppress lethality, we conclude that Nodal is not equivalent to the lra1 gene. In summary, we describe the origin of 50% lethality in lrd mutant mice not yet explained by any other 2. On q-deformed supersymmetric classical mechanical models International Nuclear Information System (INIS) Colatto, L.P.; Matheus Valle, J.L. 1995-10-01 Based on the idea of quantum groups and paragrassmann variables, we present a generalization of supersymmetric classical mechanics with a deformation parameter q=exp 2πi/k dealing with the k=3 case. The coordinates of the q-superspace are a commuting parameter t and a paragrassmann variable θ, where θ 3 =0. The generator and covariant derivative are obtained, as well as the action for some possible superfields. (author). 13 refs 3. Left-right compatibility in the processing of trading verbs. Science.gov (United States) Vicario, Carmelo M; Rumiati, Raffaella I 2014-01-01 The research investigating the nature of cognitive processes involved in the representation of economical outcomes is growing. Within this research, the mental accounting model proposes that individuals may well use cognitive operations to organize, evaluate, and keep track of their financial activities (Thaler, 1999). Here we wanted to test this hypothesis by asking to a group of participants to detect a syntax mistake of verbs indicating incoming and going out activities related to economical profit (trading verbs), swapping (swapping verbs) and thinking (thinking verbs). We reported a left-right compatibility for trading verbs (i.e., participants were faster with their right hand while detecting verb referring to a monetary gain with respect to a monetary loss; and faster with their left hand while detecting a monetary loss with respect to a monetary gain). However, this pattern of result was not reported while detecting swapping verbs. Results are discussed taking into account the mental accounting theory as well as to the spatial mapping of valence hypothesis. 4. Chiral cell sliding drives left-right asymmetric organ twisting Science.gov (United States) Inaki, Mikiko; Hatori, Ryo; Nakazawa, Naotaka; Okumura, Takashi; Ishibashi, Tomoki; Kikuta, Junichi; Ishii, Masaru 2018-01-01 Polarized epithelial morphogenesis is an essential process in animal development. While this process is mostly attributed to directional cell intercalation, it can also be induced by other mechanisms. Using live-imaging analysis and a three-dimensional vertex model, we identified ‘cell sliding,’ a novel mechanism driving epithelial morphogenesis, in which cells directionally change their position relative to their subjacent (posterior) neighbors by sliding in one direction. In Drosophila embryonic hindgut, an initial left-right (LR) asymmetry of the cell shape (cell chirality in three dimensions), which occurs intrinsically before tissue deformation, is converted through LR asymmetric cell sliding into a directional axial twisting of the epithelial tube. In a Drosophila inversion mutant showing inverted cell chirality and hindgut rotation, cell sliding occurs in the opposite direction to that in wild-type. Unlike directional cell intercalation, cell sliding does not require junctional remodeling. Cell sliding may also be involved in other cases of LR-polarized epithelial morphogenesis. PMID:29891026 5. Left-right compatibility in the processing of trading verbs Directory of Open Access Journals (Sweden) Carmelo Mario Vicario 2014-01-01 Full Text Available The research investigating the nature of cognitive processes involved in the representation of economical outcomes is growing. Within this research, the mental accounting model proposes that individuals may well use cognitive operations to organize, evaluate, and keep track of their financial activities (Thaler, 1999. Here we wanted to test this hypothesis by asking to a group of participants to detect a syntax mistake of verbs indicating incoming and going out activities related to economical profit (trading verbs, swapping (swapping verbs and thinking (thinking verbs. We reported a left-right compatibility for trading verbs (i.e. participants were faster with their right hand while detecting verb referring to a monetary gain with respect to a monetary loss; and faster with their left hand while detecting a monetary loss with respect to a monetary gain. However, this pattern of result was not reported while detecting swapping verbs. Results are discussed taking into account the mental accounting theory as well as to the spatial mapping of valence hypothesis. 6. Mass mixing, CP violation and left-right symmetry for heavy neutral mesons International Nuclear Information System (INIS) Ecker, G.; Grimus, W. 1985-01-01 We investigate M 0 - M-bar 0 mixing and CP violation in the minimal left-right symmetric gauge model with spontaneous P and CP violation. The dominant contributions to the mixing amplitude including QCD corrections are calculated explicitly for B 0 - B-bar 0 . While the amount of mixing is not much changed with respect to the standard model left-right symmetry can give rise to significantly larger CP violation in the B 0 sub(s) - B-bar 0 sub(s) system (up to two orders of magnitude for the dilepton charge asymmetry). Sizable CP violating effects require that the left-right contribution to the KsubLKsubS mass difference has the same sign as the standard model contribution. We also comment on D 0 - D-bar 0 mixing including a careful discussion of the standard model prediction. (Author) 7. Searching for beyond the minimal supersymmetric standard model at the laboratory and in the sky Energy Technology Data Exchange (ETDEWEB) Kim, Ju Min 2010-09-15 We study the collider signals as well as Dark Matter candidates in supersymmetric models. We show that the collider signatures from a supersymmetric Grand Unification model based on the SO(10) gauge group can be distinguishable from those from the (constrained) minimal supersymmetric Standard Model, even though they share some common features. The N=2 supersymmetry has the characteristically distinct phenomenology, due to the Dirac nature of gauginos, as well as the extra adjoint scalars. We compute the cold Dark Matter relic density including a class of one-loop corrections. Finally, we discuss the detectability of neutralino Dark Matter candidate of the SO(10) model by the direct and indirect Dark Matter search experiments. (orig.) 8. Searching for beyond the minimal supersymmetric standard model at the laboratory and in the sky International Nuclear Information System (INIS) Kim, Ju Min 2010-09-01 We study the collider signals as well as Dark Matter candidates in supersymmetric models. We show that the collider signatures from a supersymmetric Grand Unification model based on the SO(10) gauge group can be distinguishable from those from the (constrained) minimal supersymmetric Standard Model, even though they share some common features. The N=2 supersymmetry has the characteristically distinct phenomenology, due to the Dirac nature of gauginos, as well as the extra adjoint scalars. We compute the cold Dark Matter relic density including a class of one-loop corrections. Finally, we discuss the detectability of neutralino Dark Matter candidate of the SO(10) model by the direct and indirect Dark Matter search experiments. (orig.) 9. N = 1 supersymmetric indices and the four-dimensional A-model Science.gov (United States) Closset, Cyril; Kim, Heeyeon; Willett, Brian 2017-08-01 We compute the supersymmetric partition function of N = 1 supersymmetric gauge theories with an R-symmetry on M_4\\cong M_{g,p}× {S}^1 , a principal elliptic fiber bundle of degree p over a genus- g Riemann surface, Σ g . Equivalently, we compute the generalized supersymmetric index I_{M}{_{g,p}, with the supersymmetric three-manifold M_{g,p} as the spatial slice. The ordinary N = 1 supersymmetric index on the round three-sphere is recovered as a special case. We approach this computation from the point of view of a topological A-model for the abelianized gauge fields on the base Σ g . This A-model — or A-twisted two-dimensional N = (2 , 2) gauge theory — encodes all the information about the generalized indices, which are viewed as expectations values of some canonically-defined surface defects wrapped on T 2 inside Σ g × T 2. Being defined by compactification on the torus, the A-model also enjoys natural modular properties, governed by the four-dimensional 't Hooft anomalies. As an application of our results, we provide new tests of Seiberg duality. We also present a new evaluation formula for the three-sphere index as a sum over two-dimensional vacua. 10. Finiteness of Ricci flat supersymmetric non-linear sigma-models International Nuclear Information System (INIS) Alvarez-Gaume, L.; Ginsparg, P. 1985-01-01 Combining the constraints of Kaehler differential geometry with the universality of the normal coordinate expansion in the background field method, we study the ultraviolet behavior of 2-dimensional supersymmetric non-linear sigma-models with target space an arbitrary riemannian manifold M. We show that the constraint of N=2 supersymmetry requires that all counterterms to the metric beyond one-loop order are cohomologically trivial. It follows that such supersymmetric non-linear sigma-models defined on locally symmetric spaces are super-renormalizable and that N=4 models are on-shell ultraviolet finite to all orders of perturbation theory. (orig.) 11. Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model CERN Document Server Desrosiers, P; Mathieu, P; Desrosiers, Patrick; Lapointe, Luc; Mathieu, Pierre 2003-01-01 We present two constructions of the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement. These eigenfunctions are the superspace extension of the generalized Hermite (or Hi-Jack) polynomials. The conserved quantities of the rational supersymmetric model are first related to their trigonometric relatives through a similarity transformation. This leads to a simple expression for the generalized Hermite superpolynomials as a differential operator acting on the corresponding Jack superpolynomials. The second construction relies on the action of the Hamiltonian on the supermonomial basis. This translates into determinantal expressions for the Hamiltonian's eigenfunctions. As an aside, the maximal superintegrability of the supersymmetric rational Calogero-Moser-Sutherland model is demonstrated. 12. The determination factors of left-right asymmetry disorders- a short review. Science.gov (United States) 2017-01-01 Laterality defects in humans, situs inversus and heterotaxy, are rare disorders, with an incidence of 1:8000 to 1:10 000 in the general population, and a multifactorial etiology. It has been proved that 1.44/10 000 of all cardiac problems are associated with malformations of left-right asymmetry and heterotaxy accounts for 3% of all congenital heart defects. It is considered that defects of situs appear due to genetic and environmental factors. Also, there is evidence that the ciliopathies (defects of structure or function) are involved in development abnormalities. Over 100 genes have been reported to be involved in left-right patterning in model organisms, but only a few are likely to candidate for left-right asymmetry defects in humans. Left-right asymmetry disorders are genetically heterogeneous and have variable manifestations (from asymptomatic to serious clinical problems). The discovery of the right mechanism of left-right development will help explain the clinical complexity and may contribute to a therapy of these disorders. 13. Three-family left-right symmetry with low-scale seesaw mechanism Energy Technology Data Exchange (ETDEWEB) Reig, Mario; Valle, José W.F.; Vaquera-Araujo, C.A. [AHEP Group, Institut de Física Corpuscular - C.S.I.C., Universitat de València,Parc Científic de Paterna, C/ Catedrático José Beltrán, 2 E-46980 Paterna (Valencia) (Spain) 2017-05-18 We suggest a new left-right symmetric model implementing a low-scale seesaw mechanism in which quantum consistency requires three families of fermions. The symmetry breaking route to the Standard Model determines the profile of the “next” expected new physics, characterized either by the simplest left-right gauge symmetry or by the 3-3-1 scenario. The resulting Z{sup ′} gauge bosons can be probed at the LHC and provide a production portal for the right-handed neutrinos. On the other hand, its flavor changing interactions would affect the K, D and B neutral meson systems. 14. Predictions for m{sub t} and M{sub W} in minimal supersymmetric models Energy Technology Data Exchange (ETDEWEB) Buchmueller, O. [Imperial College, London (United Kingdom). High Energy Physics Group; Cavanaugh, R. [Fermi National Accelerator Lab., Batavia, IL (United States); Illinois Univ., Chicago, IL (United States). Dept. of Physics; Roeck, A. de [European Lab. for Particle Physics (CERN), Geneva (Switzerland); Universitaire Instelling Antwerpen, Wilrijk (Belgium); Ellis, J.R. [European Lab. for Particle Physics (CERN), Geneva (Switzerland); Flaecher, H. [Rochester Univ., NY (United States). Dept. of Physics and Astronomy; Heinemeyer, S. [Instituto de Fisica de Cantabria, Santander (Spain); Isidori, G. [INFN, Laboratori Nazionali di Frascati (Italy); Technische Univ. Muenchen (Germany). Inst. for Advanced Study; Olive, K.A. [Minnesota Univ., Minnesota, MN (United States). William I. Fine Theoretical Physics Institute; Ronga, F.J. [ETH Zuerich (Switzerland). Institute for Particle Physics; Weiglein, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany) 2009-12-15 Using a frequentist analysis of experimental constraints within two versions of the minimal supersymmetric extension of the Standard Model, we derive the predictions for the top quark mass, m{sub t}, and the W boson mass, m{sub W}. We find that the supersymmetric predictions for both m{sub t} and m{sub W}, obtained by incorporating all the relevant experimental information and state-of-the-art theoretical predictions, are highly compatible with the experimental values with small remaining uncertainties, yielding an improvement compared to the case of the Standard Model. (orig.) 15. N=12 supersymmetric four-dimensional nonlinear σ-models from nonanticommutative superspace International Nuclear Information System (INIS) Hatanaka, Tomoya; Ketov, Sergei V.; Kobayashi, Yoshishige; Sasaki, Shin 2005-01-01 The component structure of a generic N=1/2 supersymmetric nonlinear sigma-model (NLSM) defined in the four-dimensional (Euclidean) nonanticommutative (NAC) superspace is investigated in detail. The most general NLSM is described in terms of arbitrary Kahler potential, and chiral and antichiral superpotentials. The case of a single chiral superfield gives rise to splitting of the NLSM potentials, whereas the case of several chiral superfields results in smearing (or fuzziness) of the NLSM potentials, while both effects are controlled by the auxiliary fields. We eliminate the auxiliary fields by solving their algebraic equations of motion, and demonstrate that the results are dependent upon whether the auxiliary integrations responsible for the fuzziness are performed before or after elimination of the auxiliary fields. There is no ambiguity in the case of splitting, i.e., for a single chiral superfield. Fully explicit results are derived in the case of the N=1/2 supersymmetric NAC-deformed CP n NLSM in four dimensions. Here we find another surprise that our results differ from the N=1/2 supersymmetric CP n NLSM derived by the quotient construction from the N=1/2 supersymmetric NAC-deformed gauge theory. We conclude that an N=1/2 supersymmetric deformation of a generic NLSM from the NAC superspace is not unique 16. Hyperkaehlerian manifolds and exact β functions of two-dimensional N=4 supersymmetric σ models International Nuclear Information System (INIS) Morozov, A.Yu.; Perelomov, A.M. 1984-01-01 Two-dimensional supersymmetric sigma-models on cotangent bundles over CPsup(n) are investigated. These mannfolds are supplied with hyperkaehlerian metrics, and the corresponding σ-models possess N=4 supersymmetry. Also they admit instantonic solutions, which permits to apply the Novikov-Shifman-Vainshtein-Zakharov method and calculate exact β-functions. βsup(gsup(2)) = 0, as was expected 17. Bethe ansatz solution of the closed anisotropic supersymmetric U model with quantum supersymmetry International Nuclear Information System (INIS) Hibberd, Katrina; Roditi, Itzhak; Links, Jon; Foerster, Angela 1999-11-01 The nested algebraic Bethe Ansatz is presented for the anisotropic supersymmetric U model maintaining quantum a supersymmetry. The Bethe Ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for the energy is given. (author) 18. Triviality bound on lightest Higgs mass in next to minimal supersymmetric model International Nuclear Information System (INIS) Choudhury, S.R.; Mamta; Dutta, Sukanta 1998-01-01 We study the implication of triviality on Higgs sector in next to minimal supersymmetric model (NMSSM) using variational field theory. It is shown that the mass of the lightest Higgs boson in NMSSM has an upper bound ∼ 10 M w which is of the same order as that in the standard model. (author) 19. Supersymmetric flaxion Science.gov (United States) Ema, Yohei; Hagihara, Daisuke; Hamaguchi, Koichi; Moroi, Takeo; Nakayama, Kazunori 2018-04-01 Recently, a new minimal extension of the Standard Model has been proposed, where a spontaneously broken, flavor-dependent global U(1) symmetry is introduced. It not only explains the hierarchical flavor structure in the quark and lepton sector, but also solves the strong CP problem by identifying the Nambu-Goldstone boson as the QCD axion, which we call flaxion. In this work, we consider supersymmetric extensions of the flaxion scenario. We study the CP and flavor violations due to supersymmetric particles, the effects of R-parity violations, the cosmological gravitino and axino problems, and the cosmological evolution of the scalar partner of the flaxion, sflaxion. We also propose an attractor-like inflationary model where the flaxion multiplet contains the inflaton field, and show that a consistent cosmological scenario can be obtained, including inflation, leptogenesis, and dark matter. 20. Left-Right Asymmetric Morphogenesis in the Xenopus Digestive System Science.gov (United States) Muller, Jennifer K.; Prather, D.R.; Nascone-Yoder, N. M. 2003-01-01 The morphogenetic mechanisms by which developing organs become left-right asymmetric entities are unknown. To investigate this issue, we compared the roles of the left and right sides of the Xenopus embryo during the development of anatomic asymmetries in the digestive system. Although both sides contribute equivalently to each of the individual digestive organs, during the initial looping of the primitive gut tube, the left side assumes concave topologies where the right side becomes convex. Of interest, the concave surfaces of the gut tube correlate with expression of the LR gene, Pitx2, and ectopic Pitx2 mRNA induces ectopic concavities in a localized manner. A morphometric comparison of the prospective concave and convex surfaces of the gut tube reveals striking disparities in their rate of elongation but no significant differences in cell proliferation. These results provide insight into the nature of symmetry-breaking morphogenetic events during left-right asymmetric organ development. ?? 2003 Wiley-Liss, Inc. 1. Left-right entanglement entropy of Dp-branes Energy Technology Data Exchange (ETDEWEB) Zayas, Leopoldo A. Pando [The Abdus Salam International Centre for Theoretical Physics,Strada Costiera 11, 34014 Trieste (Italy); Michigan Center for Theoretical Physics, Randall Laboratory of Physics,The University of Michigan,450 Church Street, Ann Arbor, MI 48109-1120 (United States); Quiroz, Norma [Departamento de Ciencias Exactas, Tecnología y Metodología,Centro Universitario del Sur, Universidad de Guadalajara,Enrique Arreola Silva 883, C.P. 49000, Cd. Guzmán, Jalisco (Mexico) 2016-11-04 We compute the left-right entanglement entropy for Dp-branes in string theory. We employ the CFT approach to string theory Dp-branes, in particular, its presentation as coherent states of the closed string sector. The entanglement entropy is computed as the von Neumann entropy for a density matrix resulting from integration over the left-moving degrees of freedom. We discuss various crucial ambiguities related to sums over spin structures and argue that different choices capture different physics; however, we advance a themodynamic argument that seems to favor a particular choice of replica. We also consider Dp branes on compact dimensions and verify that the effects of T-duality act covariantly on the Dp brane entanglement entropy. We find that generically the left-right entanglement entropy provides a suitable generalization of boundary entropy and of the D-brane tension. 2. Non-renormalizability of supersymmetric non-linear sigma models in four dimensions International Nuclear Information System (INIS) Spence, B. 1985-01-01 The one-loop, on-shell, ultraviolet-divergent part of the effective action is calculated for the N=1 and 2 supersymmetric non-linear sigma models in four dimensions. These infinities cannot be absorbed into a redefinition of the bare Kaehler potential and the theories are not renormalizable. (orig.) 3. Production and decay of neutralinos in the nonminimal supersymmetric standard model International Nuclear Information System (INIS) Franke, F. 1995-01-01 In this thesis after a presentation of the nonminimal supersymmetric standard model the lower mass limits for neutralinos and Higgs bosons are calculated. Then some typical scenarios for the study of the neutralino production and decay at LEP2 are constructed, for which the cross sections are calculated. (HSI) 4. N=2, D=4 supersymmetric σ-models and Hamiltonian mechanics International Nuclear Information System (INIS) Galperin, A.; Ogievetsky, V. 1991-05-01 A deep similarity is established between the Hamiltonian mechanics of point particle and supersymmetric N=2, D=4 σ-models formulated within harmonic superspace. An essential part of the latter, the sphere S 2 , comes out as a counterpart of the time variable. (author). 7 refs 5. Left-right symmetry in weak interactions: present status International Nuclear Information System (INIS) Senjanovic, G. 1983-01-01 The basic features of the left-right symmetric electroweak theory are reviewed. The experimental situation regarding the scale M/sub R/ of the breakdown of parity is summarized. I further discuss in detail the connection with weak and strong CP violation and especially, grand unification. Also covered are the issues of cosmological domain walls and the compositeness of quarks and leptons. 57 references 6. Decaying dark matter in supersymmetric SU(5) models International Nuclear Information System (INIS) Luo Mingxing; Wang Liucheng; Wu Wei; Zhu Guohuai 2010-01-01 Motivated by recent observations from PAMELA, Fermi and H.E.S.S., we consider dark matter decays in the framework of supersymmetric SU(5) grand unification theories. An SU(5) singlet S is assumed to be the main component of dark matters, which decays into visible particles through dimension six operators suppressed by the grand unification scale. Under certain conditions, S decays dominantly into a pair of sleptons with universal coupling for all generations. Subsequently, electrons and positrons are produced from cascade decays of these sleptons. These cascade decay chains smooth the e + +e - spectrum, which permit naturally a good fit to the Fermi-LAT data. The observed positron fraction upturn by PAMELA can be reproduced simultaneously. We have also calculated diffuse gamma-ray spectra due to the e ± excesses and compared them with the preliminary Fermi-LAT data from 0.1 GeV to 10 GeV in the region 0 deg. ≤l≤ 360 deg., 10 deg. ≤\|b\|≤20 deg. The photon spectrum of energy above 100 GeV, mainly from final state radiations, may be checked in the near future. 7. Implications of improved Higgs mass calculations for supersymmetric models. Science.gov (United States) Buchmueller, O; Dolan, M J; Ellis, J; Hahn, T; Heinemeyer, S; Hollik, W; Marrouche, J; Olive, K A; Rzehak, H; de Vries, K J; Weiglein, G We discuss the allowed parameter spaces of supersymmetric scenarios in light of improved Higgs mass predictions provided by FeynHiggs 2.10.0. The Higgs mass predictions combine Feynman-diagrammatic results with a resummation of leading and subleading logarithmic corrections from the stop/top sector, which yield a significant improvement in the region of large stop masses. Scans in the pMSSM parameter space show that, for given values of the soft supersymmetry-breaking parameters, the new logarithmic contributions beyond the two-loop order implemented in FeynHiggs tend to give larger values of the light CP-even Higgs mass, [Formula: see text], in the region of large stop masses than previous predictions that were based on a fixed-order Feynman-diagrammatic result, though the differences are generally consistent with the previous estimates of theoretical uncertainties. We re-analyse the parameter spaces of the CMSSM, NUHM1 and NUHM2, taking into account also the constraints from CMS and LHCb measurements of [Formula: see text]and ATLAS searches for [Formula: see text] events using 20/fb of LHC data at 8 TeV. Within the CMSSM, the Higgs mass constraint disfavours [Formula: see text], though not in the NUHM1 or NUHM2. 8. Implications of improved Higgs mass calculations for supersymmetric models Energy Technology Data Exchange (ETDEWEB) Buchmueller, O. [Imperial College, London (United Kingdom). High Energy Physics Group; Dolan, M.J. [SLAC National Accelerator Laboratory, Menlo Park, CA (United States). Theory Group; Ellis, J. [King' s College, London (United Kingdom). Theoretical Particle Physics and Cosmology Group; and others 2014-03-15 We discuss the allowed parameter spaces of supersymmetric scenarios in light of improved Higgs mass predictions provided by FeynHiggs 2.10.0. The Higgs mass predictions combine Feynman-diagrammatic results with a resummation of leading and subleading logarithmic corrections from the stop/top sector, which yield a significant improvement in the region of large stop masses. Scans in the pMSSM parameter space show that, for given values of the soft supersymmetry-breaking parameters, the new logarithmic contributions beyond the two-loop order implemented in FeynHiggs tend to give larger values of the light CP-even Higgs mass, M{sub h}, in the region of large stop masses than previous predictions that were based on a fixed-order Feynman-diagrammatic result, though the differences are generally consistent with the previous estimates of theoretical uncertainties. We re-analyze the parameter spaces of the CMSSM, NUHM1 and NUHM2, taking into account also the constraints from CMS and LHCb measurements of BR(B{sub s}→μ{sup +}μ{sup -}) and ATLAS searches for E{sub T} events using 20/fb of LHC data at 8 TeV. Within the CMSSM, the Higgs mass constraint disfavours tan β 9. Complete integrability of the supersymmetric model (cos phi)/sub ell/ International Nuclear Information System (INIS) Kulish, P.P.; Tsyplyaev, S.A. 1986-01-01 Complete integrability of the supersymmetric, two-dimensional sine-Gordon model of field theory within the framework of the Hamiltonian interpretation of the method of the inverse problem is proved. The classical r-matrix of the model is computed, and its equivalence to the r-matrix the Grassmann Thirring model is established. Variables of creation-annihilation type are constructed, and the spectrum of elementary excitations of the system is obtained 10. Detailed analysis of the continuum limit of a supersymmetric lattice model in 1D International Nuclear Information System (INIS) Huijse, L 2011-01-01 We present a full identification of lattice model properties with their field theoretical counterparts in the continuum limit for a supersymmetric model for itinerant spinless fermions on a one-dimensional chain. The continuum limit of this model is described by an N=(2,2) superconformal field theory (SCFT) with central charge c = 1. We identify states and operators in the lattice model with fields in the SCFT and we relate boundary conditions on the lattice to sectors in the field theory. We use the dictionary we develop in this paper to give a pedagogical explanation of a powerful tool to study supersymmetric models based on spectral flow (Huijse 2008 Phys. Rev. Lett. 101 146406). Finally, we employ the developed machinery to explain numerically observed properties of the particle density on the open chain presented in Beccaria and De Angelis (2005 Phys. Rev. Lett. 94 100401) 11. Supersymmetric axial anomalies and the Wess-Zumino action International Nuclear Information System (INIS) 1988-01-01 We derive, by an algebraic method, a manifestly supersymmetric extension of Bardeen's minimal form of axial anomalies, which obeys the Wess-Zumino consistency condition. The left-right symmetric form of the anomalies is also obtained by a reduction procedure. We construct the supersymmetric Wess-Zumino effective action and study its low-energy features. (orig.) 12. Targeting the minimal supersymmetric standard model with the compact muon solenoid experiment Science.gov (United States) Bein, Samuel Louis An interpretation of CMS searches for evidence of supersymmetry in the context of the minimal supersymmetric Standard Model (MSSM) is given. It is found that supersymmetric particles with color charge are excluded in the mass range below about 400 GeV, but neutral and weakly-charged sparticles remain non-excluded in all mass ranges. Discussion of the non-excluded regions of the model parameter space is given, including details on the strengths and weaknesses of existing searches, and recommendations for future analysis strategies. Advancements in the modeling of events arising from quantum chromodynamics and electroweak boson production, which are major backgrounds in searches for new physics at the LHC, are also presented. These methods have been implemented as components of CMS searches for supersymmetry in proton-proton collisions resulting in purely hadronic events (i.e., events with no identified leptons) at a center of momentum energy of 13 TeV. These searches, interpreted in the context of simplified models, exclude supersymmetric gluons (gluinos) up to masses of 1400 to 1600 GeV, depending on the model considered, and exclude scalar top quarks with masses up to about 800 GeV, assuming a massless lightest supersymmetric particle. A search for non-excluded supersymmetry models is also presented, which uses multivariate discriminants to isolate potential signal candidate events. The search achieves sensitivity to new physics models in background-dominated kinematic regions not typically considered by analyses, and rules out supersymmetry models that survived 7 and 8 TeV searches performed by CMS. 13. Beta functions and central charge of supersymmetric sigma models with torsion International Nuclear Information System (INIS) 1987-01-01 We present a method for the computation of the renormalization group β-functions and the central charge in two-dimensional supersymmetric sigma models in a gravitational background. The two-loops results are exhibited. We use the Pauli-Villars regularization which preserves supersymmetry and permits an unambiguous treatment of the model with torsion. The central charge we derive for a general manifold is in agreement with the expression found on group manifolds. (orig.) 14. arXiv Supersymmetric gauged matrix models from dimensional reduction on a sphere CERN Document Server Closset, Cyril; Seong, Rak-Kyeong 2018-05-04 It was recently proposed that $\\mathcal{N}$ = 1 supersymmetric gauged matrix models have a duality of order four — that is, a quadrality — reminiscent of infrared dualities of SQCD theories in higher dimensions. In this note, we show that the zero-dimensional quadrality proposal can be inferred from the two-dimensional Gadde-Gukov-Putrov triality. We consider two-dimensional $\\mathcal{N}$ = (0, 2) SQCD compactified on a sphere with the half-topological twist. For a convenient choice of R-charge, the zero-mode sector on the sphere gives rise to a simple $\\mathcal{N}$ = 1 gauged matrix model. Triality on the sphere then implies a triality relation for the supersymmetric matrix model, which can be completed to the full quadrality. 15. Baryon-number generation in supersymmetric unified models: the effect of supermassive fermions International Nuclear Information System (INIS) Kolb, E.W.; Raby, S. 1983-01-01 In supersymmetric unified models, baryon-number-violating reactions may be mediated by supermassive fermions in addition to the usual supermassive bosons. The effective low-energy baryon-number-violating cross section for fermion-mediated reactions is sigma/sub DeltaB/approx.g 4 /m 2 , where g is a coupling constant and m is the supermassive fermion mass, as opposed to sigma/sub DeltaB/approx.g 4 s/m 4 for scalar- or vector-mediated reactions (√s is the center-of-mass energy). Since the fermion-mediated cross section is larger at low energy, it is more effective at damping the baryon number produced in decay of the supermassive particles. In this paper we calculate baryon-number generation in models with fermion-mediated baryon-number-violating reactions, and discuss implications for supersymmetric model building 16. Application to supersymmetric models of Dirac-kaehler formalism on the lattice International Nuclear Information System (INIS) Zimerman, A.H. 1987-01-01 Using Dirac-Kaehler techniques we formulate some supersymmetric models on the lattice. Specifically we consider the Wess-Zumino model with N=2 in two dimensions which is formulated on a space lattice in its Hamiltonian version (continuous time) as well as on the space-time lattice in its Lagrangean version (euclidean space). On the space lattice (Hamiltonian formulation) we study also the supersymmetric Yanh-Mills model with N=4 in four dimensions. After the introduction of lattice covariant derivatives for fields in the adjoint representation of a compact group we write down some new relations which we have obtained and which constitute generalizations on the lattice of those which are known in the continuous case. (author) [pt 17. Stochastic quantization of field theories on the lattice and supersymmetrical models International Nuclear Information System (INIS) Aldazabal, Gerardo. 1984-01-01 Several aspects of the stochastic quantization method are considered. Specifically, field theories on the lattice and supersymmetrical models are studied. A non-linear sigma model is studied firstly, and it is shown that it is possible to obtain evolution equations written directly for invariant quantities. These ideas are generalized to obtain Langevin equations for the Wilson loops of non-abelian lattice gauge theories U (N) and SU (N). In order to write these equations, some different ways of introducing the constraints which the fields must satisfy are discussed. It is natural to have a strong coupling expansion in these equations. The correspondence with quantum field theory is established, and it is noticed that at all orders in the perturbation theory, Langevin equations reduce to Schwinger-Dyson equations. From another point of view, stochastic quantization is applied to large N matrix models on the lattice. As a result, a simple and systematic way of building reduced models is found. Referring to stochastic quantization in supersymmetric theories, a simple supersymmetric model is studied. It is shown that it is possible to write an evolution equation for the superfield wich leads to quantum field theory results in equilibrium. As the Langevin equation preserves supersymmetry, the property of dimensional reduction known for the quantum model is shown to be valid at all times. (M.E.L.) [es 18. The left-right forward-backward asymmetry for B quarks at the SLD Energy Technology Data Exchange (ETDEWEB) Williams, David C. [Stanford Univ., CA (United States) 1994-05-01 The left-right asymmetry for b quarks, A{sub b}, is precisely predicted by the Weinberg-Salam-Glashow model of particle interactions, now the standard model for high-energy particle physics. As a test of this model, Ab is directly measured at the SLC Large Detector (SLD) by taking advantage of the unique polarized electron beam at the Stanford Linear Collider (SLC) and measuring the left-right forward-backward asymmetry of b quarks. To measure the asymmetry, b quarks are identified using muons of high total and transverse momenta. The result for the 1993 data sample of 37,843 hadronic Z`s is Ab = 0.91 ± 0.19 ± 0.06, where the first error is statistical and the second systematic. This result is in agreement with the standard model prediction of Ab = 0.935. 19. The left-right forward-backward asymmetry for B quarks at the SLD International Nuclear Information System (INIS) Williams, D.C. 1994-05-01 The left-right asymmetry for b quarks, A b , is precisely predicted by the Weinberg-Salam-Glashow model of particle interactions, now the standard model for high-energy particle physics. As a test of this model, A b is directly measured at the SLC Large Detector (SLD) by taking advantage of the unique polarized electron beam at the Stanford Linear Collider (SLC) and measuring the left-right forward-backward asymmetry of b quarks. To measure the asymmetry, b quarks are identified using muons of high total and transverse momenta. The result for the 1993 data sample of 37,843 hadronic Z's is A b = 0.91 ± 0.19 ± 0.06, where the first error is statistical and the second systematic. This result is in agreement with the standard model prediction of A b = 0.935 20. BRST with background field method of the (4,0) supersymmetric σ-model in two dimensions International Nuclear Information System (INIS) Lhallabi, T. 1988-08-01 A manifestly covariant background field formalism for (4,0) supersymmetric non-linear σ-model in two dimensions is presented. The BRST argument is used in order to obtain Faddeev-Popov ghost terms. (author). 13 refs 1. Horizontal, anomalous U(1) symmetry for the more minimal supersymmetric standard model International Nuclear Information System (INIS) Nelson, A.E.; Wright, D. 1997-01-01 We construct explicit examples with a horizontal, open-quotes anomalousclose quotes U(1) gauge group, which, in a supersymmetric extension of the standard model, reproduce qualitative features of the fermion spectrum and CKM matrix, and suppress FCNC and proton decay rates without the imposition of global symmetries. We review the motivation for such open-quotes moreclose quotes minimal supersymmetric standard models and their predictions for the sparticle spectrum. There is a mass hierarchy in the scalar sector which is the inverse of the fermion mass hierarchy. We show in detail why ΔS=2 FCNCs are greatly suppressed when compared with naive estimates for nondegenerate squarks. copyright 1997 The American Physical Society 2. Low-temperature specific heat of the degenerate supersymmetric t-J model in one dimension International Nuclear Information System (INIS) Lee, K.; Schlottmann, P. 1996-01-01 We consider the one-dimensional SU(N)-invariant t-J model, which consists of electrons with N spin components on a lattice with nearest-neighbor hopping t constrained by the excluded multiple occupancy of the sites and spin-exchange J between neighboring lattice sites. The model is integrable and has been diagonalized in terms of nested Bethe ansatze at the supersymmetric point t=J. The low-T specific heat is proportional to T. The γ-coefficient is extracted from the thermodynamic Bethe-ansatz equations and is expressed in terms of the spin wave velocities and the group velocity of the charges for arbitrary N, band filling, and splitting of the levels (magnetic and crystalline fields). Our results contain the following special cases: (i) For N=2 the traditional spin-1/2 supersymmetric t-J model, (ii) for exactly one electron per site the SU(N)-Heisenberg chain, and (iii) for N=4 the two-band supersymmetric t-J model with crystalline field splitting. copyright 1996 American Institute of Physics 3. Signals of dark matter in a supersymmetric two dark matter model International Nuclear Information System (INIS) Fukuoka, Hiroki; Suematsu, Daijiro; Toma, Takashi 2011-01-01 Supersymmetric radiative neutrino mass models have often two dark matter candidates. One is the usual lightest neutralino with odd R parity and the other is a new neutral particle whose stability is guaranteed by a discrete symmetry that forbids tree-level neutrino Yukawa couplings. If their relic abundance is comparable, dark matter phenomenology can be largely different from the minimal supersymmetric standard model (MSSM). We study this in a supersymmetric radiative neutrino mass model with the conserved R parity and a Z 2 symmetry weakly broken by the anomaly effect. The second dark matter with odd parity of this new Z 2 is metastable and decays to the neutralino dark matter. Charged particles and photons associated to this decay can cause the deviation from the expected background of the cosmic rays. Direct search of the neutralino dark matter is also expected to show different features from the MSSM since the relic abundance is not composed of the neutralino dark matter only. We discuss the nature of dark matter in this model by analyzing these signals quantitatively 4. Family of fish-eye-related models and their supersymmetric partners International Nuclear Information System (INIS) 2010-01-01 A large family of potentials related to the Maxwell fish-eye model is derived with the help of conformal mappings. It is shown that the whole family admits square-integrable E=0 solutions of the Schroedinger equation for discrete values of the coupling constant. A corresponding supersymmetric family of partner potentials to the preceding ones is derived as well. Some applications of the considered potentials are also discussed. 5. Decay properties of heavy leptons in the supersymmetric model of weak and electromagnetic interactions International Nuclear Information System (INIS) Egorian, Ed. 1979-01-01 Decay properties of heavy leptons in the SU(2)xSU(2)xU(1) supersymmetric model of weak and electromagnetic interactions are studied. l anti νsub(e)ν leptonic and ν(νsup(c))h semihadronic decays, where l are leptons and h are hadrons, are considered. The partial and total decay rates and the production in p anti p collision of one of them are estimated for various values of its mass 6. Impacts of supersymmetric higher derivative terms on inflation models in supergravity International Nuclear Information System (INIS) 2015-01-01 We show the effects of supersymmetric higher derivative terms on inflation models in supergravity. The results show that such terms generically modify the effective kinetic coefficient of the inflaton during inflation if the cut off scale of the higher derivative operators is sufficiently small. In such a case, the η-problem in supergravity does not occur, and we find that the effective potential of the inflaton generically becomes a power type potential with a power smaller than two 7. Duality in Left-Right Symmetric Seesaw Mechanism International Nuclear Information System (INIS) Akhmedov, E.Kh.; Frigerio, M. 2006-01-01 We consider type I+II seesaw mechanism, where the exchanges of both right-handed neutrinos and isotriplet Higgs bosons contribute to the neutrino mass. Working in the left-right symmetric framework and assuming the mass matrix of light neutrinos m ν and the Dirac-type Yukawa couplings to be known, we find the triplet Yukawa coupling matrix f, which carries the information about the masses and mixing of the right-handed neutrinos. We show that in this case there exists a duality: for any solution f, there is a dual solution f-circumflex=m ν /v L -f, where v L is the vacuum expectation value of the triplet Higgs boson. Thus, unlike in pure type I (II) seesaw, there is no unique allowed structure for the matrix f. For n lepton generations the number of solutions is 2 n . We develop an exact analytic method of solving the seesaw nonlinear matrix equation for f 8. Neutrino masses and a low breaking scale of left-right symmetry International Nuclear Information System (INIS) 2002-01-01 In left-right symmetric models (LRSMs) the light neutrino masses arise from two sources: the seesaw mechanism and a vacuum expectation value of an SU(2) L triplet. If the left-right symmetry breaking v R is low, v R (less-or-similar sign)15 TeV, the contributions to the light neutrino masses from both the seesaw mechanism and the triplet Yukawa couplings are expected to be well above the experimental bounds. We present a minimal LRSM with an additional U(1) symmetry in which the masses induced by the two sources are below the eV scale and the twofold problem is solved. We further show that, if the U(1) symmetry is also responsible for the lepton flavor structure, the model yields a small mixing angle within the first two lepton generations 9. Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry Energy Technology Data Exchange (ETDEWEB) Hikida, Yasuaki [Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan); Wada, Taiki [Department of Physical Sciences, College of Science and Engineering, Ritsumeikan University,Shiga 525-8577 (Japan) 2017-03-08 We examine the marginal deformations of double-trace type in 3d supersymmetric U(N) model with N complex free bosons and fermions. We compute the anomalous dimensions of higher spin currents to the 1/N order but to all orders in the deformation parameters by mainly applying the conformal perturbation theory. The 3d field theory is supposed to be dual to 4d supersymmetric Vasiliev theory, and the marginal deformations are argued to correspond to modifying boundary conditions for bulk scalars and fermions. Thus the modification should break higher spin gauge symmetry and generate the masses of higher spin fields. We provide supports for the dual interpretation by relating bulk computation in terms of Witten diagrams to boundary one in conformal perturbation theory. 10. Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry International Nuclear Information System (INIS) 2017-01-01 We examine the marginal deformations of double-trace type in 3d supersymmetric U(N) model with N complex free bosons and fermions. We compute the anomalous dimensions of higher spin currents to the 1/N order but to all orders in the deformation parameters by mainly applying the conformal perturbation theory. The 3d field theory is supposed to be dual to 4d supersymmetric Vasiliev theory, and the marginal deformations are argued to correspond to modifying boundary conditions for bulk scalars and fermions. Thus the modification should break higher spin gauge symmetry and generate the masses of higher spin fields. We provide supports for the dual interpretation by relating bulk computation in terms of Witten diagrams to boundary one in conformal perturbation theory. 11. FlexibleSUSY-A spectrum generator generator for supersymmetric models Science.gov (United States) Athron, Peter; Park, Jae-hyeon; Stöckinger, Dominik; Voigt, Alexander 2015-05-01 We introduce FlexibleSUSY, a Mathematica and C++ package, which generates a fast, precise C++ spectrum generator for any SUSY model specified by the user. The generated code is designed with both speed and modularity in mind, making it easy to adapt and extend with new features. The model is specified by supplying the superpotential, gauge structure and particle content in a SARAH model file; specific boundary conditions e.g. at the GUT, weak or intermediate scales are defined in a separate FlexibleSUSY model file. From these model files, FlexibleSUSY generates C++ code for self-energies, tadpole corrections, renormalization group equations (RGEs) and electroweak symmetry breaking (EWSB) conditions and combines them with numerical routines for solving the RGEs and EWSB conditions simultaneously. The resulting spectrum generator is then able to solve for the spectrum of the model, including loop-corrected pole masses, consistent with user specified boundary conditions. The modular structure of the generated code allows for individual components to be replaced with an alternative if available. FlexibleSUSY has been carefully designed to grow as alternative solvers and calculators are added. Predefined models include the MSSM, NMSSM, E6SSM, USSM, R-symmetric models and models with right-handed neutrinos. 12. Higgs Boson Properties in the Standard Model and its Supersymmetric Extensions CERN Document Server Ellis, Jonathan Richard; Zwirner, F; Ellis, John; Ridolfi, Giovanni; Zwirner, Fabio 2007-01-01 We review the realization of the Brout-Englert-Higgs mechanism in the electroweak theory and describe the experimental and theoretical constraints on the mass of the single Higgs boson expected in the minimal Standard Model. We also discuss the couplings of this Higgs boson and its possible decay modes as functions of its unknown mass. We then review the structure of the Higgs sector in the minimal supersymmetric extension of the Standard Model (MSSM), noting the importance of loop corrections to the masses of its five physical Higgs bosons. Finally, we discuss some non-minimal models. 13. Higgs boson properties in the Standard Model and its supersymmetric extensions International Nuclear Information System (INIS) Ellis, J.; Ridolfi, G.; Zwirner, F. 2007-01-01 We review the realization of the Brout-Englert-Higgs mechanism in the electroweak theory and describe the experimental and theoretical constraints on the mass of the single Higgs boson expected in the minimal Standard Model. We also discuss the couplings of this Higgs boson and its possible decay modes as functions of its unknown mass. We then review the structure of the Higgs sector in the minimal supersymmetric extension of the Standard Model (MSSM), noting the importance of loop corrections to the masses of its 5 physical Higgs bosons. Finally, we discuss some non-minimal models. (authors) 14. An Exactly Solvable Supersymmetric Model of Semimagic Nuclei International Nuclear Information System (INIS) Balantekin, A. B.; Gueven, Nurtac; Pehlivan, Yamac 2008-01-01 A simple model of nucleons coupled to angular momentum zero (s-pairs) occupying the valance shell of a semi-magic nuclei is considered. The model has a separable, orbit dependent pairing interaction which dominates over the kinetic term. It is shown that such an interaction leads to an exactly solvable model whose (0 + ) eigenstates and energies can be computed very easily with the help of the algebraic Bethe ansatz method. It is also shown that the model has a supersymmetry which connects the spectra of some semimagic nuclei. The results obtained from this model for the semimagic Ni isotopes from 58 Ni to 68 Ni are given. In addition, a new and easier technique for calculating the energy eigenvalues from the Bethe ansatz equations is also presented. 15. Cell Chirality Drives Left-Right Asymmetric Morphogenesis. Science.gov (United States) Inaki, Mikiko; Sasamura, Takeshi; Matsuno, Kenji 2018-01-01 Most macromolecules found in cells are chiral, meaning that they cannot be superimposed onto their mirror image. However, cells themselves can also be chiral, a subject that has received little attention until very recently. In our studies on the mechanisms of left-right (LR) asymmetric development in Drosophila , we discovered that cells can have an intrinsic chirality to their structure, and that this "cell chirality" is generally responsible for the LR asymmetric development of certain organs in this species. The actin cytoskeleton plays important roles in the formation of cell chirality. In addition, Myosin31DF ( Myo31DF ), which encodes Drosophila Myosin ID, was identified as a molecular switch for cell chirality. In other invertebrate species, including snails and Caenorhabditis elegans , chirality of the blastomeres, another type of cell chirality, determines the LR asymmetry of structures in the body. Thus, chirality at the cellular level may broadly contribute to LR asymmetric development in various invertebrate species. Recently, cell chirality was also reported for various vertebrate cultured cells, and studies suggested that cell chirality is evolutionarily conserved, including the essential role of the actin cytoskeleton. Although the biological roles of cell chirality in vertebrates remain unknown, it may control LR asymmetric development or other morphogenetic events. The investigation of cell chirality has just begun, and this new field should provide valuable new insights in biology and medicine. 16. LHC phenomenology and higher order electroweak corrections in supersymmetric models with and without R-parity Energy Technology Data Exchange (ETDEWEB) Liebler, Stefan Rainer 2011-09-15 The standard model of particle physics lacks on some shortcomings from experimental as well as from theoretical point of view: There is no approved mechanism for the generation of masses of the fundamental particles, in particular also not for the light, but massive neutrinos. In addition the standard model does not provide an explanation for the observance of dark matter in the universe. Moreover the gauge couplings of the three forces in the standard model do not unify, implying that a fundamental theory combining all forces can not be formulated. Within this thesis we address supersymmetric models as answers to these various questions, but instead of focusing on the most simple supersymmetrization of the standard model, we consider basic extensions, namely the next-to-minimal supersymmetric standard model (NMSSM), which contains an additional singlet field, and R-parity violating models. Using lepton number violating terms in the context of bilinear R-parity violation and the {mu}{nu}SSM we are able to explain neutrino physics intrinsically supersymmetric, since those terms induce a mixing between the neutralinos and the neutrinos. This thesis works out the phenomenology of the supersymmetric models under consideration and tries to point out differences to the well-known features of the simplest supersymmetric realization of the standard model. In case of the R-parity violating models the decays of the light neutralinos can result in displaced vertices. In combination with a light singlet state these displaced vertices might offer a rich phenomenology like non-standard Higgs decays into a pair of singlinos decaying with displaced vertices. Within this thesis we present some calculations at next order of perturbation theory, since one-loop corrections provide possibly large contributions to the tree-level masses and decay widths. We are using an on-shell renormalization scheme to calculate the masses of neutralinos and charginos including the neutrinos and 17. LHC phenomenology and higher order electroweak corrections in supersymmetric models with and without R-parity International Nuclear Information System (INIS) Liebler, Stefan Rainer 2011-09-01 The standard model of particle physics lacks on some shortcomings from experimental as well as from theoretical point of view: There is no approved mechanism for the generation of masses of the fundamental particles, in particular also not for the light, but massive neutrinos. In addition the standard model does not provide an explanation for the observance of dark matter in the universe. Moreover the gauge couplings of the three forces in the standard model do not unify, implying that a fundamental theory combining all forces can not be formulated. Within this thesis we address supersymmetric models as answers to these various questions, but instead of focusing on the most simple supersymmetrization of the standard model, we consider basic extensions, namely the next-to-minimal supersymmetric standard model (NMSSM), which contains an additional singlet field, and R-parity violating models. Using lepton number violating terms in the context of bilinear R-parity violation and the μνSSM we are able to explain neutrino physics intrinsically supersymmetric, since those terms induce a mixing between the neutralinos and the neutrinos. This thesis works out the phenomenology of the supersymmetric models under consideration and tries to point out differences to the well-known features of the simplest supersymmetric realization of the standard model. In case of the R-parity violating models the decays of the light neutralinos can result in displaced vertices. In combination with a light singlet state these displaced vertices might offer a rich phenomenology like non-standard Higgs decays into a pair of singlinos decaying with displaced vertices. Within this thesis we present some calculations at next order of perturbation theory, since one-loop corrections provide possibly large contributions to the tree-level masses and decay widths. We are using an on-shell renormalization scheme to calculate the masses of neutralinos and charginos including the neutrinos and leptons in 18. Renormalization of supersymmetric theories International Nuclear Information System (INIS) Pierce, D.M. 1998-06-01 The author reviews the renormalization of the electroweak sector of the standard model. The derivation also applies to the minimal supersymmetric standard model. He discusses regularization, and the relation between the threshold corrections and the renormalization group equations. He considers the corrections to many precision observables, including M W and sin 2 θ eff . He shows that global fits to the data exclude regions of supersymmetric model parameter space and lead to lower bounds on superpartner masses 19. Supersymmetric field-theoretic models on a supermanifold Energy Technology Data Exchange (ETDEWEB) Franco, D.H.T. [Centro de Estudos de Fisica Teorica, Belo Horizonte, MG (Brazil); Polito, Caio M.M. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas 2003-04-01 We propose an extension of some structural aspects that have successfully been applied in the development of the theory of quantum fields propagating on a general spacetime manifold so as to include superfield models on a super manifold. (author) 20. Anomaly mediated supersymmetric models and Higgs data from the LHC CERN Document Server Arbey, A; Mahmoudi, F; Tarhini, A 2013-01-01 Anomaly mediation models are well motivated supersymmetry breaking scenarios which appear as alternatives to the mSUGRA paradigm. These models are quite compelling from the theoretical point of view and it is therefore important to test if they are also viable models for phenomenology. We perform a study of these models in the light of all standard flavour, collider and dark matter constraints, including also the recent Higgs boson measurements for the mass and signal strengths in the different decay channels. The minimal AMSB scenario can satisfy in part of its parameter space the dark matter requirement but is only marginally consistent with the current Higgs boson mass value. The HyperCharge-AMSB and Mixed Moduli-AMSB scenarios can better describe present data from dark matter, flavour, low energy physics and are consistent with the measured mass of the Higgs boson. The inclusion of the preferred signal strengths for the Higgs boson decay channels shows that for tan(beta) > 5 the HC-AMSB and MM-AMSB models... 1. Sneutrino warm inflation in the minimal supersymmetric model International Nuclear Information System (INIS) Bastero-Gil, Mar; Berera, Arjun 2005-01-01 The model of RH neutrino fields coupled to the MSSM is shown to yield a large parameter regime of warm inflation. In the strong dissipative regime, it is shown that inflation, driven by a single sneutrino field, occurs with all field amplitudes below the Planck scale. Analysis is also made of leptogenesis, neutrino mass generation and gravitino constraints. A new warm inflation scenario is purposed in which one scalar field drives a period of warm inflation and a second field drives a subsequent phase of reheating. Such a model is able to reduce the final temperature after inflation, thus helping to mitigate gravitino constraints 2. Massive (p,q)-supersymmetric sigma models revisited International Nuclear Information System (INIS) 1994-06-01 We recently obtained the conditions on the couplings of the general two-dimensional massive sigma-model required by (p,q)-supersymmetry. Here wer compute the Poisson bracket algebra of the supersymmetry and central Noether charges, and show that the action is invariant under the automorphism group of this algebra. Surprisingly, for the (4,4) case the automorphism group is always a subgroup of SO(3), rather than SO(4). We also re-analyse the conditions for (2,2) and 4,4) supersymmetry of the zero torsion models without assumptions about the central charge matrix. (orig.) 3. The quantum mechanics of the supersymmetric nonlinear sigma-model International Nuclear Information System (INIS) Davis, A.C.; Macfarlane, A.J.; Popat, P.C.; Holten, J.W. van 1984-01-01 The classical and quantum mechanical formalisms of the models are developed. The quantisation is done in such a way that the quantum theory can be represented explicitly in as simple a form as possible, and the problem of ordering of operators is resolved so as to maintain the supersymmetry algebra of the classical theory. (author) 4. Non-generic couplings in supersymmetric standard models Directory of Open Access Journals (Sweden) Evgeny I. Buchbinder 2015-09-01 Full Text Available We study two phases of a heterotic standard model, obtained from a Calabi–Yau compactification of the E8×E8 heterotic string, in the context of the associated four-dimensional effective theories. In the first phase we have a standard model gauge group, an MSSM spectrum, four additional U(1 symmetries and singlet fields. In the second phase, obtained from the first by continuing along the singlet directions, three of the additional U(1 symmetries are spontaneously broken and the remaining one is a B–L symmetry. In this second phase, dimension five operators inducing proton decay are consistent with all symmetries and as such, they are expected to be present. We show that, contrary to this expectation, these operators are forbidden due to the additional U(1 symmetries present in the first phase of the model. We emphasise that such “unexpected” absences of operators, due to symmetry enhancement at specific loci in the moduli space, can be phenomenologically relevant and, in the present case, protect the model from fast proton decay. 5. On two-particle N=1 supersymmetric composite grand unified models International Nuclear Information System (INIS) Pirogov, Yu.F. 1984-01-01 A class of two-particle N=1 supersymmetric composite grand unified models, satisfying the anomaly matching and cancellation conditions, n-independence and survival hypothesis is considered. A unique admissible set of the light states, containing spectator states on a par with the composite ones is found. At low mass scales this set contains exactly four families of ordinary fermions without any additional exotics. The interactions of the light states at distances greater than the compositeness radius are described by the N=1 sypersymmetric chiral grand unified model [SU(6)] 2 (or [SU(8)] 2 with a fixed set of four second-rank tensors as matter fields 6. Repetition of the quark-lepton states in a supersymmetric composite model with complementarity International Nuclear Information System (INIS) 1986-04-01 In a supersymmetric composite model based on an SU(4) sc loc confining theory, complementarity is used to support the symmetry-breaking pattern and spectrum of massless particles in a confining phase. The model is found to accommodate two generations of quarks and leptons as quasi Nambu-Goldstone fermions and another two generations as chiral fermions. Masses of composite particles are examined and the quark-lepton generations are classified according to possible mass splittings. The suppression of dangerous flavor-changing interactions is also considered. (author) 7. Two loop effective Kahler potential of (non)-renormalizable supersymmetric models International Nuclear Information System (INIS) 2005-10-01 We perform a supergraph computation of the effective Kahler potential at one and two loops for general four dimensional N=1 supersymmetric theories described by arbitrary Kahler potential, superpotential and gauge kinetic function. We only insist on gauge invariance of the Kahler potential and the superpotential as we heavily rely on its consequences in the quantum theory. However, we do not require gauge invariance for the gauge kinetic functions, so that our results can also be applied to anomalous theories that involve the Green-Schwarz mechanism. We illustrate our two loop results by considering a few simple models: the (non-)renormalizable Wess-Zumino model and Super Quantum Electrodynamics. (author) 8. Locally supersymmetric D=3 non-linear sigma models International Nuclear Information System (INIS) Wit, B. de; Tollsten, A.K.; Nicolai, H. 1993-01-01 We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is riemannian or Kaehler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it generally decomposes, into two separate quaternionic spaces, associated with inequivalent supermultiplets. For N=5, 6, 8 there is a unique (symmetric) space for any given number of supermultiplets. Beyond that there are only theories based on a single supermultiplet for N=9, 10, 12 and 16, associated with coset spaces with the exceptional isometry groups F 4(-20) , E 6(-14) , E 7(-5) and E 8(+8) , respectively. For N=3 and N ≥ 5 the D=2 theories obtained by dimensional reduction are two-loop finite. (orig.) 9. Superfield Lax formalism of supersymmetric sigma model on symmetric spaces International Nuclear Information System (INIS) Saleem, U.; Hassan, M. 2006-01-01 We present a superfield Lax formalism of the superspace sigma model based on the target space G/H and show that a one-parameter family of flat superfield connections exists if the target space G/H is a symmetric space. The formalism has been related to the existence of an infinite family of local and non-local superfield conserved quantities. A few examples have been given to illustrate the results. (orig.) 10. A supersymmetric D4 model for μ-τ symmetry Science.gov (United States) Adulpravitchai, A.; Blum, A.; Hagedorn, C. 2009-03-01 We construct a supersymmeterized version of the model presented by Grimus and Lavoura (GL) in \\cite{GL1} which predicts θ23 maximal and θ13 = 0 in the lepton sector. For this purpose, we extend the flavor group, which is D4 × Z2(aux) in the original model, to D4 × Z5. An additional difference is the absence of right-handed neutrinos. Despite these changes the model is the same as the GL model, since θ23 maximal and θ13 = 0 arise through the same mismatch of D4 subgroups, D2 in the charged lepton and Z2 in the neutrino sector. In our setup D4 is solely broken by gauge singlets, the flavons. We show that their vacuum structure, which leads to the prediction of θ13 and θ23, is a natural result of the scalar potential. We find that the neutrino mass matrix only allows for inverted hierarchy, if we assume a certain form of spontaneous CP violation. The quantity \|mee\|, measured in neutrinoless double beta decay, is nearly equal to the lightest neutrino mass m3. The Majorana phases phi1 and phi2 are restricted to a certain range for m3lesssim0.06 eV. We discuss the next-to-leading order corrections which give rise to shifts in the vacuum expectation values of the flavons. These induce deviations from maximal atmospheric mixing and vanishing θ13. It turns out that these deviations are smaller for θ23 than for θ13. 11. A supersymmetric standard model from a local E6 GUT International Nuclear Information System (INIS) Braam, Felix Klaus 2012-02-01 In this thesis we have investigated to what extent the exceptional Lie-group E 6 can serve as unified gauge group. In the presence of the full E 6 matter content, unifcation can be realized by increasing the degree of gauge symmetry above some intermediate scale. We found that a full E 6 gauge invariant theory is disfavoured by phenomenological observations like proton stability and the smallness of flavour changing neutral currents. An appropriate framework to embed E 6 into a model for particle physics are higher dimensional orbifold constructions, where E 6 is the gauge group in the bulk and the intermediate symmetry group is the common subset of E 6 subgroups residing at the fixed-points of the orbifold. In this way the degree of symmetry in four space-time dimensions is reduced, such that the operators leading to the aforementioned dsastrous phenomenological consequences can be forbidden independently. In order to derive the implications of the model for the current experiments at the Large Hadron Collider (LHC), we developed an automated spectrum generator. It uses Monte-Carlo Markov-Chain techniques to cope with the high dimensionality of the space of input parameters and the complex interdependencies in the evolution of the Lagrangian parameters from the orbifold compactification scale to the TeV scale. For the spectra obtained with this program, we performed Monte-Carlo simulations of the production and decay of the Z ' boson stemming from the additional U(1) ' , using our own implementation of the model into the event generator WHIZARD. 12. Double suppression of FCNCs in a supersymmetric model International Nuclear Information System (INIS) Kajiyama, Yuji 2004-01-01 A concrete model which can suppress FCNCs and CP violating phenomena is suggested. It is S 3 symmetric extension of MSSM in extra dimensions where only SU(2) and SU(3) gauge multiplet are assumed to propagate in the bulk. They are suppressed due to S 3 flavor symmetry at M SUSY , and the infrared attractive force of gauge interaction in extra dimensions are used to suppress them at the compactification scale. We find that O(1) disorders of the soft parameters are allowed at the cut-off scale to suppress FCNCs and CP violating phenomena. (author) 13. Double suppression of FCNCs in a supersymmetric model Energy Technology Data Exchange (ETDEWEB) Kajiyama, Yuji [Kanazawa Univ., Dept. of Physics, Kanazawa, Ishikawa (Japan) 2004-12-01 A concrete model which can suppress FCNCs and CP violating phenomena is suggested. It is S{sub 3} symmetric extension of MSSM in extra dimensions where only SU(2) and SU(3) gauge multiplet are assumed to propagate in the bulk. They are suppressed due to S{sub 3} flavor symmetry at M{sub SUSY}, and the infrared attractive force of gauge interaction in extra dimensions are used to suppress them at the compactification scale. We find that O(1) disorders of the soft parameters are allowed at the cut-off scale to suppress FCNCs and CP violating phenomena. (author) 14. Radiative breaking of the minimal supersymmetric left–right model Directory of Open Access Journals (Sweden) 2016-05-01 Full Text Available We study a variation to the SUSY Left–Right symmetric model based on the gauge group SU(3c×SU(2L×SU(2R×U(1BL. Beyond the quark and lepton superfields we only introduce a second Higgs bidoublet to produce realistic fermion mass matrices. This model does not include any SU(2R triplets. We calculate renormalization group evolutions of soft SUSY parameters at the one-loop level down to low energy. We find that an SU(2R slepton doublet acquires a negative mass squared at low energies, so that the breaking of SU(2R×U(1BL→U(1Y is realized by a non-zero vacuum expectation value of a right-handed sneutrino. Small neutrino masses are produced through neutrino mixings with gauginos. Mass limits on the SU(2R×U(1BL sector are obtained by direct search results at the LHC as well as lepton-gaugino mixing bounds from the LEP precision data. 15. Phenomenological study of the minimal R-symmetric supersymmetric standard model International Nuclear Information System (INIS) Diessner, Philip 2016-01-01 The Standard Model (SM) of particle physics gives a comprehensive description of numerous phenomena concerning the fundamental components of nature. Still, open questions and a clouded understanding of the underlying structure remain. Supersymmetry is a well motivated extension that may account for the observed density of dark matter in the universe and solve the hierarchy problem of the SM. The minimal supersymmetric extension of the SM (MSSM) provides solutions to these challenges. Furthermore, it predicts new particles in reach of current experiments. However, the model has its own theoretical challenges and is under fire from measurements provided by the Large Hadron Collider (LHC). Nevertheless, the concept of supersymmetry has an elegance which not only shines in the MSSM. Hence, it is also of interest to examine non-minimal supersymmetric models. They have benefits similar to the MSSM and may solve its shortcomings. R-symmetry is the only global symmetry allowed that does not commutate with supersymmetry and Lorentz symmetry. Thus, extending a supersymmetric model with R-symmetry is a theoretically well motivated endeavor to achieve the complete symmetry content of a field theory. Such a model provides a natural explanation for non-discovery in the early runs of the LHC and leads to further predictions distinct from those of the MSSM. The work described in this thesis contributes to the effort by studying the minimal R-symmetric supersymmetric extension of the SM (MRSSM). Important aspects of its physics and the dependence of observables on the parameter space of the MRSSM are investigated. The discovery of a scalar particle compatible with the Higgs boson of the SM at the LHC was announced in 2012. It is the first and crucial task of this thesis to understand the underlying mechanisms leading to the correct Higgs boson mass prediction in the MRSSM. Then, the relevant regions of parameter space are investigated and it is shown that they are also in agreement 16. Phenomenological study of the minimal R-symmetric supersymmetric standard model Energy Technology Data Exchange (ETDEWEB) Diessner, Philip 2016-10-20 The Standard Model (SM) of particle physics gives a comprehensive description of numerous phenomena concerning the fundamental components of nature. Still, open questions and a clouded understanding of the underlying structure remain. Supersymmetry is a well motivated extension that may account for the observed density of dark matter in the universe and solve the hierarchy problem of the SM. The minimal supersymmetric extension of the SM (MSSM) provides solutions to these challenges. Furthermore, it predicts new particles in reach of current experiments. However, the model has its own theoretical challenges and is under fire from measurements provided by the Large Hadron Collider (LHC). Nevertheless, the concept of supersymmetry has an elegance which not only shines in the MSSM. Hence, it is also of interest to examine non-minimal supersymmetric models. They have benefits similar to the MSSM and may solve its shortcomings. R-symmetry is the only global symmetry allowed that does not commutate with supersymmetry and Lorentz symmetry. Thus, extending a supersymmetric model with R-symmetry is a theoretically well motivated endeavor to achieve the complete symmetry content of a field theory. Such a model provides a natural explanation for non-discovery in the early runs of the LHC and leads to further predictions distinct from those of the MSSM. The work described in this thesis contributes to the effort by studying the minimal R-symmetric supersymmetric extension of the SM (MRSSM). Important aspects of its physics and the dependence of observables on the parameter space of the MRSSM are investigated. The discovery of a scalar particle compatible with the Higgs boson of the SM at the LHC was announced in 2012. It is the first and crucial task of this thesis to understand the underlying mechanisms leading to the correct Higgs boson mass prediction in the MRSSM. Then, the relevant regions of parameter space are investigated and it is shown that they are also in agreement 17. Does Subjective Left-Right Position Have a Causal Effect on Support for Redistribution? DEFF Research Database (Denmark) characteristics as instruments for left-right position, can be used to estimate the causal effect of left-right position on support for redistribution. I analyze data on Sweden, Germany, and Norway from the two first waves of the European Social Survey and find first that left-right position is endogenous...... to support for redistribution, and second consistent with theory, that a causal effect of left-right position on support for redistribution exists which is stronger than previously shown.... 18. Constraints on supersymmetric flavour models from b→sγ International Nuclear Information System (INIS) Olive, Keith A.; Velasco-Sevilla, L. 2008-01-01 We consider the effects of departures from minimal flavour violations (MFV) in the context of CMSSM-like theories. Second and third generation off-diagonal elements in the Yukawa, sfermion, and trilinear mass matrices are taken to be non-zero at the GUT scale. These are run down together with MSSM parameters to the electroweak scale. We apply constraints from fermion masses and CKM matrix elements to limit the range of the new free parameters of the model. We determine the effect of the departure from MFV on the branching ratio of b→s γ. We find that only when the expansion parameter in the down-squark sector is relatively large there is a noticeable effect, which tends to relax the lower limit from b→s γ on the universal gaugino mass. We also find that the expansion parameter associated with the slepton sector needs to be smaller than the corresponding parameter in the down-squark sector in order to be compliant with the bound imposed by the branching ratio of τ→μγ. 19. Adiabatic density perturbations and matter generation from the minimal supersymmetric standard model. Science.gov (United States) Enqvist, Kari; Kasuya, Shinta; Mazumdar, Anupam 2003-03-07 We propose that the inflaton is coupled to ordinary matter only gravitationally and that it decays into a completely hidden sector. In this scenario both baryonic and dark matter originate from the decay of a flat direction of the minimal supersymmetric standard model, which is shown to generate the desired adiabatic perturbation spectrum via the curvaton mechanism. The requirement that the energy density along the flat direction dominates over the inflaton decay products fixes the flat direction almost uniquely. The present residual energy density in the hidden sector is typically shown to be small. 20. Anomaly-free gauges in superstring theory and double supersymmetric sigma-model International Nuclear Information System (INIS) Demichev, A.P.; Iofa, M.Z. 1991-01-01 Superharmonic gauge which is a nontrivial analog of the harmonic gauge in bosonic string theory is constructed for the fermionic superstrings. In contrast to the conformal gauge, the harmonic gauge in bosonic string and superharmonic gauge in superstring theory are shown to be free from previously discovered BRST anomaly (in critical dimension) in higher orders of string perturbation theory and thus provide the setup for consistent quantization of (super)string theory. Superharmonic gauge appears to be closely connected with the supersymmetric σ-model with the target space being also a supermanifold. 28 refs 1. Multichannel coupling with supersymmetric quantum mechanics and exactly-solvable model for the Feshbach resonance International Nuclear Information System (INIS) Sparenberg, Jean-Marc; Samsonov, Boris F; Foucart, Francois; Baye, Daniel 2006-01-01 A new type of supersymmetric transformations of the coupled-channel radial Schroedinger equation is introduced, which do not conserve the vanishing behaviour of solutions at the origin. Contrary to the usual transformations, these 'non-conservative' transformations allow, in the presence of thresholds, the construction of well-behaved potentials with coupled scattering matrices from uncoupled potentials. As an example, an exactly-solvable potential matrix is obtained which provides a very simple model of the Feshbach-resonance phenomenon. (letter to the editor) 2. CP asymmetry in tau slepton decay in the minimal supersymmetric standard model International Nuclear Information System (INIS) Yang Weimin; Du Dongsheng 2002-01-01 We investigate CP violation asymmetry in the decay of a tau slepton into a tau neutrino and a chargino in the minimal supersymmetric standard model. The new source of CP violation is the complex mixing in the tau slepton sector. The rate asymmetry between the decays of the tau slepton and its CP conjugate process can be of the order of 10 -3 in some region of the parameter space of the minimal supergravity scenario, which will possibly be detectable in near-future collider experiments 3. A supersymmetric matrix model: II. Exploring higher-fermion-number sectors CERN Document Server Veneziano, Gabriele 2006-01-01 Continuing our previous analysis of a supersymmetric quantum-mechanical matrix model, we study in detail the properties of its sectors with fermion number F=2 and 3. We confirm all previous expectations, modulo the appearance, at strong coupling, of {\\it two} new bosonic ground states causing a further jump in Witten's index across a previously identified critical 't Hooft coupling $\\lambda_c$. We are able to elucidate the origin of these new SUSY vacua by considering the $\\lambda \\to \\infty$ limit and a strong coupling expansion around it. 4. Solving the flavour problem in supersymmetric Standard Models with three Higgs families International Nuclear Information System (INIS) Howl, R.; King, S.F. 2010-01-01 We show how a non-Abelian family symmetry Δ 27 can be used to solve the flavour problem of supersymmetric Standard Models containing three Higgs families such as the Exceptional Supersymmetric Standard Model (E 6 SSM). The three 27-dimensional families of the E 6 SSM, including the three families of Higgs fields, transform in a triplet representation of the Δ 27 family symmetry, allowing the family symmetry to commute with a possible high energy E 6 symmetry. The Δ 27 family symmetry here provides a high energy understanding of the Z 2 H symmetry of the E 6 SSM, which solves the flavour changing neutral current problem of the three families of Higgs fields. The main phenomenological predictions of the model are tri-bi-maximal mixing for leptons, two almost degenerate LSPs and two almost degenerate families of colour triplet D-fermions, providing a clear prediction for the LHC. In addition the model predicts PGBs with masses below the TeV scale, and possibly much lighter, which appears to be a quite general and robust prediction of all models based on the D-term vacuum alignment mechanism. 5. What's Left of the Left-Right Dimension? Why the Economic Policy Positions of Europeans Do Not Fit the Left-Right Dimension. Science.gov (United States) Otjes, Simon 2018-01-01 In political science the economic left-right dimension plays a central role. A growing body of evidence shows that the economic policy preferences of a large segment of citizens do not scale sufficiently. Using Mokken scale analysis, this study determines the causes of this phenomenon. Differences in the extent to which the economic policy preferences of citizens fit the left-right dimension can be explained in terms of the interaction between individual level and political system-level variables: citizens who spend more attention to politicians with views that conform to the left-right dimension, have views that conform to the left-right dimension. There is also a role for the legacy of communist dictatorship: citizens who were socialised in democratic countries have views that fit the left-right dimension better than those socialised during communism. 6. Search for Heavy Neutrinos and $WR$ Bosons with Right-Handed Couplings in a Left-Right Symmetric Model in $pp$ Collisions at $s=7 TeV$ Energy Technology Data Exchange (ETDEWEB) 2012-12-01 Results are presented from a search for heavy, right-handed muon neutrinos, N[mu], and right-handed W[R] bosons, which arise in the left-right symmetric extensions of the standard model. The analysis is based on a 5.0 inverse femtobarn sample of proton-proton collisions at a center-of-mass energy of 7 TeV, collected by the CMS detector at the Large Hadron Collider. No evidence is observed for an excess of events over the standard model expectation. For models with exact left-right symmetry, heavy right-handed neutrinos are excluded at 95% confidence level for a range of neutrino masses below the W[R] mass, dependent on the value of M(W[R]). The excluded region in the two-dimensional (M(W[R]), M(N[mu])) mass plane extends to M(W[R]) = 2.5 TeV. 7. Topics in supersymmetric theories International Nuclear Information System (INIS) Nemeschansky, D.D. 1984-01-01 This thesis discusses four different topics in supersymmetric theories. In the first part models in which supersymmetry is broken by the Fayet-Iliopoulos mechanism are considered. The possibility that scalar quark and lepton masses might arise radiatively in such theories is explored. In the second part supersymmetric grand unified models with a sliding singlet are considered. The author reviews the argument that the sliding singlet does not work in models with large supersymmetry breaking. Then he considers the possibility of using a sliding singlet with low energy supersymmetry breaking. The third part of the thesis deals with the entropy problem of supersymmetric theories. Most supersymmetric models possess a decoupled particle with mass of order 100 GeV which is copiously produced in the early universe and whose decay produces huge amounts of entropy. The author shows how this problem can be avoided in theories in which the hidden sector contains several light fields. In the fourth part effective Lagrangians for supersymmetric theories are studied. The anomalous pion interaction for supersymmetric theories is written down. General properties of this term are studied both on compact and non-compact manifolds 8. Low-mass right-handed gauge bosons, manifest left-right symmetry, and the K/sub L/-K/sub s/ mass difference International Nuclear Information System (INIS) Datta, A.; Raychaudhuri, A. 1983-01-01 We calculate the K/sub L/-K/sub S/ mass difference in left-right-symmetric models with four quarks. It is found that a low right-handed mass scale requires strong deviations from manifest left-right symmetry 9. Supersymmetric Fits after the Higgs Discovery and Implications for Model Building CERN Document Server Ellis, John 2014-01-01 The data from the first run of the LHC at 7 and 8 TeV, together with the information provided by other experiments such as precision electroweak measurements, flavour measurements, the cosmological density of cold dark matter and the direct search for the scattering of dark matter particles in the LUX experiment, provide important constraints on supersymmetric models. Important information is provided by the ATLAS and CMS measurements of the mass of the Higgs boson, as well as the negative results of searches at the LHC for events with missing transverse energy accompanied by jets, and the LHCb and CMS measurements off BR($B_s \\to \\mu^+ \\mu^-$). Results are presented from frequentist analyses of the parameter spaces of the CMSSM and NUHM1. The global $\\chi^2$ functions for the supersymmetric models vary slowly over most of the parameter spaces allowed by the Higgs mass and the missing transverse energy search, with best-fit values that are comparable to the $\\chi^2$ for the Standard Model. The $95\\%$ CL lower... 10. Bounds on the Higgs mass in the standard model and the minimal supersymmetric standard model CERN Document Server Quiros, M. 1995-01-01 Depending on the Higgs-boson and top-quark masses, M_H and M_t, the effective potential of the {\\bf Standard Model} can develop a non-standard minimum for values of the field much larger than the weak scale. In those cases the standard minimum becomes metastable and the possibility of decay to the non-standard one arises. Comparison of the decay rate to the non-standard minimum at finite (and zero) temperature with the corresponding expansion rate of the Universe allows to identify the region, in the (M_H, M_t) plane, where the Higgs field is sitting at the standard electroweak minimum. In the {\\bf Minimal Supersymmetric Standard Model}, approximate analytical expressions for the Higgs mass spectrum and couplings are worked out, providing an excellent approximation to the numerical results which include all next-to-leading-log corrections. An appropriate treatment of squark decoupling allows to consider large values of the stop and/or sbottom mixing parameters and thus fix a reliable upper bound on the mass o... 11. The neutralino sector in the U(1)-extended supersymmetric standard model Energy Technology Data Exchange (ETDEWEB) Choi, S.Y. [Chonbuk National Univ., Jeonju (Korea). Dept. of Physics and RIPC]\|[Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Haber, H.E. [California Univ., Santa Cruz, CA (United States). SCIPP; Kalinowski, J. [Warsaw Univ. (Poland). Inst. of Theoretical Physics; Zerwas, P.M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]\|[California Univ., Santa Cruz, CA (United States). SCIPP 2006-12-15 Motivated by grand unified theories and string theories we analyze the general structure of the neutralino sector in the USSM, an extension of the Minimal Supersymmetric Standard Model that involves a broken extra U(1) gauge symmetry. This supersymmetric U(1)-extended model includes an Abelian gauge superfield and a Higgs singlet superfield in addition to the standard gauge and Higgs superfields of the MSSM. The interactions between the MSSM fields and the new fields are in general weak and the mixing is small, so that the coupling of the two subsystems can be treated perturbatively. As a result, the mass spectrum and mixing matrix in the neutralino sector can be analyzed analytically and the structure of this 6-state system is under good theoretical control. We describe the decay modes of the new states and the impact of this extension on decays of the original MSSM neutralinos, including radiative transitions in cross-over zones. Production channels in cascade decays at the LHC and pair production at e{sup +}e{sup -} colliders are also discussed. (orig.) 12. A Minimal Supersymmetric Model of Particle Physics and the Early Universe CERN Document Server Buchmüller, W; Kamada, K; Schmitz, K 2014-01-01 We consider a minimal supersymmetric extension of the Standard Model, with right-handed neutrinos and local $B$$-$$L$, the difference between baryon and lepton number, a symmetry which is spontaneously broken at the scale of grand unification. To a large extent, the parameters of the model are determined by gauge and Yukawa couplings of quarks and leptons. We show that this minimal model can successfully account for the earliest phases of the cosmological evolution: Inflation is driven by the energy density of a false vacuum of unbroken $B$$-$$L$ symmetry, which ends in tachyonic preheating, i.e.\\ the decay of the false vacuum, followed by a matter dominated phase with heavy $B$$-$$L$ Higgs bosons. Nonthermal and thermal processes produce an abundance of heavy neutrinos whose decays generate primordial entropy, baryon asymmetry via leptogenesis and dark matter consisting of gravitinos or nonthermal WIMPs. The model predicts relations between neutrino and superparticle masses and a characteristic spectrum of g... 13. A novel approach to finely tuned supersymmetric standard models: The case of the non-universal Higgs mass model Science.gov (United States) Yamaguchi, Masahiro; Yin, Wen 2018-02-01 Discarding the prejudice about fine tuning, we propose a novel and efficient approach to identify relevant regions of fundamental parameter space in supersymmetric models with some amount of fine tuning. The essential idea is the mapping of experimental constraints at a low-energy scale, rather than the parameter sets, to those of the fundamental parameter space. Applying this method to the non-universal Higgs mass model, we identify a new interesting superparticle mass pattern where some of the first two generation squarks are light whilst the stops are kept heavy as 6 TeV. Furthermore, as another application of this method, we show that the discrepancy of the muon anomalous magnetic dipole moment can be filled by a supersymmetric contribution within the 1{σ} level of the experimental and theoretical errors, which was overlooked by previous studies due to the extremely fine tuning required. 14. A Singlet Extension of the Minimal Supersymmetric Standard Model: Towards a More Natural Solution to the Little Hierarchy Problem Energy Technology Data Exchange (ETDEWEB) de la Puente, Alejandro [Univ. of Notre Dame, IN (United States) 2012-05-01 In this work, I present a generalization of the Next-to-Minimal Supersymmetric Standard Model (NMSSM), with an explicit μ-term and a supersymmetric mass for the singlet superfield, as a route to alleviating the little hierarchy problem of the Minimal Supersymmetric Standard Model (MSSM). I analyze two limiting cases of the model, characterized by the size of the supersymmetric mass for the singlet superfield. The small and large limits of this mass parameter are studied, and I find that I can generate masses for the lightest neutral Higgs boson up to 140 GeV with top squarks below the TeV scale, all couplings perturbative up to the gauge unification scale, and with no need to fine tune parameters in the scalar potential. This model, which I call the S-MSSM is also embedded in a gauge-mediated supersymmetry breaking scheme. I find that even with a minimal embedding of the S-MSSM into a gauge mediated scheme, the mass for the lightest Higgs boson can easily be above 114 GeV, while keeping the top squarks below the TeV scale. Furthermore, I also study the forward-backward asymmetry in the t¯t system within the framework of the S-MSSM. For this purpose, non-renormalizable couplings between the first and third generation of quarks to scalars are introduced. The two limiting cases of the S-MSSM, characterized by the size of the supersymmetric mass for the singlet superfield is analyzed, and I find that in the region of small singlet supersymmetric mass a large asymmetry can be obtained while being consistent with constraints arising from flavor physics, quark masses and top quark decays. 15. Using Convolutional Neural Network Filters to Measure Left-Right Mirror Symmetry in Images Directory of Open Access Journals (Sweden) Anselm Brachmann 2016-12-01 Full Text Available We propose a method for measuring symmetry in images by using filter responses from Convolutional Neural Networks (CNNs. The aim of the method is to model human perception of left/right symmetry as closely as possible. Using the Convolutional Neural Network (CNN approach has two main advantages: First, CNN filter responses closely match the responses of neurons in the human visual system; they take information on color, edges and texture into account simultaneously. Second, we can measure higher-order symmetry, which relies not only on color, edges and texture, but also on the shapes and objects that are depicted in images. We validated our algorithm on a dataset of 300 music album covers, which were rated according to their symmetry by 20 human observers, and compared results with those from a previously proposed method. With our method, human perception of symmetry can be predicted with high accuracy. Moreover, we demonstrate that the inclusion of features from higher CNN layers, which encode more abstract image content, increases the performance further. In conclusion, we introduce a model of left/right symmetry that closely models human perception of symmetry in CD album covers. 16. A K-theory anomaly free supersymmetric flipped SU(5) model from intersecting branes Energy Technology Data Exchange (ETDEWEB) Chen, C.-M. [George P. and Cynthia W. Mitchell Institute for Fundamental Physics, Texas A and M University, College Station, TX 77843 (United States)]. E-mail: [email protected]; Kraniotis, G.V. [George P. and Cynthia W. Mitchell Institute for Fundamental Physics, Texas A and M University, College Station, TX 77843 (United States)]. E-mail: [email protected]; Mayes, V.E. [George P. and Cynthia W. Mitchell Institute for Fundamental Physics, Texas A and M University, College Station, TX 77843 (United States)]. E-mail: [email protected]; Nanopoulos, D.V. [George P. and Cynthia W. Mitchell Institute for Fundamental Physics, Texas A and M University, College Station, TX 77843 (United States) and Astroparticle Physics Group, Houston Advanced Research Center (HARC), Mitchell Campus, Woodlands, TX 77381 (United States) and Academy of Athens, Division of Natural Sciences, 28 Panepistimiou Avenue, Athens 10679 (Greece)]. E-mail: [email protected]; Walker, J.W. [George P. and Cynthia W. Mitchell Institute for Fundamental Physics, Texas A and M University, College Station, TX 77843 (United States)]. E-mail: [email protected] 2005-10-06 We construct an N=1 supersymmetric three-family flipped SU(5) model from type IIA orientifolds on T{sup 6}/(Z{sub 2}xZ{sub 2}) with D6-branes intersecting at general angles. The model is constrained by the requirement that Ramond-Ramond tadpoles cancel, the supersymmetry conditions, and that the gauge boson coupled to the U(1){sub X} factor does not get a string-scale mass via a generalised Green-Schwarz mechanism. The model is further constrained by requiring cancellation of K-theory charges. The spectrum contains a complete grand unified and electroweak Higgs sector, however the latter in a non-minimal number of copies. In addition, it contains extra matter both in bi-fundamental and vector-like representations as well as two copies of matter in the symmetric representation of SU(5) 17. Twining genera of (0,4) supersymmetric sigma models on K3 International Nuclear Information System (INIS) Harrison, Sarah; Kachru, Shamit; Paquette, Natalie M. 2014-01-01 Conformal field theories with (0,4) worldsheet supersymmetry and K3 target can be used to compactify the E 8 ×E 8 heterotic string to six dimensions in a supersymmetric manner. The data specifying such a model includes an appropriate configuration of 24 gauge instantons in the E 8 ×E 8 gauge group to satisfy the constraints of anomaly cancellation. In this note, we compute twining genera — elliptic genera with appropriate insertions of discrete symmetry generators in the trace — for (0,4) theories with various instanton embeddings. We do this by constructing linear sigma models which flow to the desired conformal field theories, and using the techniques of localization. We present several examples of such twining genera which are consistent with a moonshine relating these (0,4) models to the finite simple sporadic group M 24 18. Large scale structure from the Higgs fields of the supersymmetric standard model International Nuclear Information System (INIS) Bastero-Gil, M.; Di Clemente, V.; King, S.F. 2003-01-01 We propose an alternative implementation of the curvaton mechanism for generating the curvature perturbations which does not rely on a late decaying scalar decoupled from inflation dynamics. In our mechanism the supersymmetric Higgs scalars are coupled to the inflaton in a hybrid inflation model, and this allows the conversion of the isocurvature perturbations of the Higgs fields to the observed curvature perturbations responsible for large scale structure to take place during reheating. We discuss an explicit model which realizes this mechanism in which the μ term in the Higgs superpotential is generated after inflation by the vacuum expectation value of a singlet field. The main prediction of the model is that the spectral index should deviate significantly from unity, vertical bar n-1 vertical bar ∼0.1. We also expect relic isocurvature perturbations in neutralinos and baryons, but no significant departures from Gaussianity and no observable effects of gravity waves in the CMB spectrum 19. Supersymmetric mechanics International Nuclear Information System (INIS) Stelle, Kellogg S 2007-01-01 With the development of the electronic archives in high-energy physics, there has been increasing questioning of the role of traditional publishing styles, particularly in the production of conference books. One aspect of traditional publishing that still receives wide appreciation, however, is in the production of well-focussed pedagogical material. The present two-volume edition, 'Supersymmetric Mechanics-Vol 1', edited by S Bellucci and 'Supersymmetric Mechanics-Vol 2', edited by S Bellucci, S Ferrara and A Marrani, is a good example of the kind of well-digested presentation that should still find its way into university libraries. This two-volume set presents the material of a set of pedagogical lectures presented at the INFN National Laboratory in Frascati over a two-year period on the subject of supersymmetric mechanics. The articles include the results of discussions with the attending students after the lectures. Overall, this makes for a useful compilation of material on a subject that underlies much of the current effort in supersymmetric approaches to cosmology and the unification programme. The first volume comprises articles on 'A journey through garden algebras' by S Bellucci, S J Gates Jr and E Orazi on linear supermultiplet realizations in supersymmetric mechanics,'Supersymmetric mechanics in superspace' by S Bellucci and S Krivonos, 'Noncommutative mechanics, Landau levels, twistors and Yang-Mills amplitudes' by V P Nair, 'Elements of (super) Hamiltonian formalism' by A Nersessian and 'Matrix mechanics' by C Sochichiu. The second volume consists entirely of a masterful presentation on 'The attractor mechanism and space time singularities' by S Ferrara. This presents a comprehensive and detailed overview of the structure of supersymmetric black hole solutions in supergravity, critical point structure in the scalar field moduli space and the thermodynamic consequences. This second volume alone makes the set a worthwhile addition to the research 20. Spin analysis of supersymmetric particles International Nuclear Information System (INIS) Choi, S.Y.; Martyn, H.U. 2006-12-01 The spin of supersymmetric particles can be determined at e + e - colliders unambiguously. This is demonstrated for a characteristic set of non-colored supersymmetric particles -- smuons, selectrons, and charginos/neutralinos. The analysis is based on the threshold behavior of the excitation curves for pair production in e + e - collisions, the angular distribution in the production process and decay angular distributions. In the first step we present the observables in the helicity formalism for the supersymmetric particles. Subsequently we confront the results with corresponding analyses of Kaluza-Klein particles in theories of universal extra space dimensions which behave distinctly different from supersymmetric theories. It is shown in the third step that a set of observables can be designed which signal the spin of supersymmetric particles unambiguously without any model assumptions. Finally in the fourth step it is demonstrated that the determination of the spin of supersymmetric particles can be performed experimentally in practice at an e + e - collider. (orig.) 1. BPS states in N = 2 supersymmetric G2 and F4 models Science.gov (United States) Ahl Laamara, R.; Mellal, O.; Saidi, E. H. 2017-07-01 In BPS quiver theory of N = 2 supersymmetric pure gauge models with gauge invariance G, primitive BPS quivers Q0G are of two types: Q0ADE and Q0BCFG. In this study, we first show that Q0ADE have outer-automorphism symmetries inherited from the outer-automorphisms of the Dynkin diagrams of ADE Lie algebras. Then, we extend the usual folding operation of Dynkin diagrams ADE → BCFG to obtain the two following things: (i) relate Q0BCFG quivers and their mutations to the Q0ADE ones and their mutations; and (ii) link the BPS chambers of the N = 2ADE theories with the corresponding BCFG ones. As an illustration of this construction, we derive the BPS and anti-BPS states of the strong chambers QstgG2 and QstgF4 of the 4d N = 2 pure G2 and F4 gauge models. 2. Organization of left-right coordination of neuronal activity in the mammalian spinal cord DEFF Research Database (Denmark) Shevtsova, Natalia A.; Talpalar, Adolfo E.; Markin, Sergey N. 2015-01-01 and the left-right synchronous hopping-like pattern in mutants lacking specific neuron classes, and speed-dependent asymmetric changes of flexor and extensor phase durations. The models provide insights into the architecture of spinal network and the organization of parallel inhibitory and excitatory CIN....... In this study, we construct and analyse two computational models of spinal locomotor circuits consisting of left and right rhythm generators interacting bilaterally via several neuronal pathways mediated by different CINs. The CIN populations incorporated in the models include the genetically identified...... inhibitory (V0D) and excitatory (V0V) subtypes of V0 CINs and excitatory V3 CINs. The model also includes the ipsilaterally projecting excitatory V2a interneurons mediating excitatory drive to the V0V CINs. The proposed network architectures and CIN connectivity allow the models to closely reproduce... 3. New supersymmetrizations of the generalized KDV hierarchies International Nuclear Information System (INIS) Figueroa-O'Farrill, J.M.; Stanciu, S. 1993-03-01 Recently we investigated a new supersymmetrization procedure for the KdV hierarchy inspired in some recent work on supersymmetric matrix models. We extend this procedure here for the generalized KdV hierarchies. The resulting supersymmetric hierarchies are generically nonlocal, expect for the case of Boussinesque which we treat in detail. The resulting supersymmetric hierarchy is integrable and bihamiltonian and contains the Boussinesque hierarchy as a subhierarchy. In a particular realization, we extend it by defining supersymmetric odd flows. We end with some comments on a slight modification of this supersymmetrization which yields local equations for any generalized KdV hierarchy. (orig.) 4. Measurement of the left-right asymmetry in Z boson production by electron-positron collisions International Nuclear Information System (INIS) Elia, R.D. 1994-04-01 We present the first measurement of the left-right cross-section asymmetry (A LR ) in Z boson production at the SLAC Linear Collider. The left-right asymmetry provides a direct measurement of the e - -Z coupling and thus of the effective weak mixing angle; in addition, A LR is sensitive to the unknown top-quark and Higgs-boson masses. In 1992 the SLD detector recorded 10224 Z events produced by the collision of longitudinally polarized electrons with an unpolarized positron beam at a center-of-mass energy of 91.55 GeV. The average electron beam polarization during the run was (22.4 ± 0.6)%. We measure A LR to be 0.101 ± 0.044 (stat.) ± 0.004 (syst.), which determines the effective weak mixing angle to be sin 2 θeff/W = 0.2377 ± 0.0056 (stat.) ± 0.0005 (syst.). This measurement of A LR is in agreement with comparable measurements and is consistent with Standard-Model predictions for allowed top and Higgs masses 5. microRNA function in left-right neuronal asymmetry: perspectives from C. elegans. Science.gov (United States) Alqadah, Amel; Hsieh, Yi-Wen; Chuang, Chiou-Fen 2013-09-23 Left-right asymmetry in anatomical structures and functions of the nervous system is present throughout the animal kingdom. For example, language centers are localized in the left side of the human brain, while spatial recognition functions are found in the right hemisphere in the majority of the population. Disruption of asymmetry in the nervous system is correlated with neurological disorders. Although anatomical and functional asymmetries are observed in mammalian nervous systems, it has been a challenge to identify the molecular basis of these asymmetries. C. elegans has emerged as a prime model organism to investigate molecular asymmetries in the nervous system, as it has been shown to display functional asymmetries clearly correlated to asymmetric distribution and regulation of biologically relevant molecules. Small non-coding RNAs have been recently implicated in various aspects of neural development. Here, we review cases in which microRNAs are crucial for establishing left-right asymmetries in the C. elegans nervous system. These studies may provide insight into how molecular and functional asymmetries are established in the human brain. 6. microRNA function in left-right neuronal asymmetry: perspectives from C. elegans Directory of Open Access Journals (Sweden) 2013-09-01 Full Text Available Left-right asymmetry in anatomical structures and functions of the nervous system is present throughout the animal kingdom. For example, language centers are localized in the left side of the human brain, while spatial recognition functions are found in the right hemisphere in the majority of the population. Disruption of asymmetry in the nervous system is correlated with neurological disorders. Although anatomical and functional asymmetries are observed in mammalian nervous systems, it has been a challenge to identify the molecular basis of these asymmetries. C. elegans has emerged as a prime model organism to investigate molecular asymmetries in the nervous system, as it has been shown to display functional asymmetries clearly correlated to asymmetric distribution and regulation of biologically relevant molecules. Small non-coding RNAs have been recently implicated in various aspects of neural development. Here, we review cases in which microRNAs are crucial for establishing left-right asymmetries in the C. elegans nervous system. These studies may provide insight into how molecular and functional asymmetries are established in the human brain. 7. Synaptic Plasticity and Memory: New Insights from Hippocampal Left-Right Asymmetries. Science.gov (United States) El-Gaby, Mohamady; Shipton, Olivia A; Paulsen, Ole 2015-10-01 All synapses are not the same. They differ in their morphology, molecular constituents, and malleability. A striking left-right asymmetry in the distribution of different types of synapse was recently uncovered at the CA3-CA1 projection in the mouse hippocampus, whereby afferents from the CA3 in the left hemisphere innervate small, highly plastic synapses on the apical dendrites of CA1 pyramidal neurons, whereas those originating from the right CA3 target larger, more stable synapses. Activity-dependent modification of these synapses is thought to participate in circuit formation and remodeling during development, and further plastic changes may support memory encoding in adulthood. Therefore, exploiting the CA3-CA1 asymmetry provides a promising opportunity to investigate the roles that different types of synapse play in these fundamental properties of the CNS. Here we describe the discovery of these segregated synaptic populations in the mouse hippocampus, and discuss what we have already learnt about synaptic plasticity from this asymmetric arrangement. We then propose models for how the asymmetry could be generated during development, and how the adult hippocampus might use these distinct populations of synapses differentially during learning and memory. Finally, we outline the potential implications of this left-right asymmetry for human hippocampal function, as well as dysfunction in memory disorders such as Alzheimer's disease. © The Author(s) 2014. 8. Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners International Nuclear Information System (INIS) Schulze-Halberg, Axel; Wang, Jie 2015-01-01 We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system 9. Two-parameter double-oscillator model of Mathews-Lakshmanan type: Series solutions and supersymmetric partners Energy Technology Data Exchange (ETDEWEB) Schulze-Halberg, Axel, E-mail: [email protected], E-mail: [email protected] [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Wang, Jie, E-mail: [email protected] [Department of Computer Information Systems, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States) 2015-07-15 We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system. 10. Detecting the Higgs bosons of supersymmetric models in Z0 decays International Nuclear Information System (INIS) Barnett, R.M.; Gamberini, G. 1990-01-01 We propose a method to detect the associated pair production, at the Z 0 resonance, of the light scalar and pseudoscalar Higgs bosons predicted by the minimal supersymmetric model. The method would be useful to study Higgs boson masses in the range 15-50 GeV. We consider the banti b-banti b and banti b-τ + τ - decay combinations of the Higgs pair. We exploit the angular distributions of the decay products in order to suppress the background and accurately determine the mass of the two Higgs particles. The number of events is small, but the signals are very distinct, and a limited study strongly suggests that the backgrounds will not obscure the signals. (orig.) 11. Neutrino masses and b - τ unification in the supersymmetric standard model International Nuclear Information System (INIS) Vissani, F.; Smirnov, A.Yu. 1994-05-01 There are several indications that the Majorana masses of the right-handed neutrino components, M R , are at the intermediate scale: M R ∼ (10 10 - 10 12 ) GeV or even lighter. The renormalization effects due to large Yukawa couplings of neutrinos from region of momenta M R G are studied in the supersymmetric standard model. It is shown that neutrino renormalization effect can increase the m b /m τ ratio up to (10/15)%. This strongly disfavors m b - m τ unification for low values of tan β s . Lower bound on M R and tan β from the b - τ unification condition were found. The implications of the results to the see-saw mechanism of the neutrino mass generation are discussed. (author). 17 refs, 4 figs 12. The exact mass-gap of the supersymmetric CP$^{N-1}$ sigma model CERN Document Server Evans, J M; Evans, Jonathan M; Hollowood, Timothy J 1995-01-01 A formula for the mass-gap of the supersymmetric \\CP^{n-1} sigma model (n > 1) in two dimensions is derived: m/\\Lambda_{\\overline{\\rm MS}}=\\sin(\\pi\\Delta)/(\\pi\\Delta) where \\Delta=1/n and m is the mass of the fundamental particle multiplet. This result is obtained by comparing two expressions for the free-energy density in the presence of a coupling to a conserved charge; one expression is computed from the exact S-matrix of K\\"oberle and Kurak via the thermodynamic Bethe ansatz and the other is computed using conventional perturbation theory. These calculations provide a stringent test of the S-matrix, showing that it correctly reproduces the universal part of the beta-function and resolving the problem of CDD ambiguities. 13. The exact mass-gap of the supersymmetric O(N) sigma model CERN Document Server Evans, J M; Evans, Jonathan M; Hollowood, Timothy J 1995-01-01 A formula for the mass-gap of the supersymmetric O(N) sigma model (N>4) in two dimensions is derived: m/\\Lambda_{\\overline{\\rm MS}}=2^{2\\Delta}\\sin(\\pi\\Delta)/(\\pi\\Delta), where \\Delta=1/(N-2) and m is the mass of the fundamental vector particle in the theory. This result is obtained by comparing two expressions for the free-energy density in the presence of a coupling to a conserved charge; one expression is computed from the exact S-matrix of Shankar and Witten via the the thermodynamic Bethe ansatz and the other is computed using conventional perturbation theory. These calculations provide a stringent test of the S-matrix, showing that it correctly reproduces the universal part of the beta-function and resolving the problem of CDD ambiguities. 14. Lepton electric dipole moments in non-degenerate supersymmetric Seesaw models CERN Document Server Ellis, Jonathan Richard; Raidal, Martti; Shimizu, Y; Ellis, John; Hisano, Junji; Raidal, Martti; Shimizu, Yasuhiro 2002-01-01 In the context of supersymmetric seesaw models of neutrino masses with non-degenerate heavy neutrinos, we show that Dirac Yukawa interactions N^c_i (Y_nu)_{ij} L_j H_2 induce large threshold corrections to the slepton soft masses via renormalization. While still yielding rates for lepton-flavour-violating processes below the experimental bounds, these contributions may increase the muon and electron electric dipole moments d_mu and d_e by several orders of magnitude. In the leading logarithmic approximation, this is due to three additional physical phases in Y_nu, one of which also contributes to leptogenesis. The naive relation d_mu/d_e\\approx -m_mu/m_e is violated strongly in the case of successful phenomenological textures for Y_nu, and the values of d_mu and/or d_e may be within the range of interest for the future experiments. 15. Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model Science.gov (United States) García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M. 2018-05-01 We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with infinite range interactions in 0 +1 dimensions. We have found that, close to the ground state E ≈0 , discrete symmetries alter qualitatively the spectral properties with respect to the non-supersymmetric SYK model. The average spectral density at finite N , which we compute analytically and numerically, grows exponentially with N for E ≈0 . However the chiral condensate, which is normalized with respect the total number of eigenvalues, vanishes in the thermodynamic limit. Slightly above E ≈0 , the spectral density grows exponentially with the energy. Deep in the quantum regime, corresponding to the first O (N ) eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for E ≈0 is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalue separations smaller than the Thouless energy, which seems to scale linearly with N . Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universally characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor g (t ), obtained from the connected two-level correlation function of the unfolded spectrum, decays as 1 /t2 for times shorter but comparable to the Thouless time with g (0 ) related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory. 16. All possible lightest supersymmetric particles in proton hexality violating minimal supergravity models and their signals at hadron colliders International Nuclear Information System (INIS) Grab, Sebastian 2009-08-01 The most widely studied supersymmetric scenario is the minimal supersymmetric standard model (MSSM) with more than a hundred free parameters. However for detailed phenomenological studies, the minimal supergravity (mSUGRA) model, a restricted and well-motivated framework for the MSSM, is more convenient. In this model, lepton- and baryon-number violating interactions are suppressed by a discrete symmetry, R-parity or proton-hexality, to keep the proton stable. However, it is sufficient to forbid only lepton- or baryon-number violation. We thus extend mSUGRA models by adding a proton-hexality violating operator at the grand unification scale. This can change the supersymmetric spectrum leading on the one hand to a sneutrino, smuon or squark as the lightest supersymmetric particle (LSP). On the other hand, a wide parameter region is reopened, where the scalar tau (stau) is the LSP. We investigate in detail the conditions leading to non-neutralino LSP scenarios. We take into account the restrictions from neutrino masses, the muon anomalous magnetic moment, b→sγ, and other precision measurements. We furthermore investigate existing restrictions from direct searches at LEP, the Tevatron, and the CERN p anti p collider. It is vital to know the nature of the LSP, since supersymmetric particles normally cascade decay down to the LSP at collider experiments. We present typical LHC signatures for sneutrino LSP scenarios. Promising signatures are high-p T muons and jets, like-sign muon events and detached vertices from long lived taus. We also classify the stau LSP decays and describe their dependence on the mSUGRA parameters. We then exploit our results for resonant single slepton production at the LHC. We find novel signatures with like-sign muon and three- and four-muon final states. Finally, we perform a detailed analysis for single slepton production in association with a single top quark. We show that the signal can be distinguished from the background at the LHC 17. Supersymmetric gauge field theories International Nuclear Information System (INIS) Slavnov, A.A. 1976-01-01 The paper is dealing with the role of supersymmetric gauge theories in the quantum field theory. Methods of manipulating the theories as well as possibilities of their application in elementary particle physics are presented. In particular, the necessity is explained of a theory in which there is symmetry between Fermi and Bose fields, in other words, of the supersymmetric gauge theory for construction of a scheme for the Higgs particle connecting parameters of scalar mesons with those of the rest fields. The mechanism of supersymmetry breaking is discussed which makes it possible to remain the symmetric procedure of renormalization intact. The above mechanism of spontaneous symmetry breaking is applied to demonstrate possibilities of constructing models of weak and electromagnetic interactions which would be acceptable from the point of view of experiments. It is noted that the supersymmetric gauge theories represent a natural technique for description of vector-like models 18. Constraining supersymmetric models using Higgs physics, precision observables and direct searches International Nuclear Information System (INIS) Zeune, Lisa 2014-08-01 We present various complementary possibilities to exploit experimental measurements in order to test and constrain supersymmetric (SUSY) models. Direct searches for SUSY particles have not resulted in any signal so far, and limits on the SUSY parameter space have been set. Measurements of the properties of the observed Higgs boson at ∝126 GeV as well as of the W boson mass (M W ) can provide valuable indirect constraints, supplementing the ones from direct searches. This thesis is divided into three major parts: In the first part we present the currently most precise prediction for M W in the Minimal Supersymmetric Standard Model (MSSM) with complex parameters and in the Next-to-Minimal Supersymmetric Standard Model (NMSSM). The evaluation includes the full one-loop result and all relevant available higher order corrections of Standard Model (SM) and SUSY type. We perform a detailed scan over the MSSM parameter space, taking into account the latest experimental results, including the observation of a Higgs signal. We find that the current measurements for M W and the top quark mass (m t ) slightly favour a non-zero SUSY contribution. The impact of different SUSY sectors on the prediction of M W as well as the size of the higher-order SUSY corrections are analysed both in the MSSM and the NMSSM. We investigate the genuine NMSSM contribution from the extended Higgs and neutralino sectors and highlight differences between the M W predictions in the two SUSY models. In the second part of the thesis we discuss possible interpretations of the observed Higgs signal in SUSY models. The properties of the observed Higgs boson are compatible with the SM so far, but many other interpretations are also possible. Performing scans over the relevant parts of the MSSM and the NMSSM parameter spaces and applying relevant constraints from Higgs searches, flavour physics and electroweak measurements, we find that a Higgs boson at ∝126 GeV, which decays into two photons, can in 19. Instantons in supersymmetric theories International Nuclear Information System (INIS) Novikov, V.A.; Shifman, M.A.; Vajnshtejn, A.I.; Zakharov, V.I. 1982-01-01 Instanton effects are considered for a sample of supersymmetric theories: quantum mechanics, gluodynamics. Higgs model. The problem is how to reconcile the apparent lack of the boson-fermion symmetry in the effective instanton induced interaction with supersymmetry of the corresponding lagrangians. It is shown that in case of quantum mechanics and Higgs model there is no conflict between supersymmetry and the instanton calculus since the Ward identities, associated with the supersymmetry transformations, are satisfied. In case of supersymmetric gluodynamics the standard instanton calculus explicity violates the Ward identities. This is due to the lack of symmetry in the standard class of classical solutions used in the instanton calculus 20. De novo formation of left-right asymmetry by posterior tilt of nodal cilia. Directory of Open Access Journals (Sweden) Shigenori Nonaka 2005-08-01 Full Text Available In the developing mouse embryo, leftward fluid flow on the ventral side of the node determines left-right (L-R asymmetry. However, the mechanism by which the rotational movement of node cilia can generate a unidirectional flow remains hypothetical. Here we have addressed this question by motion and morphological analyses of the node cilia and by fluid dynamic model experiments. We found that the cilia stand, not perpendicular to the node surface, but tilted posteriorly. We further confirmed that such posterior tilt can produce leftward flow in model experiments. These results strongly suggest that L-R asymmetry is not the descendant of pre-existing L-R asymmetry within each cell but is generated de novo by combining three sources of spatial information: antero-posterior and dorso-ventral axes, and the chirality of ciliary movement. 1. Gauge theories of weak interactions with left-right symmetry and the structure of neutral currents International Nuclear Information System (INIS) Mohapatra, R.N.; Sidhu, D.P. 1977-01-01 Failure to detect parity-violating effects in atomic transitions by Oxford and Washington groups would appear to rule out the Weinberg-Salam SU(2) x U(1) model as well as any variation of it that respects natural conservation laws for charm and strangeness to order a G/sub F/ (called ''natural'') and obeys quark-lepton symmetry. In this paper, a simple left-right--symmetric model based on the SU(2)/sub L/ x SU(2)/sub R/ x U(1) group with four and six quark flavors is analyzed and found to accomodate the results of the atomic experiments as well as the other features of neutral-current phenomena 2. Supersymmetric extensions of K field theories Science.gov (United States) Adam, C.; Queiruga, J. M.; Sanchez-Guillen, J.; Wereszczynski, A. 2012-02-01 We review the recently developed supersymmetric extensions of field theories with non-standard kinetic terms (so-called K field theories) in two an three dimensions. Further, we study the issue of topological defect formation in these supersymmetric theories. Specifically, we find supersymmetric K field theories which support topological kinks in 1+1 dimensions as well as supersymmetric extensions of the baby Skyrme model for arbitrary nonnegative potentials in 2+1 dimensions. 3. On the Higgs-like boson in the minimal supersymmetric 3-3-1 model Science.gov (United States) Ferreira, J. G.; Pires, C. A. de S.; da Silva, P. S. Rodrigues; Siqueira, Clarissa 2018-03-01 It is imperative that any proposal of new physics beyond the standard model possesses a Higgs-like boson with 125 GeV of mass and couplings with the standard particles that recover the branching ratios and signal strengths as measured by CMS and ATLAS. We address this issue within the supersymmetric version of the minimal 3-3-1 model. For this we develop the Higgs potential with focus on the lightest Higgs provided by the model. Our proposal is to verify if it recovers the properties of the Standard Model Higgs. With respect to its mass, we calculate it up to one loop level by taking into account all contributions provided by the model. In regard to its couplings, we restrict our investigation to couplings of the Higgs-like boson with the standard particles, only. We then calculate the dominant branching ratios and the respective signal strengths and confront our results with the recent measurements of CMS and ATLAS. As distinctive aspects, we remark that our Higgs-like boson intermediates flavor changing neutral processes and has as signature the decay t → h+c. We calculate its branching ratio and compare it with current bounds. We also show that the Higgs potential of the model is stable for the region of parameter space employed in our calculations. 4. Flavor changing processes in supersymmetric models with hybrid gauge- and gravity-mediation International Nuclear Information System (INIS) Hiller, Gudrun; Hochberg, Yonit; Nir, Yosef 2009-01-01 We consider supersymmetric models where gauge mediation provides the dominant contributions to the soft supersymmetry breaking terms while gravity mediation provides sub-dominant yet non-negligible contributions. We further assume that the gravity-mediated contributions are subject to selection rules that follow from a Froggatt-Nielsen symmetry. This class of models constitutes an example of viable and natural non-minimally flavor violating models. The constraints from K 0 -K-bar 0 mixing imply that the modifications to the Standard Model predictions for B d -B-bar d and B s - B-bar s mixing are generically at most at the percent level, but can be of order ten percent for large tan β. The modifications for D 0 -D-bar 0 mixing are generically at most of order a few percent, but in a special subclass of models they can be of order one. We point out ΔB = 1 processes relevant for flavor violation in hybrid mediation. 5. A precise measurement of the left-right cross section asymmetry in Z boson production Energy Technology Data Exchange (ETDEWEB) Lath, A. 1994-09-01 The thesis presents a measurement of the left-right asymmetry, A{sub LR}, n the production cross section of Z Bosons produced by e{sup +}e{sup -} annihilations, using polarized electrons, at a center of mass energy of 91.26 Gev. The data presented was recorded by the SLD detector at the SLAC Linear Collider during the 1993 run. The mean luminosity-weighted polarization of the electron beam was {rho}{sup lum} = (63.0{+-}1.1)%. Using a sample of 49,392 Z events, we measure A{sub LR} to be 0.1626{+-}0.0071(stat){+-}0.0030(sys.), which determined the effective weak mixing angle to be sin{sup 2} {theta}{sub W}{sup eff} = 0.2292{+-}0.0009(stat.){+-}0.0004(sys.). This result differs from that expected by the Standard Model of Particles and Fields by 2.5 standard deviations. 6. A precise measurement of the left-right cross section asymmetry in Z boson production International Nuclear Information System (INIS) Lath, A. 1994-09-01 The thesis presents a measurement of the left-right asymmetry, A LR , n the production cross section of Z Bosons produced by e + e - annihilations, using polarized electrons, at a center of mass energy of 91.26 Gev. The data presented was recorded by the SLD detector at the SLAC Linear Collider during the 1993 run. The mean luminosity-weighted polarization of the electron beam was ρ lum = (63.0±1.1)%. Using a sample of 49,392 Z events, we measure A LR to be 0.1626±0.0071(stat)±0.0030(sys.), which determined the effective weak mixing angle to be sin 2 θ W eff = 0.2292±0.0009(stat.)±0.0004(sys.). This result differs from that expected by the Standard Model of Particles and Fields by 2.5 standard deviations 7. Renormalization group running of fermion observables in an extended non-supersymmetric SO(10) model Energy Technology Data Exchange (ETDEWEB) Meloni, Davide [Dipartimento di Matematica e Fisica, Università di Roma Tre,Via della Vasca Navale 84, 00146 Rome (Italy); Ohlsson, Tommy; Riad, Stella [Department of Physics, School of Engineering Sciences,KTH Royal Institute of Technology - AlbaNova University Center,Roslagstullsbacken 21, 106 91 Stockholm (Sweden) 2017-03-08 We investigate the renormalization group evolution of fermion masses, mixings and quartic scalar Higgs self-couplings in an extended non-supersymmetric SO(10) model, where the Higgs sector contains the 10{sub H}, 120{sub H}, and 126{sub H} representations. The group SO(10) is spontaneously broken at the GUT scale to the Pati-Salam group and subsequently to the Standard Model (SM) at an intermediate scale M{sub I}. We explicitly take into account the effects of the change of gauge groups in the evolution. In particular, we derive the renormalization group equations for the different Yukawa couplings. We find that the computed physical fermion observables can be successfully matched to the experimental measured values at the electroweak scale. Using the same Yukawa couplings at the GUT scale, the measured values of the fermion observables cannot be reproduced with a SM-like evolution, leading to differences in the numerical values up to around 80%. Furthermore, a similar evolution can be performed for a minimal SO(10) model, where the Higgs sector consists of the 10{sub H} and 126{sub H} representations only, showing an equally good potential to describe the low-energy fermion observables. Finally, for both the extended and the minimal SO(10) models, we present predictions for the three Dirac and Majorana CP-violating phases as well as three effective neutrino mass parameters. 8. Supersymmetric models for quarks and leptons with nonlinearly realized E8 symmetry International Nuclear Information System (INIS) Ong, C.L. 1985-01-01 We propose three supersymmetric nonlinear sigma models with global symmetry E 8 . The models can accommodate three left-handed families of quarks and leptons without incurring the Adler-Bell-Jackiw anomaly with respect to either the standard SU(3) x SU(2) x U(1) gauge group, or the SU(5), or SO(10) grand unifying gauge group. They also predict unambiguously a right-handed, fourth family of quarks and leptons. In order to explore the structure of the models, we develop a differential-form formulation of the Kahler manifolds, resulting in general expressions for the curvature tensors and other geometrical objects in terms of the structure constants of the algebra, and the squashing parameters. These results, in turn, facilitate a general method for determining the Lagrangian to quartic order, and so the structure of the inherent four-fermion interactions of the models. We observe that the Kahlerian condition dω = 0 on the fundamental two-form ω greatly reduces the number of the independent squashing parameters. We also point out two plausible mechanisms for symmetry breaking, involving gravity 9. Supersymmetric model for dark matter and baryogenesis motivated by the recent CDMS result. Science.gov (United States) Allahverdi, Rouzbeh; Dutta, Bhaskar; Mohapatra, Rabindra N; Sinha, Kuver 2013-08-02 We discuss a supersymmetric model for cogenesis of dark and baryonic matter where the dark matter (DM) has mass in the 8-10 GeV range as indicated by several direct detection searches, including most recently the CDMS experiment with the desired cross section. The DM candidate is a real scalar field. Two key distinguishing features of the model are the following: (i) in contrast with the conventional weakly interacting massive particle dark matter scenarios where thermal freeze-out is responsible for the observed relic density, our model uses nonthermal production of dark matter after reheating of the Universe caused by moduli decay at temperatures below the QCD phase transition, a feature which alleviates the relic overabundance problem caused by small annihilation cross section of light DM particles and (ii) baryogenesis occurs also at similar low temperatures from the decay of TeV scale mediator particles arising from moduli decay. A possible test of this model is the existence of colored particles with TeV masses accessible at the LHC. 10. A minimal supersymmetric model of particle physics and the early universe International Nuclear Information System (INIS) Buchmueller, W.; Domcke, V.; Kamada, K.; Schmitz, K. 2013-11-01 We consider a minimal supersymmetric extension of the Standard Model, with right-handed neutrinos and local B-L, the difference between baryon and lepton number, a symmetry which is spontaneously broken at the scale of grand unification. To a large extent, the parameters of the model are determined by gauge and Yukawa couplings of quarks and leptons. We show that this minimal model can successfully account for the earliest phases of the cosmological evolution: Inflation is driven by the energy density of a false vacuum of unbroken B-L symmetry, which ends in tachyonic preheating, i.e. the decay of the false vacuum, followed by a matter dominated phase with heavy B-L Higgs bosons. Nonthermal and thermal processes produce an abundance of heavy neutrinos whose decays generate primordial entropy, baryon asymmetry via leptogenesis and dark matter consisting of gravitinos or nonthermal WIMPs. The model predicts relations between neutrino and superparticle masses and a characteristic spectrum of gravitational waves. 11. A minimal supersymmetric model of particle physics and the early universe Energy Technology Data Exchange (ETDEWEB) Buchmueller, W.; Domcke, V.; Kamada, K. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Schmitz, K. [Tokyo Univ., Kashiwa (Japan). Kavli IPMU, TODIAS 2013-11-15 We consider a minimal supersymmetric extension of the Standard Model, with right-handed neutrinos and local B-L, the difference between baryon and lepton number, a symmetry which is spontaneously broken at the scale of grand unification. To a large extent, the parameters of the model are determined by gauge and Yukawa couplings of quarks and leptons. We show that this minimal model can successfully account for the earliest phases of the cosmological evolution: Inflation is driven by the energy density of a false vacuum of unbroken B-L symmetry, which ends in tachyonic preheating, i.e. the decay of the false vacuum, followed by a matter dominated phase with heavy B-L Higgs bosons. Nonthermal and thermal processes produce an abundance of heavy neutrinos whose decays generate primordial entropy, baryon asymmetry via leptogenesis and dark matter consisting of gravitinos or nonthermal WIMPs. The model predicts relations between neutrino and superparticle masses and a characteristic spectrum of gravitational waves. 12. Supersymmetric Quantum Mechanics and Topology International Nuclear Information System (INIS) 2016-01-01 Supersymmetric quantum mechanical models are computed by the path integral approach. In the β→0 limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants. Explicit computation details are given for the Euler characteristics of the target manifold and the index of Dirac operator for the model on a spin manifold. 13. Supersymmetric lattices International Nuclear Information System (INIS) Catterall, Simon 2013-01-01 Discretization of supersymmetric theories is an old problem in lattice field theory. It has resisted solution until quite recently when new ideas drawn from orbifold constructions and topological field theory have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theory in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local and free of doublers and in the case of Yang-Mills theories also possess exact gauge invariance. In principle they form the basis for a truly non-perturbative definition of the continuum supersymmetric field theory. In this talk these ideas are reviewed with particular emphasis being placed on N = 4 super Yang-Mills theory. 14. Supersymmetric technicolor International Nuclear Information System (INIS) Srednicki, M. 1981-01-01 I will discuss some work I recently completed with M. Dine and W. Fischler on supersymmetric technicolor. E. Witten and S. Dimopoulos and S. Raby have considered similar ideas. Our central idea is to combine supersymmetry and technicolor to produce a natural theory which is capable of reproducing all the known phenomenology of particle physics, especially the quark-lepton mass spectrum and the absence of flavor changing neutral currents. Supersymmetry allows us to introduce fundamental scalars which are naturally light. Some of these scalars play the role of Higgs fields, and give mass to quarks and leptons via ordinary Yukawa couplings (which are chosen so that we get the correct masses and mixing angles). The supersymmetric partners of all known particles turn out to be too heavy to have been observed in experiments to data; many of them, however, weigh less than 100 GeV 15. Top quark electric dipole moment in a minimal supersymmetric standard model extension with vectorlike multiplets International Nuclear Information System (INIS) Ibrahim, Tarek; Nath, Pran 2010-01-01 The electric dipole moment (EDM) of the top quark is calculated in a model with a vector like multiplet which mixes with the third generation in an extension of the minimal supersymmetric standard model. Such mixings allow for new CP violating phases. Including these new CP phases, the EDM of the top in this class of models is computed. The top EDM arises from loops involving the exchange of the W, the Z as well as from the exchange involving the charginos, the neutralinos, the gluino, and the vector like multiplet and their superpartners. The analysis of the EDM of the top is more complicated than for the light quarks because the mass of the external fermion, in this case the top quark mass cannot be ignored relative to the masses inside the loops. A numerical analysis is presented and it is shown that the top EDM could be close to 10 -19 ecm consistent with the current limits on the EDM of the electron, the neutron and on atomic EDMs. A top EDM of size 10 -19 ecm could be accessible in collider experiments such as the International Linear Collider. 16. On SW-minimal models and N=1 supersymmetric quantum Toda-field theories International Nuclear Information System (INIS) Mallwitz, S. 1994-04-01 Integrable N=1 supersymmetric Toda-field theories are determined by a contragredient simple Super-Lie-Algebra (SSLS) with purely fermionic lowering and raising operators. For the SSLA's Osp(3/2) and D(2/1;α) we construct explicitly the higher spin conserved currents and obtain free field representations of the super W-algebras SW(3/2,2) and SW(3/2,3/2,2). In constructing the corresponding series of minimal models using covariant vertex operators, we find a necessary restriction on the Cartan matrix of the SSLA, also for the general case. Within this framework, this restriction claims that there be a minimum of one non-vanishing element on the diagonal of the Cartan matrix. This condition is without parallel in bosonic conformal field theory. As a consequence only two series of SSLA's yield minimal models, namely Osp(2n/2n-1) and Osp(2n/2n+1). Subsequently some general aspects of degenerate representations of SW-algebras, notably the fusion rules, are investigated. As an application we discuss minimal models of SW(3/2, 2), which were constructed with independent methods, in this framework. Covariant formulation is used throughout this paper. (orig.) 17. Gravitino and scalar {tau}-lepton decays in supersymmetric models with broken R-parity Energy Technology Data Exchange (ETDEWEB) Hajer, Jan 2010-06-15 Mildly broken R-parity is known to provide a solution to the cosmological gravitino problem in supergravity extensions of the Standard Model. In this work we consider new effects occurring in the R-parity breaking Minimal Supersymmetric Standard Model including right-handed neutrino superfields. We calculate the most general vacuum expectation values of neutral scalar fields including left- and right-handed scalar neutrinos. Additionally, we derive the corresponding mass mixing matrices of the scalar sector. We recalculate the neutrino mass generation mechanisms due to right- handed neutrinos as well as by cause of R-parity breaking. Furthermore, we obtain a, so far, unknown formula for the neutrino masses for the case where both mechanisms are effective. We then constrain the couplings to bilinear R-parity violating couplings in order to accommodate R-parity breaking to experimental results. In order to constrain the family structure with a U(1){sub Q} flavor symmetry we furthermore embed the particle content into an SU(5) Grand Unified Theory. In this model we calculate the signal of decaying gravitino dark matter as well as the dominant decay channel of a likely NLSP, the scalar {tau}-lepton. Comparing the gravitino signal with results of the Fermi Large Area Telescope enables us to find a lower bound on the decay length of scalar {tau}-leptons in collider experiments. (orig.) 18. Gravitino and scalar τ-lepton decays in supersymmetric models with broken R-parity International Nuclear Information System (INIS) Hajer, Jan 2010-01-01 Mildly broken R-parity is known to provide a solution to the cosmological gravitino problem in supergravity extensions of the Standard Model. In this work we consider new effects occurring in the R-parity breaking Minimal Supersymmetric Standard Model including right-handed neutrino superfields. We calculate the most general vacuum expectation values of neutral scalar fields including left- and right-handed scalar neutrinos. Additionally, we derive the corresponding mass mixing matrices of the scalar sector. We recalculate the neutrino mass generation mechanisms due to right- handed neutrinos as well as by cause of R-parity breaking. Furthermore, we obtain a, so far, unknown formula for the neutrino masses for the case where both mechanisms are effective. We then constrain the couplings to bilinear R-parity violating couplings in order to accommodate R-parity breaking to experimental results. In order to constrain the family structure with a U(1) Q flavor symmetry we furthermore embed the particle content into an SU(5) Grand Unified Theory. In this model we calculate the signal of decaying gravitino dark matter as well as the dominant decay channel of a likely NLSP, the scalar τ-lepton. Comparing the gravitino signal with results of the Fermi Large Area Telescope enables us to find a lower bound on the decay length of scalar τ-leptons in collider experiments. (orig.) 19. μ-τ symmetry and charged lepton mass hierarchy in a supersymmetric D4 model International Nuclear Information System (INIS) Hagedorn, C.; Ziegler, R. 2010-01-01 In this paper we discuss a supersymmetric D 4 xZ 5 model which leads to vanishing reactor mixing angle θ 13 =0 and maximal atmospheric mixing θ 23 =π/4 in the lepton sector at leading order, due to the preservation of nontrivial distinct D 4 subgroups in the charged lepton and neutrino sectors, respectively. The solar mixing angle θ 12 remains undetermined and is expected to be of order one. Since right-handed charged leptons transform as singlets under D 4 , the charged lepton mass hierarchy can be naturally accounted for. The model predicts inverted mass hierarchy for neutrinos. Additionally, we show that, unlike in most of the other models of this type, all vacuum expectation values of gauge singlets (flavons) can be determined through mass parameters of the superpotential. Next-to-leading order corrections to lepton masses and mixings are calculated and shown to be under control; in particular, the corrections to θ 23 =π/4 and θ 13 =0 are of the order of the generic expansion parameter ε≅0.04 and arise dominantly from the charged lepton sector. 20. Two-loop renormalization group analysis of supersymmetric SO(10) models with an intermediate scale International Nuclear Information System (INIS) Bastero-Gil, M.; Brahmachari, B. 1996-03-01 Two-loop evolutions of the gauge couplings in a class of intermediate scale supersymmetric SO(10) models including the effect of third generation Yukawa couplings are studied. The unification scale, the intermediate scale and the value of the unification gauge coupling in these models are calculated and the gauge boson mediated proton decay rates are estimated. In some cases the predicted proton lifetime turns out to be in the border-line of experimental limit. The predictions of the top quark mass, the mass ratio m b (m b )/m τ (m τ ) from the two-loop evolution of Yukawa couplings and the mass of the left handed neutrino via see-saw mechanism are summarized. The lower bounds on the ratio of the VEVs of the two low energy doublets (tan β) from the requirement of the perturbative unitarity of the top quark Yukawa coupling up to the grand unification scale are also presented. All the predictions have been compared with those of the one-step unified theory. (author). 33 refs, 5 figs, 1 tab 1. Study of Higgs self couplings of a supersymmetric E6 model at the international linear collider International Nuclear Information System (INIS) Ham, S. W.; Han, K. D.; Lee, J. I.; Oh, S. K. 2010-01-01 We study the Higgs self couplings of a supersymmetric E 6 model that has two Higgs doublets and two Higgs singlets. The lightest scalar Higgs boson in the model may be heavier than 112 GeV, at the one-loop level, where the negative results for the Higgs search at the LEP2 experiments are taken into account. The contributions from the top and scalar top quark loops are included in the radiative corrections to the one-loop mass of the lightest scalar Higgs boson in the effective potential approximation. The effect of the Higgs self couplings may be observed in the production of the lightest scalar Higgs bosons in e + e - collisions at the International Linear Collider (ILC) via the double Higgs-strahlung process. For the center of mass energy of 500 GeV with an integrated luminosity of 500 fb -1 and an efficiency of 20%, we expect that at least 5 events of the lightest scalar Higgs boson may be produced at the ILC via the double Higgs-strahlung process. 2. Z-Z' mass hierarchy in a supersymmetric model with a secluded U(1)'-breaking sector International Nuclear Information System (INIS) Erler, Jens; Langacker, Paul; Li Tianjun 2002-01-01 We consider the Z ' /Z mass hierarchy in a supersymmetric model in which the U(1) ' is broken in a secluded sector coupled to the ordinary sector only by gauge and possibly soft terms. A large mass hierarchy can be achieved while maintaining the normal sparticle spectra if there is a direction in which the tree level potential becomes flat when a particular Yukawa coupling vanishes. We describe the conditions needed for the desired breaking pattern, to avoid unwanted global symmetries, and for an acceptable effective μ parameter. The electroweak breaking is dominated by A terms rather than scalar masses, leading to tan β≅1. The spectrum of the symmetry breaking sector is displayed. There is significant mixing between the MSSM particles and new standard model singlets, for both the Higgs scalars and the neutralinos. A larger Yukawa coupling for the effective μ parameter is allowed than in the NMSSM because of the U(1) ' contribution to the running from a high scale. The upper bound on the tree-level mass of the lightest CP even Higgs doublet mass is about cx174 GeV, where c is of order unity, but the actual mass eigenvalues are generally smaller because of singlet mixing 3. A non Supersymmetric SO(10) Grand Unified Model for All the Physics below $M_{GUT}$ CERN Document Server Altarelli, Guido 2013-01-01 We present a renormalizable non supersymmetric Grand Unified SO(10) model which, at the price of a large fine tuning, is compatible with all compelling phenomenological requirements below the unification scale and thus realizes a minimal extension of the SM, unified in SO(10) and describing all known physics below $M_{GUT}$. These requirements include coupling unification at a large enough scale to be compatible with the bounds on proton decay; a Yukawa sector in agreement with all the data on quark and lepton masses and mixings and with leptogenesis as the origin of the baryon asymmetry of the Universe; an axion arising from the Higgs sector of the model, suitable to solve the strong CP problem and to account for the observed amount of Dark Matter. The above constraints imposed by the data are very stringent and single out a particular breaking chain with the Pati-Salam group at an intermediate scale $M_I\\sim10^{11}$ GeV. 4. The t-J model at small t/j: Numerical, perturbative, and supersymmetric results International Nuclear Information System (INIS) Barnes, T.; Tennessee Univ., Knoxville, TN 1991-02-01 We discuss some recent results for one- and two-hole states in the t-J model at small t/J. These include numerical results (bandwidth determinations and accurate t/J values for 4 x 4 lattice one-hole ground-state level crossings), hopping-parameter perturbation theory (which gives the small-t/J one-hole bandwidth in terms of the static-vacancy ground state), and results at the supersymmetric point t/J = 1/2 (exact results for energies and bandwidths.) The perturbative results leads us to a new conjecture regarding the staggered magnetization of higher-spin states in the two-dimensional Heisenberg model. We also discuss extrapolation of small-t/J results to high-T c parameter values; in the two-hole ground states we find (t/J) λ behavior in the rms hole-hole separation, and an extrapolation to t/J = 3 gives a bulk-limit rms hole-hole separation of ∼ 7 angstrom. 18 refs., 6 figs 5. Asymmetric dark matter from spontaneous cogenesis in the supersymmetric standard model Energy Technology Data Exchange (ETDEWEB) Kamada, Kohei [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Yamaguchi, Masahide [Tokyo Institute of Technology (Japan). Dept. of Physics 2012-01-15 The observational relation between the density of baryon and dark matter in the Universe, {omega}{sub DM}/{omega}{sub B}{approx_equal}5, is one of the most difficult problems to solve in modern cosmology. We discuss a scenario that explains this relation by combining the asymmetric dark matter scenario and the spontaneous baryogenesis associated with the flat direction in the supersymmetric standard model. A part of baryon asymmetry is transferred to charge asymmetry D that dark matter carries, if a symmetry violating interaction that works at high temperature breaks not only B-L but also D symmetries simultaneously. In this case, the present number density of baryon and dark matter can be same order if the symmetric part of dark matter annihilates sufficiently. Moreover, the baryon number density can be enhanced as compared to that of dark matter if another B-L violating interaction is still in thermal equilibrium after the spontaneous genesis of dark matter, which accommodates a TeV scale asymmetric dark matter model. (orig.) 6. Dark Matter in B – L supersymmetric Standard Model with inverse seesaw Energy Technology Data Exchange (ETDEWEB) Abdallah, W. [Department of Mathematics, Faculty of Science, Cairo University, Giza 12613 (Egypt); Khalil, S., E-mail: [email protected], E-mail: [email protected] [Center for Fundamental Physics, Zewail City of Science and Technology, 6 October City, Giza 12588 (Egypt) 2017-04-01 We show that the B – L Supersymmetric Standard Model with Inverse Seesaw (BLSSMIS) provides new Dark Matter (DM) candidates (lightest right-handed sneutrino and lightest B – L neutralino) with mass of order few hundreds GeV, while most of other SUSY spectrum can be quite heavy, consistently with the current Large Hadron Collider (LHC) constraints. We emphasize that the thermal relic abundance and direct detection experiments via relic neutralino scattering with nuclei impose stringent constraints on the B – L neutralinos. These constraints can be satisfied by few points in the parameter space where the B – L lightest neutralino is higgsino-like, which cannot explain the observed Galactic Center (GC) gamma-ray excess measured by Fermi-LAT. The lightest right-handed sneutrino DM is analysed. We show that for a wide region of parameter space the lightest right-handed sneutrino, with mass between 80 GeV and 1.2 TeV, can satisfy the limits of the relic abundance and the scattering cross section with nuclei. We also show that the lightest right-handed sneutrino with mass O(100) GeV can account for the observed GC gamma-ray results. 7. Exact scattering in the SU(n) supersymmetric principal chiral model CERN Document Server Evans, J M; Evans, Jonathan M; Hollowood, Timothy J 1997-01-01 The complete spectrum of states in the supersymmetric principal chiral model based on SU(n) is conjectured, and an exact factorizable S-matrix is proposed to describe scattering amongst these states. The SU(n)_LSU(n)_R symmetry of the lagrangian is manifest in the S-matrix construction. The supersymmetries, on the other hand, are incorporated in the guise of spin-1/2 charges acting on a set of RSOS kinks associated with su(n) at level n. To test the proposed S-matrix, calculations of the change in the ground-state energy in the presence of a coupling to a background charge are carried out. The results derived from the lagrangian using perturbation theory and from the S-matrix using the TBA are found to be in complete agreement for a variety of background charges which pick out, in turn, the highest weight states in each of the fundamental representations of SU(n). In particular, these methods rule out the possibility of additional CDD factors in the S-matrix. Comparison of the expressions found for the free-... 8. Production and detection at SSC of Higgs bosons in left-right symmetric theories International Nuclear Information System (INIS) Gunion, J.; Kayser, B.; Mohapatra, R.N.; Deshpande, N.G.; Grifols, J.; Mendez, A.; Olness, F.; Pal, P.B. 1986-12-01 We discuss the production and detection at SSC of charged and neutral Higgs bosons of the left-right symmetric theories. The H + , which is largely a member of a left-right ''bidoublet,'' should be detectable. The H 2 0 , a more unusual Higgs particle which, apart from mixing, is in a right-handed triplet and does not couple to quarks, may be detectable too 9. Fixed point and anomaly mediation in partial {\\boldsymbol{N}}=2 supersymmetric standard models Science.gov (United States) Yin, Wen 2018-01-01 Motivated by the simple toroidal compactification of extra-dimensional SUSY theories, we investigate a partial N = 2 supersymmetric (SUSY) extension of the standard model which has an N = 2 SUSY sector and an N = 1 SUSY sector. We point out that below the scale of the partial breaking of N = 2 to N = 1, the ratio of Yukawa to gauge couplings embedded in the original N = 2 gauge interaction in the N = 2 sector becomes greater due to a fixed point. Since at the partial breaking scale the sfermion masses in the N = 2 sector are suppressed due to the N = 2 non-renormalization theorem, the anomaly mediation effect becomes important. If dominant, the anomaly-induced masses for the sfermions in the N = 2 sector are almost UV-insensitive due to the fixed point. Interestingly, these masses are always positive, i.e. there is no tachyonic slepton problem. From an example model, we show interesting phenomena differing from ordinary MSSM. In particular, the dark matter particle can be a sbino, i.e. the scalar component of the N = 2 vector multiplet of {{U}}{(1)}Y. To obtain the correct dark matter abundance, the mass of the sbino, as well as the MSSM sparticles in the N = 2 sector which have a typical mass pattern of anomaly mediation, is required to be small. Therefore, this scenario can be tested and confirmed in the LHC and may be further confirmed by the measurement of the N = 2 Yukawa couplings in future colliders. This model can explain dark matter, the muon g-2 anomaly, and gauge coupling unification, and relaxes some ordinary problems within the MSSM. It is also compatible with thermal leptogenesis. 10. Nearly Supersymmetric Dark Atoms Energy Technology Data Exchange (ETDEWEB) Behbahani, Siavosh R.; Jankowiak, Martin; /SLAC /Stanford U., ITP; Rube, Tomas; /Stanford U., ITP; Wacker, Jay G.; /SLAC /Stanford U., ITP 2011-08-12 Theories of dark matter that support bound states are an intriguing possibility for the identity of the missing mass of the Universe. This article proposes a class of models of supersymmetric composite dark matter where the interactions with the Standard Model communicate supersymmetry breaking to the dark sector. In these models supersymmetry breaking can be treated as a perturbation on the spectrum of bound states. Using a general formalism, the spectrum with leading supersymmetry effects is computed without specifying the details of the binding dynamics. The interactions of the composite states with the Standard Model are computed and several benchmark models are described. General features of non-relativistic supersymmetric bound states are emphasized. 11. Reciprocal Signaling between the Ectoderm and a Mesendodermal Left-Right Organizer Directs Left-Right Determination in the Sea Urchin Embryo Science.gov (United States) Bessodes, Nathalie; Haillot, Emmanuel; Duboc, Véronique; Röttinger, Eric; Lahaye, François; Lepage, Thierry 2012-01-01 During echinoderm development, expression of nodal on the right side plays a crucial role in positioning of the rudiment on the left side, but the mechanisms that restrict nodal expression to the right side are not known. Here we show that establishment of left-right asymmetry in the sea urchin embryo relies on reciprocal signaling between the ectoderm and a left-right organizer located in the endomesoderm. FGF/ERK and BMP2/4 signaling are required to initiate nodal expression in this organizer, while Delta/Notch signaling is required to suppress formation of this organizer on the left side of the archenteron. Furthermore, we report that the H+/K+-ATPase is critically required in the Notch signaling pathway upstream of the S3 cleavage of Notch. Our results identify several novel players and key early steps responsible for initiation, restriction, and propagation of left-right asymmetry during embryogenesis of a non-chordate deuterostome and uncover a functional link between the H+/K+-ATPase and the Notch signaling pathway. PMID:23271979 12. All possible lightes supersymmetric particles in proton hexality violating minimal supergravity models and their signals at hadron colliders Energy Technology Data Exchange (ETDEWEB) Grab, Sebastian 2009-08-15 The most widely studied supersymmetric scenario is the minimal supersymmetric standard model (MSSM) with more than a hundred free parameters. However for detailed phenomenological studies, the minimal supergravity (mSUGRA) model, a restricted and well-motivated framework for the MSSM, is more convenient. In this model, lepton- and baryon-number violating interactions are suppressed by a discrete symmetry, R-parity or proton-hexality, to keep the proton stable. However, it is sufficient to forbid only lepton- or baryon-number violation. We thus extend mSUGRA models by adding a proton-hexality violating operator at the grand unification scale. This can change the supersymmetric spectrum leading on the one hand to a sneutrino, smuon or squark as the lightest supersymmetric particle (LSP). On the other hand, a wide parameter region is reopened, where the scalar tau (stau) is the LSP. We investigate in detail the conditions leading to non-neutralino LSP scenarios. We take into account the restrictions from neutrino masses, the muon anomalous magnetic moment, b{yields}s{gamma}, and other precision measurements. We furthermore investigate existing restrictions from direct searches at LEP, the Tevatron, and the CERN p anti p collider. It is vital to know the nature of the LSP, since supersymmetric particles normally cascade decay down to the LSP at collider experiments. We present typical LHC signatures for sneutrino LSP scenarios. Promising signatures are high-p{sub T} muons and jets, like-sign muon events and detached vertices from long lived taus. We also classify the stau LSP decays and describe their dependence on the mSUGRA parameters. We then exploit our results for resonant single slepton production at the LHC. We find novel signatures with like-sign muon and three- and four-muon final states. Finally, we perform a detailed analysis for single slepton production in association with a single top quark. We show that the signal can be distinguished from the background 13. Supersymmetric two-particle equations International Nuclear Information System (INIS) Sissakyan, A.N.; Skachkov, N.B.; Shevchenko, O.Yu. 1986-01-01 In the framework of the scalar superfield model, a particular case of which is the well-known Wess-Zumino model, the supersymmetric Schwinger equations are found. On their basis with the use of the second Legendre transformation the two-particle supersymmetric Edwards and Bethe-Salpeter equations are derived. A connection of the kernels and inhomogeneous terms of these equations with generating functional of the second Legendre transformation is found 14. Serotonin has early, cilia-independent roles in Xenopus left-right patterning Directory of Open Access Journals (Sweden) Laura N. Vandenberg 2013-01-01 Consistent left-right (LR patterning of the heart and viscera is a crucial part of normal embryogenesis. Because errors of laterality form a common class of birth defects, it is important to understand the molecular mechanisms and stage at which LR asymmetry is initiated. Frog embryos are a system uniquely suited to analysis of the mechanisms involved in orientation of the LR axis because of the many genetic and pharmacological tools available for use and the fate-map and accessibility of early blastomeres. Two major models exist for the origin of LR asymmetry and both implicate pre-nervous serotonergic signaling. In the first, the charged serotonin molecule is instructive for LR patterning; it is redistributed asymmetrically along the LR axis and signals intracellularly on the right side at cleavage stages. A second model suggests that serotonin is a permissive factor required to specify the dorsal region of the embryo containing chiral cilia that generate asymmetric fluid flow during neurulation, a much later process. We performed theory-neutral experiments designed to distinguish between these models. The results uniformly support a role for serotonin in the cleavage-stage embryo, long before the appearance of cilia, in ventral right blastomeres that do not contribute to the ciliated organ. 15. Online adaptive learning of Left-Right Continuous HMM for bearings condition assessment International Nuclear Information System (INIS) Cartella, F; Liu, T; Meganck, S; Lemeire, J; Sahli, H 2012-01-01 Standard Hidden Markov Models (HMMs) approaches used for condition assessment of bearings assume that all the possible system states are fixed and known a priori and that training data from all of the associated states are available. Moreover, the training procedure is performed offline, and only once at the beginning, with the available training set. These assumptions significantly impede component diagnosis applications when all of the possible states of the system are not known in advance or environmental factors or operative conditions change during the tool's usage. The method introduced in this paper overcomes the above limitations and proposes an approach to detect unknown degradation modalities using a Left-Right Continuous HMM with a variable state space. The proposed HMM is combined with Change Point Detection algorithms to (i) estimate, from historical observations, the initial number of the model's states, as well as to perform an initial guess of the parameters, and (ii) to adaptively recognize new states and, consequently, adjust the model parameters during monitoring. The approach has been tested using real monitoring data taken from the NASA benchmark repository. A comparative study with state of the art techniques shows improvements in terms of reduction of the training procedure iterations, and early detection of unknown states. 16. Suppression of the endoplasmic reticulum calcium pump during zebrafish gastrulation affects left-right asymmetry of the heart and brain. Science.gov (United States) Kreiling, Jill A; Balantac, Zaneta L; Crawford, Andrew R; Ren, Yuexin; Toure, Jamal; Zchut, Sigalit; Kochilas, Lazaros; Creton, Robbert 2008-01-01 Vertebrate embryos generate striking Ca(2+) patterns, which are unique regulators of dynamic developmental events. In the present study, we used zebrafish embryos as a model system to examine the developmental roles of Ca(2+) during gastrulation. We found that gastrula stage embryos maintain a distinct pattern of cytosolic Ca(2+) along the dorsal-ventral axis, with higher Ca(2+) concentrations in the ventral margin and lower Ca(2+) concentrations in the dorsal margin and dorsal forerunner cells. Suppression of the endoplasmic reticulum Ca(2+) pump with 0.5 microM thapsigargin elevates cytosolic Ca(2+) in all embryonic regions and induces a randomization of laterality in the heart and brain. Affected hearts, visualized in living embryos by a subtractive imaging technique, displayed either a reversal or loss of left-right asymmetry. Brain defects include a left-right reversal of pitx2 expression in the dorsal diencephalon and a left-right reversal of the prominent habenular nucleus in the brain. Embryos are sensitive to inhibition of the endoplasmic reticulum Ca(2+) pump during early and mid gastrulation and lose their sensitivity during late gastrulation and early segmentation. Suppression of the endoplasmic reticulum Ca(2+) pump during gastrulation inhibits expression of no tail (ntl) and left-right dynein related (lrdr) in the dorsal forerunner cells and affects development of Kupffer's vesicle, a ciliated organ that generates a counter-clockwise flow of fluid. Previous studies have shown that Ca(2+) plays a role in Kupffer's vesicle function, influencing ciliary motility and translating the vesicle's counter-clockwise flow into asymmetric patterns of gene expression. The present results suggest that Ca(2+) plays an additional role in the formation of Kupffer's vesicle. 17. Search for Minimal Standard Model and Minimal Supersymmetric Model Higgs Bosons in e+ e- Collisions with the OPAL detector at LEP International Nuclear Information System (INIS) Ganel, Ofer 1993-06-01 When LEP machine was turned on in August 1989, a new era had opened. For the first time, direct, model-independent searches for Higgs boson could be carried out. The Minimal Standard Model Higgs boson is expected to be produced in e + e - collisions via the H o Z o . The Minimal Supersymmetric Model Higgs boson are expected to be produced in the analogous e + e - -> h o Z o process or in pairs via the process e + e - -> h o A o . In this thesis we describe the search for Higgs bosons within the framework of the Minimal Standard Model and the Minimal Supersymmetric Model, using the data accumulated by the OPAL detector at LEP in the 1989, 1990, 1991 and part of the 1992 running periods at and around the Z o pole. An MInimal Supersymmetric Model Higgs boson generator is described as well as its use in several different searches. As a result of this work, the Minimal Standard Model Higgs boson mass is bounded from below by 54.2 GeV/c 2 at 95% C.L. This is, at present, the highest such bound. A novel method of overcoming the m τ and m s dependence of Minimal Supersymmetric Higgs boson production and decay introduced by one-loop radiative corrections is used to obtain model-independent exclusion. The thesis describes also an algorithm for off line identification of calorimeter noise in the OPAL detector. (author) 18. Precision electroweak physics with the SLD/SLC: The left-right polarization asymmetry International Nuclear Information System (INIS) Rowson, P.C. 1994-12-01 Following a brief review of a commonly used general framework for the analysis of radiative corrections and possible new physics, the recent precision results from the SLD/SLC are discussed and used to test the standard electroweak model. In the 1993 SLD/SLC run, the SLD recorded 50,000 Z events produced by the collision of longitudinally polarized electrons on unpolarized positrons at a center-of-mass energy of 91.26 GeV. The luminosity-weighted average polarization of the SLC electron beam was (63.0 ± 1.1)%. We measure the left-right cross-section asymmetry in Z boson production, A LR , to be 0.1628 ± 0.0071 (stat) ± 0.0028 (syst) which determines the effective weak mixing angle to be sin 2 θ W eff = 0.2292 ± 0.0009 (stat) ± 0.0004 (syst). When averaged with our 1992 result, we obtain sin 2 θ W eff = 0.2294 ± 0. 0010. This result differs from analogous LEP results at the level of about 2.5 σ. The world averages of electroweak data are comfortably in agreement with the standard model 19. Four generations versus left-right symmetry. A comparative numerical analysis International Nuclear Information System (INIS) Heidsieck, Tillmann J. 2012-01-01 In this work, we present a comparative numerical analysis of the Standard Model (SM) with a sequential fourth generation (SM4) and the left-right symmetric Standard model (LRM). We focus on the constraints induced by flavour violating ΔF=2 processes in the K and B system while the results of studies of collider bounds and electroweak precision tests are taken into account as external inputs. In contrast to many previous studies of both models considered in this work, we do make not any ad-hoc assumptions on the structure of the relevant mixing matrices. Therefore, we employ powerful Monte Carlo methods in order to approximate the viable parameter space of the models. In preparation of our numerical analysis, we present all relevant formulae and review the different numerical methods used in this work. In order to better understand the patterns of new effects in ΔF=2 processes, we perform a fit including all relevant ΔF=2 constraints in the context of the Standard Model. The result of this fit is then used in a general discussion on new effects in ΔF=2 processes in the context of generic extensions of the Standard Model. Our numerical analysis of the SM4 and the LRM demonstrates that in both models the existing anomalies in Δ=2 processes can easily be resolved. We transparently show how the different observables are connected to each other by their dependence on combinations of mixing parameters. In our analysis of rare decays in the SM4, we establish patterns of flavour violation that could in principle be used to disprove this model on the basis of ΔF=1 processes alone. In the LRM, we discuss the importance of the contributions originating from the exchange of heavy, flavour changing, neutral Higgs bosons as well as the inability of the LRM to entirely solve the V ub problem. 20. Four generations versus left-right symmetry. A comparative numerical analysis Energy Technology Data Exchange (ETDEWEB) Heidsieck, Tillmann J. 2012-06-18 In this work, we present a comparative numerical analysis of the Standard Model (SM) with a sequential fourth generation (SM4) and the left-right symmetric Standard model (LRM). We focus on the constraints induced by flavour violating {Delta}F=2 processes in the K and B system while the results of studies of collider bounds and electroweak precision tests are taken into account as external inputs. In contrast to many previous studies of both models considered in this work, we do make not any ad-hoc assumptions on the structure of the relevant mixing matrices. Therefore, we employ powerful Monte Carlo methods in order to approximate the viable parameter space of the models. In preparation of our numerical analysis, we present all relevant formulae and review the different numerical methods used in this work. In order to better understand the patterns of new effects in {Delta}F=2 processes, we perform a fit including all relevant {Delta}F=2 constraints in the context of the Standard Model. The result of this fit is then used in a general discussion on new effects in {Delta}F=2 processes in the context of generic extensions of the Standard Model. Our numerical analysis of the SM4 and the LRM demonstrates that in both models the existing anomalies in {Delta}=2 processes can easily be resolved. We transparently show how the different observables are connected to each other by their dependence on combinations of mixing parameters. In our analysis of rare decays in the SM4, we establish patterns of flavour violation that could in principle be used to disprove this model on the basis of {Delta}F=1 processes alone. In the LRM, we discuss the importance of the contributions originating from the exchange of heavy, flavour changing, neutral Higgs bosons as well as the inability of the LRM to entirely solve the V{sub ub} problem. 1. Dynamics of supersymmetric chameleons International Nuclear Information System (INIS) Brax, Philippe; Davis, Anne-Christine; Sakstein, Jeremy 2013-01-01 We investigate the cosmological dynamics of a class of supersymmetric chameleon models coupled to cold dark matter fermions. The model includes a cosmological constant in the form of a Fayet-Illiopoulos term, which emerges at late times due to the coupling of the chameleon to two charged scalars. Supergravity corrections ensure that the supersymmetric chameleons are efficiently screened in all astrophysical objects of interest, however this does not preclude the enhancement of gravity on linear cosmological scales. We solve the modified equations for the growth of cold dark matter density perturbations in closed form in the matter era. Using this, we go on to derive the modified linear power spectrum which is characterised by two scales, the horizon size at matter-radiation equality and at the redshift when the chameleon reaches the minimum of its effective potential. We analyse the deviations from the ΛCDM predictions in the linear regime. We find that there is generically a region in the model's parameter space where the model's background cosmology coincides with that of the ΛCDM model. Furthermore, we find that characteristic deviations from ΛCDM are present on the matter power spectrum providing a clear signature of supersymmetric chameleons 2. Dynamics of supersymmetric chameleons Energy Technology Data Exchange (ETDEWEB) Brax, Philippe [Institut de Physique Theorique, CEA, IPhT, CNRS, URA 2306, F-91191Gif/Yvette Cedex (France); Davis, Anne-Christine; Sakstein, Jeremy, E-mail: [email protected], E-mail: [email protected], E-mail: [email protected] [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom) 2013-10-01 We investigate the cosmological dynamics of a class of supersymmetric chameleon models coupled to cold dark matter fermions. The model includes a cosmological constant in the form of a Fayet-Illiopoulos term, which emerges at late times due to the coupling of the chameleon to two charged scalars. Supergravity corrections ensure that the supersymmetric chameleons are efficiently screened in all astrophysical objects of interest, however this does not preclude the enhancement of gravity on linear cosmological scales. We solve the modified equations for the growth of cold dark matter density perturbations in closed form in the matter era. Using this, we go on to derive the modified linear power spectrum which is characterised by two scales, the horizon size at matter-radiation equality and at the redshift when the chameleon reaches the minimum of its effective potential. We analyse the deviations from the ΛCDM predictions in the linear regime. We find that there is generically a region in the model's parameter space where the model's background cosmology coincides with that of the ΛCDM model. Furthermore, we find that characteristic deviations from ΛCDM are present on the matter power spectrum providing a clear signature of supersymmetric chameleons. 3. Left-right asymmetries of behaviour and nervous system in invertebrates. Science.gov (United States) Frasnelli, Elisa; Vallortigara, Giorgio; Rogers, Lesley J 2012-04-01 Evidence of left-right asymmetries in invertebrates has begun to emerge, suggesting that lateralization of the nervous system may be a feature of simpler brains as well as more complex ones. A variety of studies have revealed sensory and motor asymmetries in behaviour, as well as asymmetries in the nervous system, in invertebrates. Asymmetries in behaviour are apparent in olfaction (antennal asymmetries) and in vision (preferential use of the left or right visual hemifield during activities such as foraging or escape from predators) in animals as different as bees, fruitflies, cockroaches, octopuses, locusts, ants, spiders, crabs, snails, water bugs and cuttlefish. Asymmetries of the nervous system include lateralized position of specific brain structures (e.g., in fruitflies and snails) and of specific neurons (e.g., in nematodes). As in vertebrates, lateralization can occur both at the individual and at the population-level in invertebrates. Theoretical models have been developed supporting the hypothesis that the alignment of the direction of behavioural and brain asymmetries at the population-level could have arisen as a result of social selective pressures, when individually asymmetrical organisms had to coordinate with each other. The evidence reviewed suggests that lateralization at the population-level may be more likely to occur in social species among invertebrates, as well as vertebrates. Copyright © 2012 Elsevier Ltd. All rights reserved. 4. Early uneven ear input induces long-lasting differences in left-right motor function. Science.gov (United States) Antoine, Michelle W; Zhu, Xiaoxia; Dieterich, Marianne; Brandt, Thomas; Vijayakumar, Sarath; McKeehan, Nicholas; Arezzo, Joseph C; Zukin, R Suzanne; Borkholder, David A; Jones, Sherri M; Frisina, Robert D; Hébert, Jean M 2018-03-01 How asymmetries in motor behavior become established normally or atypically in mammals remains unclear. An established model for motor asymmetry that is conserved across mammals can be obtained by experimentally inducing asymmetric striatal dopamine activity. However, the factors that can cause motor asymmetries in the absence of experimental manipulations to the brain remain unknown. Here, we show that mice with inner ear dysfunction display a robust left or right rotational preference, and this motor preference reflects an atypical asymmetry in cortico-striatal neurotransmission. By unilaterally targeting striatal activity with an antagonist of extracellular signal-regulated kinase (ERK), a downstream integrator of striatal neurotransmitter signaling, we can reverse or exaggerate rotational preference in these mice. By surgically biasing vestibular failure to one ear, we can dictate the direction of motor preference, illustrating the influence of uneven vestibular failure in establishing the outward asymmetries in motor preference. The inner ear-induced striatal asymmetries identified here intersect with non-ear-induced asymmetries previously linked to lateralized motor behavior across species and suggest that aspects of left-right brain function in mammals can be ontogenetically influenced by inner ear input. Consistent with inner ear input contributing to motor asymmetry, we also show that, in humans with normal ear function, the motor-dominant hemisphere, measured as handedness, is ipsilateral to the ear with weaker vestibular input. 5. How to quantize supersymmetric theories International Nuclear Information System (INIS) Smilga, A.V. 1985-01-01 A recipe for resolving the ordering ambiguities in quantum hamiltonians of supersymmetric theories is suggested. The Weyl ordering procedure applied to classical supercharges expressed as functions on the phase space of a classically supersymmetric system is shown to result in quantum operators which satisfy usual SUSY algebra. The quantum hamiltonian does not always coincide with the Weyl ordered classical hamiltonian function. The difference is due to that the Weyl symbol of the supercharge anticommutator does not coincide with the Poisson bracket of their Weyl symbols (i.e. the classical hamiltonian). The procedure is applied to supersymmetric σ-models (both N=2 and N=1 cases are analyzed) and also to the supersymmetric SU(2) Yang-Mills theory. Only quantum mechanical systems following from field theories when fields are assumed to be independent of space coordinates are considered. For gauge theories thesuggested recipe for quantization leads to the same result as the well-known Dirac recipe 6. Information on the gauge principle from an N=1/2, D=2 supersymmetric model International Nuclear Information System (INIS) Dias, S.A.; Doria, R.M.; Valle, J.L.M. 1988-01-01 The gauge principle does not only work to generate interactions. It potentially yields an abundance of gauge-potential fields transforming under the same local symmetry group. In order to show evidences of this property this work gauge-covariantizes an N = 1/2, D = 2 supersymmetric theory. Then, by relaxing the so-called conventional constraint, a second gauge-potential field naturally emerges. (author) [pt 7. Duality in supersymmetric Yang-Mills theory Energy Technology Data Exchange (ETDEWEB) Peskin, M.E. 1997-02-01 These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N{sub f} < N{sub c}, in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N{sub f} large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs. 8. Duality in supersymmetric Yang-Mills theory International Nuclear Information System (INIS) Peskin, M.E. 1997-02-01 These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N f c , in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N f large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs 9. Chaos and random matrices in supersymmetric SYK Science.gov (United States) Hunter-Jones, Nicholas; Liu, Junyu 2018-05-01 We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. We find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems. 10. Contribution of hedgehog signaling to the establishment of left-right asymmetry in the sea urchin. Science.gov (United States) Warner, Jacob F; Miranda, Esther L; McClay, David R 2016-03-15 Most bilaterians exhibit a left-right asymmetric distribution of their internal organs. The sea urchin larva is notable in this regard since most adult structures are generated from left sided embryonic structures. The gene regulatory network governing this larval asymmetry is still a work in progress but involves several conserved signaling pathways including Nodal, and BMP. Here we provide a comprehensive analysis of Hedgehog signaling and it's contribution to left-right asymmetry. We report that Hh signaling plays a conserved role to regulate late asymmetric expression of Nodal and that this regulation occurs after Nodal breaks left-right symmetry in the mesoderm. Thus, while Hh functions to maintain late Nodal expression, the molecular asymmetry of the future coelomic pouches is locked in. Furthermore we report that cilia play a role only insofar as to transduce Hh signaling and do not have an independent effect on the asymmetry of the mesoderm. From this, we are able to construct a more complete regulatory network governing the establishment of left-right asymmetry in the sea urchin. Copyright © 2016 Elsevier Inc. All rights reserved. 11. Shaping the zebrafish heart: from left-right axis specification to epithelial tissue morphogenesis. NARCIS (Netherlands) Bakkers, J.; Verhoeven, M.C.; Abdelilah-Seyfried, S. 2009-01-01 Although vertebrates appear bilaterally symmetric on the outside, various internal organs, including the heart, are asymmetric with respect to their position and/or their orientation based on the left/right (L/R) axis. The L/R axis is determined during embryo development. Determination of the L/R 12. Left-right asymmetry in plants and animals: a gold mine for research NARCIS (Netherlands) Schilthuizen, M.; Gravendeel, B. 2012-01-01 Left-right asymmetry patterns in the body shapes of animals and plants have been a continuous source of interest among biologists. Recently, inroads have been made to developing a coherent research programme that makes use of the unique fact that chiral patterns may be studied (and generalities 13. Mental Rotation Does Not Account for Sex Differences in Left-Right Confusion Science.gov (United States) Ocklenburg, Sebastian; Hirnstein, Marco; Ohmann, Hanno Andreas; Hausmann, Markus 2011-01-01 Several studies have demonstrated that women believe they are more prone to left-right confusion (LRC) than men. However, while some studies report that there is also a sex difference in LRC tasks favouring men, others report that men and women perform equally well. Recently, it was suggested that sex differences only emerge in LRC tasks when they… 14. Left--right symmetric gauge theories of weak and electromagnetic interactions International Nuclear Information System (INIS) Sidhu, D.P. 1978-01-01 We review the recent progress in spontaneously broken left-right symmetric gauge theories of weak and electromagnetic interactions. Recently gauge theories based on the group SU(2)/Sub L/ x SU(2)/sub R/ x U(1) have been proposed as serious candidates for a unified description of the weak and electromagnetic interactions. Such theories have a number of attractive features which are not shared by the standard SU(2) x U(1) theories. Parity violation as well as CP-violation are spontaneous in origin and, therefore, theories are parity conserving before spontaneous breakdown of the symmetry and also afterwards at asymptotic energies. The asymmetry in low energy charged current weak interaction, i.e., predominance of left-handed charged current interactions over the right-handed ones, is a consequence of the symmetry breaking thus leading to a conceptually different picture of weak interaction at low energies. Another appealing feature of these theories is the beauty and richness of the structure of weak neutral current interactions. One can have a parity conserving structure of the neutral currents (one neutral boson (Z/sub V/) has pure vector and the other (Z/sub A/) pure axial vector coupling to quarks and leptons) which is natural in the technical sense of the word. Models of this type provide the most elegant explanation of the failure to find parity violation in atoms at the level predicted on the basis of the Weinberg-Salam model. In spite of manifestly parity conserving neutral current interactions, ν/sub μ/N and anti ν/sub μ/N (also ν/sub μ/e and anti ν/sub μ/e) neutral current cross-sections have to be unequal in these theories because of the definite parity and charge conjugation of the Z-bosons 15. The massless limit of supersymmetric QCD International Nuclear Information System (INIS) Davis, A.C.; Dine, M.; Seiberg, N. 1983-01-01 We construct an effective lagrangian for supersymmetric QCD, using a simple set of rules. The model with non-zero quark mass, msub(q), has at least N supersymmetric vacua, where N is the number of colors (in agreement with Witten's index). These vacua move to infinity as msub(q)->0. We study the possibility of supersymmetric breaking at msub(q)=0. (orig.) 16. High-precision predictions for the light CP-even Higgs boson mass of the minimal supersymmetric standard model. Science.gov (United States) Hahn, T; Heinemeyer, S; Hollik, W; Rzehak, H; Weiglein, G 2014-04-11 For the interpretation of the signal discovered in the Higgs searches at the LHC it will be crucial in particular to discriminate between the minimal Higgs sector realized in the standard model (SM) and its most commonly studied extension, the minimal supersymmetric standard model (MSSM). The measured mass value, having already reached the level of a precision observable with an experimental accuracy of about 500 MeV, plays an important role in this context. In the MSSM the mass of the light CP-even Higgs boson, Mh, can directly be predicted from the other parameters of the model. The accuracy of this prediction should at least match the one of the experimental result. The relatively high mass value of about 126 GeV has led to many investigations where the scalar top quarks are in the multi-TeV range. We improve the prediction for Mh in the MSSM by combining the existing fixed-order result, comprising the full one-loop and leading and subleading two-loop corrections, with a resummation of the leading and subleading logarithmic contributions from the scalar top sector to all orders. In this way for the first time a high-precision prediction for the mass of the light CP-even Higgs boson in the MSSM is possible all the way up to the multi-TeV region of the relevant supersymmetric particles. The results are included in the code FEYNHIGGS. 17. Heterochrony and Early Left-Right Asymmetry in the Development of the Cardiorespiratory System of Snakes Science.gov (United States) van Soldt, Benjamin J.; Metscher, Brian D.; Poelmann, Robert E.; Vervust, Bart; Vonk, Freek J.; Müller, Gerd B.; Richardson, Michael K. 2015-01-01 Snake lungs show a remarkable diversity of organ asymmetries. The right lung is always fully developed, while the left lung is either absent, vestigial, or well-developed (but smaller than the right). A ‘tracheal lung’ is present in some taxa. These asymmetries are reflected in the pulmonary arteries. Lung asymmetry is known to appear at early stages of development in Thamnophis radix and Natrix natrix. Unfortunately, there is no developmental data on snakes with a well-developed or absent left lung. We examine the adult and developmental morphology of the lung and pulmonary arteries in the snakes Python curtus breitensteini, Pantherophis guttata guttata, Elaphe obsoleta spiloides, Calloselasma rhodostoma and Causus rhombeatus using gross dissection, MicroCT scanning and 3D reconstruction. We find that the right and tracheal lung develop similarly in these species. By contrast, the left lung either: (1) fails to develop; (2) elongates more slowly and aborts early without (2a) or with (2b) subsequent development of faveoli; (3) or develops normally. A right pulmonary artery always develops, but the left develops only if the left lung develops. No pulmonary artery develops in relation to the tracheal lung. We conclude that heterochrony in lung bud development contributes to lung asymmetry in several snake taxa. Secondly, the development of the pulmonary arteries is asymmetric at early stages, possibly because the splanchnic plexus fails to develop when the left lung is reduced. Finally, some changes in the topography of the pulmonary arteries are consequent on ontogenetic displacement of the heart down the body. Our findings show that the left-right asymmetry in the cardiorespiratory system of snakes is expressed early in development and may become phenotypically expressed through heterochronic shifts in growth, and changes in axial relations of organs and vessels. We propose a step-wise model for reduction of the left lung during snake evolution. PMID:25555231 18. Heterochrony and early left-right asymmetry in the development of the cardiorespiratory system of snakes. Science.gov (United States) van Soldt, Benjamin J; Metscher, Brian D; Poelmann, Robert E; Vervust, Bart; Vonk, Freek J; Müller, Gerd B; Richardson, Michael K 2015-01-01 Snake lungs show a remarkable diversity of organ asymmetries. The right lung is always fully developed, while the left lung is either absent, vestigial, or well-developed (but smaller than the right). A 'tracheal lung' is present in some taxa. These asymmetries are reflected in the pulmonary arteries. Lung asymmetry is known to appear at early stages of development in Thamnophis radix and Natrix natrix. Unfortunately, there is no developmental data on snakes with a well-developed or absent left lung. We examine the adult and developmental morphology of the lung and pulmonary arteries in the snakes Python curtus breitensteini, Pantherophis guttata guttata, Elaphe obsoleta spiloides, Calloselasma rhodostoma and Causus rhombeatus using gross dissection, MicroCT scanning and 3D reconstruction. We find that the right and tracheal lung develop similarly in these species. By contrast, the left lung either: (1) fails to develop; (2) elongates more slowly and aborts early without (2a) or with (2b) subsequent development of faveoli; (3) or develops normally. A right pulmonary artery always develops, but the left develops only if the left lung develops. No pulmonary artery develops in relation to the tracheal lung. We conclude that heterochrony in lung bud development contributes to lung asymmetry in several snake taxa. Secondly, the development of the pulmonary arteries is asymmetric at early stages, possibly because the splanchnic plexus fails to develop when the left lung is reduced. Finally, some changes in the topography of the pulmonary arteries are consequent on ontogenetic displacement of the heart down the body. Our findings show that the left-right asymmetry in the cardiorespiratory system of snakes is expressed early in development and may become phenotypically expressed through heterochronic shifts in growth, and changes in axial relations of organs and vessels. We propose a step-wise model for reduction of the left lung during snake evolution. 19. Heterochrony and early left-right asymmetry in the development of the cardiorespiratory system of snakes. Directory of Open Access Journals (Sweden) Benjamin J van Soldt Full Text Available Snake lungs show a remarkable diversity of organ asymmetries. The right lung is always fully developed, while the left lung is either absent, vestigial, or well-developed (but smaller than the right. A 'tracheal lung' is present in some taxa. These asymmetries are reflected in the pulmonary arteries. Lung asymmetry is known to appear at early stages of development in Thamnophis radix and Natrix natrix. Unfortunately, there is no developmental data on snakes with a well-developed or absent left lung. We examine the adult and developmental morphology of the lung and pulmonary arteries in the snakes Python curtus breitensteini, Pantherophis guttata guttata, Elaphe obsoleta spiloides, Calloselasma rhodostoma and Causus rhombeatus using gross dissection, MicroCT scanning and 3D reconstruction. We find that the right and tracheal lung develop similarly in these species. By contrast, the left lung either: (1 fails to develop; (2 elongates more slowly and aborts early without (2a or with (2b subsequent development of faveoli; (3 or develops normally. A right pulmonary artery always develops, but the left develops only if the left lung develops. No pulmonary artery develops in relation to the tracheal lung. We conclude that heterochrony in lung bud development contributes to lung asymmetry in several snake taxa. Secondly, the development of the pulmonary arteries is asymmetric at early stages, possibly because the splanchnic plexus fails to develop when the left lung is reduced. Finally, some changes in the topography of the pulmonary arteries are consequent on ontogenetic displacement of the heart down the body. Our findings show that the left-right asymmetry in the cardiorespiratory system of snakes is expressed early in development and may become phenotypically expressed through heterochronic shifts in growth, and changes in axial relations of organs and vessels. We propose a step-wise model for reduction of the left lung during snake evolution. 20. Supersymmetric extension of Hopf maps: N = 4 {sigma}-models and the S{sup 3} {yields} S{sup 2} fibration Energy Technology Data Exchange (ETDEWEB) Carvalho, L. Faria; Toppan, F., E-mail: [email protected], E-mail: [email protected] [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Kuznetsova, Z., E-mail: [email protected] [Universidade Federal do ABC (UFABC), Santo Andre, SP (Brazil) 2009-07-01 We discuss four off-shell N = 4 D = 1 supersymmetry transformations, their associated one-dimensional -models and their mutual relations. They are given by I - the (4, 4){sub lin} linear 'root' supermultiplet (supersymmetric extension of R{sup 4}), II - the (3, 4, 1){sub lin} linear supermultiplet (supersymmetric extension of R3), III - the (3, 4, 1){sub nl} non-linear supermultiplet living on S{sup 3} and IV - the (2, 4, 2){sub nl} non-linear supermultiplet living on S{sup 2}. The I {yields} II map is the supersymmetric extension of the R4 {yields} R3 bilinear map, while the II {yields} IV map is the supersymmetric extension of the S{sup 3} {yields} S{sup 2} first Hopf fibration. The restrictions on the S{sup 3}, S{sup 2} spheres are expressed in terms of the stereo graphic projections. The non-linear supermultiplets, whose super transformations are local differential polynomials, are not equivalent to the linear supermultiplets with the same field content. The -models are determined in terms of an unconstrained pre potential of the target coordinates. The Uniformization Problem requires solving an inverse problem for the pre potential. The basic features of the supersymmetric extension of the second and third Hopf maps are briefly sketched. Finally, the Schur's lemma (i.e. the real, complex or quaternionic property) is extended to all minimal linear supermultiplets up to N {<=} 8. (author) 1. N-anti N oscillation in SO(10) and SU(6) supersymmetric grand unified models International Nuclear Information System (INIS) Fujimoto, Y.; Zhiyong, Z. 1982-06-01 N-anti N oscillation in SO(10) and SU(6) S.G.U.M. is considered. We find a new type of diagram leading to a faster oscillation rate than in non-supersymmetric case. It is also noted that in SO(10) S.G.U.M. with intermediate SU(4)sub(C)xSU(2)sub(L)xSU(2)sub(R) symmetry N-anti N oscillation would be highly suppressed, which may not necessarily be the case for SU(6) S.G.U.M. (author) 2. On the supersymmetric solitons and monopoles International Nuclear Information System (INIS) Hruby, J. 1978-01-01 The basic results in a new trend in supersymmetry and soliton theory are presented. It is shown that the soliton expectation value of the energy operator is mass of the soliton without the quantum corrections. A new supersymmetric monopole model in three dimensions is constructed by generalization of the supersymmetric sine-Gordon model in one space dimension 3. Modified Higgs boson phenomenology from gauge or gaugino mediation in the next-to-minimal supersymmetric standard model International Nuclear Information System (INIS) Morrissey, David E.; Pierce, Aaron 2008-01-01 In the next-to-minimal supersymmetric standard model (NMSSM), the presence of light pseudoscalars can have a dramatic effect on the decays of the standard model-like Higgs boson. These pseudoscalars are naturally light if supersymmetry breaking preserves an approximate U(1) R symmetry, spontaneously broken when the Higgs bosons take on their expectation values. We investigate two classes of theories that possess such an approximate U(1) R at the mediation scale: modifications of gauge and gaugino mediation. In the models we consider, we find two disjoint classes of phenomenologically allowed parameter regions. One of these regions corresponds to a limit where the singlet of the NMSSM largely decouples. The other can give rise to a standard model-like Higgs boson with dominant branching into light pseudoscalars. 4. Supersymmetric classical mechanics International Nuclear Information System (INIS) Biswas, S.N.; Soni, S.K. 1986-01-01 The purpose of the paper is to construct a supersymmetric Lagrangian within the framework of classical mechanics which would be regarded as a candidate for passage to supersymmetric quantum mechanics. 5 refs. (author) 5. Constraints on the rare tau decays from μ→eγ in the supersymmetric see-saw model International Nuclear Information System (INIS) Ibarra, Alejandro; Simonetto, Cristoforo 2008-01-01 It is now a firmly established fact that all family lepton numbers are violated in Nature. In this paper we discuss the implications of this observation for future searches for rare tau decays in the supersymmetric see-saw model. Using the two loop renormalization group evolution of the soft terms and the Yukawa couplings we show that there exists a lower bound on the rate of the rare process μ→eγ of the form BR(μ→eγ) ∼> C x BR(τ→μγ)BR(τ→eγ), where C is a constant that depends on supersymmetric parameters. Our only assumption is the absence of cancellations among the high-energy see-saw parameters. We also discuss the implications of this bound for future searches for rare tau decays. In particular, for large regions of the mSUGRA parameter space, we show that present B-factories could discover either τ→μγ or τ→eγ, but not both 6. Dyscalculia, Dysgraphia, and Left-Right Confusion from a Left Posterior Peri-Insular Infarct Directory of Open Access Journals (Sweden) S. Bhattacharyya 2014-01-01 Full Text Available The Gerstmann syndrome of dyscalculia, dysgraphia, left-right confusion, and finger agnosia is generally attributed to lesions near the angular gyrus of the dominant hemisphere. A 68-year-old right-handed woman presented with sudden difficulty completing a Sudoku grid and was found to have dyscalculia, dysgraphia, and left-right confusion. Magnetic resonance imaging (MRI showed a focus of abnormal reduced diffusivity in the left posterior insula and temporoparietal operculum consistent with acute infarct. Gerstmann syndrome from an insular or peri-insular lesion has not been described in the literature previously. Pathological and functional imaging studies show connections between left posterior insular region and inferior parietal lobe. We postulate that the insula and operculum lesion disrupted key functional networks resulting in a pseudoparietal presentation. 7. Organization of left-right coordination in the mammalian locomotor network DEFF Research Database (Denmark) Butt, S. J B; Lebret, James M.; Kiehn, Ole 2002-01-01 in the spinal cords of a number of aquatic vertebrates including the Xenopus tadpole and the lamprey. However, their function in left-right coordination of limb movements in mammals is poorly understood. In this review we describe the present understanding of commissural pathways in the functioning of spinal......Neuronal circuits involved in left-right coordination are a fundamental feature of rhythmic locomotor movements. These circuits necessarily include commissural interneurons (CINs) that have axons crossing the midline of the spinal cord. The properties of CINs have been described in some detail....... Spinal CINs play an important role in the generation of locomotor output. Increased knowledge as to their function in producing locomotion is likely to provide valuable insights into the spinal networks required for postural control and walking.... 8. Dyscalculia, dysgraphia, and left-right confusion from a left posterior peri-insular infarct. Science.gov (United States) Bhattacharyya, S; Cai, X; Klein, J P 2014-01-01 The Gerstmann syndrome of dyscalculia, dysgraphia, left-right confusion, and finger agnosia is generally attributed to lesions near the angular gyrus of the dominant hemisphere. A 68-year-old right-handed woman presented with sudden difficulty completing a Sudoku grid and was found to have dyscalculia, dysgraphia, and left-right confusion. Magnetic resonance imaging (MRI) showed a focus of abnormal reduced diffusivity in the left posterior insula and temporoparietal operculum consistent with acute infarct. Gerstmann syndrome from an insular or peri-insular lesion has not been described in the literature previously. Pathological and functional imaging studies show connections between left posterior insular region and inferior parietal lobe. We postulate that the insula and operculum lesion disrupted key functional networks resulting in a pseudoparietal presentation. 9. e+e- collisions at the SLC--the left-right asymmetry International Nuclear Information System (INIS) Prescott, C.Y. 1993-09-01 Recent progress with the SLC as a prototype linear collider for high energy e + e - collisions is reviewed. Recent advances in the production of high intensity beams of polarized e -s are also discussed. The SLD Collaboration has embarked on a precision measurement of the left-right polarization asymmetry A LR at the Z pole with polarized electrons. Results and future plans are presented 10. Left-right asymmetry of maturation rates in human embryonic neural development OpenAIRE De Kovel, C.; Lisgo, S.; Karlebach, G.; Ju, J.; Cheng, G.; Fisher, S.; Francks, C. 2017-01-01 Background Left-right asymmetry is a fundamental organizing feature of the human brain, and neuro-psychiatric disorders such as schizophrenia sometimes involve alterations of brain asymmetry. As early as 8 weeks post conception, the majority of human fetuses move their right arms more than their left arms, but because nerve fibre tracts are still descending from the forebrain at this stage, spinal-muscular asymmetries are likely to play an important developmental role. Methods We used RNA seq... 11. The neutron electric dipole moment in left-right symmetric low energy supergravity International Nuclear Information System (INIS) Ahn, Y.J. 1984-01-01 We compute the neutron electric dipole moment in low energy supergravity based on the gauge group SU(2)sub(L) x SU(2)sub(R) x U(1)sub(B-L). We find the electric dipole moment dsub(n) -25 e cm x (CP violating phase) provided the left-right symmetry breaking scale > or approx. 10 3 GeV. (orig.) 12. Neurally Derived Tissues in Xenopus laevis Embryos Exhibit a Consistent Bioelectrical Left-Right Asymmetry Directory of Open Access Journals (Sweden) Vaibhav P. Pai 2012-01-01 Full Text Available Consistent left-right asymmetry in organ morphogenesis is a fascinating aspect of bilaterian development. Although embryonic patterning of asymmetric viscera, heart, and brain is beginning to be understood, less is known about possible subtle asymmetries present in anatomically identical paired structures. We investigated two important developmental events: physiological controls of eye development and specification of neural crest derivatives, in Xenopus laevis embryos. We found that the striking hyperpolarization of transmembrane potential (Vmem demarcating eye induction usually occurs in the right eye field first. This asymmetry is randomized by perturbing visceral left-right patterning, suggesting that eye asymmetry is linked to mechanisms establishing primary laterality. Bilateral misexpression of a depolarizing channel mRNA affects primarily the right eye, revealing an additional functional asymmetry in the control of eye patterning by Vmem. The ATP-sensitive K+ channel subunit transcript, SUR1, is asymmetrically expressed in the eye primordia, thus being a good candidate for the observed physiological asymmetries. Such subtle asymmetries are not only seen in the eye: consistent asymmetry was also observed in the migration of differentiated melanocytes on the left and right sides. These data suggest that even anatomically symmetrical structures may possess subtle but consistent laterality and interact with other developmental left-right patterning pathways. 13. Improved perturbative calculations in field theory; Calculation of the mass spectrum and constraints on the supersymmetric standard model; Calculs perturbatifs variationnellement ameliores en theorie des champs; Calcul du spectre et contraintes sur le modele supersymetrique standard Energy Technology Data Exchange (ETDEWEB) Kneur, J.L 2006-06-15 This document is divided into 2 parts. The first part describes a particular re-summation technique of perturbative series that can give a non-perturbative results in some cases. We detail some applications in field theory and in condensed matter like the calculation of the effective temperature of Bose-Einstein condensates. The second part deals with the minimal supersymmetric standard model. We present an accurate calculation of the mass spectrum of supersymmetric particles, a calculation of the relic density of supersymmetric black matter, and the constraints that we can infer from models. 14. Left-right asymmetry is formed in individual cells by intrinsic cell chirality. Science.gov (United States) Hatori, Ryo; Ando, Tadashi; Sasamura, Takeshi; Nakazawa, Naotaka; Nakamura, Mitsutoshi; Taniguchi, Kiichiro; Hozumi, Shunya; Kikuta, Junichi; Ishii, Masaru; Matsuno, Kenji 2014-08-01 Many animals show left-right (LR) asymmetric morphology. The mechanisms of LR asymmetric development are evolutionarily divergent, and they remain elusive in invertebrates. Various organs in Drosophila melanogaster show stereotypic LR asymmetry, including the embryonic gut. The Drosophila embryonic hindgut twists 90° left-handedly, thereby generating directional LR asymmetry. We recently revealed that the hindgut epithelial cell is chiral in shape and other properties; this is termed planar cell chirality (PCC). We previously showed by computer modeling that PCC is sufficient to induce the hindgut rotation. In addition, both the PCC and the direction of hindgut twisting are reversed in Myosin31DF (Myo31DF) mutants. Myo31DF encodes Drosophila MyosinID, an actin-based motor protein, whose molecular functions in LR asymmetric development are largely unknown. Here, to understand how PCC directs the asymmetric cell-shape, we analyzed PCC in genetic mosaics composed of cells homozygous for mutant Myo31DF, some of which also overexpressed wild-type Myo31DF. Wild-type cell-shape chirality only formed in the Myo31DF-overexpressing cells, suggesting that cell-shape chirality was established in each cell and reflects intrinsic PCC. A computer model recapitulating the development of this genetic mosaic suggested that mechanical interactions between cells are required for the cell-shape behavior seen in vivo. Our mosaic analysis also suggested that during hindgut rotation in vivo, wild-type Myo31DF suppresses the elongation of cell boundaries, supporting the idea that cell-shape chirality is an intrinsic property determined in each cell. However, the amount and distribution of F-actin and Myosin II, which are known to help generate the contraction force on cell boundaries, did not show differences between Myo31DF mutant cells and wild-type cells, suggesting that the static amount and distribution of these proteins are not involved in the suppression of cell-boundary elongation 15. Fine Mapping of the Pond Snail Left-Right Asymmetry (Chirality) Locus Using RAD-Seq and Fibre-FISH Science.gov (United States) Han, Jie; Yang, Fengtang; Aboobaker, Aziz; Blaxter, Mark L.; Davison, Angus 2013-01-01 The left-right asymmetry of snails, including the direction of shell coiling, is determined by the delayed effect of a maternal gene on the chiral twist that takes place during early embryonic cell divisions. Yet, despite being a well-established classical problem, the identity of the gene and the means by which left-right asymmetry is established in snails remain unknown. We here demonstrate the power of new genomic approaches for identification of the chirality gene, “D”. First, heterozygous (Dd) pond snails Lymnaea stagnalis were self-fertilised or backcrossed, and the genotype of more than six thousand offspring inferred, either dextral (DD/Dd) or sinistral (dd). Then, twenty of the offspring were used for Restriction-site-Associated DNA Sequencing (RAD-Seq) to identify anonymous molecular markers that are linked to the chirality locus. A local genetic map was constructed by genotyping three flanking markers in over three thousand snails. The three markers lie either side of the chirality locus, with one very tightly linked (chirality gene and the variation that underpins sinistral and dextral coiling. More generally, the results also show that combining genomic technologies, such as RAD-Seq and high resolution FISH, is a robust approach for mapping key loci in non-model systems. PMID:23951082 16. The gauge technique in supersymmetric QED2 NARCIS (Netherlands) Roo, M. de; Steringa, J.J. 1988-01-01 We construct an extension of the gauge technique to two-dimensional supersymmetric gauge theories. This involves a derivation of the spectral representation of a scalar superpropagator in two dimensions. We apply the method to the massive supersymmetric Schwinger model. In the case that the gauge 17. Non-standard charged Higgs decay at the LHC in Next-to-Minimal Supersymmetric Standard Model Energy Technology Data Exchange (ETDEWEB) Bandyopadhyay, Priyotosh [Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento and INFN-Lecce,Via Arnesano, 73100 Lecce (Italy); Huitu, Katri [Department of Physics, and Helsinki Institute of Physics,P.O.B 64 (Gustaf Hällströmin katu 2), FI-00014 University of Helsinki (Finland); Niyogi, Saurabh [The Institute of Mathematical Sciences,CIT Campus, Chennai (India) 2016-07-04 We consider next-to-minimal supersymmetric standard model (NMSSM) which has a gauge singlet superfield. In the scale invariant superpotential we do not have the mass terms and the whole Lagrangian has an additional Z{sub 3} symmetry. This model can have light scalar and/or pseudoscalar allowed by the recent data from LHC and the old data from LEP. We investigate the situation where a relatively light charged Higgs can decay to such a singlet-like pseudoscalar and a W{sup ±} boson giving rise to a final state containing τ and/or b-jets and lepton(s). Such decays evade the recent bounds on charged Higgs from the LHC, and according to our PYTHIA-FastJet based simulation can be probed with 10 fb{sup −1} at the LHC center of mass energy of 13 and 14 TeV. 18. Top and Higgs mass predictions in supersymmetric SU(5) model with big top quark Yukawa coupling constant International Nuclear Information System (INIS) Krasnikov, N.V.; Rodenberg, R. 1993-01-01 From the requirement of the absence of the Landau pole singularity for the effective top quark Yukawa coupling constant up to Planck scale in SU(5) supersymmetric model we find an upper bound m t ≤ 187 GeV for the top quark mass. For the SU(5) fixed point renormalization group solution for top quark Yukawa coupling constant which can be interpreted as the case of composite superhiggs we find that m t ≥ 140 GeV. Similar bound takes place in all models with big anti h t (m t ). For m t ≤ 160 GeV we find also that the Higgs boson is lighter than m Z and hence it can be discovered at LEP2 19. Supersymmetric flipped SU(5) revitalized Energy Technology Data Exchange (ETDEWEB) Antoniadis, I.; Ellis, J.; Hagelin, J.S.; Nanopoulos, D.V. 1987-08-06 We describe a simple N = 1 supersymmetric GUT based on the group SU(5) x U(1) which has the following virtues: the gauge group is broken down to the SU(3)/sub C/ x SU(2)/sub L/ x U(1)/sub y/ of the standard model using just 10, 10 Higgs representations, and the doublet-triplet mass splitting problem is solved naturally by a very simple missing-partner mechanism. The successful supersymmetric GUT prediction for sin/sup 2/theta/sub w/ can be maintained, whilst there are no fermion mass relations. The gauge group and representation structure of the model may be obtainable from the superstring. 20. Search for neutral Higgs bosons of the minimal supersymmetric standard model in pp collisions at √s = 8 TeV with the ATLAS detector Czech Academy of Sciences Publication Activity Database Aad, G.; Abbott, B.; Abdallah, J.; Böhm, Jan; Chudoba, Jiří; Havránek, Miroslav; Hejbal, Jiří; Jakoubek, Tomáš; Kepka, Oldřich; Kupčo, Alexander; Kůs, Vlastimil; Lokajíček, Miloš; Lysák, Roman; Marčišovský, Michal; Mikeštíková, Marcela; Němeček, Stanislav; Šícho, Petr; Staroba, Pavel; Svatoš, Michal; Taševský, Marek; Vrba, Václav 2014-01-01 Roč. 2014, č. 11 (2014), s. 1-32 ISSN 1126-6708 R&D Projects: GA MŠk(CZ) LG13009 Institutional support: RVO:68378271 Keywords : scattering minimal supersymmetric standard model * parameter space * scalar particle * branching ratio * Higgs particle * ATLAS * CERN LHC Coll Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 5.618, year: 2012 1. Search for the neutral Higgs bosons of the minimal supersymmetric standard model in pp collisions at √s = 7 TeV with the ATLAS detector Czech Academy of Sciences Publication Activity Database Aad, G.; Abajyan, T.; Abbott, B.; Böhm, Jan; Chudoba, Jiří; Gunther, Jaroslav; Jakoubek, Tomáš; Juránek, Vojtěch; Kepka, Oldřich; Kupčo, Alexander; Kůs, Vlastimil; Lokajíček, Miloš; Marčišovský, Michal; Mikeštíková, Marcela; Myška, Miroslav; Němeček, Stanislav; Růžička, Pavel; Schovancová, Jaroslava; Šícho, Petr; Staroba, Pavel; Svatoš, Michal; Taševský, Marek; Tic, Tomáš; Vrba, Václav 2013-01-01 Roč. 2013, č. 2 (2013), s. 1-47 ISSN 1029-8479 R&D Projects: GA MŠk LA08032 Institutional support: RVO:68378271 Keywords : CERN * scattering * leptonic decay * Higgs particle * mass * jet * bottom * minimal supersymmetric standard model * parameter space * ATLAS Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 6.220, year: 2013 2. Fuzzy Killing spinors and supersymmetric D4 action on the fuzzy 2-sphere from the ABJM model International Nuclear Information System (INIS) Nastase, Horatiu; Papageorgakis, Constantinos 2009-01-01 Our recent construction arXiv:0903.3966 for the fuzzy 2-sphere in terms of bifundamentals, discovered in the context of the ABJM model, is shown to be explicitly equivalent to the usual (adjoint) fuzzy sphere construction. The matrices G-tilde α that define it play the role of fuzzy Killing spinors on the 2-sphere, out of which all spherical harmonics are constructed. Starting from the quadratic fluctuation action around these solutions in the mass-deformed ABJM theory, we recover a supersymmetric D4-brane action wrapping a 2-sphere, including fermions. We obtain both the usual D4 action with an unusual x-dependence on the sphere, as well as a twisted version in terms of the usual x-dependence, and contrast our result with the Maldacena-Nunez case of a D5 wrapping an S 2 . The twisted and unwisted fields are related by the same matrix G-tilde α . 3. Aspects of supersymmetric inflation International Nuclear Information System (INIS) Lindblom, P.R. 1987-01-01 A new supersymmetric inflationary model is presented and shown to possess the following features: a successful slow rollover produced by quantum corrections; an acceptable pattern of supersymmetry breaking leading to the correct value of the electroweak scale; and a stable slow rollover transition to a minimum with vanishing cosmological constant. It is demonstrated that there is a class of GUT models which are compatible with an inflationary universe scenario in which: (a) the GUT and inflationary phase transitions are distinct (as in supersymmetric inflation); and (b) an observable number of GUT monopoles are created thermally due to reheating of the GUT sector after inflation. This provides one of the few ways of reconciling an observation of GUT monopoles with inflation. New techniques are developed for constructing inflationary models with multiple inflation fields, such as generalizing the one-dimensional slow rollover constraints and estimating the contribution to δρ/ρ from fluctuations transverse to the path of the slow rollover. A new method for ending the slow rollover portion of the inflationary transition is developed 4. On quantization of supersymmetric theories International Nuclear Information System (INIS) Smilga, A.V. 1985-01-01 A recipe to resolve ordering ambiguities in the quantum hamiltonian of supersymmetric theories is suggested. The Weyl ordering prescription for supercharge operators should be employed to preserve SUSY algebra on the quantum level. The quantum hamiltonian does not generally coincide with the Weyl ordered classical hamiltonian, the difference being due to the fact that the Weyl symbol of anticommutator of supercharges does not generally coincide with the Poisson bracket of their Weyl symbols (i.e. the classical hamiltonian). The suggested procedure is applied in the examples of N=1 and N=2 supersymmetric σ-models analyzed in the constant field limit 5. Left-Right Asymmetry of Maturation Rates in Human Embryonic Neural Development. Science.gov (United States) de Kovel, Carolien G F; Lisgo, Steven; Karlebach, Guy; Ju, Jia; Cheng, Gang; Fisher, Simon E; Francks, Clyde 2017-08-01 Left-right asymmetry is a fundamental organizing feature of the human brain, and neuropsychiatric disorders such as schizophrenia sometimes involve alterations of brain asymmetry. As early as 8 weeks postconception, the majority of human fetuses move their right arms more than their left arms, but because nerve fiber tracts are still descending from the forebrain at this stage, spinal-muscular asymmetries are likely to play an important developmental role. We used RNA sequencing to measure gene expression levels in the left and right spinal cords, and the left and right hindbrains, of 18 postmortem human embryos aged 4 to 8 weeks postconception. Genes showing embryonic lateralization were tested for an enrichment of signals in genome-wide association data for schizophrenia. The left side of the embryonic spinal cord was found to mature faster than the right side. Both sides transitioned from transcriptional profiles associated with cell division and proliferation at earlier stages to neuronal differentiation and function at later stages, but the two sides were not in synchrony (p = 2.2 E-161). The hindbrain showed a left-right mirrored pattern compared with the spinal cord, consistent with the well-known crossing over of function between these two structures. Genes that showed lateralization in the embryonic spinal cord were enriched for association signals with schizophrenia (p = 4.3 E-05). These are the earliest stage left-right differences of human neural development ever reported. Disruption of the lateralized developmental program may play a role in the genetic susceptibility to schizophrenia. Copyright © 2017 Society of Biological Psychiatry. Published by Elsevier Inc. All rights reserved. 6. 1/N perturbation theory and quantum conservation laws for supersymmetrical chiral field. 2 International Nuclear Information System (INIS) Aref'eva, I.Ya.; Krivoshchekov, V.K.; Medvedev, P.B.; Gosudarstvennyj Komitet Standartov Soveta Ministrov SSSR, Moscow; Gosudarstvennyj Komitet po Ispol'zovaniyu Atomnoj Ehnergii SSSR, Moscow. Inst. Teoreticheskoj i Ehksperimental'noj Fiziki) 1980-01-01 The renormalizability of the supersymmetric chiral model (supersymmetric nonlinear σ-model) is proved in the framework of the 1/N perturbation theory expansion proposed in the previous paper. The renormalizability proof is essentially based on the quantum supersymmetric chirality condition. The supersymmetric formulation of equations of motion is given. The first non-trivial quantum conservation laws are derived 7. Measurement of the left-right asymmetry in the electrofission of the deuteron International Nuclear Information System (INIS) Frommberger, F. 1993-11-01 At the Electron Stretcher Accelerator ELSA of the Bonn University the left-right asymmetry A φ of the reaction d(e,e'p)n has been measured in quasi-free kinematics (E e =1.6 GeV, θ e =14 ). The scattered electrons were detected with a magnetic spectrometer. Due to the high duty cycle of ELSA non-magnetic proton detectors could be used. Therefore a simultaneous measurement at different proton angles was possible, leading to small systematic errors. The remaining systematic errors have been studied carefully and corrected. The experimental data are in good agreement with theoretical calculations, if relativistic corrections are taken into account. (orig.) 8. Influence of left right asymmetry degrees of freedom in self-consistent calculation of 20Ne International Nuclear Information System (INIS) Marcos, S.; Flocard, H.; Heenen, P.H. 1983-06-01 Within a constrained Hartree-Fock calculation we investigate the effects of left right asymmetric degrees of freedom associated with the channel 16 O + 4 He 20 Ne. We find a large softness of 20 Ne against octupole deformation. The optimal solution after restoration of the parity by means of a projection shows a pronouned 16 O + 4 He clustering. A generator coordinate calculation along the collective path confirms this conclusion. Once center of mass motion effects are taken into account a good agreement with experiment is found 9. Supersymmetric GUTs and cosmology International Nuclear Information System (INIS) Lazarides, G.; Shafi, Q. 1982-06-01 By examining the behaviour of supersymmetric GUTs in the very early universe we find two classes of realistic models. In one of them supersymmetry is broken at or near the superheavy GUT scale. The cosmological implications of such models are expected to be similar to those of nonsupersymmetric GUTs. In the second class of models, the superheavy GUT scale is related to the supersymmetry breaking scale a la Witten. Two types of cosmological scenarios appear possible in this case, either with or without an intermediate (new) inflationary phase. They can be experimentally distinguished, since the former predicts an absence and the latter an observable number density of superheavy monopoles. A mechanism for generating baryon asymmetry in such models is pointed out. Further constraint on model building appears if global R invariance is employed to resolve the strong CP problem. (author) 10. Supersymmetric Recipes (1/3) CERN Multimedia CERN. Geneva 2011-01-01 In these lectures, I shall describe the theory of supersymmetry accessible to people with a knowledge of basic quantum field theory. The lectures will contain recipes of how to calculate which interactions (and which special relations) are in supersymmetry, without providing detailed proofs of where they come from. We shall also cover: motivation for weak-scale supersymmetry and the minimal supersymmetric standard model. 11. Effective Lagrangian for the χi+χj0H- interaction in the minimal supersymmetric standard model and charged Higgs decays International Nuclear Information System (INIS) Ibrahim, Tarek; Nath, Pran; Psinas, Anastasios 2004-01-01 We extend previous analyses of the supersymmetric loop correction to the charged Higgs couplings to include the coupling H ± χ ± χ 0 . The analysis completes the previous analyses where similar corrections were computed for H + t-barb (H - tb-bar), and for H + τ - ν-bar τ (H - τ + ν τ ) couplings within the minimal supersymmetric standard model. The effective one loop Lagrangian is then applied to the computation of the charged Higgs decays. The sizes of the supersymmetric loop correction on branching ratios of the charged Higgs H + (H - ) into the decay modes tb-bar (t-barb), τ-barν τ (τν-bar τ ), and χ i + χ j 0 (χ i - χ j 0 )(i=1,2; j=1-4) are investigated and the supersymmetric loop correction is found to be significant, i.e., in the range 20-30 % in significant regions of the parameter space. The loop correction to the decay mode χ 1 ± χ 2 0 is examined in specific detail as this decay mode leads to a trileptonic signal. The effects of CP phases on the branching ratio are also investigated. A brief discussion of the implications of the analysis for colliders is given 12. Functional identification of interneurons responsible for left-right coordination of hindlimbs in mammals DEFF Research Database (Denmark) Butt, Simon J.B.; Kiehn, Ole 2003-01-01 Local neuronal networks that are responsible for walking are poorly characterized in mammals. Using an innovative approach to identify interneuron inputs onto motorneuron populations in a neonatal rodent spinal cord preparation, we have investigated the network responsible for left-right coordina......Local neuronal networks that are responsible for walking are poorly characterized in mammals. Using an innovative approach to identify interneuron inputs onto motorneuron populations in a neonatal rodent spinal cord preparation, we have investigated the network responsible for left......-right coordination of the hindlimbs. We demonstrate how commissural interneurons (CINs), whose axons traverse the midline to innervate contralateral neurons, are organized such that distinct flexor and extensor centers in the rostral lumbar spinal cord define activity in both flexor and extensor caudal motor pools....... In addition, the nature of some connections are reconfigured on switching from rest to locomotion via a mechanism that might be associated with synaptic plasticity in the spinal cord. These results from identified pattern-generating interneurons demonstrate how interneuron populations create an effective... 13. Cell chirality: its origin and roles in left-right asymmetric development. Science.gov (United States) Inaki, Mikiko; Liu, Jingyang; Matsuno, Kenji 2016-12-19 An item is chiral if it cannot be superimposed on its mirror image. Most biological molecules are chiral. The homochirality of amino acids ensures that proteins are chiral, which is essential for their functions. Chirality also occurs at the whole-cell level, which was first studied mostly in ciliates, single-celled protozoans. Ciliates show chirality in their cortical structures, which is not determined by genetics, but by 'cortical inheritance'. These studies suggested that molecular chirality directs whole-cell chirality. Intriguingly, chirality in cellular structures and functions is also found in metazoans. In Drosophila, intrinsic cell chirality is observed in various left-right (LR) asymmetric tissues, and appears to be responsible for their LR asymmetric morphogenesis. In other invertebrates, such as snails and Caenorhabditis elegans, blastomere chirality is responsible for subsequent LR asymmetric development. Various cultured cells of vertebrates also show intrinsic chirality in their cellular behaviours and intracellular structural dynamics. Thus, cell chirality may be a general property of eukaryotic cells. In Drosophila, cell chirality drives the LR asymmetric development of individual organs, without establishing the LR axis of the whole embryo. Considering that organ-intrinsic LR asymmetry is also reported in vertebrates, this mechanism may contribute to LR asymmetric development across phyla.This article is part of the themed issue 'Provocative questions in left-right asymmetry'. © 2016 The Authors. 14. Spontaneous mirror left-right symmetry breaking for leptogenesis parametrized by Majorana neutrino mass matrix Science.gov (United States) Gu, Pei-Hong 2017-10-01 We introduce a mirror copy of the ordinary fermions and Higgs scalars for embedding the SU(2) L × U(1) Y electroweak gauge symmetry into an SU(2) L × SU(2) R × U(1) B-L left-right gauge symmetry. We then show the spontaneous left-right symmetry breaking can automatically break the parity symmetry motivated by solving the strong CP problem. Through the SU(2) R gauge interactions, a mirror Majorana neutrino can decay into a mirror charged lepton and two mirror quarks. Consequently we can obtain a lepton asymmetry stored in the mirror charged leptons. The Yukawa couplings of the mirror and ordinary charged fermions to a dark matter scalar then can transfer the mirror lepton asymmetry to an ordinary lepton asymmetry which provides a solution to the cosmic baryon asymmetry in association with the SU(2) L sphaleron processes. In this scenario, the baryon asymmetry can be well described by the neutrino mass matrix up to an overall factor. 15. Supersymmetric particles at LEP International Nuclear Information System (INIS) Barbiellini, G.; Coignet, G.; Gaillard, M.K.; Bonneaud, G.; Ellis, J.; Matteuzzi, C.; Wiik, H. 1979-10-01 The authors examine whether the supersymmetrization of nature at a mass scale up to 100 GeV can be confirmed or excluded by experiments with LEP. They review the qualitative features of the spectroscopy suggested by supersymmetric theories. Then they discuss possible production rates and means of detection of these particles at LEP. In this framework they make some remarks about other projects for future high energy physics machines which can be used for the study of supersymmetric phenomena. (HSI) 16. Present and future K and B meson mixing constraints on TeV scale left-right symmetry Science.gov (United States) Bertolini, Stefano; Maiezza, Alessio; Nesti, Fabrizio 2014-05-01 We revisit the ΔF=2 transitions in the K and Bd ,s neutral meson systems in the context of the minimal left-right symmetric model. We take into account, in addition to up-to-date phenomenological data, the contributions related to the renormalization of the flavor-changing neutral Higgs tree-level amplitude. These contributions were neglected in recent discussions, albeit formally needed in order to obtain a gauge-independent result. Their impact on the minimal LR model is crucial and twofold. First, the effects are relevant in B meson oscillations, for both CP conserving and CP violating observables, so that for the first time these imply constraints on the LR scenario which compete with those of the K sector (plagued by long-distance uncertainties). Second, they sizably contribute to the indirect kaon CP violation parameter ɛ. We discuss the bounds from B and K mesons in both cases of LR symmetry: generalized parity (P) and charge conjugation (C). In the case of P, the interplay between the CP-violation parameters ɛ and ɛ' leads us to rule out the regime of very hierarchical bidoublet vacuum expectation values v2/v1handed currents, we find that a right-handed gauge boson WR as light as 3 TeV is allowed at the 95% C. L. This is well within the reach of direct detection at the next LHC run. If not discovered, within a decade the upgraded LHCb and Super B factories may reach an indirect sensitivity to a left-right scale of 8 TeV. 17. Phenomenological analysis of supersymmetric σ-models on coset spaces SO(10)/U(5) and E6/[SO(10)xU(1) International Nuclear Information System (INIS) Nyawelo, T.S. 2004-12-01 We discuss some phenomenological aspects of gauged supersymmetric σ-models on homogeneous coset-spaces E 6 /[SO(10)xU(1)] and SO(10)/U(5) which are some of the most interesting for phenomenology. We investigate in detail the vacuum configurations of these models, and study the resulting consequences for supersymmetry breaking and breaking of the internal symmetry. Some supersymmetric minima for both models with gauged full isometry groups E 6 and SO(10) are physically problematic as the Kaehler metric becomes singular ad hence the kinetic terms of the Goldstone boson multiplets vanish. This leads us to introduce recently proposed soft supersymmetry-breaking mass terms which displace the minimum away from the singulax point. A non-singular Kaehler metric breaks the linear subgroup SO(10)xU(1) of the E 6 model spontaneously. The particle spectrum of all these different models is computed. (author) 18. Deformed supersymmetric mechanics International Nuclear Information System (INIS) Ivanov, E.; Sidorov, S. 2013-01-01 Motivated by a recent interest in curved rigid supersymmetries, we construct a new type of N = 4, d = 1 supersymmetric systems by employing superfields defined on the cosets of the supergroup SU(2\|1). The relevant worldline supersymmetry is a deformation of the standard N = 4, d = 1 supersymmetry by a mass parameter m. As instructive examples we consider at the classical and quantum levels the models associated with the supermultiplets (1,4,3) and (2,4,2) and find out interesting interrelations with some previous works on nonstandard d = 1 supersymmetry. In particular, the d = 1 systems with 'weak supersymmetry' are naturally reproduced within our SU(2\|1) superfield approach as a subclass of the (1,4,3) models. A generalization to the N = 8, d = 1 case implies the supergroup SU(2\|2) as a candidate deformed worldline supersymmetry 19. Sign of the neutron-proton mass difference in an SU(2)xU(1) supersymmetric toy model: A possible scenario for solving the old puzzle International Nuclear Information System (INIS) Desai, B.R.; Xu, G. 1990-01-01 Based on the idea that electromagnetism is responsible for mass differences within isotopic multiplets (e.g., pointlike neutron and proton or u and d quarks), we generalize an SU(2)xU(1) model in a toy field theory of vectors to a supersymmetric model and investigate the finite mass difference within the isotopic doublet. It is found that under soft-supersymmetry breaking, a positive n-p mass difference can be obtained under reasonable assumptions for the parameters involved 20. Genetic Ablation of V2a Ipsilateral Interneurons Disrupts Left-Right Locomotor Coordination in Mammalian Spinal Cord DEFF Research Database (Denmark) Crone, Steven A.; Quinlan, Katharina A.; Zagoraiou, Laskaro 2008-01-01 The initiation and coordination of activity in limb muscles are the main functions of neural circuits that control locomotion. Commissural neurons connect locomotor circuits on the two sides of the spinal cord, and represent the known neural substrate for left-right coordination. Here we......-extensor coordination is unaffected. Anatomical tracing studies reveal a direct excitatory input of V2a interneurons onto commissural interneurons, including a set of molecularly defined V0 neurons that drive left-right alternation. Our findings imply that the neural substrate for left-right coordination consists...... of at least two components; commissural neurons and a class of ipsilateral interneurons that activate commissural pathways.... 1. Opposing nodal and BMP signals regulate left-right asymmetry in the sea urchin larva. Directory of Open Access Journals (Sweden) Yi-Jyun Luo Full Text Available Nodal and BMP signals are important for establishing left-right (LR asymmetry in vertebrates. In sea urchins, Nodal signaling prevents the formation of the rudiment on the right side. However, the opposing pathway to Nodal signaling during LR axis establishment is not clear. Here, we revealed that BMP signaling is activated in the left coelomic pouch, specifically in the veg2 lineage, but not in the small micromeres. By perturbing BMP activities, we demonstrated that BMP signaling is required for activating the expression of the left-sided genes and the formation of the left-sided structures. On the other hand, Nodal signals on the right side inhibit BMP signaling and control LR asymmetric separation and apoptosis of the small micromeres. Our findings show that BMP signaling is the positive signal for left-sided development in sea urchins, suggesting that the opposing roles of Nodal and BMP signals in establishing LR asymmetry are conserved in deuterostomes. 2. Low frequency vibrations disrupt left-right patterning in the Xenopus embryo. Directory of Open Access Journals (Sweden) Laura N Vandenberg Full Text Available The development of consistent left-right (LR asymmetry across phyla is a fascinating question in biology. While many pharmacological and molecular approaches have been used to explore molecular mechanisms, it has proven difficult to exert precise temporal control over functional perturbations. Here, we took advantage of acoustical vibration to disrupt LR patterning in Xenopus embryos during tightly-circumscribed periods of development. Exposure to several low frequencies induced specific randomization of three internal organs (heterotaxia. Investigating one frequency (7 Hz, we found two discrete periods of sensitivity to vibration; during the first period, vibration affected the same LR pathway as nocodazole, while during the second period, vibration affected the integrity of the epithelial barrier; both are required for normal LR patterning. Our results indicate that low frequency vibrations disrupt two steps in the early LR pathway: the orientation of the LR axis with the other two axes, and the amplification/restriction of downstream LR signals to asymmetric organs. 3. Measurement of the Left-Right Asymmetry in Z0 Events at SLAC Energy Technology Data Exchange (ETDEWEB) Szumilo, A 2004-01-05 Recent results from the 1992 and 1993 left-right asymmetry cross section measurements at the Stanford Linear Accelerator Center are presented. Measurements made with SLAC running with a center-of-mass energy at the Z{sup 0}-pole (91.2 GeV) by the SLD detector and an average electron beam polarization of 22.4 {+-} 0.7% for 1992 and 62.6 {+-} 1.2% for 1993. The asymmetry measured was A{sub LR} = 0.100 {+-} 0.044 and A{sub LR} = 0.1656 {+-} 0.0073 for the 1992 and 1993 runs, respectively. This in turn allows them to calculate the weak mixing angle value of sin{sup 2} {theta}{sub W} = 0.2378 {+-} 0.0056 and sin{sup 2} {theta}{sub W} = 0.2288 {+-} 0.0009 for the two data sets. 4. The first measurement of the left-right cross section asymmetry in Z0 boson production International Nuclear Information System (INIS) Ben-David, R.J. 1994-05-01 The first measurement of the left-right cross section asymmetry (A LR ) in Z degrees boson production has been made with the SLAC Large Detector (SLD) at the SLAC Linear Collider (SLC). The measurement was performed at a center-of-mass energy (E cm ) of 91.55 GeV with a longitudinally polarized electron beam. The average beam polarization was (22.4 ± 0.6)%. Using a sample of 10,224 Z degrees decays, A LR is measured to be 0.102 ± 0.044(stat) ± 0.003(syst), which determines the effective electroweak mixing angle to be sin 2 θ W eff = 0.2375 ± 0.0056(stat) ± 0.0004(syst) 5. [Analysis and research of brain-computer interface experiments for imaging left-right hands movement]. Science.gov (United States) Wu, Yazhou; He, Qinghua; Huang, Hua; Zhang, Ling; Zhuo, Yu; Xie, Qi; Wu, Baoming 2008-10-01 This is a research carried out to explore a pragmatic way of BCI based imaging movement, i. e. to extract the feature of EEG for reflecting different thinking by searching suitable methods of signal extraction and recognition algorithm processing, to boost the recognition rate of communication for BCI system, and finally to establish a substantial theory and experimental support for BCI application. In this paper, different mental tasks for imaging left-right hands movement from 6 subjects were studied in three different time sections (hint keying at 2s, 1s and 0s after appearance of arrow). Then we used wavelet analysis and Feed-forward Back-propagation Neural Network (BP-NN) method for processing and analyzing the experimental data of off-line. Delay time delta t2, delta t1 and delta t0 for all subjects in the three different time sections were analyzed. There was significant difference between delta to and delta t2 or delta t1 (P0.05). The average results of recognition rate were 65%, 86.67% and 72%, respectively. There were obviously different features for imaging left-right hands movement about 0.5-1s before actual movement; these features displayed significant difference. We got higher recognition rate of communication under the hint keying at about 1s after the appearance of arrow. These showed the feasibility of using the feature signals extracted from the project as the external control signals for BCI system, and demon strated that the project provided new ideas and methods for feature extraction and classification of mental tasks for BCI. 6. Supersymmetric domain walls NARCIS (Netherlands) Bergshoeff, Eric A.; Kleinschmidt, Axel; Riccioni, Fabio 2012-01-01 We classify the half-supersymmetric "domain walls," i.e., branes of codimension one, in toroidally compactified IIA/IIB string theory and show to which gauged supergravity theory each of these domain walls belong. We use as input the requirement of supersymmetric Wess-Zumino terms, the properties of 7. Supersymmetric family unification International Nuclear Information System (INIS) Frampton, P.H.; Kephart, T.W. 1983-01-01 The superheavy symmetry breaking of the gauge group in supersymmetrized unified theories is studied. The requirement that supersymmetry be unbroken strongly constrains the possible gauge group breaking, and we systematize such constraints group theoretically. In model building, one issue is whether to permit an adjoint matter superfield with concomitant color exotic fermions. A second issue is that of naturalness which is complicated by the well-known supersymmetry non-renormalization theorems. Both with and without an adjoint matter superfield, the most promising group appears to be SU(9) where three families can be naturally accommodated, at least for low-energy gauge group SU(3) x SU(2) x U(1). With an extra U(1) factor, as advocated by Fayet, the non-renormalization theorem must be exploited. (orig.) 8. Supersymmetric Higgs bosons and beyond International Nuclear Information System (INIS) Carena, Marcela; Kong, Kyoungchul; Ponton, Eduardo; Zurita, Jose 2010-01-01 We consider supersymmetric models that include particles beyond the minimal supersymmetric standard model (MSSM) with masses in the TeV range, and that couple significantly to the MSSM Higgs sector. We perform a model-independent analysis of the spectrum and couplings of the MSSM Higgs fields, based on an effective theory of the MSSM degrees of freedom. The tree-level mass of the lightest CP-even state can easily be above the LEP bound of 114 GeV, thus allowing for a relatively light spectrum of superpartners, restricted only by direct searches. The Higgs spectrum and couplings can be significantly modified compared to the MSSM ones, often allowing for interesting new decay modes. We also observe that the gluon fusion production cross section of the SM-like Higgs can be enhanced with respect to both the standard model and the MSSM. 9. Search for Higgs bosons of the minimal supersymmetric standard model in ppˉ collisions at √s=1.96 TeV Czech Academy of Sciences Publication Activity Database Abazov, V. M.; Abbott, B.; Acharya, B.S.; Kupčo, Alexander; Lokajíček, Miloš 2012-01-01 Roč. 710, 4-5 (2012), s. 569-577 ISSN 0370-2693 R&D Projects: GA MŠk LA08047 Institutional research plan: CEZ:AV0Z10100502 Keywords : D0 * Higgs particle * lower limit * tau * pair production * minimal supersymmetric standard model * parameter space Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 4.569, year: 2012 http://www. science direct.com/ science /article/pii/S0370269312002857 10. Consistent momentum space regularization/renormalization of supersymmetric quantum field theories: the three-loop β-function for the Wess-Zumino model International Nuclear Information System (INIS) Carneiro, David; Sampaio, Marcos; Nemes, Maria Carolina; Scarpelli, Antonio Paulo Baeta 2003-01-01 We compute the three loop β function of the Wess-Zumino model to motivate implicit regularization (IR) as a consistent and practical momentum-space framework to study supersymmetric quantum field theories. In this framework which works essentially in the physical dimension of the theory we show that ultraviolet are clearly disentangled from infrared divergences. We obtain consistent results which motivate the method as a good choice to study supersymmetry anomalies in quantum field theories. (author) 11. Search for electroweak production of supersymmetric states in Non-Universal Higgs Mass model with two extra parameters compressed scenario with the ATLAS detector CERN Document Server AUTHOR\|(INSPIRE)INSPIRE-00529728 The ATLAS and CMS collaborations announced the discovery of the Higgs boson in July 2012, completing the particle content of the Standard Model. Although the Standard Model is a great triumph, it is not considered to be the complete theory of particle physics. Several new theories have been proposed which seek to move beyond the Standard Model. Among the newly-developed theories, Supersymmetry (SUSY) is one of the most promising ones. SUSY predicts the existence of supersymmetric partner particles and it is one of the best-motivated extensions of the space-time symmetry of particle interactions. There are supersymmetric partner particles associated with each SM particles in which the spin differs by 1/2. This dissertation focuses on a search for electroweak production of supersymmetric particles with compressed mass spectra in the final states with exactly two low-momentum leptons and missing transverse momentum. The proton-proton collision data is recorded by the ATLAS detector at the Large Hadron Collider i... 12. Four-loop divergences of the two-dimensional (1,1) supersymmetric non-linear sigma model with a Wess-Zumino-Witten term International Nuclear Information System (INIS) Deriglazov, A.A.; Ketov, S.V. 1991-01-01 The four-loop divergences of the (1,1) supersymmetric two-dimensional non-linear σ-model with a Wess-Zumino-Witten term are analyzed. All the four-loop 1/ε-divergences in the general case (and an overall coefficient at the total four-loop contribution to the β-function) are shown to be reducible to only structures proportional to ζ(3). We explicitly calculate non-derivative contributions to the four-loop β-function from logarithmically divergent graphs. As a by-product, we obtain the complete four-loop β-function for the supersymmetric Wess-Zumino-Witten model. We use the partial results for the general four-loop β-function to shed some light on the structure of the (α') 3 -corrections to the superstring effective-action with antisymmetric-tensor field coupling. An inconsistency of the supersymmetrical dimensional regularisation via dimensional reduction in the presence of torsion is discovered at four loops, unless the string interpretation for the σ-model is adopted. (orig.) 13. Precise determination of the Higgs mass in supersymmetric models with vectorlike tops and the impact on naturalness in minimal GMSB CERN Document Server Nickel, Kilian 2015-01-01 We present a precise analysis of the Higgs mass corrections stemming from vectorlike top partners in supersymmetric models. We reduce the theoretical uncertainty compared to previous studies in the following aspects: (i) including the one-loop threshold corrections to SM gauge and Yukawa couplings due to the presence of the new states to obtain the $\\bar{\\text{DR}}$ parameters entering all loop calculations, (ii) including the full momentum dependence at one-loop, and (iii) including all two-loop corrections but the ones involving $g_1$ and $g_2$. We find that the additional threshold corrections are very important and can give the largest effect on the Higgs mass. However, we identify also parameter regions where the new two-loop effects can be more important than the ones of the MSSM and change the Higgs mass prediction by up to 10 GeV. This is for instance the case in the low $\\tan\\beta$, small $M_A$ regime. We use these results to calculate the electroweak fine-tuning of an UV complete variant of this mod... 14. One-loop analysis of the electroweak breaking in supersymmetric models and the fine-tuning problem CERN Document Server De Carlos, B 1993-01-01 We examine the electroweak breaking mechanism in the minimal supersymmetric standard model (MSSM) using the {\\em complete} one-loop effective potential $V_1$. First, we study what is the region of the whole MSSM parameter space (i.e. $M_{1/2},m_o,\\mu,...$) that leads to a succesful $SU(2)\\times U(1)$ breaking with an acceptable top quark mass. In doing this it is observed that all the one-loop corrections to $V_1$ (even the apparently small ones) must be taken into account in order to get reliable results. We find that the allowed region of parameters is considerably enhanced with respect to former "improved" tree level results. Next, we study the fine-tuning problem associated with the high sensitivity of $M_Z$ to $h_t$ (the top Yukawa coupling). Again, we find that this fine-tuning is appreciably smaller once the one-loop effects are considered than in previous tree level calculations. Finally, we explore the ambiguities and limitations of the ordinary criterion to estimate the degree of fine-tuning. As a r... 15. Basic model of fermion dark matter. Indirect detection of supersymmetric dark matter in γ astronomy with the CELESTE telescope International Nuclear Information System (INIS) Lavalle, J. 2004-10-01 The purpose of this thesis is to discuss both phenomenological and experimental aspects of Dark Matter, related to its indirect detection with gamma-ray astronomy. In the MSSM (Minimal Supersymmetric Standard Model) framework, neutralinos arise as natural candidates to non-baryonic and Cold Dark Matter, whose gravitational effects manifest in the Universe at different scales. As they are Majorana particles, they may in principle annihilate in high density regions, as the centres of galaxies, and produce gamma rays. Nevertheless, the expected fluxes are basically low compared to experimental sensitivities. After estimating gamma fluxes from M31 and Draco galaxies in the MSSM scheme, we first generalize the MSSM couplings by studying an effective Lagrangian. We show that the only constraint of imposing a relic abundance compatible with recent measurements obviously deplete significantly the gamma ray production, but also that predictions in this effective approach are more optimistic for indirect detection than the MSSM. In a second part, we present the indirect searches for Dark Matter performed with the CELESTE Cherenkov telescope towards the galaxy M31. We propose a statistical method to reconstruct spectra, mandatory to discriminate classical and exotic spectra. The M31 data analysis enables the extraction of an upper limit on the gamma ray flux, which is the first worldwide for a galaxy in the energy range 50-500 GeV, and whose astrophysical interest goes beyond indirect searches for Dark Matter. (author) 16. Comment on "Polarized window for left-right symmetry and a right-handed neutrino at the Large Hadron-Electron Collider" Science.gov (United States) Queiroz, Farinaldo S. 2016-06-01 Reference [1 S. Mondal and S. K. Rai, Phys. Rev. D 93, 011702 (2016).] recently argued that the projected Large Hadron Electron Collider (LHeC) presents a unique opportunity to discover a left-right symmetry since the LHeC has availability for polarized electrons. In particular, the authors apply some basic pT cuts on the jets and claim that the on-shell production of right-handed neutrinos at the LHeC, which violates lepton number in two units, has practically no standard model background and, therefore, that the right-handed nature of WR interactions that are intrinsic to left-right symmetric models can be confirmed by using colliding beams consisting of an 80% polarized electron and a 7 TeV proton. In this Comment, we show that their findings, as presented, have vastly underestimated the SM background which prevents a Left-Right symmetry signal from being seen at the LHeC. 17. Left-right squarks mixings effects in charged Higgs bosons decays H+/-->W+/-(γ,Z) in the MSSM International Nuclear Information System (INIS) Arhrib, Abdesslam; Benbrik, Rachid; Chabab, Mohamed 2007-01-01 We study the complete one loop contribution to H + /-->W + /-V, V=Z,γ, in the Minimal Supersymmetric Standard Model (MSSM). We evaluate the MSSM contributions taking into account B->X s γ constraint as well as experimental constraints on the MSSM parameters. In the MSSM, we found that in the intermediate range of tanβ-bar 10 and for large A t and large μ, where lightest stop becomes very light and hence squarks contribution is not decoupling, the branching ratio of H + /-->W + /-Z can be of the order 10 -3 while the branching ratio of H + /-->W + /-γ is of the order 10 -5 . We also study the effects of the CP violating phases of soft SUSY parameters and found that they can modify the branching ratio by about one order of magnitude 18. Supersymmetric quasipotential equations International Nuclear Information System (INIS) Zaikov, R.P. 1981-01-01 A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru 19. Stress-induced alterations of left-right electrodermal activity coupling indexed by pointwise transinformation. Science.gov (United States) Světlák, M; Bob, P; Roman, R; Ježek, S; Damborská, A; Chládek, J; Shaw, D J; Kukleta, M 2013-01-01 In this study, we tested the hypothesis that experimental stress induces a specific change of left-right electrodermal activity (EDA) coupling pattern, as indexed by pointwise transinformation (PTI). Further, we hypothesized that this change is associated with scores on psychometric measures of the chronic stress-related psychopathology. Ninety-nine university students underwent bilateral measurement of EDA during rest and stress-inducing Stroop test and completed a battery of self-report measures of chronic stress-related psychopathology. A significant decrease in the mean PTI value was the prevalent response to the stress conditions. No association between chronic stress and PTI was found. Raw scores of psychometric measures of stress-related psychopathology had no effect on either the resting levels of PTI or the amount of stress-induced PTI change. In summary, acute stress alters the level of coupling pattern of cortico-autonomic influences on the left and right sympathetic pathways to the palmar sweat glands. Different results obtained using the PTI, EDA laterality coefficient, and skin conductance level also show that the PTI algorithm represents a new analytical approach to EDA asymmetry description. 20. Common variants in left/right asymmetry genes and pathways are associated with relative hand skill. Directory of Open Access Journals (Sweden) William M Brandler Full Text Available Humans display structural and functional asymmetries in brain organization, strikingly with respect to language and handedness. The molecular basis of these asymmetries is unknown. We report a genome-wide association study meta-analysis for a quantitative measure of relative hand skill in individuals with dyslexia [reading disability (RD] (n = 728. The most strongly associated variant, rs7182874 (P = 8.68 × 10(-9, is located in PCSK6, further supporting an association we previously reported. We also confirmed the specificity of this association in individuals with RD; the same locus was not associated with relative hand skill in a general population cohort (n = 2,666. As PCSK6 is known to regulate NODAL in the development of left/right (LR asymmetry in mice, we developed a novel approach to GWAS pathway analysis, using gene-set enrichment to test for an over-representation of highly associated variants within the orthologs of genes whose disruption in mice yields LR asymmetry phenotypes. Four out of 15 LR asymmetry phenotypes showed an over-representation (FDR ≤ 5%. We replicated three of these phenotypes; situs inversus, heterotaxia, and double outlet right ventricle, in the general population cohort (FDR ≤ 5%. Our findings lead us to propose that handedness is a polygenic trait controlled in part by the molecular mechanisms that establish LR body asymmetry early in development. 1. Asymmetric inhibition of Ulk2 causes left-right differences in habenular neuropil formation. Science.gov (United States) Taylor, Robert W; Qi, Jenny Y; Talaga, Anna K; Ma, Taylur P; Pan, Luyuan; Bartholomew, Clinton R; Klionsky, Daniel J; Moens, Cecilia B; Gamse, Joshua T 2011-07-06 Studies of the zebrafish epithalamus have provided recent insights into the development of left-right brain asymmetry, which is crucial to normal human brain function. The habenular nuclei of zebrafish are robustly asymmetric, with dense elaboration of neuropil only in the left lateral subnucleus. Because this feature is tightly correlated with asymmetric expression of K(+) channel tetramerization domain-containing proteins 12.1 and 12.2 (Kctd12.1/12.2), we screened for Kctd12.1-interacting proteins to identify molecular mechanisms leading to neuropil asymmetry, and uncovered a novel interaction between Kctd12.1 and Unc-51-like kinase 2 (Ulk2). We show here that knockdown of Ulk2 or overexpression of Kctd12 proteins reduces asymmetric neuropil elaboration. Conversely, overexpression of Ulk2 or mutation of kctd12 genes causes excess neuropil elaboration. We conclude that Ulk2 activity promotes neuropil elaboration while Kctd12 proteins limit Ulk2 activity asymmetrically. This work describes a regulatory mechanism for neuronal process extension that may be conserved in other developmental contexts in addition to the epithalamus. 2. FGF signaling is required for brain left-right asymmetry and brain midline formation. Science.gov (United States) Neugebauer, Judith M; Yost, H Joseph 2014-02-01 Early disruption of FGF signaling alters left-right (LR) asymmetry throughout the embryo. Here we uncover a role for FGF signaling that specifically disrupts brain asymmetry, independent of normal lateral plate mesoderm (LPM) asymmetry. When FGF signaling is inhibited during mid-somitogenesis, asymmetrically expressed LPM markers southpaw and lefty2 are not affected. However, asymmetrically expressed brain markers lefty1 and cyclops become bilateral. We show that FGF signaling controls expression of six3b and six7, two transcription factors required for repression of asymmetric lefty1 in the brain. We found that Z0-1, atypical PKC (aPKC) and β-catenin protein distribution revealed a midline structure in the forebrain that is dependent on a balance of FGF signaling. Ectopic activation of FGF signaling leads to overexpression of six3b, loss of organized midline adherins junctions and bilateral loss of lefty1 expression. Reducing FGF signaling leads to a reduction in six3b and six7 expression, an increase in cell boundary formation in the brain midline, and bilateral expression of lefty1. Together, these results suggest a novel role for FGF signaling in the brain to control LR asymmetry, six transcription factor expressions, and a midline barrier structure. Copyright © 2013 Elsevier Inc. All rights reserved. 3. Conservation Motivation, Social Equality and Left-Right Ideological Preferences in Western and Eastern Europe. Science.gov (United States) 2017-05-01 We investigated how attitudes towards social equality can influence the relationship between conservation motivation (or openness) and personal ideological preferences on the left-right dimension, and how this relationship pattern differs between Western and Central & Eastern European (CEE) respondents. Using data from the European Social Survey (2012) we found that individual-level of conservation motivation reduces cultural egalitarianism in both the Western European and the CEE regions, but its connection with economic egalitarianism is only relevant in the CEE region where it fosters economic egalitarianism. Since both forms of egalitarianism were related to leftist ideological preferences in Western Europe, but in the CEE region only economic egalitarianism was ideologically relevant, we concluded that the classic "rigidity of the right" phenomenon is strongly related to cultural (anti)egalitarianism in Western Europe. At the same time, conservation motivation serves as a basis for the "rigidity of the left" in the post-socialist CEE region, in a great part due to the conventional egalitarian economic views. 4. Vertebrate Left-Right Asymmetry: What Can Nodal Cascade Gene Expression Patterns Tell Us? Science.gov (United States) Schweickert, Axel; Ott, Tim; Kurz, Sabrina; Tingler, Melanie; Maerker, Markus; Fuhl, Franziska; Blum, Martin 2017-12-29 Laterality of inner organs is a wide-spread characteristic of vertebrates and beyond. It is ultimately controlled by the left-asymmetric activation of the Nodal signaling cascade in the lateral plate mesoderm of the neurula stage embryo, which results from a cilia-driven leftward flow of extracellular fluids at the left-right organizer. This scenario is widely accepted for laterality determination in wildtype specimens. Deviations from this norm come in different flavors. At the level of organ morphogenesis, laterality may be inverted (situs inversus) or non-concordant with respect to the main body axis (situs ambiguus or heterotaxia). At the level of Nodal cascade gene activation, expression may be inverted, bilaterally induced, or absent. In a given genetic situation, patterns may be randomized or predominantly lacking laterality (absence or bilateral activation). We propose that the distributions of patterns observed may be indicative of the underlying molecular defects, with randomizations being primarily caused by defects in the flow-generating ciliary set-up, and symmetrical patterns being the result of impaired flow sensing, on the left, the right, or both sides. This prediction, the reasoning of which is detailed in this review, pinpoints functions of genes whose role in laterality determination have remained obscure. 5. Production and decay of supersymmetric particles at future colliders International Nuclear Information System (INIS) Bartl, A.; Majerotto, W.; Moesslacher, B. 1991-01-01 We describe how supersymmetric particles could be detected at the new colliders HERA, LEP 200, LHC, SSC, and at the possible future linear e + e - collider. We shall present theoretical predictions for production cross sections and decay probabilities, as well as for the important signatures. Our calculations will be based on the Minimal Supersymmetric Standard Model (MSSM) which is the simplest supersymmetric extension of the Standard Model. (authors) 6. Duality and supersymmetric monopoles International Nuclear Information System (INIS) Gauntlett, J.P. 1998-01-01 Exact duality in supersymmetric gauge theories leads to highly non-trivial predictions about the moduli spaces of BPS monopole solutions. These notes attempt to be a pedagogical review of the current status of these investigations. (orig.) 7. Probing the hidden Higgs bosons of the Y=0 triplet- and singlet-extended Supersymmetric Standard Model at the LHC Energy Technology Data Exchange (ETDEWEB) Bandyopadhyay, Priyotosh [Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento and INFN-Lecce,Via Arnesano, 73100 Lecce (Italy); Corianò, Claudio [Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento and INFN-Lecce,Via Arnesano, 73100 Lecce (Italy); STAG Research Centre and Mathematical Sciences, University of Southampton,Southampton SO17 1BJ (United Kingdom); Costantini, Antonio [Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento and INFN-Lecce,Via Arnesano, 73100 Lecce (Italy) 2015-12-18 We investigate the scalar sector in an extension of the Minimal Supersymmetric Standard Model (MSSM) containing a SU(2) Higgs triplet of zero hypercharge and a gauge singlet beside the SU(2) scalar doublets. In particular, we focus on a scenario of this model which allows a light pseudoscalar and/or a scalar below 100 GeV, consistent with the most recent data from the LHC and the earlier data from the LEP experiments. We analyze the exotic decay of the discovered Higgs (h{sub 125}) into two light (hidden) Higgs bosons present in the extension. The latter are allowed by the uncertainties in the Higgs decay h{sub 125}→WW{sup ∗}, h{sub 125}→ZZ{sup ∗} and h{sub 125}→γγ. The study of the parameter space for such additional scalars/pseudoscalars decay of the Higgs is performed in the gluon fusion channel. The extra hidden Higgs bosons of the enlarged scalar sector, if they exist, will then decay into lighter fermion paris, i.e., bb̄, ττ̄ and μμ̄ via the mixing with the doublets. A detailed simulation using PYTHIA of the 2b+2τ, ≥3τ, 2b+2μ and 2τ+2μ final states is presented. From our analysis we conclude that, depending on the selected benchmark points, such decay modes can be explored with an integrated luminosity of 25 fb{sup −1} at the LHC at a center of mass energy of 13 TeV. 8. Analysis of the production of Higgs boson pairs at the one-loop level in the minimal supersymmetric standard model International Nuclear Information System (INIS) Philippov, Yu. P. 2009-01-01 Within the minimal supersymmetric standard model, the amplitudes and total cross sections for the processes e + e - → hh, e + e - → hH, e + e - → HH, and e + e - → AA are calculated in the first order of perturbation theory with allowance for a complete set of one-loop diagrams in the m e → 0 approximation. Analytic expressions are obtained for the quantities under consideration; numerical results are presented in a graphical form. It is shown that the cross section for the process e + e - → hh is larger than those for the other processes (and is on the same order of magnitude as the cross section for the corresponding processes in the Standard Model). In the case of the collision energy equal to √s = 500 GeV, an integrated luminosity in the region ∫ L ≥ 500 fb -1 , and a longitudinal polarization of the e + e- beams used, 520, 320, and 300 production events are possible in the processes e + e - → hh (at M h = 115 GeV), e + e - → HH, and e + e - → AA (at M H,A = 120 GeV), respectively. Even at M H,A ∼ 500 GeV and √s = 1.5 TeV, not less than 200 events for each of the processes can be accumulated. The cross section for the process e + e - → hH is small (about 10 -2 fb), which complicates the detection of the sought signal significantly. 9. Supersymmetric extensions of Calogero-Moser-Sutherland-like models: construction and some solutions International Nuclear Information System (INIS) Kohler, Heiner; Guhr, Thomas 2005-01-01 We introduce a new class of models for interacting particles. Our construction is based on Jacobians for the radial coordinates on certain superspaces. The resulting models contain two parameters determining the strengths of the interactions. This extends and generalizes the models of the Calogero-Moser-Sutherland type for interacting particles in ordinary spaces. The latter ones are included in our models as special cases. Using results which we obtained previously for spherical functions in superspaces, we obtain various properties and some explicit forms for the solutions. We present physical interpretations. Our models involve two kinds of interacting particles. One of the models can be viewed as describing interacting electrons in a lower and upper band of a quasi-one-dimensional semiconductor. Another model is quasi-two-dimensional. Two kinds of particles are confined to two different spatial directions, the interaction contains dipole-dipole or tensor forces 10. A variant of fibroblast growth factor receptor 2 (Fgfr2 regulates left-right asymmetry in zebrafish. Directory of Open Access Journals (Sweden) Da-Wei Liu Full Text Available Many organs in vertebrates are left-right asymmetrical located. For example, liver is at the right side and stomach is at the left side in human. Fibroblast growth factor (Fgf signaling is important for left-right asymmetry. To investigate the roles of Fgfr2 signaling in zebrafish left-right asymmetry, we used splicing blocking morpholinos to specifically block the splicing of fgfr2b and fgfr2c variants, respectively. We found that the relative position of the liver and the pancreas were disrupted in fgfr2c morphants. Furthermore, the left-right asymmetry of the heart became random. Expression pattern of the laterality controlling genes, spaw and pitx2c, also became random in the morphants. Furthermore, lefty1 was not expressed in the posterior notochord, indicating that the molecular midline barrier had been disrupted. It was also not expressed in the brain diencephalon. Kupffer's vesicle (KV size became smaller in fgfr2c morphants. Furthermore, KV cilia were shorter in fgfr2c morphants. We conclude that the fgfr2c isoform plays an important role in the left-right asymmetry during zebrafish development. 11. A variant of fibroblast growth factor receptor 2 (Fgfr2) regulates left-right asymmetry in zebrafish. Science.gov (United States) Liu, Da-Wei; Hsu, Chia-Hao; Tsai, Su-Mei; Hsiao, Chung-Der; Wang, Wen-Pin 2011-01-01 Many organs in vertebrates are left-right asymmetrical located. For example, liver is at the right side and stomach is at the left side in human. Fibroblast growth factor (Fgf) signaling is important for left-right asymmetry. To investigate the roles of Fgfr2 signaling in zebrafish left-right asymmetry, we used splicing blocking morpholinos to specifically block the splicing of fgfr2b and fgfr2c variants, respectively. We found that the relative position of the liver and the pancreas were disrupted in fgfr2c morphants. Furthermore, the left-right asymmetry of the heart became random. Expression pattern of the laterality controlling genes, spaw and pitx2c, also became random in the morphants. Furthermore, lefty1 was not expressed in the posterior notochord, indicating that the molecular midline barrier had been disrupted. It was also not expressed in the brain diencephalon. Kupffer's vesicle (KV) size became smaller in fgfr2c morphants. Furthermore, KV cilia were shorter in fgfr2c morphants. We conclude that the fgfr2c isoform plays an important role in the left-right asymmetry during zebrafish development. 12. Supersymmetric color superconductivity International Nuclear Information System (INIS) Harnik, Roni; Larson, Daniel T.; Murayama, Hitoshi 2004-01-01 Recent interest in novel phases in high density QCD motivates the study of high density supersymmetric QCD (SQCD), where powerful exact results for supersymmetric gauge theories can be brought to bear in the strongly coupled regime. We begin by describing how a chemical potential can be incorporated into a supersymmetric theory as a spurion vector superfield. We then study supersymmetric SU(N c ) gauge theories with N f flavors of quarks in the presence of a baryon chemical potential mu, and describe the global symmetry breaking patterns at low energy. Our analysis requires μ f c a modified U(1) B symmetry is preserved, analogous to the non-supersymmetric 2SC phase, whereas for N f =N c there is a critical chemical potential above which the U(1) B is broken, as it is in the non-supersymmetric CFL phase. We further analyze the cases with N c +1≤ N f c and find that baryon number is broken dynamically for μ > mu c . We also give a qualitative description of the phases in the 'conformal window', 3/2 N c f c , at finite density. (author) 13. Supersymmetric color superconductivity International Nuclear Information System (INIS) Harnik, Roni; Larson, Daniel T.; Murayama, Hitoshi 2003-01-01 Recent interest in novel phases in high density QCD motivates the study of high density supersymmetric QCD (SQCD), where powerful exact results for supersymmetric gauge theories can be brought to bear in the strongly coupled regime. We begin by describing how a chemical potential can be incorporated into a supersymmetric theory as a spurion vector superfield. We then study supersymmetric SU(N c ) gauge theories with N f flavors of quarks in the presence of a baryon chemical potential μ, and describe the global symmetry breaking patterns at low energy. Our analysis requires μ > Λ. We find that for N F c a modified U(1) B symmetry is preserved, analogous to the non-supersymmetric 2SC phase, whereas for N f = N c there is a critical chemical potential above which the U(1) B is broken, as it is in the non-supersymmetric CFL phase. We further analyze the cases with N c + 1 (le) N f c and find that baryon number is broken dynamically for μ > μ c . We also give a qualitative description of the phases in the ''conformal window'', 3/2 N c f c , at finite density 14. Mapping and explaining the use of the left-right divide Directory of Open Access Journals (Sweden) André Freire 2013-12-01 Full Text Available This study is about mapping and explaining the use of the Left-Right divide across 14 countries from 5 Continents and relies on the richness of the post electoral mass surveys from the Comparative National Election Project: 14 countries and 18 elections spread over 5 continents. The paper shows not only how extensively the LR divide is used in these 14 countries, but also explains variation across both individuals and countries in terms of the factors determining LR recognition and use. Overall, it is shown that, although seen world-wide, the LR divide (both for self-placement and party placement is more present in long consolidated and middle-aged democracies and countries with freer media systems than in new democracies and societies with less free media systems. In the case of parties LR placement, party size also counts: larger parties are more easily placed. Additionally, we also show that LR recognition is more socially and politically determined in long consolidated and middle-aged democracies and in countries with more freedom of the press than in new democracies and in systems with less free media system. These findings add to the existing knowledge about these topics because previous studies were either country/Continent specific, or, if global in nature, never invested in explaining individual and system variation across 14 from 5 Continents. Besides, these findings mean that in the long term probably the new democracies will converge with the long consolidated or middle-aged ones, but this is an empirical question to be researched in future studies. 15. Mice lacking hippocampal left-right asymmetry show non-spatial learning deficits. Science.gov (United States) Shimbo, Akihiro; Kosaki, Yutaka; Ito, Isao; Watanabe, Shigeru 2018-01-15 16. Method used to test the imaging consistency of binocular camera's left-right optical system Science.gov (United States) Liu, Meiying; Wang, Hu; Liu, Jie; Xue, Yaoke; Yang, Shaodong; Zhao, Hui 2016-09-01 To binocular camera, the consistency of optical parameters of the left and the right optical system is an important factor that will influence the overall imaging consistency. In conventional testing procedure of optical system, there lacks specifications suitable for evaluating imaging consistency. In this paper, considering the special requirements of binocular optical imaging system, a method used to measure the imaging consistency of binocular camera is presented. Based on this method, a measurement system which is composed of an integrating sphere, a rotary table and a CMOS camera has been established. First, let the left and the right optical system capture images in normal exposure time under the same condition. Second, a contour image is obtained based on the multiple threshold segmentation result and the boundary is determined using the slope of contour lines near the pseudo-contour line. Third, the constraint of gray level based on the corresponding coordinates of left-right images is established and the imaging consistency could be evaluated through standard deviation σ of the imaging grayscale difference D (x, y) between the left and right optical system. The experiments demonstrate that the method is suitable for carrying out the imaging consistency testing for binocular camera. When the standard deviation 3σ distribution of imaging gray difference D (x, y) between the left and right optical system of the binocular camera does not exceed 5%, it is believed that the design requirements have been achieved. This method could be used effectively and paves the way for the imaging consistency testing of the binocular camera. 17. A precise measurement of the left-right asymmetry of Z Boson production at the SLAC linear collider International Nuclear Information System (INIS) 1994-09-01 We present a precise measurement of the left-right cross section asymmetry of Z boson production (A LR ) observed in 1993 data at the SLAC linear collider. The A LR experiment provides a direct measure of the effective weak mixing angle through the initial state couplings of the electron to the Z. During the 1993 run of the SLC, the SLD detector recorded 49,392 Z events produced by the collision of longitudinally polarized electrons on unpolarized positrons at a center-of-mass energy of 91.26 GeV. A Compton polarimeter measured the luminosity-weighted electron polarization to be (63.4±1.3)%. ALR was measured to be 0.1617±0.0071(stat.)±0.0033(syst.), which determines the effective weak mixing angle to be sin 2 θ W eff = 0.2292±0.0009(stat.)±0.0004(syst.). This measurement of A LR is incompatible at the level of two standard deviations with the value predicted by a fit of several other electroweak measurements to the Standard Model 18. An analysis on older driver's driving behavior by GPS tracking data: Road selection, left/right turn, and driving speed Directory of Open Access Journals (Sweden) Yanning Zhao 2018-02-01 Full Text Available With the high older-related accident ratio and increasing population aging problem, understanding older drivers' driving behaviors has become more and more important for building and improving transportation system. This paper examines older driver's driving behavior which includes road selection, left/right turn and driving speed. A two-month experiment of 108 participants was carried out in Aichi Prefecture, Japan. Since apparently contradictory statements were often drawn in survey-based or simulators-based studies, this study collected not only drivers' basic information but also GPS data. Analysis of road selection demonstrates that older drivers are reluctant to drive on expressway not only in short trips but also in long trips. The present study did not find significant difference between older drivers and others while turning at the intersections. To investigate the impact factors on driving speed, a random-effects regression model is constructed with explanatory variables including age, gender, road types and the interaction terms between age and road types. Compared with other variables, it fails to find that age (60 years old or over has significant impact on driving speed. Moreover, the results reflect that older drivers drive even faster than others at particular road types: national road and ordinary municipal road. The results in this study are expected to help improve transportation planning and develop driving assistance systems for older drivers. 19. A precise measurement of the left-right asymmetry of Z Boson production at the SLAC linear collider Energy Technology Data Exchange (ETDEWEB) NONE 1994-09-01 We present a precise measurement of the left-right cross section asymmetry of Z boson production (A{sub LR}) observed in 1993 data at the SLAC linear collider. The A{sub LR} experiment provides a direct measure of the effective weak mixing angle through the initial state couplings of the electron to the Z. During the 1993 run of the SLC, the SLD detector recorded 49,392 Z events produced by the collision of longitudinally polarized electrons on unpolarized positrons at a center-of-mass energy of 91.26 GeV. A Compton polarimeter measured the luminosity-weighted electron polarization to be (63.4{+-}1.3)%. ALR was measured to be 0.1617{+-}0.0071(stat.){+-}0.0033(syst.), which determines the effective weak mixing angle to be sin {sup 2}{theta}{sub W}{sup eff} = 0.2292{+-}0.0009(stat.){+-}0.0004(syst.). This measurement of A{sub LR} is incompatible at the level of two standard deviations with the value predicted by a fit of several other electroweak measurements to the Standard Model. 20. Fun with supersymmetric quantum mechanics International Nuclear Information System (INIS) Freedman, B.; Cooper, F. 1984-04-01 One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup α/ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index Δ which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if Δ is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate Δ for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references 1. Higgs bosons in the next-to-minimal supersymmetric standard model at the LHC International Nuclear Information System (INIS) Ellwanger, Ulrich 2011-01-01 We review possible properties of Higgs bosons in the NMSSM, which allow to discriminate this model from the MSSM: masses of mostly standard-model-like Higgs bosons at or above 140 GeV, or enhanced branching fractions into two photons, or Higgs-to-Higgs decays. In the case of a standard-model-like Higgs boson above 140 GeV, it is necessarily accompanied by a lighter state with a large gauge singlet component. Examples for such scenarios are presented. Available studies on Higgs-to-Higgs decays are discussed according to the various Higgs production modes, light Higgs masses and decay channels. (orig.) 2. Fixing the EW scale in supersymmetric models after the Higgs discovery CERN Document Server Ghilencea, D M 2013-01-01 TeV-scale supersymmetry was originally introduced to solve the hierarchy problem and therefore fix the electroweak (EW) scale in the presence of quantum corrections. Numerical methods testing the SUSY models often report a good likelihood L (or chi^2=-2ln L) to fit the data {\\it including} the EW scale itself (m_Z^0) with a {\\it simultaneously} large fine-tuning i.e. a large variation of this scale under a small variation of the SUSY parameters. We argue that this is inconsistent and we identify the origin of this problem. Our claim is that the likelihood (or chi^2) to fit the data that is usually reported in such models does not account for the chi^2 cost of fixing the EW scale. When this constraint is implemented, the likelihood (or chi^2) receives a significant correction (delta_chi^2) that worsens the current data fits of SUSY models. We estimate this correction for the models: constrained MSSM (CMSSM), models with non-universal gaugino masses (NUGM) or higgs soft masses (NUHM1, NUHM2), the NMSSM and the ... 3. Dark matter constraints in the minimal and nonminimal supersymmetric standard model International Nuclear Information System (INIS) Stephan, A. 1998-01-01 We determine the allowed parameter space and the particle spectra of the minimal SUSY standard model (MSSM) and nonminimal SUSY standard model (NMSSM) imposing correct electroweak gauge symmetry breaking and recent experimental constraints. The parameters of the models are evolved with the SUSY renormalization group equations assuming universality at the grand unified scale. Applying the new unbounded from below constraints we can exclude the lightest SUSY particle singlinos and light scalar and pseudoscalar Higgs singlets of the NMSSM. This exclusion removes the experimental possibility to distinguish between the MSSM and NMSSM via the recently proposed search for an additional cascade produced in the decay of the B-ino into the LSP singlino. Furthermore, the effects of the dark matter condition for the MSSM and NMSSM are investigated and the differences concerning the parameter space, the SUSY particle, and Higgs sector are discussed. thinsp copyright 1998 The American Physical Society 4. Symmetry breaking of u(6/2j+1) supersymmetric models International Nuclear Information System (INIS) Baake, M.; Reinicke, P. 1985-09-01 In this paper, we present the group theory of models with broken u(6/2j+1) supersymmetry described by the chain u(6/2j+1) contains usub(B)(6) x usub(F)(2j+1) contains usub(B)(6) x spsub(F)(2j+1) contains ... contains sosub(B)(3) x susub(F)(2) contains susub(B+F)(2) which has recently been suggested for application to nuclear physics. We present all invariants that are needed for the construction of the general Hamiltonian for this model. (orig.) 5. The Reach of CERN LEP2 and Fermilab Tevatron Upgrades for Higgs Bosons in Supersymmetric Models CERN Document Server Baer, Howard W; Tata, Xerxes; Baer, Howard; Tata, Xerxes 1999-01-01 Luminosity upgrades of the Fermilab Tevatron pbar-p collider have been shown to allow experimental detection of a Standard Model (SM) Higgs boson up to $m_{H_{SM}}\\sim 120$ GeV via $WH_{SM} \\to \\ell\ 6. Use of a variational principle for the study of supersymmetric models International Nuclear Information System (INIS) Krasnikov, N.V. 1985-01-01 A variational principle is used for study of the possibility of spontaneous symmetry breaking. It is shown that if supersymmetry in the generalized Wess-Zumino model is not broken at the classical level, taking account of quantum corrections also does not lead to symmetry breaking 7. Mono-jet, -photon and -Z signals of a supersymmetric (B−L) model at the Large Hadron Collider Energy Technology Data Exchange (ETDEWEB) Abdallah, W. [Center for Fundamental Physics, Zewail City of Science and Technology,6 October City, Giza (Egypt); Department of Mathematics, Faculty of Science, Cairo University,Giza (Egypt); Fiaschi, J. [School of Physics and Astronomy, University of Southampton,Highfield, Southampton (United Kingdom); Khalil, S. [Center for Fundamental Physics, Zewail City of Science and Technology,6 October City, Giza (Egypt); Moretti, S. [School of Physics and Astronomy, University of Southampton,Highfield, Southampton (United Kingdom) 2016-02-23 Search for invisible final states produced at the Large Hadron Collider (LHC) by new physics scenarios are normally carried out resorting to a variety of probes emerging from the initial state, in the form of single-jet, -photon and -Z boson signatures. These are particularly effective for models of Supersymmetry (SUSY) in presence of R-parity conservation, owing to the presence in their spectra of a stable neutralino as a Dark Matter (DM) candidate. We assume here as theoretical framework the Supersymmetric version of the (B−L) extension of the Standard Model (BLSSM), wherein a mediator for invisible decays can be the Z{sup ′} boson present in this scenario. The peculiarity of the signal is thus that the final state objects carry a very large (transverse) missing energy, since the Z{sup ′} is naturally massive and constrained by direct searches and Electro-Weak Precision Tests (EWPTs) to be at least in the TeV scale region. Under these circumstances the efficiency in accessing the invisible final state and rejecting the Standard Model (SM) background is very high. This somehow compensates the rather meagre production rates. Another special feature of this invisible BLSSM signal is its composition, which is often dominated by sneutrino decays (alongside the more traditional neutrino and neutralino modes). Sensitivity of the CERN machine to these two features can therefore help disentangling the BLSSM from more popular SUSY models. We assess in this analysis the scope of the LHC in establishing the aforementioned invisible signals through a sophisticated signal-to-background simulation carried out in presence of parton shower, hadronisation as well as detector effects. We find that significant sensitivity exists already after 300 fb{sup −1} during Run 2. We find that mono-jet events can be readily accessible at the LHC, so as to enable one to claim a prompt discovery, while mono-photon and -Z signals can be used as diagnostic tools of the underlying scenario. 8. Algebraic approach to q-deformed supersymmetric variants of the Hubbard model with pair hoppings International Nuclear Information System (INIS) Arnaudon, D. 1997-01-01 Two quantum spin chains Hamiltonians with quantum sl(2/1) invariance are constructed. These spin chains define variants of the Hubbard model and describe electron models with pair hoppings. A cubic algebra that admits the Birman-Wenzl-Murakami algebra as a quotient allows exact solvability of the periodic chain. The two Hamiltonians, respectively built using the distinguished and the fermionic bases of U q (sl(2/1)) differ only in the boundary terms. They are actually equivalent, but the equivalence is non local. Reflection equations are solved to get exact solvability on open chains with non trivial boundary conditions. Two families of diagonal solutions are found. The centre and the s-Casimir of the quantum enveloping algebra of sl(2/1) appear as tools for the construction of exactly solvable Hamiltonians. (author) 9. On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions Science.gov (United States) Hagendorf, Christian; Liénardy, Jean 2018-03-01 The square-lattice eight-vertex model with vertex weights a, b, c, d obeying the relation (a^2+ab)(b^2+ab) = (c^2+ab)(d^2+ab) and periodic boundary conditions is considered. It is shown that the transfer matrix of the model for L = 2n + 1 vertical lines and periodic boundary conditions along the horizontal direction possesses the doubly degenerate eigenvalue \\Thetan = (a+b){\\hspace{0pt}}2n+1 . This proves a conjecture by Stroganov from 2001. The proof uses the supersymmetry of a related XYZ spin-chain Hamiltonian. The eigenstates of the transfer matrix corresponding to \\Thetan are shown to be the ground states of the spin-chain Hamiltonian. Moreover, for positive vertex weights \\Thetan is the largest eigenvalue of the transfer matrix. 10. Analytic supersymmetric regularization for the pure N=1 super-Yang-Mills model International Nuclear Information System (INIS) Abdalla, E.; Jasinschi, R.S. 1987-01-01 We calculate for the pure N=1 super-Yang-Mills model the quantum correction to the background field strength up to two loops. In using background field method, analytic regularization and Seeley coefficient expansion we show how these corrections arise. Our method differs from the dimensional regularization via dimensional reduction scheme in various respects, in particular to the origin of the background field strength as appearing in the divergent expressions. (orig.) 11. A supersymmetric standard model from a local E{sub 6} GUT Energy Technology Data Exchange (ETDEWEB) Braam, Felix Klaus 2012-02-15 In this thesis we have investigated to what extent the exceptional Lie-group E{sub 6} can serve as unified gauge group. In the presence of the full E{sub 6} matter content, unifcation can be realized by increasing the degree of gauge symmetry above some intermediate scale. We found that a full E{sub 6} gauge invariant theory is disfavoured by phenomenological observations like proton stability and the smallness of flavour changing neutral currents. An appropriate framework to embed E{sub 6} into a model for particle physics are higher dimensional orbifold constructions, where E{sub 6} is the gauge group in the bulk and the intermediate symmetry group is the common subset of E{sub 6} subgroups residing at the fixed-points of the orbifold. In this way the degree of symmetry in four space-time dimensions is reduced, such that the operators leading to the aforementioned dsastrous phenomenological consequences can be forbidden independently. In order to derive the implications of the model for the current experiments at the Large Hadron Collider (LHC), we developed an automated spectrum generator. It uses Monte-Carlo Markov-Chain techniques to cope with the high dimensionality of the space of input parameters and the complex interdependencies in the evolution of the Lagrangian parameters from the orbifold compactification scale to the TeV scale. For the spectra obtained with this program, we performed Monte-Carlo simulations of the production and decay of the Z{sup '} boson stemming from the additional U(1){sup '}, using our own implementation of the model into the event generator WHIZARD. 12. Supersymmetric and supergravity theories International Nuclear Information System (INIS) Pernici, M. 1986-01-01 The author addressed problems in Kaluza-Klein supergravity, in supersymmetric theories and in string theories. They constructed the following supergravity theories in higher dimensions: the maximal gauged supergravities in five and seven dimensions, both related to the respective ungauged theory, though the latter cannot be obtained by putting the coupling constant of the gauged version to zero (gauge discontinuity); the ten-dimensional N = 2 non-chiral and the six-dimensional N = 4 supergravities, through trivial dimensional reduction of higher dimensional theories. They studied the Kaluza-Klein compactifications of the seven-dimensional supergravity theories and of the ten-dimensional, N = 2 non-chiral supergravity. They obtained the non-compact gaugings and the critical points of the potential of the maximal gauged supergravity in seven dimensions. They computed the non-abelian chiral anomaly in super Yang-Mills theories, using a variation of the Fujikawa method. The covariant action of the SU(2) spinning string is obtained together with its extension to non-linear sigma models. A covariant action for the free open spinning string field theory is constructed by analyzing the BRST transformations 13. Dispersive and damping properties of supersymmetric sound. 2 International Nuclear Information System (INIS) Lebedev, V.V.; Smilga, A.V. 1988-01-01 This paper is the second part of the work devoted to the massless fermionic collective excitation in supersymmetric media at nonzero temperature. The solution to generalized kinetic equations for the Wess-Zumino model at low temperatures is presented and the situation at high temperatures is discussed. Supersymmetric gauge models are also discussed 14. Serotonin signaling is a very early step in patterning of the left-right axis in chick and frog embryos NARCIS (Netherlands) Fukumoto, T; Kema, IP; Levin, M 2005-01-01 Background: Consistent left-right (LR) asymmetry is a fascinating problem in developmental and evolutionary biology. Conservation of early LR patterning steps among vertebrates as well as involvement of nonprotein small-molecule messengers are very poorly understood. Serotonin (5-HT) is a key 15. Search for Neutral Higgs Bosons of the Minimal Supersymmetric Standard Model in$e^+ e^-$Interactions at$\\sqrt{s}=192-202 GeV CERN Document Server Acciarri, M.; Adriani, O.; Aguilar-Benitez, M.; Alcaraz, J.; Alemanni, G.; Allaby, J.; Aloisio, A.; Alviggi, M.G.; Ambrosi, G.; Anderhub, H.; Andreev, Valery P.; Angelescu, T.; Anselmo, F.; Arefev, A.; Azemoon, T.; Aziz, T.; Bagnaia, P.; Bajo, A.; Baksay, L.; Balandras, A.; Baldew, S.V.; Banerjee, S.; Banerjee, Sw.; Barczyk, A.; Barillere, R.; Bartalini, P.; Basile, M.; Batalova, N.; Battiston, R.; Bay, A.; Becattini, F.; Becker, U.; Behner, F.; Bellucci, L.; Berbeco, R.; Berdugo, J.; Berges, P.; Bertucci, B.; Betev, B.L.; Bhattacharya, S.; Biasini, M.; Biland, A.; Blaising, J.J.; Blyth, S.C.; Bobbink, G.J.; Bohm, A.; Boldizsar, L.; Borgia, B.; Bourilkov, D.; Bourquin, M.; Braccini, S.; Branson, J.G.; Brochu, F.; Buffini, A.; Buijs, A.; Burger, J.D.; Burger, W.J.; Cai, X.D.; Capell, M.; Cara Romeo, G.; Carlino, G.; Cartacci, A.M.; Casaus, J.; Castellini, G.; Cavallari, F.; Cavallo, N.; Cecchi, C.; Cerrada, M.; Cesaroni, F.; Chamizo, M.; Chang, Y.H.; Chaturvedi, U.K.; Chemarin, M.; Chen, A.; Chen, G.; Chen, G.M.; Chen, H.F.; Chen, H.S.; Chiefari, G.; Cifarelli, L.; Cindolo, F.; Civinini, C.; Clare, I.; Clare, R.; Coignet, G.; Colino, N.; Costantini, S.; Cotorobai, F.; de la Cruz, B.; Csilling, A.; Cucciarelli, S.; Dai, T.S.; van Dalen, J.A.; D'Alessandro, R.; de Asmundis, R.; Deglon, P.; Degre, A.; Deiters, K.; della Volpe, D.; Delmeire, E.; Denes, P.; DeNotaristefani, F.; De Salvo, A.; Diemoz, M.; Dierckxsens, M.; van Dierendonck, D.; Dionisi, C.; Dittmar, M.; Dominguez, A.; Doria, A.; Dova, M.T.; Duchesneau, D.; Dufournaud, D.; Duinker, P.; El Mamouni, H.; Engler, A.; Eppling, F.J.; Erne, F.C.; Ewers, A.; Extermann, P.; Fabre, M.; Falagan, M.A.; Falciano, S.; Favara, A.; Fay, J.; Fedin, O.; Felcini, M.; Ferguson, T.; Fesefeldt, H.; Fiandrini, E.; Field, J.H.; Filthaut, F.; Fisher, P.H.; Fisk, I.; Forconi, G.; Freudenreich, K.; Furetta, C.; Galaktionov, Iouri; Ganguli, S.N.; Garcia-Abia, Pablo; Gataullin, M.; Gau, S.S.; Gentile, S.; Gheordanescu, N.; Giagu, S.; Gong, Z.F.; Grenier, Gerald Jean; Grimm, O.; Gruenewald, M.W.; Guida, M.; van Gulik, R.; Gupta, V.K.; Gurtu, A.; Gutay, L.J.; Haas, D.; Hasan, A.; Hatzifotiadou, D.; Hebbeker, T.; Herve, Alain; Hidas, P.; Hirschfelder, J.; Hofer, H.; Holzner, G.; Hoorani, H.; Hou, S.R.; Hu, Y.; Iashvili, I.; Jin, B.N.; Jones, Lawrence W.; de Jong, P.; Josa-Mutuberria, I.; Khan, R.A.; Kafer, D.; Kaur, M.; Kienzle-Focacci, M.N.; Kim, D.; Kim, J.K.; Kirkby, Jasper; Kiss, D.; Kittel, W.; Klimentov, A.; Konig, A.C.; Kopal, M.; Kopp, A.; Koutsenko, V.; Kraber, M.; Kraemer, R.W.; Krenz, W.; Kruger, A.; Kunin, A.; Ladron de Guevara, P.; Laktineh, I.; Landi, G.; Lebeau, M.; Lebedev, A.; Lebrun, P.; Lecomte, P.; Lecoq, P.; Le Coultre, P.; Lee, H.J.; Le Goff, J.M.; Leiste, R.; Levtchenko, P.; Li, C.; Likhoded, S.; Lin, C.H.; Lin, W.T.; Linde, F.L.; Lista, L.; Liu, Z.A.; Lohmann, W.; Longo, E.; Lu, Y.S.; Lubelsmeyer, K.; Luci, C.; Luckey, David; Lugnier, L.; Luminari, L.; Lustermann, W.; Ma, W.G.; Maity, M.; Malgeri, L.; Malinin, A.; Mana, C.; Mangeol, D.; Mans, J.; Marian, G.; Martin, J.P.; Marzano, F.; Mazumdar, K.; McNeil, R.R.; Mele, S.; Merola, L.; Meschini, M.; Metzger, W.J.; von der Mey, M.; Mihul, A.; Milcent, H.; Mirabelli, G.; Mnich, J.; Mohanty, G.B.; Moulik, T.; Muanza, G.S.; Muijs, A.J.M.; Musicar, B.; Musy, M.; Napolitano, M.; Nessi-Tedaldi, F.; Newman, H.; Niessen, T.; Nisati, A.; Kluge, Hannelies; Ofierzynski, R.; Organtini, G.; Oulianov, A.; Palomares, C.; Pandoulas, D.; Paoletti, S.; Paolucci, P.; Paramatti, R.; Park, H.K.; Park, I.H.; Passaleva, G.; Patricelli, S.; Paul, Thomas Cantzon; Pauluzzi, M.; Paus, C.; Pauss, F.; Pedace, M.; Pensotti, S.; Perret-Gallix, D.; Petersen, B.; Piccolo, D.; Pierella, F.; Pieri, M.; Piroue, P.A.; Pistolesi, E.; Plyaskin, V.; Pohl, M.; Pojidaev, V.; Postema, H.; Pothier, J.; Prokofev, D.O.; Prokofiev, D.; Quartieri, J.; Rahal-Callot, G.; Rahaman, M.A.; Raics, P.; Raja, N.; Ramelli, R.; Rancoita, P.G.; Ranieri, R.; Raspereza, A.; Raven, G.; Razis, P.; Ren, D.; Rescigno, M.; Reucroft, S.; Riemann, S.; Riles, Keith; Rodin, J.; Roe, B.P.; Romero, L.; Rosca, A.; Rosier-Lees, S.; Roth, Stefan; Rosenbleck, C.; Roux, B.; Rubio, J.A.; Ruggiero, G.; Rykaczewski, H.; Saremi, S.; Sarkar, S.; Salicio, J.; Sanchez, E.; Sanders, M.P.; Schafer, C.; Schegelsky, V.; Schmidt-Kaerst, S.; Schmitz, D.; Schopper, H.; Schotanus, D.J.; Schwering, G.; Sciacca, C.; Seganti, A.; Servoli, L.; Shevchenko, S.; Shivarov, N.; Shoutko, V.; Shumilov, E.; Shvorob, A.; Siedenburg, T.; Son, D.; Smith, B.; Spillantini, P.; Steuer, M.; Stickland, D.P.; Stone, A.; Stoyanov, B.; Straessner, A.; Sudhakar, K.; Sultanov, G.; Sun, L.Z.; Sushkov, S.; Suter, H.; Swain, J.D.; Szillasi, Z.; Sztaricskai, T.; Tang, X.W.; Tauscher, L.; Taylor, L.; Tellili, B.; Teyssier, D.; Timmermans, Charles; Ting, Samuel C.C.; Ting, S.M.; Tonwar, S.C.; Toth, J.; Tully, C.; Tung, K.L.; Uchida, Y.; Ulbricht, J.; Valente, E.; Vesztergombi, G.; Vetlitsky, I.; Vicinanza, D.; Viertel, G.; Villa, S.; Vivargent, M.; Vlachos, S.; Vodopianov, I.; Vogel, H.; Vogt, H.; Vorobev, I.; Vorobov, A.A.; Vorvolakos, A.; Wadhwa, M.; Wallraff, W.; Wang, M.; Wang, X.L.; Wang, Z.M.; Weber, A.; Weber, M.; Wienemann, P.; Wilkens, H.; Wu, S.X.; Wynhoff, S.; Xia, L.; Xu, Z.Z.; Yamamoto, J.; Yang, B.Z.; Yang, C.G.; Yang, H.J.; Yang, M.; Ye, J.B.; Yeh, S.C.; Zalite, A.; Zalite, Yu.; Zhang, Z.P.; Zhu, G.Y.; Zhu, R.Y.; Zichichi, A.; Zilizi, G.; Zimmermann, B.; Zoller, M. 2001-01-01 A search for the lightest neutral CP-even and the neutral CP-odd Higgs bosons of the Minimal Supersymmetric Standard Model is performed using 233.2 pb-1 of integrated luminosity collected with the L3 detector at LEP at centre-of-mass energies 192-202 GeV. No signal is observed and lower mass limits are given as a function of tan(beta) for two scalar top mixing hypotheses. For tan(beta) greater than 0.8, they are mh > 83.4 GeV and mA > 83.8 GeV at 95 % confidence level. 16. Supersymmetric theories of neutrino dark energy International Nuclear Information System (INIS) Fardon, Rob; Nelson, Ann E.; Weiner, Neal 2006-01-01 We present a supersymmetric model of dark energy from Mass Varying Neutrinos which is stable against radiative corrections to masses and couplings, and free of dynamical instabilities. This is the only such model of dark energy involving fields with significant couplings to any standard model particle. We briefly discuss consequences for neutrino oscillations and solar neutrinos 17. Bubbles of nothing and supersymmetric compactifications Energy Technology Data Exchange (ETDEWEB) Blanco-Pillado, Jose J. [IKERBASQUE, Basque Foundation for Science, 48011, Bilbao (Spain); Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain); Shlaer, Benjamin [Department of Physics, University of Auckland,Private Bag 92019, Auckland (New Zealand); Institute of Cosmology, Department of Physics and Astronomy,Tufts University, Medford, MA 02155 (United States); Sousa, Kepa [Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain); Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid,Cantoblanco, 28049 Madrid (Spain); Urrestilla, Jon [Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain) 2016-10-03 We investigate the non-perturbative stability of supersymmetric compactifications with respect to decay via a bubble of nothing. We show examples where this kind of instability is not prohibited by the spin structure, i.e., periodicity of fermions about the extra dimension. However, such “topologically unobstructed” cases do exhibit an extra-dimensional analog of the well-known Coleman-De Luccia suppression mechanism, which prohibits the decay of supersymmetric vacua. We demonstrate this explicitly in a four dimensional Abelian-Higgs toy model coupled to supergravity. The compactification of this model to M{sub 3}×S{sub 1} presents the possibility of vacua with different windings for the scalar field. Away from the supersymmetric limit, these states decay by the formation of a bubble of nothing, dressed with an Abelian-Higgs vortex. We show how, as one approaches the supersymmetric limit, the circumference of the topologically unobstructed bubble becomes infinite, thereby preventing the realization of this decay. This demonstrates the dynamical origin of the decay suppression, as opposed to the more familiar argument based on the spin structure. We conjecture that this is a generic mechanism that enforces stability of any topologically unobstructed supersymmetric compactification. 18. Applications of supersymmetric quantum mechanics International Nuclear Information System (INIS) Rietdijk, R.H. 1992-01-01 The central subject of the thesis is the spinning particle model. It is a theory describing in a pseudoclassical way a Dirac particle which moves in an arbitrary d-dimensional space-time.In addition to space-time coordinates, the particle has spin which is described in terms of anti-commuting coordinates. Along the particles world line there is a super-symmetry between the fermionic spin variables and the bosonic position coordinates of the particle. It is straightforward to quantisize this model giving rise to supersymmetric quantum mechanics. The model does indeed describe a particle with spin 1/2, like a quark or an electron. There are two aspects of this model which is studied extensively in this thesis. First, to investigate the symmetries of the spinning particle on an arbitrary Riemannian manifold. Second, attention is drawn to the application of supersymmetric quantum mechanical models (i.e. spinning particle models) defined on an arbitrary Riemannian manifold to the calculation of anomalies in quantum field theories defined on the same manifold. (author). 49 refs.; 7 figs 19. Supersymmetric quantum mechanics International Nuclear Information System (INIS) Crombrugghe, M. de; Rittenberg, V. 1982-12-01 We give a general construction for supersymmetric Hamiltonians in quantum mechanics. We find that N-extended supersymmetry imposes very strong constraints, and for N > 4 the Hamiltonian is integrable. We give a variety of examples, for one-particle and for many-particle systems, in different numbers of dimensions. (orig.) 20. Supersymmetric reflection matrices International Nuclear Information System (INIS) Moriconi, M.; Schoutens, K. 1997-04-01 We briefly review the general structure of integrable particle theories in 1 + 1 dimensions having N = 1 supersymmetry. Examples are specific perturbed superconformal field theories (of Yang-Lee type) and the N = 1 supersymmetric sine-Gordon theory. We comment on the modifications that are required when the N = 1 supersymmetry algebra contains non-trivial topological charges. (author). 8 refs, 2 figs 1. Supersymmetric leptogenesis with a light hidden sector International Nuclear Information System (INIS) De Simone, Andrea 2010-04-01 Supersymmetric scenarios incorporating thermal leptogenesis as the origin of the observed matter-antimatter asymmetry generically predict abundances of the primordial elements which are in conflict with observations. In this paper we pro- pose a simple way to circumvent this tension and accommodate naturally ther- mal leptogenesis and primordial nucleosynthesis. We postulate the existence of a light hidden sector, coupled very weakly to the Minimal Supersymmetric Standard Model, which opens up new decay channels for the next-to-lightest supersymmetric particle, thus diluting its abundance during nucleosynthesis. We present a general model-independent analysis of this mechanism as well as two concrete realizations, and describe the relevant cosmological and astrophysical bounds and implications for this dark matter scenario. Possible experimental signatures at colliders and in cosmic-ray observations are also discussed. (orig.) 2. Vector supersymmetric multiplets in two dimensions International Nuclear Information System (INIS) Khattab, Mohammad 1990-01-01 Author.The invariance of both, N=1 supersymmetric yang-Mills theory and N-1 supersymmetric off-shell Wess-Zumino model in four dimensions is proved. Dimensional reduction is then applied to obtain super Yang-Mills theory with extended supersymmetry, N=2, in two dimensions. The resulting theory is then truncated to N=1 super Yang-Mills and with further truncation, N=1/2 supersymmetry is shown to be possible. Then, using the duality transformations, we find the off-shell supersymmetry algebra is closed and that the auxiliary fields are replaced by four-rank antisymmetric tensors with Gauge symmetry. Finally, the mechanism of dimensional reduction is then applied to obtain N=2 extended off-shell supersymmetric model with two gauge vector fields 3. Supersymmetric quantum mechanics: another nontrivial quantum superpotential International Nuclear Information System (INIS) Cervero, J.M. 1991-01-01 A nontrivial example of a quantum superpotential in the framework of supersymmetric quantum mechanics is constructed using integrable soliton-like functions. The model is shown to be fully solvable and some consequences regarding the physical properties of the model such as transparence and boundary effects are discussed. (orig.) 4. Removing left-right asymmetry in a Sagnac interferometer applied to cancel its reflectance dependence on birefringence. Science.gov (United States) Golub, Ilya; Exir, Hourieh 2013-05-01 We present a left-right symmetry restoring method, which removes the detrimental birefringence in the single-mode fiber Sagnac interferometer, achieved with the aid of a half waveplate oriented at a specific angle. We show theoretically and demonstrate experimentally that adding a π-shift between clockwise and counterclockwise propagating, horizontally (in fiber loop plane) polarized field components, the Sagnac loop mirror's reflection becomes independent on birefringence of an element placed in the loop. 5. Tbx6 regulates left/right patterning in mouse embryos through effects on nodal cilia and perinodal signaling. Directory of Open Access Journals (Sweden) Anna-Katerina Hadjantonakis Full Text Available BACKGROUND: The determination of left/right body axis during early embryogenesis sets up a developmental cascade that coordinates the development of the viscera and is essential to the correct placement and alignment of organ systems and vasculature. Defective left-right patterning can lead to congenital cardiac malformations, vascular anomalies and other serious health problems. Here we describe a novel role for the T-box transcription factor gene Tbx6 in left/right body axis determination in the mouse. RESULTS: Embryos lacking Tbx6 show randomized embryo turning and heart looping. Our results point to multiple mechanisms for this effect. First, Dll1, a direct target of Tbx6, is down regulated around the node in Tbx6 mutants and there is a subsequent decrease in nodal signaling, which is required for laterality determination. Secondly, in spite of a lack of expression of Tbx6 in the node, we document a profound effect of the Tbx6 mutation on the morphology and motility of nodal cilia. This results in the loss of asymmetric calcium signaling at the periphery of the node, suggesting that unidirectional nodal flow is disrupted. To carry out these studies, we devised a novel method for direct labeling and live imaging cilia in vivo using a genetically-encoded fluorescent protein fusion that labels tubulin, combined with laser point scanning confocal microscopy for direct visualization of cilia movement. CONCLUSIONS: We conclude that the transcription factor gene Tbx6 is essential for correct left/right axis determination in the mouse and acts through effects on notch signaling around the node as well as through an effect on the morphology and motility of the nodal cilia. 6. Left-Right Asymmetry Is Required for the Habenulae to Respond to Both Visual and Olfactory Stimuli OpenAIRE Dreosti, Elena; Vendrell Llopis, Nuria; Carl, Matthias; Yaksi, Emre; Wilson, Stephen W. 2014-01-01 Summary Left-right asymmetries are most likely a universal feature of bilaterian nervous systems and may serve to increase neural capacity by specializing equivalent structures on left and right sides for distinct roles [1]. However, little is known about how asymmetries are encoded within vertebrate neural circuits and how lateralization influences processing of information in the brain. Consequently, it remains unclear the extent to which lateralization of the nervous system is important fo... 7. Solvable potentials derived from supersymmetric quantum mechanics International Nuclear Information System (INIS) Levai, G. 1994-01-01 The introduction of supersymmetric quantum mechanics has generated renewed interest in solvable problems of non-relativistic quantum mechanics. This approach offers an elegant way to describe different, but isospectral potentials by interpreting the degeneracy of their energy levels in terms of supersymmetry. The original ideas of supersymmetric quantum mechanics have been developed further in many respects in the past ten years, and have been applied to a large variety of physical problems. The purpose of this contribution is to give a survey of supersymmetric quantum mechanics and its applications to solvable quantum mechanical potentials. Its relation to other models describing isospectral potentials is also discussed here briefly, as well as some of its practical applications in various branches of physics. (orig.) 8. Supersymmetric Higgs boson production in Z decays International Nuclear Information System (INIS) Gamberini, G.; Giudice, G.F.; Ridolfi, G. 1987-01-01 The problem of distinguishing between the standard model and the supersymmetric Higgs bosons is considered in the context of Z 0 decays. We find that, for some choices of the parameters, the branching ratio for Z 0 → H 0 γ is strongly enhanced by the exchange of supersymmetric fermions as virtual particles. This makes the study of this process at LEP very interesting, since other Z 0 branching modes into Higgs bosons, such as Z 0 → H 0 μ + μ - , are not so clearly modified by supersymmetry. (orig.) 9. Indirect detection of heavy supersymmetric dark matter International Nuclear Information System (INIS) Kamionkowski, M. 1991-02-01 If neutralinos reside in the galactic halo they will be captured in the Sun and annihilate therein producing high-energy neutrinos. Present limits on the flux of such neutrinos from underground detectors such as IMB and Kamiokande 2 may be used to rule out certain supersymmetric dark-matter candidates, while in many other supersymmetric models the rates are large enough that if neutralinos do reside in the galactic halo, observation of a neutrino signal may be possible in the near future. 10 refs., 2 figs 10. R&D; studies on the hadronic calorimeter and physics simulations on the Standard Model and minimal supersymmetric Standard Model Higgs bosons in the CMS experiment CERN Document Server Duru, Firdevs 2007-01-01 This thesis consists of two main parts: R&D; studies done on the Compact Muon Solenoid (CMS) Hadronic Calorimeter (HCAL) and physics simulations on the Higgs boson for a Minimal Supersymmetric Standard Model (MSSM) and a Standard Model (SM) channel. In the first part, the air core light guides used in the read-out system of the Hadronic Forward (HF) calorimeter and the reflective materials used in them are studied. Then, tests and simulations were performed to find the most efficient way to collect Cerenkov light from the quartz plates, which are proposed as a substitute for the scintillator tiles in the Hadronic Endcap (HE) calorimeter due to radiation damage problems. In the second part physics simulations and their results are presented. The MSSM channel H/A[arrow right]ττ [arrow right]l l v v v v is studied to investigate the jet and missing transverse energy (MET) reconstruction of the CMS detector. The effects of the jet and MET corrections on the Higgs boson mass reconstruction are investigated. ... 11. Supersymmetric symplectic quantum mechanics Science.gov (United States) de Menezes, Miralvo B.; Fernandes, M. C. B.; Martins, Maria das Graças R.; Santana, A. E.; Vianna, J. D. M. 2018-02-01 Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function. 12. Ultraviolet divergences in non-renormalizable supersymmetric theories International Nuclear Information System (INIS) Smilga, A. 2017-01-01 We present a pedagogical review of our current understanding of the ultraviolet structure of N =(1, 1) 6D supersymmetric Yang-Mills theory and of N = 8 4D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higher-dimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially of extended supersymmetric theories) is that these counterterms may not be invariant off-shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on-shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behavior. 13. Supersymmetrically transformed periodic potentials OpenAIRE C, David J. Fernandez 2003-01-01 The higher order supersymmetric partners of a stationary periodic potential are studied. The transformation functions associated to the band edges do not change the spectral structure. However, when the transformation is implemented for factorization energies inside of the forbidden bands, the final potential will have again the initial band structure but it can have bound states encrusted into the gaps, giving place to localized periodicity defects. 14. Planarizable Supersymmetric Quantum Toboggans Czech Academy of Sciences Publication Activity Database Znojil, Miloslav 2011-01-01 Roč. 7, - (2011), 018/1-018/23 ISSN 1815-0659. [Workshop on Supersymmetric Quantum Mechanics and Spectral Design. Benasque, 18.07.2010-30.07. 2010] R&D Projects: GA ČR GAP203/11/1433 Institutional research plan: CEZ:AV0Z10480505 Keywords : supersymmetry * Schrodinger equation * complexified coordinates Subject RIV: BE - Theoretical Physics Impact factor: 1.071, year: 2011 15. The calculation of sparticle and Higgs decays in the minimal and next-to-minimal supersymmetric standard models: SOFTSUSY4.0 Science.gov (United States) Allanach, B. C.; Cridge, T. 2017-11-01 We describe a major extension of the SOFTSUSY spectrum calculator to include the calculation of the decays, branching ratios and lifetimes of sparticles into lighter sparticles, covering the next-to-minimal supersymmetric standard model (NMSSM) as well as the minimal supersymmetric standard model (MSSM). This document acts as a manual for the new version of SOFTSUSY, which includes the calculation of sparticle decays. We present a comprehensive collection of explicit expressions used by the program for the various partial widths of the different decay modes in the appendix. Program Files doi:http://dx.doi.org/10.17632/5hhwwmp43g.1 Licensing provisions: GPLv3 Programming language:C++, fortran Nature of problem: Calculating supersymmetric particle partial decay widths in the MSSM or the NMSSM, given the parameters and spectrum which have already been calculated by SOFTSUSY. Solution method: Analytic expressions for tree-level 2 body decays and loop-level decays and one-dimensional numerical integration for 3 body decays. Restrictions: Decays are calculated in the real R -parity conserving MSSM or the real R -parity conserving NMSSM only. No additional charge-parity violation (CPV) relative to the Standard Model (SM). Sfermion mixing has only been accounted for in the third generation of sfermions in the decay calculation. Decays in the MSSM are 2-body and 3-body, whereas decays in the NMSSM are 2-body only. Does the new version supersede the previous version?: Yes. Reasons for the new version: Significantly extended functionality. The decay rates and branching ratios of sparticles are particularly useful for collider searches. Decays calculated in the NMSSM will be a particularly useful check of the other programs in the literature, of which there are few. Summary of revisions: Addition of the calculation of sparticle and Higgs decays. All 2-body and important 3-body tree-level decays, including phenomenologically important loop-level decays (notably, Higgs decays to 16. Supersymmetric quantum corrections and Poisson-Lie T-duality International Nuclear Information System (INIS) Assaoui, F.; Lhallabi, T.; Abdus Salam International Centre for Theoretical Physics, Trieste 2000-07-01 The quantum actions of the (4,4) supersymmetric non-linear sigma model and its dual in the Abelian case are constructed by using the background superfield method. The propagators of the quantum superfield and its dual and the gauge fixing actions of the original and dual (4,4) supersymmetric sigma models are determined. On the other hand, the BRST transformations are used to obtain the quantum dual action of the (4,4) supersymmetric nonlinear sigma model in the sense of Poisson-Lie T-duality. (author) 17. Influence of Left-Right Asymmetries on Voice Quality in Simulated Paramedian Vocal Fold Paralysis Science.gov (United States) Samlan, Robin A.; Story, Brad H. 2017-01-01 Purpose: The purpose of this study was to determine the vocal fold structural and vibratory symmetries that are important to vocal function and voice quality in a simulated paramedian vocal fold paralysis. Method: A computational kinematic speech production model was used to simulate an exemplar "voice" on the basis of asymmetric… 18. Planar cell polarity enables posterior localization of nodal cilia and left-right axis determination during mouse and Xenopus embryogenesis. Directory of Open Access Journals (Sweden) Dragana Antic 2010-02-01 Full Text Available Left-right asymmetry in vertebrates is initiated in an early embryonic structure called the ventral node in human and mouse, and the gastrocoel roof plate (GRP in the frog. Within these structures, each epithelial cell bears a single motile cilium, and the concerted beating of these cilia produces a leftward fluid flow that is required to initiate left-right asymmetric gene expression. The leftward fluid flow is thought to result from the posterior tilt of the cilia, which protrude from near the posterior portion of each cell's apical surface. The cells, therefore, display a morphological planar polarization. Planar cell polarity (PCP is manifested as the coordinated, polarized orientation of cells within epithelial sheets, or as directional cell migration and intercalation during convergent extension. A set of evolutionarily conserved proteins regulates PCP. Here, we provide evidence that vertebrate PCP proteins regulate planar polarity in the mouse ventral node and in the Xenopus gastrocoel roof plate. Asymmetric anterior localization of VANGL1 and PRICKLE2 (PK2 in mouse ventral node cells indicates that these cells are planar polarized by a conserved molecular mechanism. A weakly penetrant Vangl1 mutant phenotype suggests that compromised Vangl1 function may be associated with left-right laterality defects. Stronger functional evidence comes from the Xenopus GRP, where we show that perturbation of VANGL2 protein function disrupts the posterior localization of motile cilia that is required for leftward fluid flow, and causes aberrant expression of the left side-specific gene Nodal. The observation of anterior-posterior PCP in the mouse and in Xenopus embryonic organizers reflects a strong evolutionary conservation of this mechanism that is important for body plan determination. 19. Search for Neutral Higgs Bosons of the Minimal Supersymmetric Standard Model ine^{+}e^{-}$Interactions at$\\sqrt{s}$up to 209 GeV CERN Document Server Achard, P; Aguilar-Benítez, M; Alcaraz, J; Alemanni, G; Allaby, James V; Aloisio, A; Alviggi, M G; Anderhub, H; Andreev, V P; Anselmo, F; Arefev, A; Azemoon, T; Aziz, T; Bagnaia, P; Bajo, A; Baksay, G; Baksay, L; Baldew, S V; Banerjee, S; Banerjee, Sw; Barczyk, A; Barillère, R; Bartalini, P; Basile, M; Batalova, N; Battiston, R; Bay, A; Becattini, F; Becker, U; Behner, F; Bellucci, L; Berbeco, R; Berdugo, J; Berges, P; Bertucci, B; Betev, B L; Biasini, M; Biglietti, M; Biland, A; Blaising, J J; Blyth, S C; Bobbink, Gerjan J; Böhm, A; Boldizsar, L; Borgia, B; Bottai, S; Bourilkov, D; Bourquin, Maurice; Braccini, S; Branson, J G; Brochu, F; Burger, J D; Burger, W J; Cai, X D; Capell, M; Cara Romeo, G; Carlino, G; Cartacci, A M; Casaus, J; Cavallari, F; Cavallo, N; Cecchi, C; Cerrada, M; Chamizo-Llatas, M; Chang, Y H; Chemarin, M; Chen, A; Chen, G; Chen, G M; Chen, H F; Chen, H S; Chiefari, G; Cifarelli, Luisa; Cindolo, F; Clare, I; Clare, R; Coignet, G; Colino, N; Costantini, S; de la Cruz, B; Cucciarelli, S; van Dalen, J A; De Asmundis, R; Déglon, P L; Debreczeni, J; Degré, A; Dehmelt, K; Deiters, K; Della Volpe, D; Delmeire, E; Denes, P; De Notaristefani, F; De Salvo, A; Diemoz, M; Dierckxsens, M; Dionisi, C; Dittmar, Michael; Doria, A; Dova, M T; Duchesneau, D; Echenard, B; Eline, A; El-Mamouni, H; Engler, A; Eppling, F J; Ewers, A; Extermann, Pierre; Falagán, M A; Falciano, S; Favara, A; Fay, J; Fedin, O; Felcini, Marta; Ferguson, T; Fesefeldt, H S; Fiandrini, E; Field, J H; Filthaut, Frank; Fisher, P H; Fisher, W; Fisk, I; Forconi, G; Freudenreich, Klaus; Furetta, C; Galaktionov, Yu; Ganguli, S N; García-Abia, P; Gataullin, M; Gentile, S; Giagu, S; Gong, Z F; Grenier, G; Grimm, O; Grünewald, M W; Guida, M; van Gulik, R; Gupta, V K; Gurtu, A; Gutay, L J; Haas, D; Hakobyan, R S; Hatzifotiadou, D; Hebbeker, T; Hervé, A; Hirschfelder, J; Hofer, H; Hohlmann, M; Holzner, G; Hou, S R; Hu, Y; Jin, B N; Jones, L W; de Jong, P; Josa-Mutuberria, I; Käfer, D; Kaur, M; Kienzle-Focacci, M N; Kim, J K; Kirkby, Jasper; Kittel, E W; Klimentov, A; König, A C; Kopal, M; Koutsenko, V F; Kräber, M H; Krämer, R W; Krenz, W; Krüger, A; Kunin, A; Ladrón de Guevara, P; Laktineh, I; Landi, G; Lebeau, M; Lebedev, A; Lebrun, P; Lecomte, P; Lecoq, P; Le Coultre, P; Le Goff, J M; Leiste, R; Levtchenko, M; Levchenko, P M; Li, C; Likhoded, S A; Lin, C H; Lin, W T; Linde, Frank L; Lista, L; Liu, Z A; Lohmann, W; Longo, E; Lü, Y S; Lübelsmeyer, K; Luci, C; Luminari, L; Lustermann, W; Ma Wen Gan; Malgeri, L; Malinin, A; Maña, C; Mangeol, D J J; Mans, J; Martin, J P; Marzano, F; Mazumdar, K; McNeil, R R; Mele, S; Merola, L; Meschini, M; Metzger, W J; Mihul, A; Milcent, H; Mirabelli, G; Mnich, J; Mohanty, G B; Muanza, G S; Muijs, A J M; Musicar, B; Musy, M; Nagy, S; Natale, S; Napolitano, M; Nessi-Tedaldi, F; Newman, H; Niessen, T; Nisati, A; Nowak, H; Ofierzynski, R A; Organtini, G; Palomares, C; Pandoulas, D; Paolucci, P; Paramatti, R; Passaleva, G; Patricelli, S; Paul, T; Pauluzzi, M; Paus, C; Pauss, Felicitas; Pedace, M; Pensotti, S; Perret-Gallix, D; Petersen, B; Piccolo, D; Pierella, F; Pioppi, M; Piroué, P A; Pistolesi, E; Plyaskin, V; Pohl, M; Pozhidaev, V; Pothier, J; Prokofiev, D O; Prokofev, D; Quartieri, J; Rahal-Callot, G; Rahaman, M A; Raics, P; Raja, N; Ramelli, R; Rancoita, P G; Ranieri, R; Raspereza, A V; Razis, P A; Ren, D; Rescigno, M; Reucroft, S; Riemann, S; Riles, K; Roe, B P; Romero, L; Rosca, A; Rosier-Lees, S; Roth, S; Rosenbleck, C; Roux, B; Rubio, Juan Antonio; Ruggiero, G; Rykaczewski, H; Sakharov, A; Saremi, S; Sarkar, S; Salicio, J; Sánchez, E; Sanders, M P; Schäfer, C; Shchegelskii, V; Schmidt-Kärst, S; Schmitz, D; Schopper, Herwig Franz; Schotanus, D J; Schwering, G; Sciacca, C; Servoli, L; Shevchenko, S; Shivarov, N; Shoutko, V; Shumilov, E; Shvorob, A V; Siedenburg, T; Son, D; Souga, C; Spillantini, P; Steuer, M; Stickland, D P; Stoyanov, B; Strässner, A; Sudhakar, K; Sultanov, G G; Sun, L Z; Sushkov, S V; Suter, H; Swain, J D; Szillási, Z; Tang, X W; Tarjan, P; Tauscher, Ludwig; Taylor, L; Tellili, B; Teyssier, D; Timmermans, C; Ting, Samuel C C; Ting, S M; Tonwar, S C; Tóth, J; Tully, C; Tung, K L; Ulbricht, J; Valente, E; Van de Walle, R T; Vásquez, R P; Veszpremi, V; Vesztergombi, G; Vetlitskii, I; Vicinanza, D; Viertel, Gert M; Villa, S; Vivargent, M; Vlachos, S; Vodopyanov, I; Vogel, H; Vogt, H; Vorobev, I; Vorobyov, A A; Wadhwa, M; Wallraff, W; Wang, X L; Wang, Z M; Weber, M; Wienemann, P; Wilkens, H; Wynhoff, S; Xia, L; Xu, Z Z; Yamamoto, J; Yang, B Z; Yang, C G; Yang, H J; Yang, M; Yeh, S C; Zalite, A; Zalite, Yu; Zhang, Z P; Zhao, J; Zhu, G Y; Zhu, R Y; Zhuang, H L; Zichichi, A; Zimmermann, B; Zöller, M 2002-01-01 A search for the lightest neutral CP-even and neutral CP-odd Higgs bosons of the Minimal Supersymmetric Standard Model is performed using 216.6 pb-1 of data collected with the L3 detector at LEP at centre-of-mass energies between 203 and 209 GeV. No indication of a signal is found. Including our results from lower centre-of-mass energies, lower limits on the Higgs boson masses are set as a function of tan(beta) for several scenarios. For tan(beta) greater than 0.7 they are mh > 84.5 GeV and mA > 86.3 GeV at 95% confidence level. 20. Effects of the R-parity violation in the minimal supersymmetric standard model on dilepton pair production at the CERN LHC CERN Document Server Jun, Y; Lang-Hui, W; Ren Zhao You; Jun, Yin; Wen-Gan, Ma; Lang-Hui, Wan; Ren-You, Zhang 2002-01-01 We investigate in detail the effects of the R-parity lepton number violation in the minimal supersymmetric standard model (MSSM) on the parent process$pp \\to e^+ e^- + X$at the CERN Large Hadron Collider (LHC). The numerical comparisons between the contributions of the R-parity violating effects to the parent process via the Drell-Yan subprocess and the gluon-gluon fusion are made. We find that the R-violating effects on$e^+ e^-$pair production at the LHC could be significant. The results show that the cross section of the$ e^+ e^-$pair productions via gluon-gluon collision at the LHC can be of the order of$10^2$fb, and this subprocess maybe competitive with the production mechanism via the Drell-Yan subprocess. We give also quantitatively the analysis of the effects from both the mass of sneutrino and coupling strength of the R-parity violating interactions. 1. Search for neutral minimal supersymmetric standard model Higgs bosons decaying to tau pairs in pp collisions at √s=7 TeV. Science.gov (United States) Chatrchyan, S; Khachatryan, V; Sirunyan, A M; Tumasyan, A; Adam, W; Bergauer, T; Dragicevic, M; Erö, J; Fabjan, C; Friedl, M; Frühwirth, R; Ghete, V M; Hammer, J; Hänsel, S; Hoch, M; Hörmann, N; Hrubec, J; Jeitler, M; Kasieczka, G; Kiesenhofer, W; Krammer, M; Liko, D; Mikulec, I; Pernicka, M; Rohringer, H; Schöfbeck, R; Strauss, J; Teischinger, F; Wagner, P; Waltenberger, W; Walzel, G; Widl, E; Wulz, C-E; Mossolov, V; Shumeiko, N; Suarez Gonzalez, J; Benucci, L; De Wolf, E A; Janssen, X; Maes, T; Mucibello, L; Ochesanu, S; Roland, B; Rougny, R; Selvaggi, M; Van Haevermaet, H; Van Mechelen, P; Van Remortel, N; Blekman, F; Blyweert, S; D'Hondt, J; Devroede, O; Gonzalez Suarez, R; Kalogeropoulos, A; Maes, J; Maes, M; Van Doninck, W; Van Mulders, P; Van Onsem, G P; Villella, I; Charaf, O; Clerbaux, B; De Lentdecker, G; Dero, V; Gay, A P R; Hammad, G H; Hreus, T; Marage, P E; Thomas, L; Vander Velde, C; Vanlaer, P; Adler, V; Cimmino, A; Costantini, S; Grunewald, M; Klein, B; Lellouch, J; Marinov, A; McCartin, J; Ryckbosch, D; Thyssen, F; Tytgat, M; Vanelderen, L; Verwilligen, P; Walsh, S; Zaganidis, N; Basegmez, S; Bruno, G; Caudron, J; Ceard, L; Cortina Gil, E; De Favereau De Jeneret, J; Delaere, C; Favart, D; Giammanco, A; Grégoire, G; Hollar, J; Lemaitre, V; Liao, J; Militaru, O; Ovyn, S; Pagano, D; Pin, A; Piotrzkowski, K; Schul, N; Beliy, N; Caebergs, T; Daubie, E; Alves, G A; Damiao, D De Jesus; Pol, M E; Souza, M H G; Carvalho, W; Da Costa, E M; Martins, C De Oliveira; De Souza, S Fonseca; Mundim, L; Nogima, H; Oguri, V; Da Silva, W L Prado; Santoro, A; Do Amaral, S M Silva; Sznajder, A; De Araujo, F Torres Da Silva; Dias, F A; Tomei, T R Fernandez Perez; Gregores, E M; Lagana, C; Marinho, F; Mercadante, P G; Novaes, S F; Padula, Sandra S; Darmenov, N; Dimitrov, L; Genchev, V; Iaydjiev, P; Piperov, S; Rodozov, M; Stoykova, S; Sultanov, G; Tcholakov, V; Trayanov, R; Vankov, I; Dimitrov, A; Hadjiiska, R; Karadzhinova, A; Kozhuharov, V; Litov, L; Mateev, M; Pavlov, B; Petkov, P; Bian, J G; Chen, G M; Chen, H S; Jiang, C H; Liang, D; Liang, S; Meng, X; Tao, J; Wang, J; Wang, J; Wang, X; Wang, Z; Xiao, H; Xu, M; Zang, J; Zhang, Z; Ban, Y; Guo, S; Guo, Y; Li, W; Mao, Y; Qian, S J; Teng, H; Zhang, L; Zhu, B; Zou, W; Cabrera, A; Moreno, B Gomez; Rios, A A Ocampo; Oliveros, A F Osorio; Sanabria, J C; Godinovic, N; Lelas, D; Lelas, K; Plestina, R; Polic, D; Puljak, I; Antunovic, Z; Dzelalija, M; Brigljevic, V; Duric, S; Kadija, K; Morovic, S; Attikis, A; Galanti, M; Mousa, J; Nicolaou, C; Ptochos, F; Razis, P A; Finger, M; Finger, M; Assran, Y; Khalil, S; Mahmoud, M A; Hektor, A; Kadastik, M; Müntel, M; Raidal, M; Rebane, L; Azzolini, V; Eerola, P; Fedi, G; Czellar, S; Härkönen, J; Heikkinen, A; Karimäki, V; Kinnunen, R; Kortelainen, M J; Lampén, T; Lassila-Perini, K; Lehti, S; Lindén, T; Luukka, P; Mäenpää, T; Tuominen, E; Tuominiemi, J; Tuovinen, E; Ungaro, D; Wendland, L; Banzuzi, K; Korpela, A; Tuuva, T; Sillou, D; Besancon, M; Choudhury, S; Dejardin, M; Denegri, D; Fabbro, B; Faure, J L; Ferri, F; Ganjour, S; Gentit, F X; Givernaud, A; Gras, P; de Monchenault, G Hamel; Jarry, P; Locci, E; Malcles, J; Marionneau, M; Millischer, L; Rander, J; Rosowsky, A; Shreyber, I; Titov, M; Verrecchia, P; Baffioni, S; Beaudette, F; Benhabib, L; Bianchini, L; Bluj, M; Broutin, C; Busson, P; Charlot, C; Dahms, T; Dobrzynski, L; Elgammal, S; de Cassagnac, R Granier; Haguenauer, M; Miné, P; Mironov, C; Ochando, C; Paganini, P; Sabes, D; Salerno, R; Sirois, Y; Thiebaux, C; Wyslouch, B; Zabi, A; Agram, J-L; Andrea, J; Bloch, D; Bodin, D; Brom, J-M; Cardaci, M; Chabert, E C; Collard, C; Conte, E; Drouhin, F; Ferro, C; Fontaine, J-C; Gelé, D; Goerlach, U; Greder, S; Juillot, P; Karim, M; Le Bihan, A-C; Mikami, Y; Van Hove, P; Fassi, F; Mercier, D; Baty, C; Beauceron, S; Beaupere, N; Bedjidian, M; Bondu, O; Boudoul, G; Boumediene, D; Brun, H; Chierici, R; Contardo, D; Depasse, P; El Mamouni, H; Fay, J; Gascon, S; Ille, B; Kurca, T; Le Grand, T; Lethuillier, M; Mirabito, L; Perries, S; Sordini, V; Tosi, S; Tschudi, Y; Verdier, P; Lomidze, D; Anagnostou, G; Edelhoff, M; Feld, L; Heracleous, N; Hindrichs, O; Jussen, R; Klein, K; Merz, J; Mohr, N; Ostapchuk, A; Perieanu, A; Raupach, F; Sammet, J; Schael, S; Sprenger, D; Weber, H; Weber, M; Wittmer, B; Ata, M; Bender, W; Dietz-Laursonn, E; Erdmann, M; Frangenheim, J; Hebbeker, T; Hinzmann, A; Hoepfner, K; Klimkovich, T; Klingebiel, D; Kreuzer, P; Lanske, D; Magass, C; Merschmeyer, M; Meyer, A; Papacz, P; Pieta, H; Reithler, H; Schmitz, S A; Sonnenschein, L; Steggemann, J; Teyssier, D; Tonutti, M; Bontenackels, M; Davids, M; Duda, M; Flügge, G; Geenen, H; Giffels, M; Ahmad, W Haj; Heydhausen, D; Kress, T; Kuessel, Y; Linn, A; Nowack, A; Perchalla, L; Pooth, O; Rennefeld, J; Sauerland, P; Stahl, A; Thomas, M; Tornier, D; Zoeller, M H; Martin, M Aldaya; Behrenhoff, W; Behrens, U; Bergholz, M; Bethani, A; Borras, K; Cakir, A; Campbell, A; Castro, E; Dammann, D; Eckerlin, G; Eckstein, D; Flossdorf, A; Flucke, G; Geiser, A; Hauk, J; Jung, H; Kasemann, M; Katkov, I; Katsas, P; Kleinwort, C; Kluge, H; Knutsson, A; Krämer, M; Krücker, D; Kuznetsova, E; Lange, W; Lohmann, W; Mankel, R; Marienfeld, M; Melzer-Pellmann, I-A; Meyer, A B; Mnich, J; Mussgiller, A; Olzem, J; Pitzl, D; Raspereza, A; Raval, A; Rosin, M; Schmidt, R; Schoerner-Sadenius, T; Sen, N; Spiridonov, A; Stein, M; Tomaszewska, J; Walsh, R; Wissing, C; Autermann, C; Blobel, V; Bobrovskyi, S; Draeger, J; Enderle, H; Gebbert, U; Kaschube, K; Kaussen, G; Klanner, R; Lange, J; Mura, B; Naumann-Emme, S; Nowak, F; Pietsch, N; Sander, C; Schettler, H; Schleper, P; Schröder, M; Schum, T; Schwandt, J; Stadie, H; Steinbrück, G; Thomsen, J; Barth, C; Bauer, J; Buege, V; Chwalek, T; De Boer, W; Dierlamm, A; Dirkes, G; Feindt, M; Gruschke, J; Hackstein, C; Hartmann, F; Heinrich, M; Held, H; Hoffmann, K H; Honc, S; Komaragiri, J R; Kuhr, T; Martschei, D; Mueller, S; Müller, Th; Niegel, M; Oberst, O; Oehler, A; Ott, J; Peiffer, T; Piparo, D; Quast, G; Rabbertz, K; Ratnikov, F; Ratnikova, N; Renz, M; Saout, C; Scheurer, A; Schieferdecker, P; Schilling, F-P; Schmanau, M; Schott, G; Simonis, H J; Stober, F M; Troendle, D; Wagner-Kuhr, J; Weiler, T; Zeise, M; Zhukov, V; Ziebarth, E B; Daskalakis, G; Geralis, T; Karafasoulis, K; Kesisoglou, S; Kyriakis, A; Loukas, D; Manolakos, I; Markou, A; Markou, C; Mavrommatis, C; Ntomari, E; Petrakou, E; Gouskos, L; Mertzimekis, T J; Panagiotou, A; Stiliaris, E; Evangelou, I; Foudas, C; Kokkas, P; Manthos, N; Papadopoulos, I; Patras, V; Triantis, F A; Aranyi, A; Bencze, G; Boldizsar, L; Hajdu, C; Hidas, P; Horvath, D; Kapusi, A; Krajczar, K; Sikler, F; Veres, G I; Vesztergombi, G; Beni, N; Molnar, J; Palinkas, J; Szillasi, Z; Veszpremi, V; Raics, P; Trocsanyi, Z L; Ujvari, B; Bansal, S; Beri, S B; Bhatnagar, V; Dhingra, N; Gupta, R; Jindal, M; Kaur, M; Kohli, J M; Mehta, M Z; Nishu, N; Saini, L K; Sharma, A; Singh, A P; Singh, J B; Singh, S P; Ahuja, S; Bhattacharya, S; Choudhary, B C; Gupta, P; Jain, S; Jain, S; Kumar, A; Ranjan, K; Shivpuri, R K; Choudhury, R K; Dutta, D; Kailas, S; Kumar, V; Mohanty, A K; Pant, L M; Shukla, P; Aziz, T; Guchait, M; Gurtu, A; Maity, M; Majumder, D; Majumder, G; Mazumdar, K; Mohanty, G B; Saha, A; Sudhakar, K; Wickramage, N; Banerjee, S; Dugad, S; Mondal, N K; Arfaei, H; Bakhshiansohi, H; Etesami, S M; Fahim, A; Hashemi, M; Jafari, A; Khakzad, M; Mohammadi, A; Najafabadi, M Mohammadi; Mehdiabadi, S Paktinat; Safarzadeh, B; Zeinali, M; Abbrescia, M; Barbone, L; Calabria, C; Colaleo, A; Creanza, D; De Filippis, N; De Palma, M; Fiore, L; Iaselli, G; Lusito, L; Maggi, G; Maggi, M; Manna, N; Marangelli, B; My, S; Nuzzo, S; Pacifico, N; Pierro, G A; Pompili, A; Pugliese, G; Romano, F; Roselli, G; Selvaggi, G; Silvestris, L; Trentadue, R; Tupputi, S; Zito, G; Abbiendi, G; Benvenuti, A C; Bonacorsi, D; Braibant-Giacomelli, S; Brigliadori, L; Capiluppi, P; Castro, A; Cavallo, F R; Cuffiani, M; Dallavalle, G M; Fabbri, F; Fanfani, A; Fasanella, D; Giacomelli, P; Giunta, M; Marcellini, S; Masetti, G; Meneghelli, M; Montanari, A; Navarria, F L; Odorici, F; Perrotta, A; Primavera, F; Rossi, A M; Rovelli, T; Siroli, G; Travaglini, R; Albergo, S; Cappello, G; Chiorboli, M; Costa, S; Tricomi, A; Tuve, C; Barbagli, G; Ciulli, V; Civinini, C; D'Alessandro, R; Focardi, E; Frosali, S; Gallo, E; Gonzi, S; Lenzi, P; Meschini, M; Paoletti, S; Sguazzoni, G; Tropiano, A; Benussi, L; Bianco, S; Colafranceschi, S; Fabbri, F; Piccolo, D; Fabbricatore, P; Musenich, R; Benaglia, A; De Guio, F; Di Matteo, L; Ghezzi, A; Malvezzi, S; Martelli, A; Massironi, A; Menasce, D; Moroni, L; Paganoni, M; Pedrini, D; Ragazzi, S; Redaelli, N; Sala, S; Tabarelli de Fatis, T; Tancini, V; Buontempo, S; Montoya, C A Carrillo; Cavallo, N; De Cosa, A; Fabozzi, F; Iorio, A O M; Lista, L; Merola, M; Paolucci, P; Azzi, P; Bacchetta, N; Bellan, P; Bisello, D; Branca, A; Carlin, R; Checchia, P; De Mattia, M; Dorigo, T; Dosselli, U; Fanzago, F; Gasparini, F; Gasparini, U; Lacaprara, S; Lazzizzera, I; Margoni, M; Mazzucato, M; Meneguzzo, A T; Nespolo, M; Perrozzi, L; Pozzobon, N; Ronchese, P; Simonetto, F; Torassa, E; Tosi, M; Vanini, S; Zotto, P; Zumerle, G; Baesso, P; Berzano, U; Ratti, S P; Riccardi, C; Torre, P; Vitulo, P; Viviani, C; Biasini, M; Bilei, G M; Caponeri, B; Fanò, L; Lariccia, P; Lucaroni, A; Mantovani, G; Menichelli, M; Nappi, A; Romeo, F; Santocchia, A; Taroni, S; Valdata, M; Azzurri, P; Bagliesi, G; Bernardini, J; Boccali, T; Broccolo, G; Castaldi, R; D'Agnolo, R T; Dell'Orso, R; Fiori, F; Foà, L; Giassi, A; Kraan, A; Ligabue, F; Lomtadze, T; Martini, L; Messineo, A; Palla, F; Segneri, G; Serban, A T; Spagnolo, P; Tenchini, R; Tonelli, G; Venturi, A; Verdini, P G; Barone, L; Cavallari, F; Del Re, D; Di Marco, E; Diemoz, M; Franci, D; Grassi, M; Longo, E; Nourbakhsh, S; Organtini, G; Pandolfi, F; Paramatti, R; Rahatlou, S; Amapane, N; Arcidiacono, R; Argiro, S; Arneodo, M; Biino, C; Botta, C; Cartiglia, N; Castello, R; Costa, M; Demaria, N; Graziano, A; Mariotti, C; Marone, M; Maselli, S; Migliore, E; Mila, G; Monaco, V; Musich, M; Obertino, M M; Pastrone, N; Pelliccioni, M; Romero, A; Ruspa, M; Sacchi, R; Sola, V; Solano, A; Staiano, A; Vilela Pereira, A; Belforte, S; Cossutti, F; Della Ricca, G; Gobbo, B; Montanino, D; Penzo, A; Heo, S G; Nam, S K; Chang, S; Chung, J; Kim, D H; Kim, G N; Kim, J E; Kong, D J; Park, H; Ro, S R; Son, D; Son, D C; Son, T; Kim, Zero; Kim, J Y; Song, S; Choi, S; Hong, B; Jeong, M S; Jo, M; Kim, H; Kim, J H; Kim, T J; Lee, K S; Moon, D H; Park, S K; Rhee, H B; Seo, E; Shin, S; Sim, K S; Choi, M; Kang, S; Kim, H; Park, C; Park, I C; Park, S; Ryu, G; Choi, Y; Choi, Y K; Goh, J; Kim, M S; Kwon, E; Lee, J; Lee, S; Seo, H; Yu, I; Bilinskas, M J; Grigelionis, I; Janulis, M; Martisiute, D; Petrov, P; Sabonis, T; Castilla-Valdez, H; De La Cruz-Burelo, E; Lopez-Fernandez, R; Magaña Villalba, R; Sánchez-Hernández, A; Villasenor-Cendejas, L M; Carrillo Moreno, S; Vazquez Valencia, F; Salazar Ibarguen, H A; Casimiro Linares, E; Morelos Pineda, A; Reyes-Santos, M A; Krofcheck, D; Tam, J; Butler, P H; Doesburg, R; Silverwood, H; Ahmad, M; Ahmed, I; Asghar, M I; Hoorani, H R; Khan, W A; Khurshid, T; Qazi, S; Brona, G; Cwiok, M; Dominik, W; Doroba, K; Kalinowski, A; Konecki, M; Krolikowski, J; Frueboes, T; Gokieli, R; Górski, M; Kazana, M; Nawrocki, K; Romanowska-Rybinska, K; Szleper, M; Wrochna, G; Zalewski, P; Almeida, N; Bargassa, P; David, A; Faccioli, P; Parracho, P G Ferreira; Gallinaro, M; Musella, P; Nayak, A; Ribeiro, P Q; Seixas, J; Varela, J; Afanasiev, S; Belotelov, I; Bunin, P; Golutvin, I; Kamenev, A; Karjavin, V; Kozlov, G; Lanev, A; Moisenz, P; Palichik, V; Perelygin, V; Shmatov, S; Smirnov, V; Volodko, A; Zarubin, A; Golovtsov, V; Ivanov, Y; Kim, V; Levchenko, P; Murzin, V; Oreshkin, V; Smirnov, I; Sulimov, V; Uvarov, L; Vavilov, S; Vorobyev, A; Vorobyev, A; Andreev, Yu; Dermenev, A; Gninenko, S; Golubev, N; Kirsanov, M; Krasnikov, N; Matveev, V; Pashenkov, A; Toropin, A; Troitsky, S; Epshteyn, V; Gavrilov, V; Kaftanov, V; Kossov, M; Krokhotin, A; Lychkovskaya, N; Popov, V; Safronov, G; Semenov, S; Stolin, V; Vlasov, E; Zhokin, A; Boos, E; Dubinin, M; Dudko, L; Ershov, A; Gribushin, A; Kodolova, O; Lokhtin, I; Markina, A; Obraztsov, S; Perfilov, M; Petrushanko, S; Sarycheva, L; Savrin, V; Snigirev, A; Andreev, V; Azarkin, M; Dremin, I; Kirakosyan, M; Leonidov, A; Rusakov, S V; Vinogradov, A; Azhgirey, I; Bitioukov, S; Grishin, V; Kachanov, V; Konstantinov, D; Korablev, A; Krychkine, V; Petrov, V; Ryutin, R; Slabospitsky, S; Sobol, A; Tourtchanovitch, L; Troshin, S; Tyurin, N; Uzunian, A; Volkov, A; Adzic, P; Djordjevic, M; Krpic, D; Milosevic, J; Aguilar-Benitez, M; Alcaraz Maestre, J; Arce, P; Battilana, C; Calvo, E; Cepeda, M; Cerrada, M; Chamizo Llatas, M; Colino, N; De La Cruz, B; Delgado Peris, A; Diez Pardos, C; Domínguez Vázquez, D; Fernandez Bedoya, C; Fernández Ramos, J P; Ferrando, A; Flix, J; Fouz, M C; Garcia-Abia, P; Gonzalez Lopez, O; Goy Lopez, S; Hernandez, J M; Josa, M I; Merino, G; Puerta Pelayo, J; Redondo, I; Romero, L; Santaolalla, J; Soares, M S; Willmott, C; Albajar, C; Codispoti, G; de Trocóniz, J F; Cuevas, J; Fernandez Menendez, J; Folgueras, S; Gonzalez Caballero, I; Lloret Iglesias, L; Vizan Garcia, J M; Brochero Cifuentes, J A; Cabrillo, I J; Calderon, A; Chuang, S H; Duarte Campderros, J; Felcini, M; Fernandez, M; Gomez, G; Gonzalez Sanchez, J; Jorda, C; Lobelle Pardo, P; Lopez Virto, A; Marco, J; Marco, R; Martinez Rivero, C; Matorras, F; Munoz Sanchez, F J; Piedra Gomez, J; Rodrigo, T; Rodríguez-Marrero, A Y; Ruiz-Jimeno, A; Scodellaro, L; Sobron Sanudo, M; Vila, I; Vilar Cortabitarte, R; Abbaneo, D; Auffray, E; Auzinger, G; Baillon, P; Ball, A H; Barney, D; Bell, A J; Benedetti, D; Bernet, C; Bialas, W; Bloch, P; Bocci, A; Bolognesi, S; Bona, M; Breuker, H; Bunkowski, K; Camporesi, T; Cerminara, G; Coarasa Perez, J A; Curé, B; D'Enterria, D; De Roeck, A; Di Guida, S; Elliott-Peisert, A; Frisch, B; Funk, W; Gaddi, A; Gennai, S; Georgiou, G; Gerwig, H; Gigi, D; Gill, K; Giordano, D; Glege, F; Garrido, R Gomez-Reino; Gouzevitch, M; Govoni, P; Gowdy, S; Guiducci, L; Hansen, M; Hartl, C; Harvey, J; Hegeman, J; Hegner, B; Hoffmann, H F; Honma, A; Innocente, V; Janot, P; Kaadze, K; Karavakis, E; Lecoq, P; Lourenço, C; Mäki, T; Malberti, M; Malgeri, L; Mannelli, M; Masetti, L; Maurisset, A; Meijers, F; Mersi, S; Meschi, E; Moser, R; Mozer, M U; Mulders, M; Nesvold, E; Nguyen, M; Orimoto, T; Orsini, L; Perez, E; Petrilli, A; Pfeiffer, A; Pierini, M; Pimiä, M; Polese, G; Racz, A; Antunes, J Rodrigues; Rolandi, G; Rommerskirchen, T; Rovelli, C; Rovere, M; Sakulin, H; Schäfer, C; Schwick, C; Segoni, I; Sharma, A; Siegrist, P; Simon, M; Sphicas, P; Spiropulu, M; Stoye, M; Tropea, P; Tsirou, A; Vichoudis, P; Voutilainen, M; Zeuner, W D; Bertl, W; Deiters, K; Erdmann, W; Gabathuler, K; Horisberger, R; Ingram, Q; Kaestli, H C; König, S; Kotlinski, D; Langenegger, U; Meier, F; Renker, D; Rohe, T; Sibille, J; Starodumov, A; Bortignon, P; Caminada, L; Chanon, N; Chen, Z; Cittolin, S; Dissertori, G; Dittmar, M; Eugster, J; Freudenreich, K; Grab, C; Hervé, A; Hintz, W; Lecomte, P; Lustermann, W; Marchica, C; Del Arbol, P Martinez Ruiz; Meridiani, P; Milenovic, P; Moortgat, F; Nägeli, C; Nef, P; Nessi-Tedaldi, F; Pape, L; Pauss, F; Punz, T; Rizzi, A; Ronga, F J; Rossini, M; Sala, L; Sanchez, A K; Sawley, M-C; Stieger, B; Tauscher, L; Thea, A; Theofilatos, K; Treille, D; Urscheler, C; Wallny, R; Weber, M; Wehrli, L; Weng, J; Aguiló, E; Amsler, C; Chiochia, V; De Visscher, S; Favaro, C; Rikova, M Ivova; Mejias, B Millan; Otiougova, P; Regenfus, C; Robmann, P; Schmidt, A; Snoek, H; Chang, Y H; Chen, K H; Kuo, C M; Li, S W; Lin, W; Liu, Z K; Lu, Y J; Mekterovic, D; Volpe, R; Wu, J H; Yu, S S; Bartalini, P; Chang, P; Chang, Y H; Chang, Y W; Chao, Y; Chen, K F; Hou, W-S; Hsiung, Y; Kao, K Y; Lei, Y J; Lu, R-S; Shiu, J G; Tzeng, Y M; Wang, M; Adiguzel, A; Bakirci, M N; Cerci, S; Dozen, C; Dumanoglu, I; Eskut, E; Girgis, S; Gokbulut, G; Guler, Y; Gurpinar, E; Hos, I; Kangal, E E; Karaman, T; Topaksu, A Kayis; Nart, A; Onengut, G; Ozdemir, K; Ozturk, S; Polatoz, A; Sogut, K; Cerci, D Sunar; Tali, B; Topakli, H; Uzun, D; Vergili, L N; Vergili, M; Zorbilmez, C; Akin, I V; Aliev, T; Bilmis, S; Deniz, M; Gamsizkan, H; Guler, A M; Ocalan, K; Ozpineci, A; Serin, M; Sever, R; Surat, U E; Yildirim, E; Zeyrek, M; Deliomeroglu, M; Demir, D; Gülmez, E; Isildak, B; Kaya, M; Kaya, O; Ozkorucuklu, S; Sonmez, N; Levchuk, L; Bostock, F; Brooke, J J; Cheng, T L; Clement, E; Cussans, D; Frazier, R; Goldstein, J; Grimes, M; Hansen, M; Hartley, D; Heath, G P; Heath, H F; Jackson, J; Kreczko, L; Metson, S; Newbold, D M; Nirunpong, K; Poll, A; Senkin, S; Smith, V J; Ward, S; Basso, L; Bell, K W; Belyaev, A; Brew, C; Brown, R M; Camanzi, B; Cockerill, D J A; Coughlan, J A; Harder, K; Harper, S; Kennedy, B W; Olaiya, E; Petyt, D; Radburn-Smith, B C; Shepherd-Themistocleous, C H; Tomalin, I R; Womersley, W J; Worm, S D; Bainbridge, R; Ball, G; Ballin, J; Beuselinck, R; Buchmuller, O; Colling, D; Cripps, N; Cutajar, M; Davies, G; Della Negra, M; Ferguson, W; Fulcher, J; Futyan, D; Gilbert, A; Bryer, A Guneratne; Hall, G; Hatherell, Z; Hays, J; Iles, G; Jarvis, M; Karapostoli, G; Lyons, L; Macevoy, B C; Magnan, A-M; Marrouche, J; Mathias, B; Nandi, R; Nash, J; Nikitenko, A; Papageorgiou, A; Pesaresi, M; Petridis, K; Pioppi, M; Raymond, D M; Rogerson, S; Rompotis, N; Rose, A; Ryan, M J; Seez, C; Sharp, P; Sparrow, A; Tapper, A; Tourneur, S; Acosta, M Vazquez; Virdee, T; Wakefield, S; Wardle, N; Wardrope, D; Whyntie, T; Barrett, M; Chadwick, M; Cole, J E; Hobson, P R; Khan, A; Kyberd, P; Leslie, D; Martin, W; Reid, I D; Teodorescu, L; Hatakeyama, K; Bose, T; Jarrin, E Carrera; Fantasia, C; Heister, A; St John, J; Lawson, P; Lazic, D; Rohlf, J; Sperka, D; Sulak, L; Avetisyan, A; Bhattacharya, S; Chou, J P; Cutts, D; Ferapontov, A; Heintz, U; Jabeen, S; Kukartsev, G; Landsberg, G; Narain, M; Nguyen, D; Segala, M; Sinthuprasith, T; Speer, T; Tsang, K V; Breedon, R; Sanchez, M Calderon De La Barca; Chauhan, S; Chertok, M; Conway, J; Cox, P T; Dolen, J; Erbacher, R; Friis, E; Ko, W; Kopecky, A; Lander, R; Liu, H; Maruyama, S; Miceli, T; Nikolic, M; Pellett, D; Robles, J; Salur, S; Schwarz, T; Searle, M; Smith, J; Squires, M; Tripathi, M; Sierra, R Vasquez; Veelken, C; Andreev, V; Arisaka, K; Cline, D; Cousins, R; Deisher, A; Duris, J; Erhan, S; Farrell, C; Hauser, J; Ignatenko, M; Jarvis, C; Plager, C; Rakness, G; Schlein, P; Tucker, J; Valuev, V; Babb, J; Chandra, A; Clare, R; Ellison, J; Gary, J W; Giordano, F; Hanson, G; Jeng, G Y; Kao, S C; Liu, F; Liu, H; Long, O R; Luthra, A; Nguyen, H; Shen, B C; Stringer, R; Sturdy, J; Sumowidagdo, S; Wilken, R; Wimpenny, S; Andrews, W; Branson, J G; Cerati, G B; Dusinberre, E; Evans, D; Golf, F; Holzner, A; Kelley, R; Lebourgeois, M; Letts, J; Mangano, B; Padhi, S; Palmer, C; Petrucciani, G; Pi, H; Pieri, M; Ranieri, R; Sani, M; Sharma, V; Simon, S; Tu, Y; Vartak, A; Wasserbaech, S; Würthwein, F; Yagil, A; Yoo, J; Barge, D; Bellan, R; Campagnari, C; D'Alfonso, M; Danielson, T; Flowers, K; Geffert, P; Incandela, J; Justus, C; Kalavase, P; Koay, S A; Kovalskyi, D; Krutelyov, V; Lowette, S; McColl, N; Pavlunin, V; Rebassoo, F; Ribnik, J; Richman, J; Rossin, R; Stuart, D; To, W; Vlimant, J R; Apresyan, A; Bornheim, A; Bunn, J; Chen, Y; Gataullin, M; Ma, Y; Mott, A; Newman, H B; Rogan, C; Shin, K; Timciuc, V; Traczyk, P; Veverka, J; Wilkinson, R; Yang, Y; Zhu, R Y; Akgun, B; Carroll, R; Ferguson, T; Iiyama, Y; Jang, D W; Jun, S Y; Liu, Y F; Paulini, M; Russ, J; Vogel, H; Vorobiev, I; Cumalat, J P; Dinardo, M E; Drell, B R; Edelmaier, C J; Ford, W T; Gaz, A; Heyburn, B; Lopez, E Luiggi; Nauenberg, U; Smith, J G; Stenson, K; Ulmer, K A; Wagner, S R; Zang, S L; Agostino, L; Alexander, J; Cassel, D; Chatterjee, A; Das, S; Eggert, N; Gibbons, L K; Heltsley, B; Hopkins, W; Khukhunaishvili, A; Kreis, B; Kaufman, G Nicolas; Patterson, J R; Puigh, D; Ryd, A; Salvati, E; Shi, X; Sun, W; Teo, W D; Thom, J; Thompson, J; Vaughan, J; Weng, Y; Winstrom, L; Wittich, P; Biselli, A; Cirino, G; Winn, D; Abdullin, S; Albrow, M; Anderson, J; Apollinari, G; Atac, M; Bakken, J A; Banerjee, S; Bauerdick, L A T; Beretvas, A; Berryhill, J; Bhat, P C; Bloch, I; Borcherding, F; Burkett, K; Butler, J N; Chetluru, V; Cheung, H W K; Chlebana, F; Cihangir, S; Cooper, W; Eartly, D P; Elvira, V D; Esen, S; Fisk, I; Freeman, J; Gao, Y; Gottschalk, E; Green, D; Gunthoti, K; Gutsche, O; Hanlon, J; Harris, R M; Hirschauer, J; Hooberman, B; Jensen, H; Johnson, M; Joshi, U; Khatiwada, R; Klima, B; Kousouris, K; Kunori, S; Kwan, S; Leonidopoulos, C; Limon, P; Lincoln, D; Lipton, R; Lykken, J; Maeshima, K; Marraffino, J M; Mason, D; McBride, P; Miao, T; Mishra, K; Mrenna, S; Musienko, Y; Newman-Holmes, C; O'Dell, V; Pordes, R; Prokofyev, O; Saoulidou, N; Sexton-Kennedy, E; Sharma, S; Spalding, W J; Spiegel, L; Tan, P; Taylor, L; Tkaczyk, S; Uplegger, L; Vaandering, E W; Vidal, R; Whitmore, J; Wu, W; Yang, F; Yumiceva, F; Yun, J C; Acosta, D; Avery, P; Bourilkov, D; Chen, M; De Gruttola, M; Di Giovanni, G P; Dobur, D; Drozdetskiy, A; Field, R D; Fisher, M; Fu, Y; Furic, I K; Gartner, J; Kim, B; Konigsberg, J; Korytov, A; Kropivnitskaya, A; Kypreos, T; Matchev, K; Mitselmakher, G; Muniz, L; Prescott, C; Remington, R; Schmitt, M; Scurlock, B; Sellers, P; Skhirtladze, N; Snowball, M; Wang, D; Yelton, J; Zakaria, M; Ceron, C; Gaultney, V; Kramer, L; Lebolo, L M; Linn, S; Markowitz, P; Martinez, G; Mesa, D; Rodriguez, J L; Adams, T; Askew, A; Bandurin, D; Bochenek, J; Chen, J; Diamond, B; Gleyzer, S V; Haas, J; Hagopian, S; Hagopian, V; Jenkins, M; Johnson, K F; Prosper, H; Quertenmont, L; Sekmen, S; Veeraraghavan, V; Baarmand, M M; Dorney, B; Guragain, S; Hohlmann, M; Kalakhety, H; Ralich, R; Vodopiyanov, I; Adams, M R; Anghel, I M; Apanasevich, L; Bai, Y; Bazterra, V E; Betts, R R; Callner, J; Cavanaugh, R; Dragoiu, C; Gauthier, L; Gerber, C E; Hofman, D J; Khalatyan, S; Kunde, G J; Lacroix, F; Malek, M; O'Brien, C; Silvestre, C; Smoron, A; Strom, D; Varelas, N; Akgun, U; Albayrak, E A; Bilki, B; Clarida, W; Duru, F; Lae, C K; McCliment, E; Merlo, J-P; Mermerkaya, H; Mestvirishvili, A; Moeller, A; Nachtman, J; Newsom, C R; Norbeck, E; Olson, J; Onel, Y; Ozok, F; Sen, S; Wetzel, J; Yetkin, T; Yi, K; Barnett, B A; Blumenfeld, B; Bonato, A; Eskew, C; Fehling, D; Giurgiu, G; Gritsan, A V; Guo, Z J; Hu, G; Maksimovic, P; Rappoccio, S; Swartz, M; Tran, N V; Whitbeck, A; Baringer, P; Bean, A; Benelli, G; Grachov, O; Kenny Iii, R P; Murray, M; Noonan, D; Sanders, S; Wood, J S; Zhukova, V; Barfuss, A F; Bolton, T; Chakaberia, I; Ivanov, A; Khalil, S; Makouski, M; Maravin, Y; Shrestha, S; Svintradze, I; Wan, Z; Gronberg, J; Lange, D; Wright, D; Baden, A; Boutemeur, M; Eno, S C; Ferencek, D; Gomez, J A; Hadley, N J; Kellogg, R G; Kirn, M; Lu, Y; Mignerey, A C; Rossato, K; Rumerio, P; Santanastasio, F; Skuja, A; Temple, J; Tonjes, M B; Tonwar, S C; Twedt, E; Alver, B; Bauer, G; Bendavid, J; Busza, W; Butz, E; Cali, I A; Chan, M; Dutta, V; Everaerts, P; Ceballos, G Gomez; Goncharov, M; Hahn, K A; Harris, P; Kim, Y; Klute, M; Lee, Y-J; Li, W; Loizides, C; Luckey, P D; Ma, T; Nahn, S; Paus, C; Ralph, D; Roland, C; Roland, G; Rudolph, M; Stephans, G S F; Stöckli, F; Sumorok, K; Sung, K; Wenger, E A; Xie, S; Yang, M; Yilmaz, Y; Yoon, A S; Zanetti, M; Cooper, S I; Cushman, P; Dahmes, B; De Benedetti, A; Dudero, P R; Franzoni, G; Haupt, J; Klapoetke, K; Kubota, Y; Mans, J; Rekovic, V; Rusack, R; Sasseville, M; Singovsky, A; Cremaldi, L M; Godang, R; Kroeger, R; Perera, L; Rahmat, R; Sanders, D A; Summers, D; Bloom, K; Bose, S; Butt, J; Claes, D R; Dominguez, A; Eads, M; Keller, J; Kelly, T; Kravchenko, I; Lazo-Flores, J; Malbouisson, H; Malik, S; Snow, G R; Baur, U; Godshalk, A; Iashvili, I; Jain, S; Kharchilava, A; Kumar, A; Shipkowski, S P; Smith, K; Alverson, G; Barberis, E; Baumgartel, D; Boeriu, O; Chasco, M; Reucroft, S; Swain, J; Trocino, D; Wood, D; Zhang, J; Anastassov, A; Kubik, A; Odell, N; Ofierzynski, R A; Pollack, B; Pozdnyakov, A; Schmitt, M; Stoynev, S; Velasco, M; Won, S; Antonelli, L; Berry, D; Hildreth, M; Jessop, C; Karmgard, D J; Kolb, J; Kolberg, T; Lannon, K; Luo, W; Lynch, S; Marinelli, N; Morse, D M; Pearson, T; Ruchti, R; Slaunwhite, J; Valls, N; Wayne, M; Ziegler, J; Bylsma, B; Durkin, L S; Gu, J; Hill, C; Killewald, P; Kotov, K; Ling, T Y; Rodenburg, M; Williams, G; Adam, N; Berry, E; Elmer, P; Gerbaudo, D; Halyo, V; Hebda, P; Hunt, A; Jones, J; Laird, E; Pegna, D Lopes; Marlow, D; Medvedeva, T; Mooney, M; Olsen, J; Piroué, P; Quan, X; Saka, H; Stickland, D; Tully, C; Werner, J S; Zuranski, A; Acosta, J G; Huang, X T; Lopez, A; Mendez, H; Oliveros, S; Vargas, J E Ramirez; Zatserklyaniy, A; Alagoz, E; Barnes, V E; Bolla, G; Borrello, L; Bortoletto, D; Everett, A; Garfinkel, A F; Gutay, L; Hu, Z; Jones, M; Koybasi, O; Kress, M; Laasanen, A T; Leonardo, N; Liu, C; Maroussov, V; Merkel, P; Miller, D H; Neumeister, N; Shipsey, I; Silvers, D; Svyatkovskiy, A; Yoo, H D; Zablocki, J; Zheng, Y; Jindal, P; Parashar, N; Boulahouache, C; Cuplov, V; Ecklund, K M; Geurts, F J M; Padley, B P; Redjimi, R; Roberts, J; Zabel, J; Betchart, B; Bodek, A; Chung, Y S; Covarelli, R; de Barbaro, P; Demina, R; Eshaq, Y; Flacher, H; Garcia-Bellido, A; Goldenzweig, P; Gotra, Y; Han, J; Harel, A; Miner, D C; Orbaker, D; Petrillo, G; Vishnevskiy, D; Zielinski, M; Bhatti, A; Ciesielski, R; Demortier, L; Goulianos, K; Lungu, G; Malik, S; Mesropian, C; Yan, M; Atramentov, O; Barker, A; Duggan, D; Gershtein, Y; Gray, R; Halkiadakis, E; Hidas, D; Hits, D; Lath, A; Panwalkar, S; Patel, R; Richards, A; Rose, K; Schnetzer, S; Somalwar, S; Stone, R; Thomas, S; Cerizza, G; Hollingsworth, M; Spanier, S; Yang, Z C; York, A; Asaadi, J; Eusebi, R; Gilmore, J; Gurrola, A; Kamon, T; Khotilovich, V; Montalvo, R; Nguyen, C N; Osipenkov, I; Pakhotin, Y; Pivarski, J; Safonov, A; Sengupta, S; Tatarinov, A; Toback, D; Weinberger, M; Akchurin, N; Bardak, C; Damgov, J; Jeong, C; Kovitanggoon, K; Lee, S W; Roh, Y; Sill, A; Volobouev, I; Wigmans, R; Yazgan, E; Appelt, E; Brownson, E; Engh, D; Florez, C; Gabella, W; Issah, M; Johns, W; Kurt, P; Maguire, C; Melo, A; Sheldon, P; Snook, B; Tuo, S; Velkovska, J; Arenton, M W; Balazs, M; Boutle, S; Cox, B; Francis, B; Hirosky, R; Ledovskoy, A; Lin, C; Neu, C; Yohay, R; Gollapinni, S; Harr, R; Karchin, P E; Lamichhane, P; Mattson, M; Milstène, C; Sakharov, A; Anderson, M; Bachtis, M; Bellinger, J N; Carlsmith, D; Dasu, S; Efron, J; Flood, K; Gray, L; Grogg, K S; Grothe, M; Hall-Wilton, R; Herndon, M; Klabbers, P; Klukas, J; Lanaro, A; Lazaridis, C; Leonard, J; Loveless, R; Mohapatra, A; Palmonari, F; Reeder, D; Ross, I; Savin, A; Smith, W H; Swanson, J; Weinberg, M 2011-06-10 A search for neutral minimal supersymmetric standard model (MSSM) Higgs bosons in pp collisions at the LHC at a center-of-mass energy of 7 TeV is presented. The results are based on a data sample corresponding to an integrated luminosity of 36 pb(-1) recorded by the CMS experiment. The search uses decays of the Higgs bosons to tau pairs. No excess is observed in the tau-pair invariant-mass spectrum. The resulting upper limits on the Higgs boson production cross section times branching fraction to tau pairs, as a function of the pseudoscalar Higgs boson mass, yield stringent new bounds in the MSSM parameter space. 2. Search for Higgs bosons of the minimal supersymmetric standard model in p(bar p) collisions at √s = 1.96 TeV International Nuclear Information System (INIS) 2012-01-01 We report results from searches for neutral Higgs bosons produced in p(bar p) collisions recorded by the D0 experiment at the Fermilab Tevatron Collider. We study the production of inclusive neutral Higgs boson in the ττ final state and in association with a b quark in the bττ and bbb final states. These results are combined to improve the sensitivity to the production of neutral Higgs bosons in the context of the minimal supersymmetric standard model (MSSM). The data are found to be consistent with expectation from background processes. Upper limits on MSSM Higgs boson production are set for Higgs boson masses ranging from 90 to 300 GeV. We exclude tan β > 20-30 for Higgs boson masses below 180 GeV. These are the most stringent constraints on MSSM Higgs boson production in p(bar p) collisions. 3. Precise measurement of the left-right cross section asymmetry in Z boson production by electron-positron collisions International Nuclear Information System (INIS) Frey, R.E. 1994-03-01 A precise measurement of the left-right cross section asymmetry (A LR ) for Z boson production by e + e - collisions has been attained at the Slac Linear Collider with the SLD detector. We describe this measurement for the 1993 data run, emphasizing the significant improvements in polarized beam operation which took place for this run, where the luminosity-weighted electron beam polarization averaged 62.6 ± 1.2 %. Preliminary 1993 results for A LR are presented. When combined with the (less precise) 1992 result, the preliminary result for the effective weak mixing angle is sin 2 θ W eff = 0.2290 ± 0.0010 4. Klf8 regulates left-right asymmetric patterning through modulation of Kupffer's vesicle morphogenesis and spaw expression. Science.gov (United States) Lin, Che-Yi; Tsai, Ming-Yuan; Liu, Yu-Hsiu; Lu, Yu-Fen; Chen, Yi-Chung; Lai, Yun-Ren; Liao, Hsin-Chi; Lien, Huang-Wei; Yang, Chung-Hsiang; Huang, Chang-Jen; Hwang, Sheng-Ping L 2017-07-17 Although vertebrates are bilaterally symmetric organisms, their internal organs are distributed asymmetrically along a left-right axis. Disruption of left-right axis asymmetric patterning often occurs in human genetic disorders. In zebrafish embryos, Kupffer's vesicle, like the mouse node, breaks symmetry by inducing asymmetric expression of the Nodal-related gene, spaw, in the left lateral plate mesoderm (LPM). Spaw then stimulates transcription of itself and downstream genes, including lft1, lft2, and pitx2, specifically in the left side of the diencephalon, heart and LPM. This developmental step is essential to establish subsequent asymmetric organ positioning. In this study, we evaluated the role of krüppel-like factor 8 (klf8) in regulating left-right asymmetric patterning in zebrafish embryos. Zebrafish klf8 expression was disrupted by both morpholino antisense oligomer-mediated knockdown and a CRISPR-Cas9 system. Whole-mount in situ hybridization was conducted to evaluate gene expression patterns of Nodal signalling components and the positions of heart and visceral organs. Dorsal forerunner cell number was evaluated in Tg(sox17:gfp) embryos and the length and number of cilia in Kupffer's vesicle were analyzed by immunocytochemistry using an acetylated tubulin antibody. Heart jogging, looping and visceral organ positioning were all defective in zebrafish klf8 morphants. At the 18-22 s stages, klf8 morphants showed reduced expression of genes encoding Nodal signalling components (spaw, lft1, lft2, and pitx2) in the left LPM, diencephalon, and heart. Co-injection of klf8 mRNA with klf8 morpholino partially rescued spaw expression. Furthermore, klf8 but not klf8△zf overexpressing embryos showed dysregulated bilateral expression of Nodal signalling components at late somite stages. At the 10s stage, klf8 morphants exhibited reductions in length and number of cilia in Kupffer's vesicle, while at 75% epiboly, fewer dorsal forerunner cells were observed 5. Measurement of the left-right forward-backward asymmetry for charm quarks with D+ and D+ mesons International Nuclear Information System (INIS) Abe, K.; Abt, I.; Ahn, C.J.; Akagi, T.; Allen, N.J.; Ash, W.W.; Aston, D.; Baird, K.G.; Baltay, C.; Band, H.R.; Barakat, M.B.; Baranko, G.; Bardon, O.; Barklow, T.; Bazarko, A.O.; Ben-David, R.; Benvenuti, A.C.; Bienz, T.; Bilei, G.M.; Bisello, D.; Blaylock, G.; Bogart, J.R.; Bolton, T.; Bower, G.R.; Brau, J.E.; Breidenbach, M.; Bugg, W.M.; Burke, D.; Burnett, T.H.; Burrows, P.N.; Busza, W.; Calcaterra, A.; Caldwell, D.O.; Calloway, D.; Camanzi, B.; Carpinelli, M.; Cassell, R.; Castaldi, R.; Castro, A.; Cavalli-Sforza, M.; Church, E.; Cohn, H.O.; Coller, J.A.; Cook, V.; Cotton, R.; Cowan, R.F.; Coyne, D.G.; D'Oliveira, A.; Damerell, C.J.S.; Daoudi, M.; De Sangro, R.; De Simone, P.; Dell'Orso, R.; Dima, M.; Du, P.Y.C.; Dubois, R.; Eisenstein, B.I.; Elia, R.; Falciai, D.; Fan, C.; Fero, M.J.; Frey, R.; Furuno, K.; Gillman, T.; Gladding, G.; Gonzalez, S.; Hallewell, G.D.; Hart, E.L.; Hasegawa, Y.; Hedges, S.; Hertzbach, S.S.; Hildreth, M.D.; Huber, J.; Huffer, M.E.; Hughes, E.W.; Hwang, H.; Iwasaki, Y.; Jackson, D.J.; Jacques, P.; Jaros, J.; Johnson, A.S.; Johnson, J.R.; Johnson, R.A.; Junk, T.; Kajikawa, R.; Kalelkar, M.; Karliner, I.; Kawahara, H.; Kendall, H.W.; Kim, Y.; King, M.E.; King, R.; Kofler, R.R.; Krishna, N.M.; Kroeger, R.S.; Labs, J.F.; Langston, M.; Lath, A.; Lauber, J.A.; Leith, D.W.G.; Liu, X.; Loreti, M.; Lu, A.; Lynch, H.L.; Ma, J.; Mancinelli, G.; Manly, S.; Mantovani, G.; Markiewicz, T.W.; Maruyama, T.; Massetti, R.; Masuda, H.; Mazzucato, E.; McKemey, A.K.; Meadows, B.T.; Messner, R.; Mockett, P.M.; Moffeit, K.C.; Mours, B.; Mueller, G.; Muller, D.; Nagamine, T.; Nauenberg, U.; Neal, H.; Nussbaum, M.; Ohnishi, Y.; Osborne, L.S.; Panvini, R.S.; Park, H.; Pavel, T.J.; Peruzzi, I.; Piccolo, M.; Piemontese, L.; Pieroni, E.; Pitts, K.T.; Plano, R.J.; Prepost, R.; Prescott, C.Y.; Punkar, G.D.; Quigley, J.; Ratcliff, B.N.; Reeves, T.W.; Rensing, P.E.; Rochester, L.S.; Rothberg, J.E.; Rowson, P.C.; Russell, J.J.; Saxton, O.H.; Schalk, T. 1995-01-01 We present a direct measurement of A c =2v c a c /(v 2 c +a 2 c ) from the left-right forward-backward asymmetry of D + and D + mesons in Z 0 events produced with the longitudinally polarized SLAC Linear Collider beam. These Z 0 →c over bar events are tagged on the basis of event kinematics and decay topology from a sample of hadronic Z 0 decays recorded by the SLAC Large Detector. We measure A 0 c = 0.73 ± 0.22(stat) ± 0.10(syst). copyright 1995 The American Physical Society 6. A Wnt5 Activity Asymmetry and Intercellular Signaling via PCP Proteins Polarize Node Cells for Left-Right Symmetry Breaking. Science.gov (United States) Minegishi, Katsura; Hashimoto, Masakazu; Ajima, Rieko; Takaoka, Katsuyoshi; Shinohara, Kyosuke; Ikawa, Yayoi; Nishimura, Hiromi; McMahon, Andrew P; Willert, Karl; Okada, Yasushi; Sasaki, Hiroshi; Shi, Dongbo; Fujimori, Toshihiko; Ohtsuka, Toshihisa; Igarashi, Yasunobu; Yamaguchi, Terry P; Shimono, Akihiko; Shiratori, Hidetaka; Hamada, Hiroshi 2017-03-13 Polarization of node cells along the anterior-posterior axis of mouse embryos is responsible for left-right symmetry breaking. How node cells become polarized has remained unknown, however. Wnt5a and Wnt5b are expressed posteriorly relative to the node, whereas genes for Sfrp inhibitors of Wnt signaling are expressed anteriorly. Here we show that polarization of node cells is impaired in Wnt5a -/- Wnt5b -/- and Sfrp mutant embryos, and also in the presence of a uniform distribution of Wnt5a or Sfrp1, suggesting that Wnt5 and Sfrp proteins act as instructive signals in this process. The absence of planar cell polarity (PCP) core proteins Prickle1 and Prickle2 in individual cells or local forced expression of Wnt5a perturbed polarization of neighboring wild-type cells. Our results suggest that opposing gradients of Wnt5a and Wnt5b and of their Sfrp inhibitors, together with intercellular signaling via PCP proteins, polarize node cells along the anterior-posterior axis for breaking of left-right symmetry. Copyright © 2017 Elsevier Inc. All rights reserved. 7. Embryonic left-right separation mechanism allows confinement of mutation-induced phenotypes to one lateral body half of bilaterians. Science.gov (United States) Ma, Kun 2013-12-01 A fundamental question in developmental biology is how a chimeric animal such as a bilateral gynandromorphic animal can have different phenotypes confined to different lateral body halves, and how mutation-induced phenotypes, such as genetic diseases, can be confined to one lateral body half in patients. Here, I propose that embryos of many, if not all, bilaterian animals are divided into left and right halves at a very early stage (which may vary among different types of animals), after which the descendants of the left-sided and right-sided cells will almost exclusively remain on their original sides, respectively, throughout the remaining development. This embryonic left-right separation mechanism allows (1) mutations and the mutation-induced phenotypes to be strictly confined to one lateral body half in animals and humans; (2) mothers with bilateral hereditary primary breast cancer to transmit their disease to their offspring at twofold of the rate compared to mothers with unilateral hereditary breast cancer; and (3) a mosaic embryo carrying genetic or epigenetic mutations to develop into either an individual with the mutation-induced phenotype confined unilaterally, or a pair of twins displaying complete, partial, or mirror-image discordance for the phenotype. Further, this left-right separation mechanism predicts that the two lateral halves of a patient carrying a unilateral genetic disease can each serve as a case and an internal control, respectively, for genetic and epigenetic comparative studies to identify the disease causations. © 2013 Wiley Periodicals, Inc. 8. Supersymmetric reciprocal transformation and its applications International Nuclear Information System (INIS) Liu, Q. P.; Popowicz, Ziemowit; Tian Kai 2010-01-01 The supersymmetric analog of the reciprocal transformation is introduced. This is used to establish a transformation between one of the supersymmetric Harry Dym equations and the supersymmetric modified Korteweg-de Vries equation. The reciprocal transformation, as a Baecklund-type transformation between these two equations, is adopted to construct a recursion operator for the supersymmetric Harry Dym equation. By proper factorization of the recursion operator, a bi-Hamiltonian structure is found for the supersymmetric Harry Dym equation. Furthermore, a supersymmetric Kawamoto equation is proposed and is associated with the supersymmetric Sawada-Kotera equation. The recursion operator and odd bi-Hamiltonian structure of the supersymmetric Kawamoto equation are also constructed. 9. A new supersymmetric index International Nuclear Information System (INIS) Cecotti, S.; Fendley, P.; Intriligator, K.; Vafa, C. 1992-01-01 We show that Tr(-1) F F e -βH is an index for N = 2 supersymmetric theories in two dimensions, in the sense that it is independent of almost all deformations of the theory. This index is related to the geometry of the vacua (Berry's curvature) and satisfies an exact differential equation as a function of β. For integrable theories we can also compute the index thermodynamically, using the exact S-matrix. The equivalence of these two results implies a highly non-trivial equivalence of a set of coupled integral equations with these differential equations, among them Painleve III and the affine Toda equations. (orig.) 10. Supersymmetric inflation: Recent progress International Nuclear Information System (INIS) Ovrut, B.A.; Steinhardt, P.J. 1986-01-01 The new inflationary universe scenario is, in principle, a simple and powerful approach to resolving a large number of fundamental cosmological problems. However, in order for the scenario to be considered a complete theory, one critical question remains to be answered: What is the physics responsible for the phase transition that triggers the exponential expansion (inflation) of the universe? One possibility that the authors and several other groups have been pursuing is that the physics responsible for the phase transition involves (local) supersymmetry. The goal of this paper is to review the present status of ''Supersymmetric Inflation'', particularly emphasizing some very exciting results that they recently obtained 11. Supersymmetric Extension of Technicolor & Fermion Mass Generation DEFF Research Database (Denmark) Antola, Matti; Di Chiara, Stefano; Sannino, Francesco 2012-01-01 We provide a complete extension of Minimal Walking Technicolor able to account for the standard model fermion masses. The model is supersymmetric at energies greater or equal to the technicolor compositeness scale. We integrate out, at the supersymmetry breaking scale, the elementary Higgses. We...... tests and experimental bounds on the mass spectrum. We then turn to the composite Higgs phenomenology at the LHC and show that current data are already constraining the parameter space of the model.... 12. Small numbers in supersymmetric theories of nature International Nuclear Information System (INIS) Graesser, Michael L. 1999-01-01 The Standard Model of particle interactions is a successful theory for describing the interactions of quarks, leptons and gauge bosons at microscopic distance scales. Despite these successes, the theory contains many unsatisfactory features. The origin of particle masses is a central mystery that has eluded experimental elucidation. In the Standard Model the known particles obtain their mass from the condensate of the so-called Higgs particle. Quantum corrections to the Higgs mass require an unnatural fine tuning in the Higgs mass of one part in 10 -32 to obtain the correct mass scale of electroweak physics. In addition, the origin of the vast hierarchy between the mass scales of the electroweak and quantum gravity physics is not explained in the current theory. Supersymmetric extensions to the Standard Model are not plagued by this fine tuning issue and may therefore be relevant in Nature. In the minimal supersymmetric Standard Model there is also a natural explanation for electroweak symmetry breaking. Supersymmetric Grand Unified Theories also correctly predict a parameter of the Standard Model. This provides non-trivial indirect evidence for these theories. The most general supersymmetric extension to the Standard Model however, is excluded by many physical processes, such as rare flavor changing processes, and the non-observation of the instability of the proton. These processes provide important information about the possible structure such a theory. In particular, certain parameters in this theory must be rather small. A physics explanation for why this is the case would be desirable. It is striking that the gauge couplings of the Standard Model unify if there is supersymmetry close to the weak scale. This suggests that at high energies Nature is described by a supersymmetric Grand Unified Theory. But the mass scale of unification must be introduced into the theory since it does not coincide with the probable mass scale of strong quantum gravity. The subject 13. Supersymmetric hadronic mechanics and procedures for isosupersymmetrization International Nuclear Information System (INIS) Ntibashirakandi, L.; Callebaut, D.K. 1994-01-01 In this paper the authors present the Lie-Santilli lifting of Witten's one-dimensional supersymmetric quantum mechanical model within the context of supersymmetric hadronic mechanics and extended it to three dimensions. They show that the model describes the motion of a spin one-half particle in a central isosuperpotential. Choosing this isosuperpotential within the specific isosupersymmetrization procedure, their theory produces the model of hadronic harmonic oscillator plus isotopic spin-orbit couplings. They finally indicate that their model describes a particle under conventional potentials plus nonlocal-nonhamiltonian corrections expected in deep penetrations of the wavepackets. As such, the model appears to be significant for the recently proposed chemical synthesis of unstable hadrons via lighter hadrons, which is prohibited by quantum mechanics, but permitted by the covering hadronic mechanics. 16 refs 14. Vacuum fluctuations of the supersymmetric field in curved background International Nuclear Information System (INIS) Bilić, Neven; Domazet, Silvije; Guberina, Branko 2012-01-01 We study a supersymmetric model in curved background spacetime. We calculate the effective action and the vacuum expectation value of the energy momentum tensor using a covariant regularization procedure. A soft supersymmetry breaking induces a nonzero contribution to the vacuum energy density and pressure. Assuming the presence of a cosmic fluid in addition to the vacuum fluctuations of the supersymmetric field an effective equation of state is derived in a self-consistent approach at one loop order. The net effect of the vacuum fluctuations of the supersymmetric fields in the leading adiabatic order is a renormalization of the Newton and cosmological constants. 15. Vacuum fluctuations of the supersymmetric field in curved background Energy Technology Data Exchange (ETDEWEB) Bilic, Neven, E-mail: [email protected] [Rudjer Boskovic Institute, POB 180, HR-10002 Zagreb (Croatia); Domazet, Silvije, E-mail: [email protected] [Rudjer Boskovic Institute, POB 180, HR-10002 Zagreb (Croatia); Guberina, Branko, E-mail: [email protected] [Rudjer Boskovic Institute, POB 180, HR-10002 Zagreb (Croatia) 2012-01-16 We study a supersymmetric model in curved background spacetime. We calculate the effective action and the vacuum expectation value of the energy momentum tensor using a covariant regularization procedure. A soft supersymmetry breaking induces a nonzero contribution to the vacuum energy density and pressure. Assuming the presence of a cosmic fluid in addition to the vacuum fluctuations of the supersymmetric field an effective equation of state is derived in a self-consistent approach at one loop order. The net effect of the vacuum fluctuations of the supersymmetric fields in the leading adiabatic order is a renormalization of the Newton and cosmological constants. 16. Supersymmetric U boson and the old U(1) problem International Nuclear Information System (INIS) Kim, B.R. 1983-01-01 In the supersymmetric SU(3)xSU(2)xU(1)xUsup(')(1) model the new gauge group Usup(')(1) enforces the introduction of mirror fermions. In this note we address the inverse question. If one starts with SU(3)xSU(2)xU(1) including mirror fermions, what physical arguments other than the supersymmetric require the introduction of a new gauge group Usup(')(1). It turns out that the old U(1) problem is closely related with this question. Further we give an estimate for the upper bound for the parameter of the supersymmetric U boson r and x. (orig.) 17. Supersymmetric seesaw inflection International Nuclear Information System (INIS) Aulakh, Charanjit S.; Garg, Ila 2013-01-01 We showed that Supersymmetric Unified theories which explain small neutrino masses via renormalizable Type-I-see-saw mechanism can also support slow roll inflection point inflation. In such a scenario inflation occurs along a MSSM D-flat direction associated with gauge invariant combination of Higgs, slepton and right handed sneutrino. The scale of inflation is set by right handed neutrino mass M υc ∼10 6 10 12 GeV and inflation parameters are determined in terms of Dirac and Majorana couplings responsible for neutrino masses. The fine tuning conditions to have effective slow roll inflation are determined in terms of superpotential parameters (Dirac and Majorana couplings). This is in contrast to MSSM or Dirac neutrino inflection scenarios where fine tuning conditions are on soft Susy breaking parameters. In our case M υc ≫ M Susy , so soft Susy breaking parameters have hardly any role to play in fine tuning. The fine tuning conditions are thus radiatively stable due to nonrenormalization theorems. Reheating occurs via instant preheating which dumps all the inflation energy into MSSM degrees of freedom giving a high reheat temperature T rh ≅ M υc 10 6 GeV ∼ 10 1l 10 15 GeV. We also examined how this scenario can be embedded in realistic New Minimal Supersymmetric SO(10) Grand Unified Theory. (author) 18. First measurement of the left-right Z cross section asymmetry in polarized e+e- collisions at the SLC International Nuclear Information System (INIS) Swartz, M.L. 1993-01-01 The SLAC Linear Collider (SLC) has recently been upgraded to produce, accelerate, and collide a spin polarized electron beam. The average beam polarization during the 1992 run was (22.4 ± 0.7)%. The SLD Collaboration used the polarized beam to perform the first measurement of the left-right cross section asymmetry (A LR ) for Z boson production by e + e - collisions. The measurement was performed at a center-of-mass energy of 91.55 GeV with a sample of 10,224 Z decays. The measured value of A LR is 0.100 ± 0.044(stat.) ± O.004(syst.) which determines the effective weak mixing angle to be sin 2 θ W eff = 0.2378 ± 0.0056(stat.) ± 0.0005(syst.) 19. Precise measurement of the left-right cross section asymmetry in Z boson production by electron-positron collisions Energy Technology Data Exchange (ETDEWEB) Frey, R.E. [Univ. of Oregon, Eugene, OR (United States) 1994-12-01 A precise measurement of the left-right cross section asymmetry (A{sub LR}) for Z boson production by e{sup +}e{sup {minus}} collisions has been attained at the SLAC Linear Collider with the SLD detector. The author describes this measurement for the 1993 data run, emphasizing the significant improvements in polarized beam operation which took place for this run, where the luminosity-weighted electron beam polarization averaged 62.6 {+-} 1.2%. Preliminary 1993 results for A{sub LR} are presented. When combined with the (less precise) 1992 result, the preliminary result for the effective weak mixing angle is sin{sup 2}{theta}{sub W}{sup eff} = 0.2290 {+-} 0.0010. 20. Size and receptor density of glutamatergic synapses: a viewpoint from left-right asymmetry of CA3-CA1 connections Directory of Open Access Journals (Sweden) Yoshiaki Shinohara 2009-07-01 Full Text Available Synaptic plasticity is considered to be the main mechanism for learning and memory. Excitatory synapses in the cerebral cortex and hippocampus undergo plastic changes during development and in response to electric stimulation. It is widely accepted that this process is mediated by insertion and elimination of various glutamate receptors. In a series of recent investigations on left-right asymmetry of hippocampal CA3-CA1 synapses, glutamate receptor subunits have been found to have distinctive expression patterns that depend on the postsynaptic density (PSD area. Particularly notable are the GluR1 AMPA receptor subunit and NR2B NMDA receptor subunit, where receptor density has either a supra-linear (GluR1 AMPA or inverse (NR2B NMDAR relationship to the PSD area. We review current understanding of structural and physiological synaptic plasticity and propose a scheme to classify receptor subtypes by their expression pattern with respect to PSD area. 1. Left-right asymmetry for pion and kaon production in the semi-inclusive deep-inelastic scattering process International Nuclear Information System (INIS) Sun, Bo; She, Jun; Zhang, Bing; Mao, Ya-Jun; Ma, Bo-Qiang 2010-01-01 We analyze the left-right asymmetry in the semi-inclusive deep-inelastic scattering (SIDIS) process without introducing any weighting functions. With the current theoretical understanding, we find that the Sivers effect plays a key role in our analysis. We use the latest parametrization of the Sivers and fragmentation functions to reanalyze the π ± production process and find that the results are sensitive to the parametrization. We also extend our calculation on the K ± production, which can help us know more about the Sivers distribution of the sea quarks and the unfavored fragmentation processes. HERMES kinematics with a proton target, COMPASS kinematics with a proton, deuteron, and neutron target (the information on the neutron target can be effectively extracted from the 3 He target), and JLab kinematics (both 6 GeV and 12 GeV) with a proton and neutron target are considered in our paper. (orig.) 2. Supersymmetric Majoron inflation Energy Technology Data Exchange (ETDEWEB) King, Stephen F.; Ludl, Patrick Otto [School of Physics and Astronomy, University of Southampton,Southampton, SO17 1BJ (United Kingdom) 2017-03-31 We propose supersymmetric Majoron inflation in which the Majoron field Φ responsible for generating right-handed neutrino masses may also be suitable for giving low scale “hilltop” inflation, with a discrete lepton number ℤ{sub N} spontaneously broken at the end of inflation, while avoiding the domain wall problem. In the framework of non-minimal supergravity, we show that a successful spectral index can result with small running together with small tensor modes. We show that a range of heaviest right-handed neutrino masses can be generated, m{sub N}∼10{sup 1}−10{sup 16} GeV, consistent with the constraints from reheating and domain walls. 3. New Supersymmetric String Compactifications Energy Technology Data Exchange (ETDEWEB) Kachru, Shamit 2002-11-25 We describe a new class of supersymmetric string compactifications to 4d Minkowski space. These solutions involve type II strings propagating on (orientifolds of) non Calabi-Yau spaces in the presence of background NS and RR fluxes. The simplest examples have descriptions as cosets, generalizing the three-dimensional nilmanifold. They can also be thought of as twisted tori. We derive a formula for the (super)potential governing the light fields, which is generated by the fluxes and certain ''twists'' in the geometry. Detailed consideration of an example also gives strong evidence that in some cases, these exotic geometries are related by smooth transitions to standard Calabi-Yau or G2 compactifications of M-theory. 4. SO(10) supersymmetric grand unified theories Science.gov (United States) Dermisek, Radovan The origin of the fermion mass hierarchy is one of the most challenging problems in elementary particle physics. In the standard model fermion masses and mixing angles are free parameters. Supersymmetric grand unified theories provide a beautiful framework for physics beyond the standard model. In addition to gauge coupling unification these theories provide relations between quark and lepton masses within families, and with additional family symmetry the hierarchy between families can be generated. We present a predictive SO(10) supersymmetric grand unified model with D 3 x U(1) family symmetry. The hierarchy in fermion masses is generated by the family symmetry breaking D 3 x U(1) → ZN → nothing. This model fits the low energy data in the charged fermion sector quite well. We discuss the prediction of this model for the proton lifetime in light of recent SuperKamiokande results and present a clear picture of the allowed spectra of supersymmetric particles. Finally, the detailed discussion of the Yukawa coupling unification of the third generation particles is provided. We find a narrow region is consistent with t, b, tau Yukawa unification for mu > 0 (suggested by b → sgamma and the anomalous magnetic moment of the muon) with A0 ˜ -1.9m16, m10 ˜ 1.4m16, m16 ≳ 1200 GeV and mu, M1/2 ˜ 100--500 GeV. Demanding Yukawa unification thus makes definite predictions for Higgs and sparticle masses. 5. Properties of supersymmetric particles and processes International Nuclear Information System (INIS) Barnett, R.M. 1986-01-01 The motivations for experimental searches for supersymmetric particles are discussed. The role of R-parity in these searches is described. The production and decay characteristics of each class of supersymmetric particles are investigated in the context of both e+e- and hadron machines. There is a detailed presentation of a sample calculation of a supersymmetric process. Emphasis is given to the signatures for detection of supersymmetric particles and processes. The current limits for supersymmetric particles are given. 125 refs., 50 figs 6. On negative norm states in supersymmetric theories International Nuclear Information System (INIS) Ellwanger, U. 1983-01-01 We study the effective kinetic energy of scalar fields for two classes of supersymmetric theories. In theories with very large VEVs of scalar fields, as proposed by Witten, the use of the renormalization group improved effective action prevents the appearance of negative norm states. For simpler theories a general criterium for the absence of negative norm states is given, which is violated in a model with O(N)-symmetry proposed recently. (orig.) 7. The Supersymmetric Top-Ten Lists OpenAIRE Haber, Howard E. 1993-01-01 Ten reasons are given why supersymmetry is the leading candidate for physics beyond the Standard Model. Ultimately, the experimental discovery of supersymmetric particles at future colliders will determine whether supersymmetry is relevant for TeV scale physics. The grand hope of supersymmetry enthusiasts is to connect TeV scale supersymmetry with Planck scale physics. The ten most pressing theoretical problems standing in the way of this goal are briefly described. 8. On supersymmetric effective theories of axion Energy Technology Data Exchange (ETDEWEB) Higaki, Tetsutaro [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Kitano, Ryuichiro [Tohoku Univ., Sendai (Japan). Dept. of Physics 2011-04-15 We study effective theories of an axion in spontaneously broken supersymmetric theories. We consider a system where the axion supermultiplet is directly coupled to a supersymmetry breaking sector whereas the standard model sector is communicated with those sectors through loops of messenger fields. The gaugino masses and the axion-gluon coupling necessary for solving the strong CP problem are both obtained by the same effective interaction. We discuss cosmological constraints on this framework. (orig.) 9. Supersymmetric SU(5) GUT with Stabilized Moduli CERN Document Server Antoniadis, Ignatios; Panda, Binata 2008-01-01 We construct a minimal example of a supersymmetric grand unified model in a toroidal compactification of type I string theory with magnetized D9-branes. All geometric moduli are stabilized in terms of the background internal magnetic fluxes which are of "oblique" type (mutually non-commuting). The gauge symmetry is just SU(5) and the gauge non-singlet chiral spectrum contains only three families of quarks and leptons transforming in the$10+{\\bar 5}$representations. 10. Planar Quantum Mechanics: an Intriguing Supersymmetric Example CERN Document Server Veneziano, Gabriele 2006-01-01 After setting up a Hamiltonian formulation of planar (matrix) quantum mechanics, we illustrate its effectiveness in a non-trivial supersymmetric example. The numerical and analytical study of two sectors of the model, as a function of 't Hooft's coupling$\\lambda$, reveals both a phase transition at$\\lambda=1$(disappearence of the mass gap and discontinuous jump in Witten's index) and a new form of strong-weak duality for$\\lambda \\to 1/\\lambda\$. 11. Supersymmetric field theories at finite temperature International Nuclear Information System (INIS) Dicus, D.A.; Tata, X.R. 1983-01-01 We show by explicit calculations to second and third order in perturbation theory, that finite temperature effects do not break the supersymmetry Ward-Takahashi identities of the Wess-Zumino model. Moreover, it is argued that this result is true to all orders in perturbation theory, and further, true for a wide class of supersymmetric theories. We point out, however, that these identities can be broken in the course of a phase transition that restores an originally broken internal symmetry 12. Collisional processes in supersymmetric plasma International Nuclear Information System (INIS) Czajka, Alina; Mrowczynski, Stanislaw 2011-01-01 Collisional processes in ultrarelativistic N=1 supersymmetric QED plasma are studied and compared to those in an electromagnetic plasma of electrons, positrons and photons. Cross sections of all binary interactions which occur in the supersymmetric plasma at the order of e 4 are computed. Some processes, in particular, the Compton scattering on selectrons, appear to be independent of momentum transfer and thus they are qualitatively different from processes in an electromagnetic plasma. It suggests that the transport properties of the supersymmetric plasma are different than those of its nonsupersymmetric counterpart. Energy loss and momentum broadening of a particle traversing the supersymmetric plasma are discussed in detail and the characteristics are shown to be surprisingly similar to those of QED plasma. 13. Basic hypergeometry of supersymmetric dualities Energy Technology Data Exchange (ETDEWEB) Gahramanov, Ilmar, E-mail: [email protected] [Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D14476 Potsdam (Germany); Institut für Physik und IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Grossen Windkanal 6, D12489 Berlin (Germany); Institute of Radiation Problems ANAS, B.Vahabzade 9, AZ1143 Baku (Azerbaijan); Department of Mathematics, Khazar University, Mehseti St. 41, AZ1096, Baku (Azerbaijan); Rosengren, Hjalmar, E-mail: [email protected] [Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96 Göteborg (Sweden) 2016-12-15 We introduce several new identities combining basic hypergeometric sums and integrals. Such identities appear in the context of superconformal index computations for three-dimensional supersymmetric dual theories. We give both analytic proofs and physical interpretations of the presented identities. 14. Continuous degeneracy of non-supersymmetric vacua International Nuclear Information System (INIS) Sun Zheng 2009-01-01 In global supersymmetric Wess-Zumino models with minimal Kaehler potentials, F-type supersymmetry breaking always yields instability or continuous degeneracy of non-supersymmetric vacua. As a generalization of the original O'Raifeartaigh's result, the existence of instability or degeneracy is true to any higher order corrections at tree level for models even with non-renormalizable superpotentials. The degeneracy generically coincides the R-axion direction under some assumptions of R-charge assignment, but generally requires neither R-symmetries nor any assumption of generic superpotentials. The result also confirms the well-known fact that tree level supersymmetry breaking is a very rare occurrence in global supersymmetric theories with minimal Kaehler potentials. The implication for effective field theory method in the landscape is discussed and we point out that choosing models with minimal Kaehler potentials may result in unexpected answers to the vacuum statistics. Supergravity theories or theories with non-minimal Kaehler potentials in general do not suffer from the existence of instability or degeneracy. But very strong gauge dynamics or small compactification dimension reduces the Kaehler potential from non-minimal to minimal, and gravity decoupling limit reduces supergravity to global supersymmetry. Instability or degeneracy may appear in these limits. Away from these limits, a large number of non-SUSY vacua may still be found in an intermediate region. 15. A review of supersymmetric GUT and its implication to proton decay International Nuclear Information System (INIS) Sakai, N. 1983-01-01 Supersymmetric grand unification and its implication to proton decay are reviewed. The author discusses prototype models and reviews recent studies of model building, in particular models with an intermediate scale (10/sup 10/ -- 10/sup 12/ Gev) supersymmetry breaking. Finally proton decay in supersymmetric models is reviewed 16. Search for supersymmetric particles at CDF International Nuclear Information System (INIS) Wagner, R.G. 1989-01-01 Analyses of events with large unbalanced transverse energy from the 1987 and 1988-89 CDF data runs have set limits on the masses of supersymmetric squarks and gluinos. In a simple model with a stable photino as the lightest supersymmetric particle, the 1987 data with an integrated luminosity of 25.3 nb -1 have excluded at the 90% CL, squarks of mass less than 73 GeV/c 2 and gluinos of mass less than 74 GeV/c 2 . Preliminary results from an analysis of 1 pb -1 of data from the current 1988-89 run imply that the existence of a squark of mass less than 150 GeV/c 2 is unlikely. 4 refs., 2 fig., 1 tab 17. Supersymmetric extensions of Schrodinger-invariance International Nuclear Information System (INIS) Henkel, Malte; Unterberger, Jeremie 2006-01-01 The set of dynamic symmetries of the scalar free Schrodinger equation in d space dimensions gives a realization of the Schrodinger algebra that may be extended into a representation of the conformal algebra in d+2 dimensions, which yields the set of dynamic symmetries of the same equation where the mass is not viewed as a constant, but as an additional coordinate. An analogous construction also holds for the spin-12 Levy-Leblond equation. An N=2 supersymmetric extension of these equations leads, respectively, to a 'super-Schrodinger' model and to the (3 vertical bar 2)-supersymmetric model. Their dynamic supersymmetries form the Lie superalgebras osp(2 vertical bar 2)-bar sh(2 vertical bar 2) and osp(2 vertical bar 4), respectively. The Schrodinger algebra and its supersymmetric counterparts are found to be the largest finite-dimensional Lie subalgebras of a family of infinite-dimensional Lie superalgebras that are systematically constructed in a Poisson algebra setting, including the Schrodinger-Neveu-Schwarz algebra sns (N) with N supercharges. Covariant two-point functions of quasiprimary superfields are calculated for several subalgebras of osp(2 vertical bar 4). If one includes both N=2 supercharges and time-inversions, then the sum of the scaling dimensions is restricted to a finite set of possible values 18. Effective Higgs theories in supersymmetric grand unification Energy Technology Data Exchange (ETDEWEB) Zheng, Sibo [Chongqing University, Department of Physics, Chongqing (China) 2017-09-15 The effective Higgs theories at the TeV scale in supersymmetric SU(5) grand unification models are systematically derived. Restricted to extensions on 5{sub H} containing the Higgs sector we show that only two types of real (vector-like) models and one type of chiral model are found to be consistent with perturbative grand unification. While the chiral model has been excluded by the LHC data, the fate of perturbative unification will be uniquely determined by the two classes of vector-like models. (orig.) 19. Quantum integrability and supersymmetric vacua International Nuclear Information System (INIS) Nekrasov, Nikita; Shatashvili, Samson 2009-01-01 Supersymmetric vacua of two dimensional N=4 gauge theories with matter, softly broken by the twisted masses down to N=2, are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. Examples include: the Heisenberg SU(2) XXX spin chain which is mapped to the two dimensional U(N) theory with fundamental hypermultiplets, the XXZ spin chain which is mapped to the analogous three dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model which are related to the four dimensional theory compactified on T 2 . A consequence of our correspondence is the isomorphism of the quantum cohomology ring of various quiver varieties, such as T * Gr(N,L) and the ring of quantum integrals of motion of various spin chains. The correspondence extends to any spin group, representations, boundary conditions, and inhomogeneity, it includes Sinh-Gordon and non-linear Schroedinger models as well as the dynamical spin chains like Hubbard model. These more general spin chains correspond to quiver gauge theories with twisted masses, with classical gauge groups. We give the gauge-theoretic interpretation of Drinfeld polynomials and Baxter operators. In the classical weak coupling limit our results make contact with Nakajima constructions. Toric compactifications of four dimensional N=2 theories lead to the instanton corrected Bethe equations. (author) 20. Bethe Ansatz and supersymmetric vacua International Nuclear Information System (INIS) Nekrasov, Nikita; Shatashvili, Samson 2009-01-01 Supersymmetric vacua of two dimensional N = 4 gauge theories with matter, softly broken by the twisted masses down to N = 2, are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. Examples include: the Heisenberg SU(2)XXX spin chain which is mapped to the two dimensional U(N) theory with fundamental hypermultiplets, the XXZ spin chain which is mapped to the analogous three dimensional super-Yang-Mills theory compactified on a circle, the XYZ spin chain and eight-vertex model which are related to the four dimensional theory compactified on T 2 . A consequence of our correspondence is the isomorphism of the quantum cohomology ring of various quiver varieties, such as cotangent bundles to (partial) flag varieties and the ring of quantum integrals of motion of various spin chains. The correspondence extends to any spin group, representations, boundary conditions, and inhomogeneity, it includes Sinh-Gordon and non-linear Schroedinger models as well as the dynamical spin chains like Hubbard model. Compactifications of four dimensional N = 2 theories on a two-sphere lead to the instanton-corrected Bethe equations.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9146796464920044, "perplexity": 2482.1471420325915}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583516003.73/warc/CC-MAIN-20181023023542-20181023045042-00322.warc.gz"}
https://agrubertx.github.io/Active-Manifolds/	# Active Manifolds: Reducing high-dimensional data to 1-D When fitting the parameters of a scientific model, it may be the case that real data is expensive or difficult to acquire. A natural question then arises – how can one get the most accurate understanding of a physical situation when given sparse or limited data? Active Manifolds (AM) is a technique for reducing the dimension of regression problems when the function in question involves a high number of input dimensions relative to the data acquired. In this fashion, Active Manifolds extends the Active Subspace methods of Paul Constantine, which use techniques from principal component analysis (PCA) applied to the gradient of a model function in order to compute a lower-dimensional affine subspace where the unknown function changes most on average. Similarly, AM seeks to find and exploit a 1-D submanifold on which the function exhibits the most change. More precisely, given samples of an unknown function $f:\mathbb{R}^m \to \mathbb{R}$ and its gradient $\nabla f$, our method computes an integral curve of $\nabla f$ (an active manifold) inside the function domain. This provides a 1-D object that encompasses almost all of the change in $f$, and which can be used to (formally) construct the quotient space $\mathbb{R}^m/{\sim}$ (isomorphic to $\mathbb{R}$) where each point $x_0 \in \mathbb{R}^m$ is identified with its level set submanifold $\{ y \in \mathbb{R}^m \vert \, f(y) = f(x_0) \}$. The utility of this is that, with a suitable approximation of the quotient map $\pi: \mathbb{R}^m \to \mathbb{R}^m /{\sim}$, the arbitrarily large regression problem in question becomes essentially one-dimensional; recovering $f$ along the active manifold is analogous to recovering the factorization map $\hat f: \mathbb{R}^m/{\sim} \to \mathbb{R}$ which completely characterizes the range of $f$. We provide a mathematical justification for this method, a basic algorithm for running the program, and a comparison against previous results involving magnetohydrodynamic simulations which were obtained using Active Subspaces. The benefits of the AM method include increased accuracy (at more computational cost), greatly improved visualization capabilities, more refined sensitivity analysis, and complete reduction to a 1-D problem. On the other hand, very little is known about the algorithmic accuracy or dependence on data, so further work in this area should include obtaining rigorous estimates on these quantities, as well as investigating method sensitivity with respect to the amount/spread of data, and bounding the complexity and convergence of the involved algorithms. # Relevant Publications Robert A. Bridges, Anthony D. Gruber, Christopher Felder, Miki Verma, Chelsey Hoff. Active Manifolds: A non-linear analogue to Active Subspaces, Volume 97: International Conference on Machine Learning (2019). Preprint version available here.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.829035758972168, "perplexity": 484.4680868905834}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153392.43/warc/CC-MAIN-20210727135323-20210727165323-00353.warc.gz"}
http://math.stackexchange.com/questions/299811/find-all-the-elements-in-the-intersection-langle-alpha-rangle-cap-langle-b	Find all the elements in the intersection $\langle \alpha\rangle \cap \langle \beta \rangle$ Find all the elements in the intersection $\langle \alpha\rangle \cap \langle \beta \rangle$ of $\langle \alpha \rangle , \langle \beta \rangle$ where $\alpha, \beta \in S_9$. $\beta =(521)(96347)(8), \alpha = (15)(37964)(8)(2)$ I know that $\|\beta\|=15, \|\alpha\|=10$, so $\langle \beta \rangle = ( \beta, \beta^1..., \beta^{15})$ and $\langle \alpha \rangle = ( \alpha, \alpha^1..., \alpha^{9})$ and so I could just check manually, but is there a more efficient solution that i am not seeing? Any input would be appreciated, Thanks - How come $\alpha\in S_4$ and 9 appears in the product of cycles of $\alpha$ ? – Amr Feb 10 '13 at 23:50 @Amr you are right, my mistake, fixed it – bobdylan Feb 10 '13 at 23:53 I will assume that you meant $S_9$. By Lagrange's theorem we know that $\|<\alpha>\cap<\beta>\|$ divides $\|<\alpha>\|,\|<\beta>\|$. Thus, $\|<\alpha>\cap<\beta>\|$ divides $10,15$. Hence $\|<\alpha>\cap<\beta>\|$ divides 5. Now there are two cases. Either $\|<\alpha>\cap<\beta>\|$ is trivial (Now things become easy) or $\|<\alpha>\cap<\beta>\|$ is cyclic of order 5. In the second case it suffices to find only one non-identity element $x\in <\alpha>\cap<\beta>$ to find $<\alpha>\cap<\beta>$, because $<\alpha>\cap<\beta>=\{e,x,x^2,x^3,x^4\}$ (This is because 5 is prime) If $<\alpha>\cap<\beta>$ is not trivial: Let $x\in\|<\alpha>\cap<\beta>\|$. Thus, $x=\alpha^i$ for some $i\in\{1,2,...,9\}$. Since $(\alpha^i)^5=e$, thus $i\in\{0,2,4,6,8\}$. Hence $<\alpha>\cap<\beta>\leq<\,\alpha^2>$. Since $\|<\alpha>\cap<\beta>\|=\|<\alpha^2>\|=5$, thus $<\alpha^2>=<\alpha>\cap<\beta>$. Hence, $\alpha^2\in\alpha>\cap<\beta>$. Conclusion: $<\alpha>\cap<\beta>$ is not trivial implies $\alpha^2\in<\beta>$. So you just need to check if $\alpha^2\in<\beta>$ - Thats excellent, im checking if $\alpha^2 \in \langle B \rangle$ but i have an intuition that this can never be since $\beta$ can be expressed as 6, 2 cycles and $\alpha$ can be expressed as 5, 2 cyles so it has to be the trivial case, Is my logic correct? – bobdylan Feb 11 '13 at 2:23 Your observation on the orders of the two permutations is correct, $\|\alpha\|=10$ and $\|\beta\|=15$. By Lagrange's theorem, $\|<\alpha>\cap<\beta>\|$ must divide the greatest common divisor of these two numbers, which is the prime number 5. To see if there is a common element in $<\alpha>\cap<\beta>$ raise $\alpha$ to a power that will make all but the 5-cycle singletons. Do the same for $\beta$. Now look to see if the two 5-cycles represent powers of the same permutation. The only operations you need to use are compositions of permutations in cycle notation. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9537973403930664, "perplexity": 128.5465143815049}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398468396.75/warc/CC-MAIN-20151124205428-00232-ip-10-71-132-137.ec2.internal.warc.gz"}
http://www.cjss.ac.cn/EN/volumn/volumn_1325.shtml	CNKI期刊全文数据库《中国学术期刊文摘》《中国物理文摘》《中国天文学文摘》 #### Table of Content 15 March 2020, Volume 40 Issue 2 Research Aeticles Exploring Greenhouse Gases Water and Climate Changes: Scientific Opportunities for the Climate and Atmospheric Composition Exploring Satellites Mission LIU Congliang, KIRCHENGAST Gottfried, SUN Yueqiang, WANG Xin, Lü Daren, BAI Weihua, DU Qifei, L?SCHER Armin, SYNDERGAARD Stig, TIAN Longfei, ZHANG Zhihua 2020, 40 (2): 151-168. doi: 10.11728/cjss2020.02.151 Abstract ( 463 ) PDF (6103KB) ( 112 ) The Essential Climate Variables (ECVs), such as the atmospheric thermodynamic state variables and greenhouse gases, play an important role in the atmosphere physical processes and global climate change. Given the need of improvements in existing ground-based and satellite observations to successfully deliver atmosphere and climate benchmark data and reduce data ambiguity, the Climate and Atmospheric Composition Exploring Satellites mission (CACES) was proposed and selected as a candidate mission of the Strategic Priority Research Program of Chinese Academy Science (SPRPCAS). This paper presents an overview of the key scientific questions and responses of ECVs in relation to global change; the principles, algorithms, and payloads of microwave occultation using centimeter and millimeter wave signals between low Earth orbit satellites (LEO-LEO microwave occultation, LMO) as well as of the LEO-LEO infrared-laser occultation (LIO); the CACES mission with its scientific objectives, mission concept, spacecraft and instrumentation. Parallel Computing Technology for CME Parameter Detection Model Based on MapReduce YANG Shitong, CAI Yanxia, LU Guorui, WANG Jingjing 2020, 40 (2): 169-175. doi: 10.11728/cjss2020.02.169 Abstract ( 355 ) PDF (3204KB) ( 85 ) Space environment prediction model is an important part of space environment business. Coronal Mass Ejection (CME) is the source of many space events and near-Earth space environment disturbances. The CME parameter detection model is an important part of the solar wind forecasting process. In order to improve the accuracy of solar wind forecasting in space environment forecasting, it is necessary to improve the accuracy of CME parameter detection. However, the model runs in serial mode with low calculating efficiency, which leads to long operation time of the model and can not meet the requirement. Based on the parallel computing framework of MapReduce, according to the characteristics of CME parameter detection model, the calculation flow of CME parameter detection model is improved. A CDMR (CME Detection under MapReduce) method is presented, which can realize the parallel computing of CME parameter detection model. Moreover, the running time of the CME parameter detection model between serial computing and MapReduce parallel computing is compared. The experimental results show that the running time is reduced by using MapReduce parallel computing, and the detection accuracy and calculation efficiency of the model are improved. Application of LSTM Neural Network in F10.7 Solar Radio Flux Mid-term Forecast YANG Xu, ZHU Yaguang, YANG Shenggao, WANG Xijing, ZHONG Qiuzhen 2020, 40 (2): 176-185. doi: 10.11728/cjss2020.02.176 Abstract ( 330 ) PDF (4297KB) ( 62 ) The F10.7 index is an important input parameter for the empirical models of atmospheric density, and its prediction accuracy directly affects the accuracy of spacecraft orbit prediction. The solar activity exhibited an average of 11 years on a long-term scale and a 27-day periodic variation on a short-term scale. Based on this observational fact, a l Long and Short Term Memory (LSTM) recurrent neural network method is proposed to conduct the mid-term forecast of F10.7 index for the next 27 days. Using a continuous long period of F10.7 data as training data, the LSTM neural network training is constructed, and the upper and lower bounds of model parameters based on empirical formula are determined. The method of trial and error is used to select the optimal model parameters, and the prediction models to predict solar activity of high and low years F10.7 index in the next 27 days are constructed. The results show that the average relative error of the 27th day F10.7 index forecast for solar activity in the high year can reach about 10%, and can reach 2% or less in the low year. In 1998, the correlation coefficient between the predicted value of the F10.7 index on the 27th day and the measured value was 0.60. Hemispheric Distribution of Lower-band Chorus Waves Observed by Van Allen Probes CHENG Xiaowei, GU Xudong, NI Binbin, ZHANG Yang 2020, 40 (2): 186-196. doi: 10.11728/cjss2020.02.186 Abstract ( 375 ) PDF (14865KB) ( 26 ) Whistler mode chorus waves are important electromagnetic emissions due to their dual roles in acceleration and loss processes of Earth’s radiation belt electrons. A detailed global survey of lower-band chorus is performed using EMFISIS data from Van Allen Probes in near-equatorial orbits. In addition to the confirmation of the positive correlation of chorus wave intensities to geomagnetic activity and dayside-nightside distribution asymmetry of wave amplitude and occurrence probability, the analysis results find that in statistics lower-band chorus emissions exhibit higher wave occurrence rates and larger normalized peak wave frequencies in the magnetically northern hemisphere but somehow stronger peak wave intensities in the magnetically southern hemisphere. While overall the differences between the two magnetically hemispheric distributions tend to be not significant, it is important to establish the magnetically hemispheric distribution profiles of lowerband chorus with respect to L-shell, magnetic local time, and geomagnetic latitude for improved understanding of chorus-induced dynamics of radiation belt electrons. Analysis of Spatial Variation Characteristics of Regional Ionospheric TEC Grid Based on Crustal Movement Observation Network of China LI Yongtao, ZHOU Wei, LI Jianwen, CHE Tongyu, JING Xin 2020, 40 (2): 197-206. doi: 10.11728/cjss2020.02.197 Abstract ( 350 ) PDF (4771KB) ( 209 ) In order to study the variation characteristics and the applicable accuracy range of ionospheric TEC in small-scale, high-resolution space in the Crustal Movement Observation Network of China (CMONOC) region of China, 260 CORS data of the CMONOC are used to generate the 731-day CMONOC ionospheric RIM grids from 2016 to 2017, and the accuracy is verified. In the same RIM grid, the TEC grid points with different latitudinal and longitudinal are analyzed in the longitude and latitude directions respectively. The results show that the maximum change rate of the TEC difference in the longitudinal direction of the CMONOC region is about 0.3TECU·(°)-1, and the average rate of TEC change is about 0.11TECU·(°)-1. When the longitude interval is 1°, the TEC difference is less than 2TECU. As the longitude interval increases, its TEC difference also increases and shows a certain half-year and annual variation. The maximum value of the TEC difference in the latitudinal direction is about 1.7TECU·(°)-1. The average change rate of TEC is approximately 0.46TECU·(°)-1. The ionospheric TEC in the CMONOC region increases with the decrease of latitude. When the latitude interval is 1°, 99.4% TEC differences are less than 4TECU. As the latitude interval increases, the TEC difference also increases. It also shows a certain half-year and annual variation law. In the case of the same degree of interval, the change of TEC in the latitudinal direction is larger than that in the longitudinal direction. Seasonal Variations of Mesospheric Densities Observed by Rayleigh Lidar at Golmud, Qinghai DAI Yaru, PAN Weilin, QIAO Shuai, HU Xiong, YAN Zhaoai, BAN Chao 2020, 40 (2): 207-214. doi: 10.11728/cjss2020.02.207 Abstract ( 311 ) PDF (4785KB) ( 40 ) From Aug. 2013 to Oct. 2015, a Rayleigh lidar has been used to study the middle atmosphere at Golmud (36.25°N, 94.54°E), Qinghai, located in the northeastern part of the Tibetan Plateau. Mesospheric density profiles from 50 to 90 km were retrieved based on 205 nights of lidar observation, with a total of 1616 hours of operation. We compared our lidar density measurements with SABER observations onboard TIMED satellite and MSIS-00 model data. The results showed that the annual mean density measured by lidar agreed well with SABER data, but both were lower than that of MSIS-00. All datasets exhibited dominant annual oscillation in the mesosphere. From 63 to 85 km, the annual amplitude of lidar density is larger than those of SABER and MSIS-00. PDD (Percentage of Density Difference) was calculated to investigate the mesospheric density climatology. The largest density variations of lidar, MSIS-00, and SABER occurred at around 72 km. Both lidar and SABER PDD reached their maximum in May, about one month earlier than the MSIS-00; while the minimum PDD appeared in late December for all datasets. Daytime Sodium Lidar Observations and Studies of the Tidal Characteristics in Winter over Beijingormalsize LU Zhenghua, YANG Guotao, WANG Jihong, JIAO Jing, XUN Yuchang 2020, 40 (2): 215-222. doi: 10.11728/cjss2020.02.215 Abstract ( 294 ) PDF (2890KB) ( 49 ) Based on continuous observation of the sodium layer from lidar located in Yanqing, Beijing, the diurnal variation of the sodium layer and its relevant parameters can be analyzed. Comparing the phase information of sodium density from every altitude with the information from meridian wind at the same time, it can be found that the two diurnal phases are consistent with each other. Although the two semi-diurnal phases exist a little bit difference, as a whole, they two agree very well. Extracting the phase and amplitude from continuous sodium observation data from October to January from 2014 to 2016, tidal characters in fall over Beijing can be studied. The results show diurnal tide phases have unobvious seasonal variation and propagate upward with vertical wavelengths between 30 and 50km. Besides, the diurnal tide is stronger than the semidiurnal tide. Study on Charge of Dust Particles in Lower Polar Region of Double Maxwell Distributionormalsize PATIMAN A, WANG Yantong, SHI Yanxiang 2020, 40 (2): 223-226. doi: 10.11728/cjss2020.02.223 Abstract ( 451 ) PDF (1152KB) ( 33 ) Polar Mesosphere Summer Echoes (PMSE) will disappear immediately under the condition of high power microwave irradiation, which is called heating phenomenon in the polar mesosphere. When the high power microwave irradiate the polar mesosphere, the directional motion velocity of the electrons under the acceleration of microwave electric field can be compared with the thermal motion velocity, and the dust plasma in the polar mesosphere obeys the dual Maxwell distribution. The charge distribution of dust particles in the polar mesosphere is given based on the charge theory of dust particles under double Maxwell distribution. The charge changes of dust particles and the electron concentration are compared before and during the high power microwave heating the polar mesosphere. The results show that heating the polar mesosphere with a high-power microwave device will affect the charge of electrons to dust particles and lead to the change of electron concentration, which is of great significance to further explain the phenomenon of heating in the polar mesosphere. Assimilation of Near Space Temperature Data from SABER and MLS Observations into the Whole Atmosphere Community Climate Model and Data Assimilation Research Test-bed JING Wenqi, CUI Yuanyuan, WANG Yegui, JIANG Huiming, CAI Qifa, LAN Weiren 2020, 40 (2): 227-241. doi: 10.11728/cjss2020.02.227 Abstract ( 540 ) PDF (9004KB) ( 63 ) This study performs SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) and MLS (Microwave Limb Sounder) temperature data assimilation experiments to simulate a SSW (Stratospheric Sudden Warming) process occurred in February 2016, based on WACCM+DART (Whole Atmosphere Community Climate Model, Data Assimilation Research Test-bed). The following main conclusions are obtained. First, assimilating SABER and MLS temperature observations significantly reduces WACCM's forecast error of temperature fields in mesosphere and middle-upper stratosphere (0.001～10hPa), and effectively improves control experiment's several discrepancies with observations and reanalysis, such as colder mesosphere during SSW, lower layer height that zonal wind direction firstly changes when SSW occurs, east zonal wind layers in 0.1～10hPa prematurely vanishing, stronger zonal wind and higher stratopause height during SSW recovery phase. The verification based on ERA5 reanalysis suggests that assimilating SABER and MLS temperature observations is in favor of reducing analysis error of zonal wind in low mesosphere and middle-upper stratosphere (0.1～14hPa) and temperature in stratosphere and middle-lower mesosphere (0.01～100hPa) above high-latitude areas (60°-90°N)in the northern hemisphere. In addition, assimilating low atmospheric observations is also beneficial for reducing analysis error of zonal wind in 0.1～14hPa and temperature in 0.01～100hPa, but this reduction effect is not as significant as that of assimilating SABER and MLS temperature observations. Adaptability Analysis of GPT2w Model in High Latitudes YAO Xiang, CHEN Mingjian, WANG Jianguang, CHEN Rui 2020, 40 (2): 242-249. doi: 10.11728/cjss2020.02.242 Abstract ( 397 ) PDF (2503KB) ( 58 ) The GPT2w model is the most accurate zenith tropospheric model in current, but there exists large error at high latitudes. In order to better ensure the high-precision application of satellite navigation and positioning system in high latitudes, the accuracy of GPT2w model in high latitudes is evaluated, and GPT2w model is used to obtain zenith tropospheric wet delay, dry delay and total delay, and the impact of GPT2w model correction on precise point positioning is explored. The test results show that the accuracy of GPT2w model in high latitudes is in the centimeter level, which is better than that in the middle and low latitudes. The zenith tropospheric delay in the Antarctic and Arctic regions has obvious seasonal variation characteristics and regional consistency characteristics. The total tropospheric delay in summer is higher than that in winter. The tropospheric delay in the Arctic region is significantly higher than that in the Antarctic region, and the zenith tropospheric delay in the Arctic region varies with the seasons more than the Antarctic region. The PPP test results show that the GPT2w model can effectively improve the positioning accuracy and adapt to high-precision positioning in high latitudes. Electric Fields Distribution of Zhinyu Crater in Chang’E-4 Landing Area GAN Hong, LI Xiongyao, WEI Guangfei 2020, 40 (2): 250-263. doi: 10.11728/cjss2020.02.250 Abstract ( 342 ) PDF (7732KB) ( 38 ) Solar radiation and solar wind create a complex dust-plasma environment in lunar crater. Based on the elevation data obtained from the Lunar Orbiter Laser Altimeter (LOLA) onboard Lunar Reconnaissance Orbiter (LRO), we constructed a three-dimensional model of Zhinyu crater which located in the Chang'E-4 landing area, and then calculated the effective solar irradiance and the percentage of illuminated area at different local time in the lunar daytime. The results show that the crater self-shading effect plays an important role in crater illumination conditions, and the percentage of illuminated area reaches 100% only during 10:30LT-13:30LT. In addition, we calculated the distributions of equilibrium surface potential, Debye length and electric field at different local time, which were found to be highly dependent on the crater self-shading effect. Finally, we discussed the relationship of equilibrium surface potential, Debye length and electric field at the bottom of Zhinyu-like crater with local time and latitude. The results show that the distributions of equilibrium surface potential, Debye length and electric field are symmetric along the time of 12:00LT and lunar equator. These values almost remain unchanged on the shadow areas and change slightly on the sunlit areas, but change dramatically at the dead zone. Characteristics of Moonquake and Its Comparison with Earthquakeormalsize ZHAO Na 2020, 40 (2): 264-272. doi: 10.11728/cjss2020.02.264 Abstract ( 725 ) PDF (5409KB) ( 95 ) The study on lunar internal structure is the hot issue. Seismology is one of the best methods for studying lunar internal structure. In this paper, the moonquake data and parameters are reanalyzed, and the characteristics of moonquake signal, distribution and mechanism are discussed in detail and compared with earthquake. By combining with previous studies, it is concluded that the moonquake is quite different from earthquake. Moonquake signals are typically of very long duration. Deep moonquakes and thermal moonquakes show evident wave form matching feature. Most of moonquakes detected are deep moonquakes which mainly distribute on the nearside of the Moon. The largest number of deep moonquakes which emanate from source nest are caused by tidal. Thermal moonquake also occurs periodically, resulting from temperature variation during one lunation. Performance Analysis of BDS/GPS Single Frequency RTK Based on MLAMBDA Methodormalsize SHEN Xiaoyun, BAO Ningxin, JIAO Weidong, WANG Wei 2020, 40 (2): 273-279. doi: 10.11728/cjss2020.02.273 Abstract ( 602 ) PDF (2970KB) ( 57 ) GNSS RTK technology is widely used in aerospace, high-precision mapping, transportation and other industries due to its high precision, high efficiency and real-time performance. At present, dual-frequency RTK technology is very mature and widely used. Single-frequency GNSS RTK has difficulties in data quality control and positioning error processing. Therefore, the accuracy of single-frequency RTK service may be limited, and its positioning performance remains to be studied. Based on the extended Kalman filter model, the MLAMBDA ambiguity search method and the ratio test method are combined with the measured data to compare and analyze the single-frequency RTK positioning performance of BDS, GPS and BDS/GPS. The results show that the single-frequency RTK positioning accuracy of the three modes is in the centimeter level in the static scene, which can meet the high-precision positioning requirements. In the dynamic scene, the ambiguity fixed rate of the three modes is above 70%, which can meet the daily positioning requirements. Regardless of static or dynamic application scenes, BDS has the highest fixed rate of ambiguity, and the time used for ambiguity resolution is short, which can enable fast RTK positioning. Design and Implementation of Signal Processing System for Radio Spectrometer Based on Casper and Simulink ZHAO Cuixia, ZHAO Fei, YAN Jingye 2020, 40 (2): 280-288. doi: 10.11728/cjss2020.02.280 Abstract ( 415 ) PDF (4716KB) ( 50 ) The digital system of radio telescope based on Casper library is being widely used. In the Simulink, complex digital signal design can be realized by calling the Casper module. This module enables the development of signal processing functions in the Simulink graphical environment with the help of the System Generator tool, greatly improving the development efficiency of radio astronomy equipment. The Casper and Xilinx modules in Simulink are used to design the digital signal processing unit of the radio telescope unit prototype, and realize the sub-band extraction, down-conversion and overall spectrum analysis. The simulation of related functions are realized on the Casper general hardware platform ZYNQ7020, which verifies the feasibility and high efficiency for designing the digital signal processing system of radio telescope unit prototype based on FPGA by using Casper and Xilinx module. Contour Detection of Disk Resolved Objects in Cassini ISS Image Using Deep Neural Network ZHANG Qingfen, ZHENG Yang, CHENG Guohao, LU Zhicong, ZHOU Xiaomei, WANG Yuchen 2020, 40 (2): 289-295. doi: 10.11728/cjss2020.02.289 Abstract ( 485 ) PDF (2363KB) ( 91 ) In the astrometry of CCD image, it is important to match image stars with catalogue stars to correct the camera's pointing. The onboard Imaging Science Subsystem (ISS) in Cassini orbiter has taken a large number of images of targets which are disk resolved. In the astrometry of these images, the false image stars are often detected in the disk. It disturbs the pointing correction of camera and decline the precision of the astrometry. Therefore, it is helpful to find the contours of the disk to remove the false image stars. One method based on deep learning is proposed to detect the contour of disk resolved object in ISS images. A convolutional neural network was set up by the framework TensorFlow, in which the input is the nine features of each pixel, and the output is the classification of each pixel: contour pixel or non-contour pixel. The neural network is trained by about 36000 pixels, and then it is used to detect the contour pixels in 380 ISS images. Compared with the contour pixels labeled by hand, the contour pixels detected by neural network have the precision of 78.26% and the recall ratio of 73.32%. It proved that the proposed method is available to find the contour of disk resolved target in ISS images.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8302502632141113, "perplexity": 4412.759527562956}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057337.81/warc/CC-MAIN-20210922072047-20210922102047-00404.warc.gz"}
https://www.quantumdiaries.org/2014/04/09/major-harvest-of-four-leaf-clover/	## View Blog \| Read Bio ### Major harvest of four-leaf clover The LHCb Collaboration at CERN has just confirmed the unambiguous observation of a very exotic state, something that looks strangely like a particle being made of four quarks. As exotic as it might be, this particle is sternly called Z(4430), which gives its mass at 4430 MeV, roughly four times heavier than a proton, and indicates it is has a negative electric charge. The letter Z shows that it belongs to a strange series of particles that are referred to as XYZ states. So what’s so special about this state? The conventional and simple quark model states that there are six different quarks, each quark coming with its antiparticle. All these particles form bound states by either combining two or three of them. Protons and neutrons for example are made of three quarks. All states made of three quarks are called baryons. Other particles like pions and kaons, which are often found in the decays of heavier particles, are made of one quark and one antiquark. These form the mesons category. Until 2003, the hundreds of particles observed were classified either as mesons or baryons. And then came the big surprise: in 2003, the BELLE experiment found a state that looked like a bound state of four quarks. Many other exotic states have been observed since. These states often look like charmonium or bottomonium states, which contain a charm quark and a charm antiquark, or a bottom and antibottom quarks. Last spring, the BESIII collaboration from Beijing confirmed the observation of the Zc(3900)+ state also seen by BELLE. On April 8, the LHCb collaboration reported having found the Z(4430) with ten times more events than all other groups before. The data sample is so large that it enabled LHCb to measure some of its properties unambiguously. Determining the exact quantum numbers of a particle is like getting its fingerprints: it allows physicists to find out exactly what kind of particle it is. Hence, the Z(4430)state appears to be made of a charm, an anti-charm, a down and an anti up quarks. Their measurement rules out several other possibilities. The squared mass distribution for the 25,200 B meson decays to ψ’ π found by LHCb in their entire data set. The black points represent the data, the red curve the result of the simulation when including the presence of the Z(4430)state. The dashed light brown curve below shows that the simulation fails to reproduce the data if no contribution from Z(4430)is included, establishing the clear presence of this particle with 13.9σ (that is, the signal is 13.9 times stronger than all possible combined statistical fluctuations. These are the error bars represented by the small vertical line attached to each point). Theorists are hard at work now trying to come up with a model to describe these new states. Is this a completely new tetraquark, a bound state of four quarks, or some strange combination of two charmed mesons (mesons containing at least one charm quark)? The question is still open. Pauline Gagnon To be alerted of new postings, follow me on Twitter: @GagnonPauline  or sign-up on this mailing list to receive and e-mail notification. For more information, see the LHCb website Tags: , ,	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9045140147209167, "perplexity": 1210.9372904067627}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107891228.40/warc/CC-MAIN-20201026115814-20201026145814-00425.warc.gz"}
https://www.physicsforums.com/threads/quick-general-question-about-induction-problem.272772/	# Quick general question about induction problem 1. Nov 17, 2008 ### bcjochim07 1. The problem statement, all variables and given/known data I have a problem where a 40 turn coil surrounds a a 200 turn solenoid and I am asked to find the maximum induced emf. Without going into exact details, to get the EMF do I need to multiply my expression for the change in flux w/ respect to time by 40? Also, The area in dflux/dt = dB/dt dot A is the cross sectional area of the solenoid, not the coil, correct? 2. Relevant equations 3. The attempt at a solution 2. Nov 17, 2008 ### JWDavid I believe you are forgetting the turn ratio 3. Nov 19, 2008 ### unscientific e = -N*d(BA)/dt Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook Similar Discussions: Quick general question about induction problem	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8851510286331177, "perplexity": 2410.4402433627047}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818689102.37/warc/CC-MAIN-20170922183303-20170922203303-00365.warc.gz"}
https://www.physicsforums.com/threads/weak-analog-of-the-strong-cp-problem.281925/	# Weak analog of the 'Strong CP Problem' 1. Dec 29, 2008 ### TriTertButoxy I understand that there is an issue about the FF-dual term in the strong sector. But I believe I can write an analogous term in the SU(2) part of the electroweak sector. Why don't people worry quite as much about this term (the Weak analog of the 'Strong CP Problem')? 2. Dec 29, 2008 ### blechman I remember wondering this very question. There are two answers I have in my mind, neither of which I can back up with the current state of my brain (sorry). (1) You can always remove this term by field redefinitions. (2) On the off chance (1) is wrong, remember that the electroweak couplings are much smaller than the QCD coupling, so any contributions from this term are invisible in experiment, and there is no "problem." The strong CP problem is b/c the contribution to the neutron EDM is much too big, which is not the case for the analogous electroweak term. Well, I'll let someone else back these statements up (or correct them). But there are two quick thoughts. 3. Dec 29, 2008 ### TriTertButoxy I also thought I had an answer to this question but I now doubt it is correct: Recall that one possible resolution of the strong CP problem is that one of the quarks have a vanishing mass parameter (with the up quark being the best candidate). Lattice simulations indicate that not even the up quark is massless, so the strong CP problem isn't resolved. As far the weak anolog of the problem is concerned, recall that neutrinos are massless in the Standard Model. I thought this would resolve the weak anolog of the CP problem. However, by the turn of the millennium, neutrinos were found to oscillate, implying them to have a small mass. However, this didn't seem to raise the issue about the weak CP problem, so something else must be at work... 4. Dec 29, 2008 ### blechman It's a little more subtle than that, I think. Let me try to repeat the argument that lives on the surface of my brain, with the caveat that it's only the surface thoughts I'm talking about here... The reason why the strong CP problem is a "problem" is that you cannot set $\theta_{\rm QCD}=0$ naturally, since the physical phase is actually $$\theta_{\rm QCD}+{\rm Arg~det}M$$ so as long as you write down the most general Yukawa couplings (and why wouldn't you?) you will always get the effective vacuum angle to be nonzero, unless the Yukawa's have real determinant. This relationship follows from an instanton calculation and is related to the fact that the axial symmetry is anomalous. So far, all facts. My confused memory is saying something like, SU(2)_W vacuum angle does not have this kind of relationship. Recall that QCD has a U(3)xU(3) vectorlike symmetry that is broken by a quark condensate (the chiral Lagrangian story) and the U(1)_A lives inside this symmetry group. EW does not have this kind of symmetry structure, so I'm not sure how it works. All still very vague, but I think that's how the argument goes. Again, take all this with a grain of salt. But I don't think the neutrinos are the key. I think is has more to do with how there is only one vacuum angle, and we can always choose it to be the QCD angle by suitable axial field redefinitions. Enough rambling. Hope this helps (and doesn't make things worse!). 5. Dec 30, 2008 ### BDOA Blechman above is right, The weak force has no CP problem, because it explicitly breaks CP. its group is SU(2)_L acting only on left handed particle and right handed antiparticles. This is maximal CP violation. Now it might be that there is also a right handed version of weak force carriers. The mass limit for them are currently that they must be heavier than about 800Gev, so there not very ruled out at all. In the case with both left and right handed carriers we can ask what happens if we swap handness, U(1)_A would exist for particles effected by the weak force(s). In fact it seems to me, that we would need U(1)_A as a local symmetry i.e. as a force, In the independent research forum I've a paper about what it would entail to have U(1)_A as a independent force. It has been looked at by other researchers, but so far many buried in very obscure or old journals. See however: <A HREF="http://lanl.arxiv.org/abs/hep-ph/0512324">L.M. [Broken] Slads</A> paper, where is seems to show that U(1)_A is demended as a local symmetry for any theory with both left and right handed weak carrier. Last edited by a moderator: Apr 24, 2017 at 9:47 AM 6. Dec 30, 2008 Staff Emeritus 7. Dec 30, 2008 Staff Emeritus Blechman is correct about the symmetry structure: in chiral QCD you end up with a leftover U(1) (and it must be a U(1), since you need the generator to be a number, $$\theta$$ and not a matrix) and that gives you a term in the Lagrangian like $$\frac{\theta}{16\pi^2} F^a_{\mu \nu} \tilde{F}^{\mu \nu a}$$. That term is the troublemaker, because it can give rise to a non-zero neutron EDM. As an aside, that's the real problem here - not that there is strong CP violation, but that CP violation can give rise to a neutron electric dipole moment, where the experimental constraints are extraordinarily strong. If I have an ordinary U(1) theory, this term doesn't contribute: you'll get something like $$\int d^4x F \tilde{F}$$ and since $$F \tilde{F} = \vec{E} \cdot \vec{B} = \frac{1}{2} \partial_\mu \epsilon^\mu_{\nu \rho \sigma} A^{\nu} F^{\rho \sigma}$$: an integral of a total divergence. Now, since dimensionally F falls off faster than 1/r2 and A falls off faster than 1/r, you're left with something that falls off too fast to give you any surface term. So, what you need is a non-Abelian theory that has an approximate U(1) built in. You get that in chiral QCD. You don't get that in GWS weak theory, because U(1) hypercharge is an exact symmetry, but so is U(1) electromagnetism. Now, you do get a neutron EDM from electroweak effects. It's very small, because it can only come in loops, and relies on an intereference from all three families. I would estimate the size of the effect to be of order: $$\left[ \frac{\alpha}{16 \pi^2} \left( \frac{m^2_u - m^2_d}{M^2_W} \right) \left(\frac{m^2_c - m^2_s}{M^2_W}\right) \left(\frac{m^2_t - m^2_b}{M^2_W}\right) (3.0 \pm 0.3) \times 10^{-5} \right] ea_0 \approx 10^{-31}$$ which is, in fact, the SM prediction. (In units of e-cm) Experimental limits are about a million times larger. 8. Dec 30, 2008 ### TriTertButoxy Thanks for the enlightening responses. I'd like to summarize your claim, Vanadium, to see if I understand this properly: The chiral limit of QCD is a non-abelian gauge theory with an exact U(1) flavor symmetry. Therefore, I may rotate away the theta term (and hence, it is unobservable). In the real-world QCD, the U(1) flavor symmetry is approximate. Hence, the theta may not be rotated away, as the angle will simply get transferred to the quark mass matrices: the phase is an observable. On the other hand, GWS theory is a non-ablelian gauge theory with an exact U(1) of hypercharge. I believe now I should claim that I should be able to rotate away the theta term for weak isospin. However, since the U(1) symmetry is not even anomalous (required for consistency of the GWS theory), doesn't that mean performing a rotation leaves the theta term untouched? So did you mean that I need an approximate global (not local) U(1) symmetry? In that cause we have the anomalous B+L symmetry to remove the theta term; right? I believe I'm finally understanding the issue; thanks! 9. Dec 30, 2008 ### blechman I just want to emphasize his point that a U(1) has no physical vacuum angle. A slick way to see that goes as follows: Even if you ignore the phase in the mass matrices for a moment, you might think that you can just set $\theta=0$ -- we're theorists, we can do what we want! The problem is that even if you try to do this by "playing G-d," you will just regenerate the theta term from instanton effects in the gauge theory. That is why it is not "natural" to set the vacuum angle to zero. However, there are no U(1) instantons, since you cannot embed a circle into a 3-sphere in a nontrivial way. Therefore the abelian vacuum angle has no physical meaning. You really need a nonabelian gauge theory to get a nontrivial vacuum angle. This is just what Vanadium-50 is saying. This leaves the SU(2) and SU(3) theories. Vanadium-50: can I ask you to just go through the argument for needing an "approximate U(1)" again? Under an ANOMALOUS U(1) symmetry, $\theta\rightarrow\theta+\alpha$ where $e^{i\alpha}$ is the U(1) phase. Using this explicitly broken symmetry we can set a phase convention where $\theta\rightarrow 0$ but since the mass matrix also rotates under this symmetry we will reintroduce it there, and so the effect does not just go away. What part of this argument goes wrong if we replace SU(3) with SU(2)? U(1)_{Y,EM} are not the anomalous symmetries we are using to remove the vacuum angle... As far as it being a "problem" -- well, I agree that IF we saw a sizable neutron EDM then we would say, "Wonderful! QCD predicts that, and we have a great theory!" Unfortunately, we don't see this, and now we are left with asking where the small value of $\theta$ comes from. 10. Dec 30, 2008 ### blechman you have it backwards: if you have an EXACT symmetry, any "rotation" does not do anything to the parameters, since it is an exact symmetry!! You need the symmetry to be BROKEN, so that the parameters become "spurions" of the broken symmetry and therefore can be rotated away. This is, for example, how the usual flavor symmetry works when diagonalizing the mass matrices in the SM - the U(3)^5 symmetry is explicitly broken by the Yukawa matrices, and so we can use that symmetry to do field redefinitions and therefore remove the off-diagonal masses (up to the CKM matrix). BY THE WAY: It is important that the symmetry is broken EXPLICITLY, either by anomalies or spurions, not spontaneously. Remember: if the symmetry is broken spontaneously, it is still an "exact" symmetry, only realized nonlinearly. For this argument to work, you need an explicit breaking. again, I'm a little confused by that. I have asked Vanadium-50 to go into more detail. But I bet you are right - it is probably B+L that does it! AHAH! Yes, I bet you got it in one! The B+L U(1) can rotate away the EW vacuum angle, and since the mass terms are invariant under this symmetry, it does not come back in the form of a phase like in the QCD case! I bet that's the answer. Anyone want to have a go at my guess? 11. Dec 30, 2008 ### humanino Very interesting discussion. Thanks guys. I've been re-reading a little since the beginning of the discussion. I think I still need to check in Coleman's "symmetry", but from what I collected so far, I think your bet is correct Maybe Vanadium has a better reference ? 12. Dec 30, 2008 ### blechman Coleman is, of course, great! I'm doing all this from home, so I don't have any textbooks readily available to me and have been doing it all from memory (why I've been sure to include all those caveats about possibly being wrong). here's an amusing question: we don't REALLY believe that the SM Lagrangian is the full story; we know that the infamous (unique) dimension 5 operator gives Majorana neutrino masses and explicitly breaks L (and therefore B+L). dimension 6 operators also break these symmetries. Does that mean, by my half-brained arguments above, that when including these higher-dimension operators, the electroweak vacuum angle is no longer unphysical? I imagine it is still irrelevant since its contributions to physics are highly suppressed... Thoughts, anyone? Last edited: Dec 30, 2008 13. Dec 30, 2008 Staff Emeritus Actually, at the time I wrote this, I thought it was obvious. Now I am not so sure. As a former professor once said, "It's obvious. Um...I think it's obvious. It's either obvious or wrong - I'm not sure which." 14. Dec 30, 2008 ### blechman yeah, the more obvious it is, the more likely it's wrong! I think I have it though - see my other posts and feel free to rip them apart if you disagree. I don't think it has to do with hypercharge, though. that makes me suspicious... Similar Discussions: Weak analog of the 'Strong CP Problem'	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9465604424476624, "perplexity": 689.5119998537898}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917120349.46/warc/CC-MAIN-20170423031200-00300-ip-10-145-167-34.ec2.internal.warc.gz"}
https://brilliant.org/discussions/thread/best-books-for-physics-and-maths/?sort=new	# Best Books For Physics And Maths Could you please suggest the best books for : Algebra and Number theory , Geometry and combinatorics and Mechanics and Electricity & magnetism.... Note by Pratik Acharya 7 years, 9 months ago This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science. When posting on Brilliant: • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused . • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone. • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge. MarkdownAppears as italics or _italics_ italics bold or __bold__ bold - bulleted - list • bulleted • list 1. numbered 2. list 1. numbered 2. list Note: you must add a full line of space before and after lists for them to show up correctly paragraph 1 paragraph 2 paragraph 1 paragraph 2 > This is a quote This is a quote # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" # I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world" MathAppears as Remember to wrap math in $$...$$ or $...$ to ensure proper formatting. 2 \times 3 $2 \times 3$ 2^{34} $2^{34}$ a_{i-1} $a_{i-1}$ \frac{2}{3} $\frac{2}{3}$ \sqrt{2} $\sqrt{2}$ \sum_{i=1}^3 $\sum_{i=1}^3$ \sin \theta $\sin \theta$ \boxed{123} $\boxed{123}$ Sort by: Hi - 2 years ago My favorite physics book: The Feynman Lectures on Physics FEYNMAN ROCKS! THE BEST PHYSICS TEACHER THERE EVER WAS! - 7 years, 9 months ago Best for any amateur to Number Theory is David Burton's book : Elementary Number Theory ........ an excellent read And for Physics I'd suggest Halliday, Resnick and Walker's : Fundamentals of Physics ... the best explanantion of rudimentary physics For further detailed reading, Richard Feynman's Lectures on Physics is literally mind-blowing ! - 7 years, 9 months ago Bal ka pratik - 2 years ago Hprpa physique;TecDoc maths - 7 years, 9 months ago Has anyone here solved the Harder problems in Mechanics from IE Irodov? - 7 years, 9 months ago Feynman's Lectures on physics vol 1 is great for mechanics, from the basics to the intermediate. I think Vol 2 deals with electricity and magnetism in detail but he uses more advanced math so it's hard to get through. - 7 years, 9 months ago Hello all, Here are some old threads we have had over the past month offering good book suggestions. Pratik, since it sounds like you are interested in all books to help you with everything on Brilliant, I have tried to collate most of our book threads. Everybody, please feel free to recommend any other books you like, that are not on the old threads or this one. It will probably be helpful to somebody. Books for Combinatorics Mathematical Circles Number theory books Electricity and Magnetism Books Beginning trigonometry books Staff - 7 years, 9 months ago sir,this week one physics question is wrong(fluorescent tube qn.) ,so can u change that with another correct question,so that those who don't know to do such incorrect question can solve the new correct queation. - 7 years, 9 months ago Thank you, Peter. - 7 years, 9 months ago No problem:) Staff - 7 years, 9 months ago why - 7 years, 9 months ago "No problem" is an American colloquial figure of speech used when somebody thanks you and you would like to stress that you do not mind doing something for them, and that it was no big deal. It is often used interchangeably with "your welcome." Staff - 7 years, 9 months ago sorry.I joked - 7 years, 9 months ago Mathematical circles by Fomin ,Genkin and Itenberg is very good for problem solving in maths. - 7 years, 9 months ago Try Challenge and Thrill of pre college mathematics, published by the national board of higher math. Also consider Resnick and Halliday's Fundamentals of Physics and Sears and Zemansky University Physics. Problem Peimer for the Olympiad is also a good book for previous math olympiad problems. India and International Math Olympiads b Arihant Publications is also very good. I have used these books myself and find them quite good. All these books are available on flipkart.com for nominal rates, or can be bought as ebooks if you prefer. - 7 years, 9 months ago [Comment edited out for rudeness]-Peter - 7 years, 9 months ago sorry for that - 7 years, 9 months ago brother...there's a limit.and you're crossing it. - 7 years, 9 months ago could you please suggest me best books regarding quantitative aptitude - 7 years, 9 months ago R.S. AGGARWAL and EDGAR THORPE - 7 years, 9 months ago if you like popular standard textbooks, university physics by young and freedman. if you want some elegant text and problems, physics for scientists and engineers by serway. - 7 years, 9 months ago good. I have them - 7 years, 9 months ago	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 8, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9109838604927063, "perplexity": 3481.3552932580105}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141681209.60/warc/CC-MAIN-20201201170219-20201201200219-00143.warc.gz"}
http://mathhelpforum.com/advanced-algebra/180673-bijective-map-su-2-u-1-a.html	# Math Help - Bijective Map from SU(2) to U(1) 1. ## Bijective Map from SU(2) to U(1) how do i define a bijective map form SU(2) to U(1) where SU(2) is the special unitary 2x2 matrix and U(1) is the unitary 1x1 matrix? 2. U(1) consists of complex numbers which are the inverse of their conjugate. An element of SU(2) has the form $\left(\begin{array}{cc}\alpha&-\overline\beta\\ \beta&\overline\alpha\end{array}\right)$ such that the determinant is 1. Can you finish from there? 3. Not really. I was thinking of the determinant map but the determinant of all elements in su(n) is 1. Can i instead define it as a map from the matrix ( tt you defined, which is in su(n) ) to the first element a ? Seems wrong to me though.. 4. i was thinking, can i define it from cos(a) -isin(a) isin(a) cos(a) seen as a matrix to exp(ia) which is in U(1)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9906058311462402, "perplexity": 906.6288564765817}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609535535.6/warc/CC-MAIN-20140416005215-00106-ip-10-147-4-33.ec2.internal.warc.gz"}
http://mathhelpforum.com/calculus/89924-help-confusing-integration-question.html	# Thread: Help on a confusing Integration question 1. ## Help on a confusing Integration question I've got one question left on my assignment, and I'm not too sure what the questions even asking. Here's the question: Can somebody help me understand this question? And is the question asking about 2D or 3D models? I can understand how 2D might be possible to work out, but have no idea about 3D, since the height (z-axis) is not specified. Maybe I'm just looking at the question the wrong way! Any help is accepted . 2. Originally Posted by Phatmat I've got one question left on my assignment, and I'm not too sure what the questions even asking. Here's the question: Can somebody help me understand this question? And is the question asking about 2D or 3D models? I can understand how 2D might be possible to work out, but have no idea about 3D, since the height (z-axis) is not specified. Maybe I'm just looking at the question the wrong way! Any help is accepted . a): for a fixed $0 \leq x \leq \pi$ find the area of an equilateral triangle with each side of length $6 \sqrt{\sin x}.$ then integrate the result on the interval $[0,\pi]$ to find the volume. it's as simple as that! b): the same idea as a). 3. I'm still confused.. What do you mean by: "then integrate the result on the interval to find the volume. it's as simple as that!"? Is the triangle only 2D then? Because how can each side of the triangle be of length 6sqrt(sin x) when that's a semi-circle shape? 4. Originally Posted by Phatmat I'm still confused.. What do you mean by: "then integrate the result on the interval to find the volume. it's as simple as that!"? Is the triangle only 2D then? Because how can each side of the triangle be of length 6sqrt(sin x) when that's a semi-circle shape? for a fixed $x_0,$ the triangle is in the plane $x=x_0.$ you leaned in high school or earlier that the area of an equilateral triangle with each side of length $a$ is $\frac{\sqrt{3}}{4}a^2.$ so in your example the area of each cross section is $A(x)=\frac{\sqrt{3}}{4}(6 \sqrt{\sin x})^2=9\sqrt{3} \sin x.$ the volume you're looking for is $\int_0^{\pi} A(x) \ dx= 18 \sqrt{3}.$ 5. Thanks for your help, your answer was right. I used the same method for the square (part b), and it was right aswell.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8177643418312073, "perplexity": 352.174610899696}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948516843.8/warc/CC-MAIN-20171212114902-20171212134902-00612.warc.gz"}
https://advances.sciencemag.org/content/2/4/e1501693?ijkey=76f15be5fd1cee684dbe2d0bc9b5c546099609c8&keytype2=tf_ipsecsha	Research ArticleCLIMATOLOGY # Climate-driven polar motion: 2003–2015 See allHide authors and affiliations Vol. 2, no. 4, e1501693 ## Abstract Earth’s spin axis has been wandering along the Greenwich meridian since about 2000, representing a 75° eastward shift from its long-term drift direction. The past 115 years have seen unequivocal evidence for a quasi-decadal periodicity, and these motions persist throughout the recent record of pole position, in spite of the new drift direction. We analyze space geodetic and satellite gravimetric data for the period 2003–2015 to show that all of the main features of polar motion are explained by global-scale continent-ocean mass transport. The changes in terrestrial water storage (TWS) and global cryosphere together explain nearly the entire amplitude (83 ± 23%) and mean directional shift (within 5.9° ± 7.6°) of the observed motion. We also find that the TWS variability fully explains the decadal-like changes in polar motion observed during the study period, thus offering a clue to resolving the long-standing quest for determining the origins of decadal oscillations. This newly discovered link between polar motion and global-scale TWS variability has broad implications for the study of past and future climate. Keywords • Earth sciences • climatology • earth’s spin axis • polar motion • space geodesy • terrestrial water storage • polar ice sheets • hydrology ## INTRODUCTION Polar motion is the movement of Earth’s spin axis as it wanders through the crust. Observations have tracked this motion for more than 100 years. Astrometric data, when combined with space methods, form a continuous time series since 1899 (14) and have sufficient signal-to-noise ratio to accurately determine the pole position to a level much less than 1 millisecond of arc (mas; 1 mas ≈ 3.09 cm). The time variations in pole position are described by the Cartesian orthogonal vector positions and Y(t) ŷ, with vector dyads and ŷ pointing along the longitudes of mean Greenwich and 90° East, respectively. When this time series is filtered to remove the 433-day Chandler and annual wobbles and shorter time-scale variability, a clear linear drift in X(t) and Y(t) is revealed (1, 2, 4, 5), with interannual variability dominated by a 25- to 35-year periodicity (called the Markowitz wobble) and 6- to 14-year decadal periodicities (4, 6). The origins of linear drift (1, 2, 5, 7) are far better understood than are interannual variability seen in the data (8, 9). Here, we identify the mechanisms that largely explain all of the observed polar motions during a 13-year time span, from April 2002 to March 2015, by analyzing monthly data from the Gravity Recovery and Climate Experiment (GRACE) mission (10). We develop our analysis from observed pole positions, or Earth Orientation Parameters (EOP), that are provided by the International Earth Rotation and Reference Systems Service (IERS) and compute corresponding polar motion excitations, with components χ1(t) and χ2(t), from EOP 08 C04 solutions (https://hpiers.obspm.fr/eop-pc/analysis/excitactive.html) by setting the Chandler period to 433 days and its quality factor to 179 (4). Because we are interested in frequencies below that of the Chandler wobble, it is reasonable to approximate [X(t) Y(t)]T ≈ [χ1(t) χ2(t)]T (see Materials and Methods). Figure 1 shows observed polar motion excitations χ1(t) and χ2(t) since 1976, when satellite measurements were first available. The 20th century linear drift is generally explained by the glacial isostatic adjustment (GIA) processes (1, 2, 5) associated with 100,000 years of waxing and waning of the Pleistocene great ice sheets that periodically covered northern hemispheric landmasses (7). Strong deviation in linear drift since about 2000 is likely related to climate-induced mass redistribution (5), including the melting of polar ice sheets (11). Both Markowitz and decadal variabilities are thought to have excitation mechanisms that originate either from the subtle dynamics of Earth’s fluid core or from large-scale global mass transport at Earth’s surface. However, core mechanisms fail to explain the amplitudes of the observed decadal motions by more than an order of magnitude (9), and a comprehensive search for decadal-scale atmosphere-ocean mass transport and angular momentum exchange demonstrated that these fail to explain the decadal amplitudes by more than a factor of 3 (8, 12). Here, we demonstrate for the first time that both the strong deviation in linear drift since about 2000 (5, 11) and the decadal-like variability are explained by global-scale continent-ocean mass transport, with robust changes in terrestrial water storage (TWS) playing an unexpectedly large role. Rigorous incorporation of TWS changes reduces the variance of a fit to the polar drift data by about 66% for χ1(t) and by about 92% for χ2(t), a great reduction over those incorporating only cryospheric changes (11). The variability in TWS excitation signal fully explains the ~20-mas amplitude of the observed change in χ2(t) during the study period, offering a clue as to the origins of decadal-scale oscillations that are so ubiquitous in the 115-year polar motion record (3, 4, 6). ## RESULTS We compute the variations in polar motion from the changes in Earth’s inertia tensor caused by the climate-driven surface mass redistribution (see Materials and Methods). It is therefore important to understand the spatiotemporal variability in the transport of water mass between the continents and the oceans. For convenience, we define a mass-conserving loading function, L(θ, λ, t), with dimensions of water equivalent height (WEH) as follows(1)Here, H(θ, λ, t) is the change in WEH on the continents with mask , S(θ, λ, t) is the associated change in sea level with ocean mask , and (θ, λ) represents the geographic coordinates on Earth’s surface. We compute H(θ, λ, t) by analyzing the GRACE Release-05 Level-2 monthly GSM data products provided by the Center for Space Research (available at http://www.csr.utexas.edu/grace/RL05.html). We use the standard processing of GRACE data, which are distributed in the form of monthly varying Stokes coefficients, as described in Materials and Methods. Briefly, we replace the degree 1 and degree 2 Stokes coefficients with more accurate values (13, 14), including those derived from satellite laser ranging (SLR) observations. We then calculate the total WEH gravity signal from Stokes coefficient anomalies, using a Gaussian filter with a 300-km radius. Finally, we remove the GIA signal (15) and scale the remaining WEH. This procedure forms our climate-driven surface loading H(θ, λ, t). Following Schrama et al. (16), we individually scale H(θ, λ, t) for the entire Greenland Ice Sheet (GIS), three nonoverlapping subdomains of the Antarctic Ice Sheet (AIS), and 15 regions of global glaciers and ice caps (GICs), with corresponding uncertainties arising from a suite of GIA computations and the choice of degree 1 and degree 2 Stokes coefficients. We scale H(θ, λ, t) for TWS over the noncryospheric continental domain using the so-called gain factors (17) to account for leakage errors and to restore the attenuated signals. The budget of continental mass directly contributes to the sea-level change. Continental mass variability, along with this ocean loading, induces perturbations in the gravitational and rotational potentials of the planet, causing the further redistribution of S(θ, λ, t), which is gravitationally self-consistent. Here, we compute S(θ, λ, t) by solving the perturbation theory of relative sea level on an elastically compressible rotating Earth (18). Figure 2 shows the least-squares retrieval of linear trend in L(θ, λ, t) during the study period, using the monthly GRACE solutions and associated sea-level computations. The GIS has lost ice mass at a pace of about −278 ± 19 Gt/year. Much of this loss comes from southern Greenland, where pervasive thinning occurs as a result of collective surface mass balance changes and increased outflux (19). The AIS has also lost mass, but at a more modest rate of −92 ± 26 Gt/year. However, there is great contrast in regional patterns, and coastal East AIS has mainly gained mass, especially in and adjacent to Dronning Maud Land and Enderby Land, as a result of increased precipitation (19). The AIS is losing mass from the Amundsen Sea Sector and the Antarctic Peninsula at a rapid rate. These two loss areas involve changing ice dynamics and, to a lesser degree, surface mass balance (19, 20). Other continental signals in Fig. 2A are composed of those associated with TWS and global GICs. Among the features that stand out are the negative TWS signals around Eurasia (the Indian subcontinent and the Caspian Sea). Relatively large negative signals appear around the Canadian Arctic (−61 ± 5.2 Gt/year), Alaska (−42.1 ± 6.8 Gt/year), and Patagonia (−22.1 ± 6.6 Gt/year), reflecting the large mass loss from these glaciated regions (16, 20, 21). All of these features are consistent with numerous reports of cryospheric and hydrographic mass changes that are comparable to the time span of our study (1923). A total mass loss from the continents of about −530 Gt/year raises the global mean sea level at a rate of about 1.46 mm/year. The linear trend in S(θ, λ, t) of Fig. 2D shows a large drop in local sea level around the GIS and along the Amundsen Sea Sector, and an enhanced sea-level rise in the corridor between South Africa and Dronning Maud Land. The pattern of in the corridor is caused, in nearly equal measure, by changes in gravitational attraction between the oceans and the continents [as induced by ] and by rotational feedback (see Materials and Methods). Although the values of S(θ, λ, t) are generally one order of magnitude smaller than the values of global H(θ, λ, t), they have a very long wavelength character and form an important component of polar motion excitations (24). The variations in polar motion induced by polar ice sheets, global GICs, and TWS are shown in Fig. 3A. Because the pole excitations are related to the degree 2 order 1 spherical harmonic (SH) coefficients of L(θ, λ, t), χ1(t) and χ2(t) are greatly sensitive to mass changes occurring around ±45° latitudes (fig. S1). Despite the proximity to the poles, the mass of ice sheets is changing so rapidly that they contribute greatly to drift in the pole position. Mass loss from the GIS yields positive and negative values of similar magnitudes. Positive trends for the AIS-associated χ1(t) and χ2(t) are driven by the combination of mass loss from the Amundsen Sea Sector and mass gain in Dronning Maud Land and Enderby Land. Mass loss from the Antarctic Peninsula acts to diminish while enhancing , contributing to a muted rate of χ1(t) compared to χ2(t) for the whole of the AIS. A similar interpretation can be made for TWS and global GICs. A large-scale water mass loss from Eurasia, as well as losses from southern South America, produce a large positive TWS-induced . Glacial mass loss signals of Alaska and Patagonia collectively drive a negative . In contrast, driven by GICs in Alaska, the Canadian Arctic, High Mountain Asia, and Patagonia tend to operate with differing signs and, consequently, yield a muted negative excitation. As the space gravimetry time series lengthens, it might be possible to use observations of changes in the spin rate of the pole, proportional to the change in length of day ΔLOD(t), as additional constraints on continent-ocean mass transport. However, the interannual variability of this component of rotation is more strongly influenced by axial angular momentum transfer. Models of this angular momentum transfer currently lack the sophistication required for isolating surface mass transport from these ΔLOD(t) data (25). A separation would allow isolation of the change in Earth’s oblateness ΔJ2(t), which is fully independent of the SLR-based ΔJ2(t) used in our analysis. We elaborate on this issue in Materials and Methods. To model the more complete picture of climate-driven surface mass redistribution, we also consider (nontidal) atmospheric and oceanic mass (AOM) contributions that were removed from the GRACE GSM data products. We use complementary GRACE Release-05 Level-2 GAC solutions to compute the AOM-associated polar motion and to find that its contributions, particularly to χ2(t), provide some nonnegligible excitations (see Materials and Methods). We now combine the individual contributions of polar ice sheets, global GICs, TWS, and AOM to reconstruct the total climate-driven polar motion. Figure 3B compares our reconstructions with the corresponding components of observed data that are obtained after removing long-term linear trends. Henceforth, we deal only with these detrended time series, unless otherwise specified. The solutions provide an excellent reconciliation of the data: The TWS and the three cryospheric components together explain 88 ± 18% and 70 ± 34% of observed and , respectively. Adding global AOM contribution further improves the fit to by an additional 7%. We are also able to reconstruct the sharp changes in direction for χ2(t) at around 2005 and 2012; although the onset of eastward motion (positive ) at around 2005 is well documented (11), this reversal of polar motion toward the west after 2012 is a new observation with a causal origin that we can clearly isolate in this analysis. The large amplitude (~20 mas) of the reversal in χ2(t) in 2012 is comparable to those associated with observed decadal variabilities of polar motion over the past 115 years (3, 4, 6), thus suggesting that it is an emergent decadal-like oscillation. The complete picture of the redirected polar motion is more complicated than can be derived solely from changes in the ice sheets, and the large-amplitude swings must include noncryospheric mechanisms. Comparing polar motion excitations of Fig. 3 (A and B) reveals that TWS is the most plausible causal mechanism for the decadal-like oscillation during the study period (see also table S1); it has previously been identified as the dominant mechanism for annual and semiannual wobbles (26). This discovery requires a detailed analysis of the spatiotemporal variability of TWS: The trend in the global mass budget of TWS during the study period is small, and there is no anomalous variability in it at around 2012 (see Materials and Methods). However, we find that the spatial patterns of mass redistribution are strikingly different before and after 2012. As seen in Fig. 4, there is almost a complete reversal in wet (excess water mass) and dry (water mass deficit) patterns, and the intensity of wetness and drought has strengthened during 2012–2015. Mass gain in Asia and southern South America, accompanied by enhanced mass loss from western North America and Australia, is collectively consistent with the observed westward drift in polar motion since 2012. ## SUMMARY AND DISCUSSION Figure 5 summarizes our key discoveries about the changes in polar motion. Mean rates of change in the polar motion vector during 2003–2015, after removing the long-term linear drift signals, are shown in Fig. 5A. The total reconstructed signal has been partitioned to highlight the relative excitation strength of five major climatological components. The global cryospheric excitations alone explain 66 ± 7% of the observed magnitude of the polar motion vector, but the associated drift direction deviates by 38° ± 11°. Combining TWS excitations with cryospheric signals greatly reduces the variance of a fit to the amplitude and direction of polar motion: The reconstructed motion has 83 ± 23% magnitude and is within 5.9° ± 7.6° of the observed (detrended) polar motion (5.52 mas/year along 33.6° East longitude). The data fit to the magnitude is slightly improved (by 1.5%) when we add global AOM contributions, and the direction is better aligned toward the observations by 2.6°. The discrepancies between the observed motion and the reconstructed motion may be partially explained by the uncertainty in the assumed long-term linear trend (see Materials and Methods) or by the net effect of other smaller (motion) excitation mechanisms, including wind stress and ocean current variability. Figure 5B shows a comparison between the total observed mean annual pole position (including the long-term linear trend) and the total reconstructed mean annual pole position. The observed east-west wander of the pole during 2003–2015 is reproduced—owing to the excitation strength of variability in the spatial distribution of TWS—about the mean drift direction that is roughly along the Greenwich meridian. Near-decadal shifts in large-scale global wet and dry patterns (Fig. 4), which fully explain an emergent decadal-like oscillation of polar motion, are quite similar to those mapped as a drought index during 1900–1995 based on monthly air temperature and precipitation records (27). We propose that these form the causal mechanism for the long-sought origins of 10- to 20-mas decadal oscillations seen throughout the 115-year polar motion record (3, 4, 6). These are consistent with our current notional understanding of near-decadal shifts in patterns of ocean storage of thermal energy which characterize the current paradigm of decadal changes in continental rainfall and drought (28). The polar motion record may therefore offer yet unexploited information about the intensities, duration, and globality of wet and dry periods, providing possible data constraints on models of past changes in horizontal water vapor transport (29). Such model quantification will have important ramifications for climate change during the 21st century, as we now face an increased intensity of the global water cycle (30, 31). ## MATERIALS AND METHODS ### Polar motion: Theory and methods Euler’s equations of classical mechanics that conserve angular momentum form the fundamental equations of motion for a rotating body. Consider body-fixed right-handed Cartesian coordinates with the origin located at the center of mass of the planet. In the present context, where the external torque is absent, we may express Euler’s equations as (32, 33)(2)Here, ω(t) is the angular velocity vector, I(t) is the inertia tensor that changes as a result of the redistribution of Earth’s (surface and interior) mass, and h(t) is the change in angular momentum attributable to motion relative to the rotating reference frame. Because the polar motion is minimally affected by the motion-induced change in angular momentum in the lower-frequency domains (lower than the Chandler wobble frequency) that we are interested in, the following discussion is based on the assumption that h(t) ≅ 0. In the chosen body-fixed coordinates and assumed initial equilibrium state, the products of inertia tensor vanish (that is, Iij = 0 for ij = 1, 2, 3) and the moments of inertia tensor for (assumed) rotationally symmetric Earth are given by Iii = A (for i = 1, 2) and I33 = C, where A is the mean equatorial and C is the polar moment of inertia. Similarly, components of angular velocity vector are given by ωi = δi3Ω (for i = 1, 2, 3), where δi3 is the Kronecker delta and Ω is the mean rotational velocity of Earth. Following the mass redistribution on Earth’s surface, both I(t) and ω(t) are perturbed from their initial equilibrium states. Let and Ωmi be the respective perturbation terms, where mi are nondimensional and typically on the order of ≤ 10−6. Inserting these perturbation terms into Eq. 2 and dropping second- or higher-order terms give the following coupled equation to be solved for m1(t) and m2(t) characterizing the rotational pole (32, 33)(3)Here, σr is the Chandler wobble frequency for an elastic Earth (with 433-day periodicity) and ke is an effective degree 2 Love number that accounts for rotation-induced perturbations in gravitational and rotational potentials (18, 32, 33). The excitation functions are given by(4)Here, the first terms on the right-hand side are directly induced by mass redistribution and, hence, are often called “mass excitation functions” (33). The IERS reports the pole position vector, with components [X(t) Y(t)]T, in the celestial reference frame, whereas rotational pole [m1(t) m2(t)]T and excitation pole [χ1(t) χ2(t)]T are computed in the body-fixed terrestrial reference frame. However, for frequencies much lower than the Chandler wobble frequency that we are interested in, the celestial intermediate pole, the rotational pole, and the excitation pole all have virtually the same motion (4, 33), that is(5)The low-frequency polar motion estimates provided in this study are essentially those computed from Eq. 4. To evaluate perturbations in the product of inertia (particularly and appearing in Eq. 4) induced by climate-driven surface mass redistribution, we defined a mass-conserving loading function, L(θ, λ, t), as in Eq. 1. The loading function and the relevant components of inertia tensor are related as (18)(6)Here, a is the mean radius of Earth, ρw is the water density, and L21n(t) represents degree 2 order 1 SH coefficients of L(θ, λ, t), which follows from the following orthogonal relationship(7)Here, 𝒴21n(θ, λ) represents the 4π-normalized degree 2 order 1 SHs, with cosine and sine components denoted by n = 1 and n = 2, respectively (18, 34). As shown in fig. S1, the inertia tensor, and hence polar motion, are greatly sensitive to mass changes occurring around ±45° latitudes. The integral appearing in Eq. 7 is applied over the surface domain of a unit sphere . Computation of H(θ, λ, t). To fully define the global loading function (Eq. 1), we computed H(θ, λ, t) by analyzing the GRACE Release-05 Level-2 monthly GSM data products provided by the Center for Space Research at the University of Texas at Austin. The monthly time series of these data were distributed in the form of Stokes coefficients up to SH degree and order 60 (10, 34). Here, we covered a 13-year period, from April 2002 to March 2015. There were only partial or no data available for a few months during the study period, and we filled these data gaps through linear scaling or interpolation between adjacent monthly data, as appropriate. Because GRACE cannot measure the degree 1 Stokes coefficients as a result of its sensitivity only to the center of mass frame, we used those obtained from the analysis of SLR observations (35) or those inferred from the GRACE solutions and ocean model outputs (13). We also replaced degree 2 Stokes coefficients with more accurate SLR-based estimates (14, 36). We did not apply the pole tide correction (37) because its effects on the continental WEH were minimal (on the order of 1%) and our estimates of oceanic mass variations [S(θ, λ, t)] follow from the solutions of the sea-level equation [see Computation of S(θ, λ, t)] that are independent of GRACE-inferred ocean mass redistribution. Nonetheless, the pole tide–associated errors should be within our uncertainty estimates, which were constrained by, among other factors, the plausible range of degree 1 and degree 2 Stokes coefficients (see Polar Motion: Results). After filling the data gaps and inserting more accurate degree 1 and degree 2 Stokes coefficients as summarized above, we followed the standard procedure to retrieve climate-driven monthly WEH signals, as discussed elsewhere (34, 38). We first obtained the Stokes coefficient anomalies by removing the corresponding mean values during the study period. We calculated the total WEH caused by both the surface mass redistribution and the GIA processes embedded in GRACE data, using a Gaussian filter with a 300-km radius. We isolated the climate-driven WEH by removing the GIA signals provided by A et al. (15) and finally applied appropriate (regional) scaling to account for the so-called leakage effects and attenuated signals. A detailed description of solution scaling and uncertainties thereof is provided in Polar Motion: Results. Computation of S(θ, λ, t). The budget of continental mass directly contributes to the sea-level change, via mass conservation. The variability in H(θ, λ, t) on the continents, along with this ocean loading, induces perturbations in the gravitational and rotational potentials of the planet, causing the further redistribution of S(θ, λ, t), which is gravitationally self-consistent. For an elastically compressible rotating Earth, the gravitationally consistent S(θ, λ, t) is given by (18)(8)Here, M is the total mass of Earth, is the acceleration resulting from gravity, is the Green’s function for an elastically compressible Earth that parameterizes the perturbations in gravitational potential and associated solid-Earth deformation, Λ2mn(t) represents the degree 2 SH coefficients related to perturbations in rotational potential and associated solid-Earth deformation, and E(t) is the eustatic term that follows from the mass conservation constraint. The operator ⊗ appearing in Eq. 8 signifies the spatial convolution over the surface of a unit sphere . Computation of S(θ, λ, t) requires a priori knowledge of L(θ, λ, t), which in turn depends on S(θ, λ, t) itself (cf. Eq. 1). We therefore solved the coupled system of Eqs. 1 and 8 using a recursive scheme. All of our calculations were based on a novel mesh-based approach (18), which, unlike contemporary pseudo-spectral methods, remained numerically accurate and computationally efficient as the resolution requirements approached those of contemporary ice sheets or ocean models (on the order of a few kilometers). ### Polar motion: Results Accurate estimates of polar motion induced by the climate-driven global change in L(θ, λ, t) require careful retrieval of H(θ, λ, t) from the GRACE observations. A common practice is to directly compare H(θ, λ, t) obtained from the standard GRACE processing (hereafter termed “original” signal) with more accurate field- and model-based estimates and to scale it accordingly. In this section, we summarize our scaling approach and present estimates of polar motion (Eq. 4). To understand the origins of observed polar motion during the study period (Fig. 1), we partitioned the continental domain into the following four nonoverlapping subdomains that represent unique components of Earth’s climate system: the GIS, the AIS, GICs, and the continental hydrosphere. Although the first three components together characterized the global cryospheric changes, the fourth component accounted for the variability in TWS. Cryospheric changes. The largest uncertainty in the original H(θ, λ, t) is perhaps related to the GIA correction (15, 38, 39), especially for the AIS (19, 40). The choice of degree 1 and degree 2 Stokes coefficients is also shown to have a considerable impact on WEH estimates for polar ice sheets (16, 38). Using a suite of GIA models and various choices of low-degree Stokes coefficients, Schrama et al. (16) provided a rigorous estimate of mass evolution and uncertainties thereof for the entire GIS, three nonoverlapping subdomains of the AIS, and 15 glaciated regions that cover the global GICs. Their estimates are generally consistent with other published results (1923, 38, 40), and we scaled our estimates such that the trend in total mass and uncertainties thereof were reproduced during the common time span. The corresponding solutions and uncertainties of χ1(t) and χ2(t) presented below account for the lump-sum effects of GIA, degree 1 and degree 2 Stokes coefficients, leakage errors, and signal attenuation. Our domain of the GIS covered the ice sheet and peripheral GICs. We scaled the original H(θ, λ, t) for the entire domain by a factor of 1.64 (16, 19) so that the total mass loss during the study period is about −278 ± 19 Gt/year (fig. S2). Pervasive and sustained thinning of the southern GIS, as seen in the figure, was consistent with other published results (19, 22, 40) and was attributed to the combination of negative surface mass balance and enhanced outflux (19). The associated loss in gravity anomaly was reflected in the “sea-level fingerprint” (fig. S2A) that shows the drop in local sea level and the rise elsewhere, particularly around East Asia and the Drake Passage between the Antarctic Peninsula and southern South America. Our estimates of GIS-driven polar motion are shown in fig. S2B. We found that the GIS promoted a positive (2.82 ± 0.19 mas/year) and a negative (−2.20 ∓ 0.15 mas/year), consistent with the signatures of relevant SHs (cf. fig. S1). Because our error estimates were based on the basic assumption that the spatial pattern of H(θ, λ, t) is relatively stable, these could not fully quantify the uncertainties in drift direction. However, here, we considered the maximum uncertainty obtained from four possible combinations of limiting values of and . Consequently, the GIS causes the pole position vector to drift along 37.96° ± 3.82° West longitude at a rate of 3.58 ± 0.24 mas/year during the study period. Our AIS domain comprised the continental ice sheet and the relatively small peripheral GICs. We applied scaling factors of 1.16, 1.43, and 2.08 for the West AIS, the East AIS, and the Antarctic Peninsula, respectively (16, 19, 38). Although the net budget of the entire AIS is negative (−92 ± 26 Gt/year), the East AIS has gained mass at a rate of about 80 ± 16 Gt/year as a result of increased precipitation (19). Large losses are recorded for the West AIS (−137 ± 7 Gt/year) and the Antarctic Peninsula (−35 ± 3 Gt/year) as a consequence of accelerated ice dynamics and, to a lesser degree, increasingly negative surface mass balance (19, 20). The spatial distribution of for the entire AIS is shown in fig. S3. High rates of ice loss along the Amundsen Sea Sector and the moderate rates of loss in the Antarctic Peninsula and gain in Dronning Maud Land and Enderby Land, as seen in the figure, are consistent with numerous reports of mass changes that are comparable to the time span of our study (19, 20, 22, 40). The associated shown also suggests a large drop in local sea level around the Amundsen Sea Sector and a rise around Dronning Maud Land and Enderby Land. We computed the corresponding polar motion and found that mas/year and mas/year (fig. S3C). The positive rates for both χ1(t) and χ2(t) were consistent with mass loss from the Amundsen Sea Sector and mass gain in Dronning Maud Land and Enderby Land. Mass loss from the Antarctic Peninsula acted to diminish while enhancing , contributing to a muted rate of χ1(t) that was causally related to the entire AIS (cf. fig. S1). Following the same approach as for the GIS, we sourced the AIS-driven components of the polar motion vector to a direction along 64.24° ± 3.37° East longitude of amplitude 2.23 ± 0.18 mas/year during the study period. We formed a global GIC domain by creating 15 nonoverlapping regions (fig. S4). Our regional masks for mass change determination were based on the fraction of 0.5° × 0.5° global grids covered by regional GICs (21). We mapped this gridded information onto our computational mesh (18) by using an anisotropic mesh refinement algorithm so that the finer mesh, with a characteristic element size on the order of 10 km, is used in the glaciated regions. We then assumed that any element with ≥ 1% ice coverage has a GRACE signal dominated by GIC changes, and we defined the regional mask accordingly. Some of these regions have lost mass at a great pace, whereas others did not exhibit significant long-term trends during the span of our study (fig. S5). Alaska (−42.1 ± 6.8 Gt/year), the North Canadian Arctic (−33.9 ± 3.3 Gt/year), the South Canadian Arctic (−28.4 ± 1.9 Gt/year), Patagonia (−19.5 ± 4.8 Gt/year), and High Mountain Asia (−8.6 ± 0.6 Gt/year) are the areas with the greatest loss. We individually scaled all of these 15 regions to derive H(θ, λ, t) for global GICs. (See fig. S4A for during the study period.) The associated computation of suggests a considerable sea-level drop in the region north of ≈ 45° latitude. Figure S4B summarizes our estimates of polar motion excitations. By combining polar motions driven by individual regions, we found minimal overall contributions of global GICs with relatively large uncertainties: mas/year and mas/year. Figure S1 shows that glacial mass loss in Alaska and Patagonia collectively drives a negative . Similarly, χ2(t) caused by GICs in Alaska, the Canadian Arctic, High Mountain Asia, and Patagonia tends to operate with differing signs, and hence yields a rather muted (negative) . TWS changes. Excluding the cryospheric domains, the mass redistribution in the continents may be interpreted as the TWS changes. By definition, we may express the TWS, W(θ, λ, t), as follows (41)(9)Here, V(θ, λ, t) is the vertically integrated water vapor anomaly, ∇Q(θ, λ, t) is the divergence of the horizontal water transport, and R(θ, λ, t) is the runoff. The first term on the right-hand side is equivalent to the difference between precipitation and evapotranspiration. If we evaluate Eq. 9 on a monthly time interval during the study period, the TWS signal would essentially be the same as the monthly WEH signal derived from the GRACE observations, or W(θ, λ, t) ≡ H(θ, λ, t). Figure S6A shows the linear trend in the original H(θ, λ, t) that needs to be scaled appropriately. Landerer and Swenson (17) analyzed monthly TWS signals obtained from the GRACE observations and the Noah land surface model, simulated within the Global Land Data Assimilation System (GLDAS-Noah), and derived global gridded gain factors (fig. S6B). These scaling factors, when applied to the original H(θ, λ, t), helped to correct for the leakage errors and to restore the attenuated signals. Relatively large gain factors along the coasts, as seen in the figure, implied that a large signal loss prevails between the oceans and the continents. Figure S6C shows the corrected and associated variations in during the study period. The feature that stands out in the present context of polar motion is a strong and large-scale, negative TWS signal around Eurasia (the Indian subcontinent and the Caspian Sea). This and the global signals are consistent with the general picture that has emerged from the GRACE monthly variability on continental land masses (23, 42, 43). Such variability in global TWS induces changes in sea level such that it rises in the Atlantic Ocean and falls around the Drake Passage and the Asia Pacific. The total TWS mass evolution and our estimates of polar motion are plotted in fig. S6D. The trends in global mass budget are small for both the original and the corrected TWS signals, implying that the net contribution of TWS to the global mean sea level is minimal. The patterns of polar motion are generally unaffected by the gain factors: The reversal in χ2(t) since about 2012, for example, is apparent for both the original and the corrected TWS changes. However, we found some sensitivity of gain factors on the solved-for linear trend in polar motion, particularly for χ1(t), and this forms the basis of our uncertainty estimates. There is no physically or statistically rigorous basis for defining the uncertainties for TWS-driven polar motion, and we simply considered the solutions associated with the original TWS signals as the limiting values. Consequently, the respective contributions of TWS variability and uncertainties to and are 0.40 ± 0.43 and 2.40 ± 0.39 mas/year. This suggests that the robust changes in TWS cause the polar motion vector to drift along 80.5° ± 8.7° East longitude at a rate of about 2.43 ± 0.45 mas/year during the study period. Nontidal AOM variability. There is nontidal AOM contribution to Earth’s surface mass redistribution that is not included in the GRACE GSM solutions. The AOM-associated Stokes coefficients, which are provided as complementary GRACE GAC solutions, are computed from the European Centre for Medium-Range Weather Forecast (ECMWF) operational atmospheric model and the baroclinic Ocean Model for Circulation and Tides (OMCT) driven by the same atmospheric model. We estimated corresponding polar excitations using the following linear relationship (11)(10)Here, ΔC21(t) and ΔS21(t) are the Stokes coefficients and is the degree 2 load Love number. Results are shown in fig. S7. The figure shows, as expected, that the global AOM variability induces high (seasonal) amplitude excitations. We found that the AOM had negligible contribution to (−0.03 mas/year), but it had sizable effects on (0.22 mas/year) during the study period. Observed and reconstructed polar motion. To compare our estimates of polar motion with the observed data (Fig. 1), it is first necessary to remove the long-term trends from the observations. Here, we considered the GIA-driven true polar wander along 75° West longitude at a rate of 0.85° (great-circle distance) per million years (5) as the long-term trend of the pole position vector. Other estimates that are mostly inferred from ~100 years of polar motion record are generally within the 25% uncertainties (1, 2, 44, 45). Therefore, we used mas/year and mas/year as the long-term trends. Subtracting these from the observed rates of mas/year and mas/year (during 2003–2015) gave mas/year and mas/year. In what follows, we quantify how much of these detrended motions are explained by the cryospheric mass changes alone (11) and how many improvements we make to a data fit through rigorous incorporation of TWS and global AOM signals. Table S1 summarizes and during the study period. By combining the AIS, the GIS, and global GIC signals, we found that the total cryospheric changes accounted for mas/year and mas/year, and caused the pole position vector to drift along 4.4° ± 11.4° West longitude at a rate of 3.65 ± 0.38 mas/year. This suggests that the global cryospheric changes explain only about 66.0 ± 6.8% of the observed (detrended) polar motion and predict the mean drift direction within 38.0° ± 11.4°. By adding TWS signals, we obtained mas/year and mas/year, which is a great reduction in the variance of a fit to the data (by about 66% for χ1 and by about 92% for χ2). As a consequence, our total reconstruction of the pole position vector predicted a drift along 27.7° ± 7.6° East longitude at a rate of 4.56 ± 1.26 mas/year. This means that the TWS excitations, when combined with cryospheric signals, reduce the variance of a fit to the magnitude of the pole position vector by 74% and to the direction of the pole position vector by 97%, and explain nearly the entire amplitude (82.6 ± 22.8%) and mean directional shift (within 5.9° ± 7.6°) of the observed (detrended) polar motion. The data fit to the magnitude was slightly improved (by 1.5%) as we added the global AOM contributions, and the direction was further aligned toward the observations by 2.6°. ### Use of ΔLOD(t) as an additional constraint on ΔJ2(t) Lunar Laser Ranging (LLR) has been operating since 1970 and has provided accurate determination of the rate of slowing of the axial rotation by the transfer of angular momentum from Earth to the lunar orbit by tidal dissipation (46). The slowing may, for example, be expressed as ω3(t) = Ω[1 + m3(t)]. The rate of deceleration is effectively secular on a time scale of 10 million years. Although the rate of slowing is roughly consistent with ancient eclipse observations that constrain the secular ΔLOD(t) (33), there is a systematic offset in the time of recorded eclipses (47). The offset in the LLR-determined m3(t) (from that observed in eclipse data) is, in fact, consistent with an additional slight secular increase in the rotation rate caused by a change in the polar moment of inertia C due to GIA (48). GIA processes are uncomplicated by angular momentum transfer, and a linear relation exists between the change in Earth’s gravitational bulge [that is, ] and the associated secular nontidal ΔLODGIA(t). A natural question to ask concerning our focus on the period of space geodetic observations is whether a ΔLOD(t) time series might contain additional information that constrains cryospheric and hydrological mass variability on interannual time scales. However, the motion terms in the excitation function associated with zonal winds and ocean currents have a relatively strong influence on the ΔLOD(t) time series (4). On centennial time scales, these angular momentum exchanges have comparatively short periods, and ΔLOD(t) can be adequately described by the mass terms in the excitation function. However, for data taken since the mid-1970s, when SLR data first became available for directly constraining , angular momentum (motion) terms have a non-negligible contribution to ΔLOD(t) observations, and the physical models that drive such motions must be carefully considered. A recent analysis (49) of the IERS time series for ΔLOD(t) has attempted to isolate the motion excitations and thus deduce a ΔLOD(t) proxy for ΔJ2(t), potentially providing a consistency check on SLR-based ΔJ2(t) observations (36, 49, 50). However, in addition to the angular momentum transfer within Earth’s surface fluid envelope, a relatively poorly modeled angular momentum coupling between the mantle and the core must also be considered. This fact necessitates using a filter to remove 7-year and longer periodicities (49) from ΔLOD(t) and suggests that useful inferences of large-scale surface mass transport from axial changes in rotation during the 13-year GRACE time series considered in our analysis will be quite difficult to obtain. ## SUPPLEMENTARY MATERIALS Fig. S1. SHs of degree 2 order 1. Fig. S2. GIS and polar motion excitations. Fig. S3. AIS and polar motion excitations. Fig. S4. Global GICs and polar motion excitations. Fig. S5. Mass evolution of regional GICs. Fig. S6. TWS and polar motion excitations. Fig. S7. Polar motion excitations due to nontidal AOM variability. Table S1. Polar motion excitation rates for different time periods. This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited. ## REFERENCES AND NOTES Acknowledgments: We wish to thank E. Larour for his contribution to solving the sea-level equation. Conversations with J. Mitrovica and J. Chen are also acknowledged. Funding: This research was carried out at the Jet Propulsion Laboratory of the California Institute of Technology, under a contract with the National Aeronautics and Space Administration (NASA) and with funding from the Cryosphere Program and the Earth Surface and Interior Focus Area as part of the GRACE Science Team and NASA Sea-level Change Team efforts. S.A. was supported through a fellowship from the NASA Postdoctoral Program. Author contributions: S.A. performed all of the calculations. Both authors contributed to the analysis of the results and to the writing of the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors. View Abstract	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9132073521614075, "perplexity": 2513.6099729416237}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578548241.22/warc/CC-MAIN-20190422075601-20190422101601-00243.warc.gz"}
https://en.wikiversity.org/wiki/Numerical_Analysis/Householder_transformation_exercises	# Householder's method Exercises ## Exercise 1 This exercise will help you in introducing how to perform the Householder's method to transform a symmetric matrix A into the tridiagonal form. All of the notations and computations in this Exercise follow from those in Section 9.3, Numerical Analysis, Burden and Faires, 8th Edition. It's recommended that you read that section before solving the problem. It's also recommended that you read the following useful links 1. Householder's method for symmetric matrices, J. H. Wilkinson, Handbook Series Linear Algebra, Volume 4, Number 1 / December, 1962, Springer Berlin / Heidelberg. 2. Module for Householder Transformations, Mathematics Department, California State University, Fullerton. Problem Let ${\displaystyle A={\begin{bmatrix}5&-1&-4&2\\-1&3&2&3\\-4&2&4&-3\\2&3&-3&2\end{bmatrix}}.}$ Perform Householder's method to bring A into a tridiagonal form. Solution Step 1: k = 1 (Meaning: Making 0's for the third and fourth rows of the first column) 1 ${\displaystyle \displaystyle \alpha =-sgn(a_{k+1,k}){\sqrt {\sum _{j=k+1}^{n}a_{jk}^{2}}}}$ is . 2 ${\displaystyle r={\sqrt {{\frac {1}{2}}(\alpha ^{2}-a_{k+1,k}\alpha )}}}$ is . 3 Now, we are going to find the vector ${\displaystyle w^{(1)}={\begin{bmatrix}w_{1}^{(1)}\\w_{2}^{(1)}\\w_{3}^{(1)}\\w_{4}^{(1)}\end{bmatrix}}}$ Set ${\displaystyle w_{1}^{(1)}=0}$, we need to find ${\displaystyle w_{2}^{(1)},w_{3}^{(1)},w_{4}^{(1)}}$ ${\displaystyle w_{2}^{(1)}={\frac {a_{2,1}-\alpha }{2r}}=}$ . ${\displaystyle w_{j}^{(1)}={\frac {a_{j,1}}{2r}}}$ for j = 3 and 4 gives ${\displaystyle w_{3}^{(1)}={\frac {a_{3,1}}{2r}}=}$ ${\displaystyle w_{4}^{(1)}={\frac {a_{4,1}}{2r}}=}$ 4 The orthogonal matrix ${\displaystyle \displaystyle P^{1}}$, defined as ${\displaystyle \displaystyle P^{1}=I-2w^{(1)}(w^{(1)})^{t}}$ is (click Submit to see the answer) 5 The new matrix ${\displaystyle \displaystyle A^{(1)}}$, defined as ${\displaystyle \displaystyle A^{(1)}=P^{1}AP^{1}}$, should be in the form ${\displaystyle A^{(1)}={\begin{bmatrix}&&0&0\\*&&&\\0&&&\\0&&&\end{bmatrix}}}$ This is the end of Step 1. Step 2: k = 2 (Meaning: Making 0's for the fourth row of the second column) In Step 2, we redo the computations in Step 1 with the matrix ${\displaystyle \displaystyle A=A^{(1)}}$ 1 ${\displaystyle \displaystyle \alpha =-sgn(a_{k+1,k}){\sqrt {\sum _{j=k+1}^{n}a_{jk}^{2}}}}$ is . 2 ${\displaystyle r={\sqrt {{\frac {1}{2}}(\alpha ^{2}-a_{k+1,k}\alpha )}}}$ is . 3 Now, find the vector ${\displaystyle w^{(2)}={\begin{bmatrix}w_{1}^{(2)}\\w_{2}^{(2)}\\w_{3}^{(2)}\\w_{4}^{(2)}\end{bmatrix}}}$ Set ${\displaystyle w_{1}^{(2)}=w_{2}^{(2)}=0}$, we need to find ${\displaystyle w_{3}^{(2)},w_{4}^{(2)}}$ ${\displaystyle w_{3}^{(2)}={\frac {a_{2,1}-\alpha }{2r}}=}$ . ${\displaystyle w_{4}^{(2)}={\frac {a_{4,1}}{2r}}=}$ 4 The orthogonal matrix ${\displaystyle \displaystyle P^{2}}$, defined as ${\displaystyle \displaystyle P^{2}=I-2w^{(2)}(w^{(2)})^{t}}$ is (click Submit to see the answer) 5 The new matrix ${\displaystyle \displaystyle A^{(2)}}$, defined as ${\displaystyle \displaystyle A^{(2)}=P^{2}A^{(1)}P^{2}}$, should be in the form ${\displaystyle A^{(2)}={\begin{bmatrix}&&0&0\\*&&&0\\0&&&\\0&0&&\end{bmatrix}}}$ This is the end of Step 2. Now the matrix ${\displaystyle \displaystyle A^{(2)}}$ is in a tridiagonal form. The Householder's method is complete. ## Exercise 2 1 Householder's method is for Any matrix. A non-symmetric positive define matrix. A symmetric matrix. A non-symmetric diagonally dominant matrix. 2 The goal of Householder's method is for Finding the determinant of a matrix. Transforming a matrix to tridiagonal form. Finding eigenvalues of a matrix. Finding the LU decomposition of a matrix. 3 How many steps do we need to perform in Householder's method n steps (where n is the size of the matrix). 2n steps. ${\displaystyle {\frac {n}{2}}}$ steps. n-2 steps. 4 What should be performed after Householder's method LU decomposition. Support Vector Decomposition (SVD). Power method. QR decomposition. 5 Will the Householder's method ever fail Yes No. ## Exercise 3 Problem Based on the computations performed in Exercise 1, write code in Matlab to perform the Householder's method for an input symmetric matrix A. Solution 132.235.39.18 19:02, 28 May 2009 (UTC) Nam Nguyen	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 30, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8682637214660645, "perplexity": 649.9014371341583}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574665.79/warc/CC-MAIN-20190921211246-20190921233246-00213.warc.gz"}
https://math.stackexchange.com/questions/808711/non-linear-second-order-differential-equation	# Non-linear Second Order Differential equation I want to ask for a hint in solving the following ODE, $y'' (1+x^2) + y' (x) = C$, where C is a constant. I've tried a couple of ways to manipulate this ODE; such as letting v = y' $v' (1+x^2) + v (x) = C$ but I can't see a way to solve the equation for y • Your idea is good. Note that you can divide by $1+x^2$. Then use your favorite method to solve a first degree ODE. – Git Gud May 25 '14 at 11:54 • To me it looks similar to Euler-type equation which can be simplified and solved by the substitution $x=e^t$, $t = \ln x$ (so that in case of $y''x^2 + y'x$ you get $g'' + g'$ instead). Cannot be sure it is going to work in this case. – Shady_arc May 25 '14 at 12:12 ## 1 Answer $$\left(1+x^2\right)v' + xv = C$$ we can obtain $$v\sqrt{1+x^2} = C\int\frac{1}{\sqrt{1+x^2}}dx + \lambda_{1}$$ or $$\frac{dy}{dx} = \frac{C}{\sqrt{1+x^2}}\int\frac{1}{\sqrt{1+x^2}}dx + \frac{\lambda_{1}}{\sqrt{1+x^2}} = \frac{1}{\sqrt{1+x^2}}\left[C\sinh^{-1}(x) + \lambda_1\right]$$ so $$y = \lambda_1\int \frac{1}{\sqrt{1+x^2}} + C\int \frac{1}{\sqrt{1+x^2}}\sinh^{-1}(x)$$ the first integral evaluates to $\sinh^{-1}x$ the second can be evaluated as follows $$\int \frac{1}{\sqrt{1+x^2}}\sinh^{-1}(x) = \int \sinh^{-1}(x) \frac{d}{dx}\sinh^{-1}(x) dx = \frac{1}{2}\left(\sinh^{-1}x\right)^{2} + \lambda_2$$ $$y(x) = \lambda_1 \sinh^{-1}(x) + \frac{C}{2}\left(\sinh^{-1}x\right)^{2} + \lambda_3$$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.925421416759491, "perplexity": 179.9379136763287}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526799.4/warc/CC-MAIN-20190720235054-20190721021054-00351.warc.gz"}
http://www.navipedia.net/index.php/Relativistic_Clock_Correction	If you wish to contribute or participate in the discussions about articles you are invited to join Navipedia as a registered user # Relativistic Clock Correction Fundamentals Title Relativistic Clock Correction Author(s) J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain. Level Intermediate Year of Publication 2011 The rate of advance of two identical clocks, placed one in the satellite and the other on the terrestrial surface, will differ due to the difference of the gravitational potential (general relativity) and to the relative speed between them (special relativity). This difference can be split into [1]: • A constant component that only depends on the nominal value of the semi-major axis of the satellite orbit, which is adjusted modifying (in factory) the clock oscillating frequency of the satellite[footnotes 1]: $\frac{f_0'-f_0}{f_0}=\frac{1}{2} \left( \frac{v}{c} \right) ^2+\frac{\triangle U}{c^2} \simeq -4.464 \cdot 10^{-10} \qquad \mbox{(1)}$ • A periodical component due to the orbit eccentricity (that must be applied by the user receiver software): $\Delta_{rel}=- 2\, \frac{\mathbf{r}^{sat} \cdot \mathbf{v}^{sat}}{c^2} \qquad \mbox{(2)}$ where ${\mathbf r}^{sat}$ and ${\mathbf v}^{sat}$ are the satellite position ($\displaystyle m$) and velocity ($\displaystyle m/s$) vectors, in an inertial system[footnotes 2]. The scalar ${\mathbf r}^{sat}\cdot{\mathbf v}^{sat}$ can be evaluated either in a CRS or TRS (i.e., ECEF) system. Notice that in a ECEF system, the earth rotation ${\boldsymbol \omega}_E \times {\mathbf r}^{sat}$ should be discounted from ${\mathbf v}^{sat}$, but it cancels in the scalar product with ${\mathbf r}^{sat}$. Unlike in GPS, relativistic corrections to GLONASS orbits eccentricity are transmitted within the navigation message into the satellite clock corrections ($\displaystyle \tau_n$, $\displaystyle \gamma_n$). Thence, (2) is not needed with such broadcast message [1]. Figure 1 illustrates the effect of neglecting the relativistic correction given by equation (2) on the user position. As it is shown, range errors up to 13 meters and vertical errors over 20 meters can be experienced when neglecting this correction. First row shows the horizontal (left) and vertical (right) positioning error using (blue) or not using (red) the relativistic correction 2. The variation in range, in meters units, is shown in the second row at left. ## Notes 1. ^ Being $\displaystyle f_0=10.23 MHz$, one has $\Delta f_0= 4.464 \cdot 10^{-10}\, f_0=4.57 \cdot 10^{-3} Hz$ thus the satellite must use $f_0'=10.22999999543\,Mhz$. Notice that $\displaystyle f_0^'$ is the frequency "emitted" by the satellite and $\displaystyle f_0$ is the one "received" on the terrestrial surface, i.e., an apparent increase of the frequency is of $4.57 \cdot 10^{-3} Hz$. That is, the clock on satellite appear to run faster ($\simeq 38 \mu s/day$) than on ground [note: $\displaystyle \Delta f/f=\Delta T/T$]. This effect is corrected (in factory) decreasing the oscillating frequency of the satellite by this amount $4.57 \cdot 10^{-3} Hz$. 2. ^ Note: Over the osculating orbit, $\sqrt{\mu a}\,e\sin E={\mathbf r} \cdot {\mathbf v}$. Thence, $\Delta_{rel}=- 2\, \frac{\mathbf{r} \cdot \mathbf{v}}{c^2}= -2\,\frac{\sqrt{\mu\, a}}{c^2} \, e\, \sin(E)$, where $\displaystyle \mu$ the (geocentric) gravitational constant, $\displaystyle c$ the speed of light in a vacuum, $\displaystyle a$ and $\displaystyle e$ the semi-major axis and eccentricity of the osculating orbit and $\displaystyle E$ the eccentric anomaly. ## References 1. ^ a b Ashby, N., 2003 Relativity in the Global Positioning System	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 28, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9233224391937256, "perplexity": 1252.802671293293}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131296587.89/warc/CC-MAIN-20150323172136-00121-ip-10-168-14-71.ec2.internal.warc.gz"}
https://www.coursehero.com/file/62593003/allpdf/	all.pdf - College Algebra 1 of 458 College Algebra Course Instructions Please read the instructions given below related to Course\"College Algebra There all.pdf - College Algebra 1 of 458 College Algebra Course... • 458 This preview shows page 1 - 5 out of 458 pages. College Algebra 1 of 458 College Algebra Course Instructions Please read the instructions given below related to Course "College Algebra" There are 5 sections in this course. All sections are mandatory. In Section 1 of this course you will cover these topics: Fundamental Concepts Of Algebra 1 Fundamental Concepts Of Algebra 2 In Section 2 of this course you will cover these topics: Graphs And Graphing Utilities Functions And Graphs In Section 3 of this course you will cover these topics: Polynomial And Rational Functions Exponential And Logarithmic Functions In Section 4 of this course you will cover these topics: Systems Of Equations And Inequalities Matrices And Determinants In Section 5 of this course you will cover these topics: Conic Sections Sequences, Induction, And Probability 2 of 458 College Algebra > Section 1 Section 1- Instructions In Section 1 of this course you will cover these topics: Fundamental Concepts Of Algebra 1 Fundamental Concepts Of Algebra 2 You may take as much time as you want to complete the topic coverd in section 1. There is no time limit to finish any Section, However you must finish All Sections before semester end date. 3 of 458 College Algebra > Section 1 > Topic 1 Topic 1: Fundamental Concepts Of Algebra 1 Topic Objective: At the end of this topic, students will be able to understand: 1. Algebraic Expressions 2. Formulas and Mathematical Models 3. Sets 4. Properties of Real Numbers and Algebraic Expressions 5. Simplifying Algebraic Expressions 6. Exponents and Scientific Notation 7. Radicals and Rational Exponents 8. Polynomials Topic Introduction: Algebra uses letters, such as x and y to represent numbers. If a letter is used to represent various numbers, it is called a variable. Topic Overview: 1. Algebraic Expressions For example, imagine that you are basking in the sun on the beach. We can let x represent the number of minutes that you can stay in the sun without burning with no sunscreen. With a number 6 sunscreen, exposure time without burning is six times as long, or 6 times x . This can be written 6 · x but it is usually expressed as 6 x. Placing a number and a letter next to one another indicates multiplication. Notice that 6 x combines the number 6 and the variable using the operation of multiplication. A combination of variables and numbers using the operations of addition, subtraction, multiplication, or division, as well as powers or roots, is called an algebraic expression . Here are some examples of algebraic expressions: Many algebraic expressions involve exponents . For example, the algebraic Expression 17 x 2 + 261 x = 3257 approximates the average cost of tuition and fees at public U.S. colleges for the school year ending years x after 2000. The expression x 2 means x · x , and is read “ x to the second power” or “ x squared.” The exponent, 2, indicates that the base, x , appears as a factor two times.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8575400114059448, "perplexity": 697.1400303378022}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150266.65/warc/CC-MAIN-20210724125655-20210724155655-00050.warc.gz"}
https://www.physicsforums.com/threads/calculation-of-bolt-angle.258590/	Calculation of bolt angle 1. Sep 23, 2008 MJCfromCT I have a flange of known thickness, with a bolt hole of a known diameter through it. I am trying to calculate the maximum angle off from the centerline through the bolt hole that the bolt will be able to pass ( I know the max diameter of the bolt as well ). Is there a formula for this, given that I know the flange thickness, bolt hole diameter, and bolt diameter? Thanks in advance. 2. Sep 23, 2008 mgb_phys I would just draw a picture. You have a striaght hole of known width and depth, a straight bolt of known width. The angle should come out easily - probably more easily than describing the question. 3. Sep 23, 2008 MJCfromCT Thanks. Yeah, as soon after I posted this, I drew it out and it became a lot clearer :) 4. Sep 23, 2008 Mech_Engineer Yup, trig = friend Counter-sinks on the hole can also have a large effect on max angle, so you might look into that. Similar Discussions: Calculation of bolt angle	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8651390075683594, "perplexity": 1361.6455905418964}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608984.81/warc/CC-MAIN-20170527171852-20170527191852-00391.warc.gz"}
http://math.stackexchange.com/questions/247918/unexplainable-noise-graph-function/247929	# Unexplainable noise graph function. I'm sorry for the ambiguity here but I've recently discovered a function which plots, what seems to be either a fractal or simply noise in a selected area. Can anyone explain this function: $\sqrt{x^2+y^2} = \frac{1}{(\cos(\tan^{-1}(x/y)+\tan^{-1}(y/x)))}$ Graph it and see what you make of it. I was trying to find the locus of a square, but instead found the equation of parallel lines through $abs(x) = a$ $\sqrt{x^2+y^2} = \frac{a}{\cos(\tan^{-1}(x/y))}$ and then added in an extra $\tan^{-1}(y/x)$, the reciprocal of $\tan^{-1}(x/y)$ and thats how I discovered this strange graph. I'm in only in high school, so I'm sorry if my question is a a bit simple. - How did you plot it? Via MATLAB, etc? – Gautam Shenoy Nov 30 '12 at 8:48 I must confess, there is a certain similarity on different scales - though I guess this is due to the number of roots of the trigonometric functions. – S.D. Nov 30 '12 at 8:59 I used grapher on mac – Jordan Brown Nov 30 '12 at 9:00 a screenshot would have been welcome, to help interpret it. – comprehensible Mar 19 '14 at 12:19 $$\tan^{-1}(x) + \tan^{-1}(y) = \tan^{-1}\left(\frac{x+y}{1-xy}\right)$$ $$x^2 +y^2 = \sec^2(\tan^{-1}(x/y)+\tan^{-1}(y/x))$$ $$= 1 + \tan^2\left(\tan^{-1}\left(\frac{x/y + y/x}{1-1}\right)\right) = \infty$$ In the last step, I have implicitly taken a left hand limit to arrive at the result. Now This represents(as a locus) a circle with infinite radius which some would say technically is a line. Just like a circle with zero radius(radius tends to 0) is a point. So the software you are using could be giving weird results due to this anomaly. Unfortunately I do not know how the software plots these functions...	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9040805101394653, "perplexity": 368.6844347585091}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645208021.65/warc/CC-MAIN-20150827031328-00190-ip-10-171-96-226.ec2.internal.warc.gz"}
http://ospapergyby.n2g.us/writing-batch-files.html	# Writing batch files Batch files are the computer handyman's way of getting things done they can automate everyday tasks, shorten the required time to do something, and translate a complex process into something anyone could operate in this article, i 'll show you how to write a simple batch file you'll learn the basics of what batch files can. Learn by example: examine these batch files, see how they work, then write your own batch files (this page lists all batch samples. Windows is a fact of life for most professionals writing code for coporate customers this series aims to make life with windows a little easier why dos- style batch files this series will share some conventions i picked up along the way for scripting in windows via command prompt batch files the windows. In this video we show you how to automate your android command by writing a batch file so if you wanted to learn to write a batch file, check it out. Batch scripts are stored in simple text files containing lines with commands that get executed in sequence, one after the other scripting is a way by which one can alleviate this necessity by automating these command sequences in order to make one's life at the shell easier and more productive this tutorial discusses the. Dos batch files are written in plain text any text editor that can store plain text can be used to create a new dos batch file dos batch files use the file extension bat or cmd in our simple example we will use notepad to create a batch file right on the desktop the notepad program is available on all windows platforms. Batch files in windows 10 can help to ease your efforts here is an easy guide on how you can create a batch (bat) file in windows 10 with images. Subscribe now: http://wwwyoutubecom/subscription_centeradd_user= ehowtech watch more: http://wwwyoutubecom/ehowtech writing a batch file in the cmd promp. Generally speaking, batch files (files with the bat extension such as autoexec bat) are text files that can contain a list of multiple commands to be executed for example, you could write a bat file to copy multiple files or change the directory or anything you can do using the command/dos prompt commands it's very. A batch file a windows file with the bat extension it's used as an input file for the command-line interpreter cmd to run a set of commands this helps in automating things and reduced the need to physically typing the commands you can easily create a batch file to automate tasks on a windows pc. Step 6: done well done please continue to the not so basic batch tutorial for some cool batch commands if you want to try something offline, i recommend getting learn batch file programming by john albert, really simple, easy to follow and great if you want to get better. • People that make computers make them act a lot like people the if else statement helps a computer act a lot like people act when faced with various conditions the format is simple: if (condition) then dothis, else dothat the parentheses must enclose things just as shown in the next example let's create a batch file. • These are simple text files containing some lines with commands that get executed in sequence, one after the other these files have the special extension bat or cmd files of this type are recognized and executed through an interface (sometimes called a shell) provided by a system file called the command interpreter. • Batch file best practices dos and don'ts when writing batch files batch files may be a convenient way to glue commands together, thus easily automating repetitive tasks, they can also be a pain in the [beep] if you have to maintain them if you think understanding someone else's batch files can be. Batch files do not contain compiled code like c++ so they can be opened, copied and edited they are usually used for simple routines and low-level machine instruction, but they can be very powerful if you look in your c:\, c:\ windows, or c:\winnt folder you will see a multitude of bat, sys, cfg, inf and other types. Hello guys today i will be showing you how to create a simple batch file on windows 7 professional the truth is that windows is being simulated on my mac by a program called virtualbox thank you for watching and remember to share , like, favourite and subscribe for more. Do you know how to use the command prompt if you do, you can write a batch file in its simplest form, a batch file (or batch script) is a list of several commands that are executed when you double-click the file batch files go all the way back to dos, but still work on modern versions of windows. Writing batch files Rated 5/5 based on 30 review	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8268527984619141, "perplexity": 1725.1108390676063}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814827.46/warc/CC-MAIN-20180223174348-20180223194348-00766.warc.gz"}
http://www.ck12.org/book/CK-12-Algebra-I-Concepts/section/2.2/	<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" /> # 2.2: Additive Inverses and Absolute Values Difficulty Level: At Grade Created by: CK-12 Estimated5 minsto complete % Progress Practice Additive Inverses and Absolute Values Progress Estimated5 minsto complete % What if you had a number like \begin{align}- \frac{3}{4}\end{align}. How could you find its opposite and its absolute value? After completing this Concept, you'll be able to find both values for any number. ### Watch This CK-12 Foundation: 0202S Opposites and Absolute Values ### Guidance Every number has an opposite. On the number line, a number and its opposite are, predictably, opposite each other. In other words, they are the same distance from zero, but on opposite sides of the number line. The opposite of zero is defined to be simply zero. #### Example A The sum of a number and its opposite is always zero, as shown in Example B. #### Example B The numbers 3 and -3 are opposites because: \begin{align}3 + -3 = 0\end{align} The numbers 4.2 and -4.2 are opposites because: \begin{align}4.2 + -4.2 = 0\end{align} This is because adding 3 and -3 is like moving 3 steps to the right along the number line, and then 3 steps back to the left. The number and its opposite cancel each other out, leaving zero. Another way to think of the opposite of a number is that it is simply the original number multiplied by -1. #### Example C The opposite of 4 is \begin{align}4 \times -1\end{align} or -4, and the opposite of -2.3 is \begin{align}-2.3 \times -1\end{align} or just 2.3. Another term for the opposite of a number is the additive inverse. #### Example D Find the opposite of each of the following: a) 19.6 b) \begin{align}- \frac{4}{9}\end{align} c) \begin{align}x\end{align} d) \begin{align}xy^2\end{align} e) \begin{align}(x - 3)\end{align} Solution Since we know that opposite numbers are on opposite sides of zero, we can simply multiply each expression by -1. This changes the sign of the number to its opposite—if it’s negative, it becomes positive, and vice versa. a) The opposite of 19.6 is -19.6. b) The opposite of is \begin{align}-\frac{4}{9}\end{align} is \begin{align}\frac{4}{9}\end{align}. c) The opposite of \begin{align}x\end{align} is \begin{align}-x\end{align}. d) The opposite of \begin{align}xy^2\end{align} is \begin{align}-xy^2\end{align}. e) The opposite of \begin{align}(x - 3)\end{align} is \begin{align}-(x - 3)\end{align}, or \begin{align}(3 - x)\end{align}. Note: With the last example you must multiply the entire expression by -1. A common mistake in this example is to assume that the opposite of \begin{align}(x-3)\end{align} is \begin{align}(x + 3)\end{align}. Avoid this mistake! Find Absolute Values When we talk about absolute value, we are talking about distances on the number line. For example, the number 7 is 7 units away from zero—and so is the number -7. The absolute value of a number is the distance it is from zero, so the absolute value of 7 and the absolute value of -7 are both 7. We write the absolute value of -7 as \begin{align}\| -7 \|\end{align}. We read the expression \begin{align}\| x \|\end{align} as “the absolute value of \begin{align}x\end{align}.” • Treat absolute value expressions like parentheses. If there is an operation inside the absolute value symbols, evaluate that operation first. • The absolute value of a number or an expression is always positive or zero. It cannot be negative. With absolute value, we are only interested in how far a number is from zero, and not in which direction. #### Example E Evaluate the following absolute value expressions. a) \begin{align}\|5 + 4\|\end{align} b) \begin{align}- \|7 - 22\|\end{align} (Remember to treat any expressions inside the absolute value sign as if they were inside parentheses, and evaluate them first.) Solution a) \begin{align}\| 5 + 4\| = \| 9 \| = 9\end{align} b) \begin{align}-\| 7 - 22 \| = - \| -15 \| = -(15) = -15\end{align} Watch this video for help with the Examples above. CK-12 Foundation: Opposites and Absolute Values ### Guided Practice 1. Find the opposite of each of the following: a) \begin{align}x\end{align} b) \begin{align}xy^2\end{align} 2. Evaluate the following absolute value expressions. a) \begin{align}3 - \|4 - 9\|\end{align} b) \begin{align}\|-5 - 11\|\end{align} Solution 1. Since we know that opposite numbers are on opposite sides of zero, we can simply multiply each expression by -1. This changes the sign of the number to its opposite—if it’s negative, it becomes positive, and vice versa. a) The opposite of \begin{align}x\end{align} is \begin{align}-x\end{align}. b) The opposite of \begin{align}xy^2\end{align} is \begin{align}-xy^2\end{align}. 2. a) \begin{align} 3 - \| 4 - 9 \| = 3 - \| -5 \| = 3 - 5 = -2\end{align} b) \begin{align}\| -5 - 11 \| = \| -16 \| = 16\end{align} ### Explore More Find the opposite of each of the following. 1. 1.001 2. \begin{align} (5 - 11)\end{align} 3. \begin{align}( x + y )\end{align} 4. \begin{align}(x - y)\end{align} 5. \begin{align}(x + y - 4)\end{align} 6. \begin{align}(-x + 2y)\end{align} Simplify the following absolute value expressions. 1. \begin{align}11 - \| -4 \| \end{align} 2. \begin{align}\| 4 - 9 \| - \| -5 \| \end{align} 3. \begin{align}\| -5 - 11 \|\end{align} 4. \begin{align}7 - \| 22 - 15 - 19 \|\end{align} 5. \begin{align}- \| -7 \|\end{align} 6. \begin{align}\| -2 - 88 \| - \| 88 + 2 \|\end{align} ### Answers for Explore More Problems To view the Explore More answers, open this PDF file and look for section 2.2. ### My Notes/Highlights Having trouble? Report an issue. Color Highlighted Text Notes Show Hide Details Description Difficulty Level: Authors: Tags: Subjects:	{"extraction_info": {"found_math": true, "script_math_tex": 48, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8465437293052673, "perplexity": 1405.9016201222537}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257828313.74/warc/CC-MAIN-20160723071028-00285-ip-10-185-27-174.ec2.internal.warc.gz"}
https://statisticshelper.com/raw-score-calculator/	This raw score calculator will find a raw score given a z-score, mean, and standard deviation. Enter the three values, then you will get an answer and step-by-step explanation on how you can convert a z-score to a raw score yourself. Afterward, take a look at the Z-Score Calculator to convert raw scores to z-scores. You GOT this! The raw score formula is simply the z-score formula solved for x, the raw score. Depending on what your distribution represents, start by either writing the formula for the raw score of a population: $$x = \mu + z{\sigma}$$ or the formula for the z-score of a sample: $$x = \bar{x} + zs$$ Substitute in values for this problem (z-score, mean, and standard deviation) into the formula: $$x = 142 + (2)(18)$$ $$x = 178$$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9306280612945557, "perplexity": 1171.2347198132973}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103036363.5/warc/CC-MAIN-20220626010644-20220626040644-00306.warc.gz"}
https://socratic.org/questions/how-do-you-find-an-equation-of-a-line-containing-the-point-2-2-and-parallel-to-t#452866	Algebra Topics # How do you find an equation of a line containing the point (-2, 2), and parallel to the line 2(y + 1) = x? Jul 17, 2017 $y = \frac{1}{2} x + 3$ #### Explanation: We are given a point on the line and have indirectly been given the slope as well, because lines that are parallel have the same slope. Simplify the equation of the given line. $2 \left(y + 1\right) = x \text{ } \rightarrow y + 1 = \frac{1}{2} x$ Then: $y = \frac{1}{2} x - 1 \text{ } \leftarrow$ this gives the slope as $m = \frac{1}{2}$ Now use the point slope formula for a line: $y - {y}_{1} = m \left(x - {x}_{1}\right) \text{ }$with $\left(- 2 , 2\right) \mathmr{and} m = \frac{1}{2}$ $y - 2 = \frac{1}{2} \left(x - \left(- 2\right)\right)$ $y = \frac{1}{2} x + 1 + 2$ $y = \frac{1}{2} x + 3$ ##### Impact of this question 967 views around the world	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 9, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9272744655609131, "perplexity": 562.4210756631475}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301670.75/warc/CC-MAIN-20220120005715-20220120035715-00634.warc.gz"}
http://onewebglobal.com/burst-error/burst-error-detection-codes.php	Home > Burst Error > Burst Error Detection Codes # Burst Error Detection Codes ## Contents There exist codes for correcting such burst errors. If l e n g t h ( P 1 ) + l e n g t h ( P 2 ) ⩽ n + 1 , {\displaystyle \mathrm γ 3 The codewords of this cyclic code are all the polynomials that are divisible by this generator polynomial. Let a burst error of length ℓ {\displaystyle \ell } occur. get redirected here Recommended Foundations of Programming: Databases Foundations of Programming: Object-Oriented Design Foundations of Programming: Fundamentals Error Detection And Correction Renu Kewalramani Computer Networks - Error Detection & Error Correction Saikrishna Tanguturu Errror Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. Thus, the separation between consecutive inputs = n d {\displaystyle nd} symbols Let the length of codeword ⩽ n . {\displaystyle \leqslant n.} Thus, each symbol in the input codeword will Thus, a linear code C {\displaystyle C} is an ℓ {\displaystyle \ell } -burst-error-correcting code if and only if all the burst errors of length ⩽ ℓ {\displaystyle \leqslant \ell } ## Burst Error Detection And Correction Pattern of burst - A burst pattern of a burst of length l is defined as the polynomial b(x) of degree l − 1. To be able to detect or correct errors, we need to send some extra bits with our data. This site stores nothing other than an automatically generated session ID in the cookie; no other information is captured. e1 = p1^(m0^m3^m6^m9) e2 = p2^(m1^m4^m7^m10) e3 = p3^(m2^m5^m8^m11) If any of these equations is not equal to zero, an error has occurred. If your computer's clock shows a date before 1 Jan 1970, the browser will automatically forget the cookie. Correcting Burst Errors: Consider a linear code C. Burst Error Correcting Convolutional Codes Theorem (Burst error codeword classification). CIRC (Cross-Interleaved Reed–Solomon code) is the basis for error detection and correction in the CD process. Crc Burst Error Detection In this case, when the input multiplexer switch completes around half switching, we can read first row at the receiver. If one bit has an error, it is likely that the adjacent bits could also be corrupted. http://epubs.siam.org/doi/pdf/10.1137/0113076 Moreover, we have ( n − ℓ ) q ℓ − 2 ⩽ \| B ( c ) \| {\displaystyle (n-\ell )q^{\ell -2}\leqslant \|B(\mathbf {c} )\|} . The trick is that if there occurs a burst of length h {\displaystyle h} in the transmitted word, then each row will contain approximately h λ {\displaystyle {\tfrac {h}{\lambda }}} consecutive Burst Error Example Following are typical parameters that a burst can have 1. Sincerely yours, Tanzila Islam ID#2012000000022 30th Batch, Sec-01 Dept. First we observe that a code can correct all bursts of length ⩽ ℓ {\displaystyle \leqslant \ell } if and only if no two codewords differ by the sum of two ## Crc Burst Error Detection Upon receiving c 1 {\displaystyle \mathbf − 3 _ − 2} , we can not tell whether the transmitted word is indeed c 1 {\displaystyle \mathbf γ 9 _ γ 8} We have q n − r {\displaystyle q^ − 3} such polynomials. Burst Error Detection And Correction We call the set of indices corresponding to this run as the zero run. Burst Error Correcting Codes Ppt In other words, what is the upper bound on the length ℓ {\displaystyle \ell } of bursts that we can detect using any ( n , k ) {\displaystyle (n,k)} code? If your browser does not accept cookies, you cannot view this site. http://onewebglobal.com/burst-error/burst-error-codes.php To remedy the issues that arise by the ambiguity of burst descriptions with the theorem below, however before doing so we need a definition first. Notice the indices are 0 {\displaystyle 0} -based, that is, the first element is at position 0 {\displaystyle 0} . In general, only the information that you provide, or the choices you make while visiting a web site, can be stored in a cookie. Burst Error Correcting Codes Pdf Many codes have been designed to correct random errors. r = n − k {\displaystyle r=n-k} is called the redundancy of the code and in an alternative formulation for the Abramson's bounds is r ⩾ ⌈ log 2 ⁡ ( The sound wave is sampled for amplitude (at 44.1kHz or 44,100 pairs, one each for the left and right channels of the stereo sound). http://onewebglobal.com/burst-error/burst-error-detection-correction.php The concept of including extra information in the transmission for error detection is a good one. I have prepared this report with my utmost earnestness and sincere effort. Burst Error Correction Using Hamming Code The system returned: (22) Invalid argument The remote host or network may be down. Let C {\displaystyle C} be a linear ℓ {\displaystyle \ell } -burst-error-correcting code. ## Random errors include those due to jitter of reconstructed signal wave and interference in signal. These errors may be due to physical damage such as scratch on a disc or a stroke of lightning in case of wireless channels. Select another clipboard × Looks like you’ve clipped this slide to already. Clipping is a handy way to collect important slides you want to go back to later. Burst Error Correction Example Share Email Error Detection And Correction byRenu Kewalramani 41305views Computer Networks - Error Detection... Therefore, a ( x ) + x b b ( x ) {\displaystyle a(x)+x^{b}b(x)} is either divisible by x 2 ℓ − 1 + 1 {\displaystyle x^{2\ell -1}+1} or is 0 With these requirements in mind, consider the irreducible polynomial p ( x ) = 1 + x 2 + x 5 {\displaystyle p(x)=1+x^{2}+x^{5}} , and let ℓ = 5 {\displaystyle \ell To define a cyclic code, we pick a fixed polynomial, called generator polynomial. this page Generated Tue, 04 Oct 2016 18:43:29 GMT by s_hv997 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.8/ Connection Allowing a website to create a cookie does not give that or any other site access to the rest of your computer, and only the site that created the cookie can For w = 0 , 1 , {\displaystyle w=0,1,} there is nothing to prove. For example, E = ( 0 1000011 0 ) {\displaystyle E=(0{\textbf γ 5}0)} is a burst of length ℓ = 7. {\displaystyle \ell =7.} Although this definition is sufficient to describe CD's, for example, are particularly vulnerable to burst errors (from a scratch on the disc).	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.943617582321167, "perplexity": 1965.3955030192847}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887414.4/warc/CC-MAIN-20180118131245-20180118151245-00712.warc.gz"}
http://math.stackexchange.com/questions/7413/meaning-of-convolution/7416	# Meaning of convolution? I am currently learning about the concept of convolution between two functions in my university course. The course notes are vague about what convolution is, so I was wondering if anyone could give me a good explanation. I can't seem to grasp other than the fact that it is just a particular integral of two functions. What is the physical meaning of convolution and why is it useful? Thanks a lot. - Have a look here: ...and lots of good answers here: http://mathoverflow.net/questions/5892/what-is-convolution-intuitively - Thanks for the links. From the two, I found the second link to be better for understanding. Now I have some sort of "intuition" for convolutions! =) – thomas1234 Oct 21 '10 at 15:18 I'd suggest these lectures by professor Osgood here particularly lectures 8 and 9. - If $X$ and $Y$ are random variables, then their sum $X+Y$ is the convolution of their distributions. The way you have stated this is a bit unclear. the distribution of the variable $Z = X + Y$ is the convolution of the distributions of $X$ and $Y$. This is true only when $X$ and $Y$ are independent. – svenkatr Oct 25 '10 at 19:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.850047767162323, "perplexity": 157.7142739088029}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1404776439916.87/warc/CC-MAIN-20140707234039-00027-ip-10-180-212-248.ec2.internal.warc.gz"}
http://www.gabormelli.com/RKB/2001_IntroductiontoSequenceLearning	# 2001 IntroductiontoSequenceLearning Jump to: navigation, search ## Quotes ### Abstract Sequential behavior is essential to intelligence, and it is a fundamental part of human activities ranging from reasoning to language, and from everyday skills to complex problem solving. In particular, sequence learning is an important component of learning in many task domains - planning, reasoning, robotics, natural language processing, speech recognition, adaptive control, time series prediction, financial engineering, DNA sequencing, and so on. ### 1 Introduction Sequential behavior is essential to intelligence, and it is a fundamental part of human activities ranging from reasoning to language, and from everyday skills to complex problem solving. In particular, sequence learning is an important component of learning in many task domains — planning, reasoning, robotics, natural language processing, speech recognition, adaptive control, time series prediction, financial engineering, DNA sequencing, and so on. Naturally, there are many different approaches towards sequence learning, resulting from different perspectives taken in different task domains. These approaches deal with somewhat differently formulated sequential learning problems (for example, some with actions and some without), and/or different aspects of sequence learning (for example, sequence prediction vs. sequence recognition). Sequence learning is clearly a difficult task. More powerful algorithms for sequence learning are needed in all of these afore-mentioned domains. It is our view that the right approach to develop better techniques, algorithms, models, and theories is to first better understand the state of the art in different disciplines related to this topic. There seems to be a need to compare, contrast, and combine different existing techniques, approaches, and paradigms, in order to develop better and more powerful algorithms. Currently, existing techniques and algorithms include recurrent neural networks, hidden Markov models, dynamic programming, reinforcement learning, graph theoretical models, search based models, evolutionary computational models, symbolic planning models, production rule based models, and so on. Especially important to this topic area is the fact that work on sequence learning has been going on in several different disciplines such as artificial intelligence, neural networks, cognitive science (human sequence learning, e.g., in skill acquisition), and engineering. We need to examine the field in a cross-disciplinary way and take into consideration all of these different perspectives on sequence learning. Thus, we need interdisciplinary gatherings that include researchers from all of these orientations and disciplines, beyond narrowly focused meetings on specialized topics such as reinforcement learning or recurrent neural networks. A workshop on neural, symbolic, and reinforcement methods for sequence learning (co-chaired by Ron Sun and Lee Giles) was held on August 1st, 1999, preceding IJCAr99, in Stockholm, Sweden. The following issues concerning sequence learning were raised and addressed: (...) ### 2 Problem Formulations and Their Relationships One aim of the present volume is to better understand different formulations of sequence learning problems. With some necessary simplification, we can categorize various sequence learning problems that have been tackled into the following categories: (1) sequence prediction, in which, we want to predict elements of a sequence based on the preceding element(s): (2) sequence generation, in which we want to generate elements of a sequence one by one in their natural order: and (3) sequence recognition, in which we want to determine if a sequence is a legitimate one according to some criteria: in addition, (4) sequential decision making involves selecting sequence of actions, to accomplish a goal, to follow a trajectory, or to maximize (or minimize) a reinforcement (or cost) function that is normally the (discounted) sum of reinforcements (costs) that are received along the way (see Bellman 1957, Bertsekas and Tsitsiklis 1995) (...) These different sequence learning problems can be more precisely formulated as follows (assume a deterministic world for now): • Sequence prediction: Si, Si+i, Sj — > Sj-i-ii where 1 < i < j < oo; that is, given Si, Si+i, Sj, we want to predict Sj+i. When i = 1, we make predictions based on all of the previously seen elements of the sequence. When i = j, we make predictions based only on the immediately preceding element. • Sequence generation: Si, Si+i, ...., Sj — > Sj-i-i) where 1 < i < j < oo; that is, given Si, Si+i, ...., Sj, we want to generate Sj+i. (Put in this way, it is clear that sequence prediction and generation are essentially the same task.) • Sequence recognition]: Si, Si+i, Sj — > yes or no, where 1 < i < j < oo; that is, given Si, Si+i, Sj, we want to determine if this subsequence is legitimate or not. (There are alternative ways of formulating the sequence recognition problem, for example, as an one-shot recognition process, as opposed to an incremental step-by-step recognition process as formulated here.) With this formulation, sequence recognition can be turned into sequence generation/prediction, by basing recognition on prediction (see the chapter by D. Wang in this volume); that is, Si,Si+i, — > yes (a recognition problem), if and only if Si, Si+i, ...., Sj-i — > Sj (a prediction problem) and Sj = Sj, where Sj is the prediction and is the actual element. Sequence learning (either generation, prediction, or recognition) is usually based on models of legitimate sequences, which can be developed through training with exemplars. Models may be in the form of Markov chains, hidden Markov models, recurrent neural networks, and a variety of other forms. Expectation-maximization, gradient descent, or clustering may be used in training (see e.g. the chapters by Oates and Cohen and by Sebastiani et al in this volume). Such training may extract “central tendencies” from a set of exemplars. (...) ## References ; volumeDate ValuetitletypejournaltitleUrldoinoteyear 2001 IntroductiontoSequenceLearningIntroduction to Sequence Learning10.1007/3-540-44565-X_12001 Author Ron Sun + doi 10.1007/3-540-44565-X_1 + title Introduction to Sequence Learning + year 2001 +	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8237455487251282, "perplexity": 1822.9134314795422}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540569146.17/warc/CC-MAIN-20191213202639-20191213230639-00048.warc.gz"}
http://scistatcalc.blogspot.co.uk/2013/03/blog-post.html	## Friday, 29 March 2013 ### The normalised incomplete gamma function and its inverse. The Scientific calculator has the two types of normalised incomplete gamma function (in addition to the single-parameter Gamma function $\Gamma(x)$ itself) - the lower and upper functions, denoted by $P(a,x)$ and $Q(a,x)$ respectively. These are accessible using the fourth segment, as shown below:- The functions take in two arguments, so you need to enter a number (the $a$ parameter), then press the relevant function button, followed by another number ($x$), then press the equal button to obtain the result. The (complete) Gamma function is:- $\Gamma(a)=\int_0^\infty t^{a-1}e^{-t}dt$ The equation for the Lower Normalised Incomplete Gamma function is:- $P(a,x)=\frac{1}{\Gamma(a)}\int_0^xt^{a-1}e^{-t}dt$ while that for the Upper Normalised Incomplete Gamma function is:- $Q(a,x)=\frac{1}{\Gamma(a)}\int_x^{\infty}t^{a-1}e^{-t}dt$ Note that $P(a,x) + Q(a,x) = 1$. The Lower Normalised Incomplete Gamma function is the CDF of the Gamma probability density function $\Gamma(\alpha,\beta)$, with $\beta$ set to 1, so we can use the landscape mode CDF/inverse-CDF calculator to find its inverse with respect to $x$. Thus, to invert the lower function (i.e. to find $x$), enter the $\alpha$ parameter, put the input in the probability field, put 1 into the $\beta$ parameter, and set the lower limit to 0. The result will populate the Upper Limit, once the calculate button is pressed. For a worked example, finding $x$ such that $P(3,x) = 0.5$ (i.e. $\alpha = 3$), see screenshot below (the result is approx. 2.6741):- As the underlying algorithm is quite numerically intensive for yielding high precision results, there will be a delay of a few seconds. To invert the upper normalised function, simply subtract its value from 1 and enter the result into the probability field. As a side note, you can use the Gamma function to evaluate the Beta function ($B(a,b)=\int_0^1t^{(a-1)}(1-t)^{(b-1)}dt$) as follows:- $B(a,b) = \frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)}$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9637492299079895, "perplexity": 511.4947867440628}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560279379.41/warc/CC-MAIN-20170116095119-00081-ip-10-171-10-70.ec2.internal.warc.gz"}
https://scicomp.stackexchange.com/questions/19377/estimating-the-local-compression-expansion-ratio-for-a-transformation-on-a-point	# Estimating the local compression/expansion ratio for a transformation on a point cloud Let's say we have an unorganized point cloud P1 with N points, each with coordinates {x,y,z}. We apply non-rigid transformation to P1 (translation + rotation + warping), to obtain point cloud P2. Given a pair of corresponding points in P1 and P2, how can we efficiently estimate the change in local point density around this point without performing explicit meshing? In other words, how to estimate the local space compression/expansion around each point after the transformation? Consider that the expansion/compression may not be isotropic. If you also wish to know about the anisotropy of the stretching you should look at computing the right Cauchy-Green deformation tensor, $\Delta$, and it's associated eigenvalues and eigenvectors. The eigenvectors of this tensor define the primary axes of deformation and the eigenvalues are equal to the squares of the stretching ratios along these axes. The density ratio is given by the square root of the determinant of $\Delta$ which equals the square root of the eigenvalues: $\rho_2/\rho_1 = \sqrt{\det(\Delta)}= \sqrt{\lambda_1 \lambda_2 \lambda_3}$. If you are not able to perform the transformation on arbitrary points you can use the points you know to estimate the deformation tensor. The simplest method involves choosing N neighbors of a given point and using those to estimate the deformation tensor. This can be formulated as a least-squares problem to determine the components of a 3x3 transformation matrix, $\Phi$, such that $\Phi~(\text{P}1_i-\text{P}1_0) = (\text{P}2_i-\text{P}2_0)$ where subscript $0$ denotes the point of interest and $i$ denotes the neighbors. In 3D you will need a minimum of 3 neighbors to determine $\Phi$ (3 points x 3 components {x,y,z} gives 9 linear equations for the 9 entries in $\Phi$). The deformation tensor is then given by $\Delta = \Phi^\intercal \Phi$. This method is first order accurate in the point spacing and quickly loses accuracy when the points are far enough apart so that the transformation is not locally linear on the neighborhood being used. If my memory is correct, this is the method that is used for computing the deformation tensor to find LCS on unstructured meshes in this paper. As a side note, this method is provably equivalent to using centered finite differences (and recovers second order accuracy) if the you use 6 neighbors at the locations of the points in the finite difference stencil.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9573892951011658, "perplexity": 225.10005945656732}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057615.3/warc/CC-MAIN-20210925082018-20210925112018-00042.warc.gz"}
https://blog.asarkar.com/algorithms-design-analysis/hw-5-opt/	# Homework 5 Optional Problems In lecture we define the length of a path to be the sum of the lengths of its edges. Define the bottleneck of a path to be the maximum length of one of its edges. A mininum-bottleneck path between two vertices $s$ and $t$ is a path with bottleneck no larger than that of any other $s-t$ path. Show how to modify Dijkstra’s algorithm to compute a minimum-bottleneck path between two given vertices. The running time should be $O(m\log n)$, as in lecture. ANSWER: Each iteration is analogous to finding the winner of a two-round tournament. In the first round, we find the bottlenecks for all the paths until that point; in the second round, we find the minimum of all such bottlenecks. $\begin{multline} dist(v) = \min(dist(v), \max(dist(u), weight(u, v))) \\ \forall u \in X, v \in V - X \end{multline}$ We start by inserting $(\infty, u) \ u \in V$ in a min-heap. We decrease the key of the source to $-\infty$. Then in each iteration, we extract the minimum from the heap, add it to set $X$, and update the keys for the adjacent vertices according to the formula above. The only thing we changed from Dijkstra’s algorithm is the scoring formula, which now involves some constant time operations for $\min$ and $\max$. Thus, running time of the above algorithm is the same as that of Dijkstra’s, $O(m\log n)$. This problem is also known as the minimax path problem. A variation of it is the widest path problem, or the maximum-capacity problem, where we try to maximize the capacity of a path, which in turn is defined as the minimum length of one of its edges. We can do better. Suppose now that the graph is undirected. Give a linear-time $O(m)$ algorithm to compute a minimum-bottleneck path between two given vertices. ANSWER: The idea is as follows: 1: CRITICAL-EDGE(G, s, t) 2: if \|E(G)\| == 1 3: return the only edge 4: else 5: x = median of all edge weights 6: X = E - (v, w) s.t. weight(v, w) > x 7: G' = G(V, X) 8: exists = is there a path from s to t in G' 9: if (exists == FALSE) 10: C = {C₁, C₂, ..., Cₖ} s.t. Cᵢ is a connected component of G 11: G' = G(V, E - X) 12: for i = 1 to \|C\| 13: G' = SHRINK(G', C, i) 14: else if X == E // no edges were deleted 15: X = {(v, w)} s.t. weight(v, w) = x 16: G' = G(V, X) 17: return CRITICAL-EDGE(G', s, t) 18: SHRINK(G, C, i) 20: V* = {V(G) - C[i]} ∪ {leaderᵢ} 21: E* = {} 22: for each (v, w) ∈ E(G) 23: if v ∈ C[i], w ∈ C[j] 24: E* = E* ∪ {(leaderᵢ, leaderⱼ, min(weight(u, w)))} ∀ u ∈ C[i] 25: else if v, w ∉ C[i] E * = E* ∪ {(v, w, weight(v, w))} 26: return G(V, E*) • 5: can be done using Randomized Linear-Time Selection; $O(m)$ • 8: can be done by running BFS and stopping when $t$ is visited; $O(m + n)$ • 10: can be done using Kosaraju’s algorithm; $O(m + n)$ • 11: can be done in $O(\frac{m}{2})$ • 20: can be done in linear time of $V(C[i])$ • 22: can be done in $O(\frac{m}{2})$ • 24: can be done by knowing all edges incident with $w$; the graph would need to support such query in constant time, likely at the expense of increased memory usage • 13: $O(m)$ (max work done in $SHRINK$) The correctness of $CRITICAL-EDGE$ can be argued as follows: If in line 8 it turns out that the graph still is s-t-connected, then deleting the edges of weights greater than $x$ in line 6 did not affect the optimal solution. By recursing on the resulting graph, we converge on smaller edge weights that possibly maintain s-t-connectivity. Otherwise, clearly $s$ and $t$ are in different connected components, and the bottleneck of path $s-t$ is at least $x$. In line 24, if there are more than one edges between two connected components, choosing the minimum is consistent with our goal find the minimum bolttleneck. If we chose the maximum instead, we would lose the path that has a smaller edge weight, and could eventually become the minimum bolttleneck path. The algorithm runs in time $O(m)$, where $m = \|E\|$ denotes the number of edges: The crucial observation is that in every recursive call, half of the edges are removed from the graph, either by shrinking all “thin” edges or by dropping all “thick” edges. As shown above, the work done outside the recursive call is $O(m)$. Thus, the total running time is bounded by: $O(m) + O(\frac{m}{2}) + O(\frac{m}{4}) + ... = O(m)$ Having found the critical edge, we run BFS ignoring all edges with weight greater than the cricital edge. That takes linear time ($O(m)$). What if the graph is directed? Can you compute a minimum-bottleneck path between two given vertices faster than $O(m\log n)$? ANSWER: This paper argues that the above algorithm doesn’t work for directed graphs because: the shrinking step in line 13 will not significantly reduce the number of edges, since it need not to be true that every “thin” edge is contained in some strongly connected component. However, I have yet to convince myself of the above argument. The paper also offers a linear-time algorithm for computing a minimum-bottleneck path in directed graphs but it looks quite complicated. If the edge weights are integral and drawn from a small range such that the maximum edge weight is known, then this lecture presents a modified Dijkstra’s algorithm using buckets, aka Dial’s implementation. There are a few ways of improving the time complexity of this algorithm. 1. We can use a circular queue of size $W + 2$, where $W$ is the maximum edge weight. The bucket corresponding to $dist(v)$ is simply $dist(v)\ mod\ (W + 1)$. Last bucket contains the vertices not yet visited, corresponding to distance $\infty$. 2. By maintaining a distance to heap index hash table, we can do distance updates in constant time. Note that the heap property is not violated if a vertex is moved bwteen buckets. It’s only when a buket is inserted or deleted, we need to worry about restoring the heap property. Since the heap always contains no more than $W + 2$ buckets, any operation takes $O(\log W)$ time, thus giving us a running time of $O(m + n)\log W = O(m\log W)$, based on the assumption that every vertex is reachable from the source vertex $s$, and thus, $m \geq n - 1$ (see lecture video for details).	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8376064896583557, "perplexity": 634.8933459619167}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178355944.41/warc/CC-MAIN-20210226001221-20210226031221-00452.warc.gz"}
https://stacks.math.columbia.edu/tag/033D	\begin{equation} \DeclareMathOperator\Coim{Coim} \DeclareMathOperator\Coker{Coker} \DeclareMathOperator\Ext{Ext} \DeclareMathOperator\Hom{Hom} \DeclareMathOperator\Im{Im} \DeclareMathOperator\Ker{Ker} \DeclareMathOperator\Mor{Mor} \DeclareMathOperator\Ob{Ob} \DeclareMathOperator\Sh{Sh} \DeclareMathOperator\SheafExt{\mathcal{E}\mathit{xt}} \DeclareMathOperator\SheafHom{\mathcal{H}\mathit{om}} \DeclareMathOperator\Spec{Spec} \newcommand\colim{\mathop{\mathrm{colim}}\nolimits} \newcommand\lim{\mathop{\mathrm{lim}}\nolimits} \newcommand\Qcoh{\mathit{Qcoh}} \newcommand\Sch{\mathit{Sch}} \newcommand\QCohstack{\mathcal{QC}\!\mathit{oh}} \newcommand\Cohstack{\mathcal{C}\!\mathit{oh}} \newcommand\Spacesstack{\mathcal{S}\!\mathit{paces}} \newcommand\Quotfunctor{\mathrm{Quot}} \newcommand\Hilbfunctor{\mathrm{Hilb}} \newcommand\Curvesstack{\mathcal{C}\!\mathit{urves}} \newcommand\Polarizedstack{\mathcal{P}\!\mathit{olarized}} \newcommand\Complexesstack{\mathcal{C}\!\mathit{omplexes}} \newcommand\Pic{\mathop{\mathrm{Pic}}\nolimits} \newcommand\Picardstack{\mathcal{P}\!\mathit{ic}} \newcommand\Picardfunctor{\mathrm{Pic}} \newcommand\Deformationcategory{\mathcal{D}\!\mathit{ef}} \end{equation} ## 10.158 Descending properties In this section we start proving some algebraic facts concerning the “descent” of properties of rings. It turns out that it is often “easier” to descend properties than it is to ascend them. In other words, the assumption on the ring map $R \to S$ are often weaker than the assumptions in the corresponding lemma of the preceding section. However, we warn the reader that the results on descent are often useless unless the corresponding ascent can also be shown! Here is a typical result which illustrates this phenomenon. Lemma 10.158.1. Let $R \to S$ be a ring map. Assume that 1. $R \to S$ is faithfully flat, and 2. $S$ is Noetherian. Then $R$ is Noetherian. Proof. Let $I_0 \subset I_1 \subset I_2 \subset \ldots$ be a growing sequence of ideals of $R$. By assumption we have $I_ nS = I_{n +1}S = I_{n + 2}S = \ldots$ for some $n$. Since $R \to S$ is flat we have $I_ kS = I_ k \otimes _ R S$. Hence, as $R \to S$ is faithfully flat we see that $I_ nS = I_{n +1}S = I_{n + 2}S = \ldots$ implies that $I_ n = I_{n +1} = I_{n + 2} = \ldots$ as desired. $\square$ Lemma 10.158.2. Let $R \to S$ be a ring map. Assume that 1. $R \to S$ is faithfully flat, and 2. $S$ is reduced. Then $R$ is reduced. Proof. This is clear as $R \to S$ is injective. $\square$ Lemma 10.158.3. Let $R \to S$ be a ring map. Assume that 1. $R \to S$ is faithfully flat, and 2. $S$ is a normal ring. Then $R$ is a normal ring. Proof. Since $S$ is reduced it follows that $R$ is reduced. Let $\mathfrak p$ be a prime of $R$. We have to show that $R_{\mathfrak p}$ is a normal domain. Since $S_{\mathfrak p}$ is faithfully over $R_{\mathfrak p}$ too we may assume that $R$ is local with maximal ideal $\mathfrak m$. Let $\mathfrak q$ be a prime of $S$ lying over $\mathfrak m$. Then we see that $R \to S_{\mathfrak q}$ is faithfully flat (Lemma 10.38.17). Hence we may assume $S$ is local as well. In particular $S$ is a normal domain. Since $R \to S$ is faithfully flat and $S$ is a normal domain we see that $R$ is a domain. Next, suppose that $a/b$ is integral over $R$ with $a, b \in R$. Then $a/b \in S$ as $S$ is normal. Hence $a \in bS$. This means that $a : R \to R/bR$ becomes the zero map after base change to $S$. By faithful flatness we see that $a \in bR$, so $a/b \in R$. Hence $R$ is normal. $\square$ Lemma 10.158.4. Let $R \to S$ be a ring map. Assume that 1. $R \to S$ is faithfully flat, and 2. $S$ is a regular ring. Then $R$ is a regular ring. Proof. We see that $R$ is Noetherian by Lemma 10.158.1. Let $\mathfrak p \subset R$ be a prime. Choose a prime $\mathfrak q \subset S$ lying over $\mathfrak p$. Then Lemma 10.109.9 applies to $R_\mathfrak p \to S_\mathfrak q$ and we conclude that $R_\mathfrak p$ is regular. Since $\mathfrak p$ was arbitrary we see $R$ is regular. $\square$ Lemma 10.158.5. Let $R \to S$ be a ring map. Assume that 1. $R \to S$ is faithfully flat, and 2. $S$ is Noetherian and has property $(S_ k)$. Then $R$ is Noetherian and has property $(S_ k)$. Proof. We have already seen that (1) and (2) imply that $R$ is Noetherian, see Lemma 10.158.1. Let $\mathfrak p \subset R$ be a prime ideal. Choose a prime $\mathfrak q \subset S$ lying over $\mathfrak p$ which corresponds to a minimal prime of the fibre ring $S \otimes _ R \kappa (\mathfrak p)$. Then $A = R_{\mathfrak p} \to S_{\mathfrak q} = B$ is a flat local ring homomorphism of Noetherian local rings with $\mathfrak m_ AB$ an ideal of definition of $B$. Hence $\dim (A) = \dim (B)$ (Lemma 10.111.7) and $\text{depth}(A) = \text{depth}(B)$ (Lemma 10.157.2). Hence since $B$ has $(S_ k)$ we see that $A$ has $(S_ k)$. $\square$ Lemma 10.158.6. Let $R \to S$ be a ring map. Assume that 1. $R \to S$ is faithfully flat, and 2. $S$ is Noetherian and has property $(R_ k)$. Then $R$ is Noetherian and has property $(R_ k)$. Proof. We have already seen that (1) and (2) imply that $R$ is Noetherian, see Lemma 10.158.1. Let $\mathfrak p \subset R$ be a prime ideal and assume $\dim (R_{\mathfrak p}) \leq k$. Choose a prime $\mathfrak q \subset S$ lying over $\mathfrak p$ which corresponds to a minimal prime of the fibre ring $S \otimes _ R \kappa (\mathfrak p)$. Then $A = R_{\mathfrak p} \to S_{\mathfrak q} = B$ is a flat local ring homomorphism of Noetherian local rings with $\mathfrak m_ AB$ an ideal of definition of $B$. Hence $\dim (A) = \dim (B)$ (Lemma 10.111.7). As $S$ has $(R_ k)$ we conclude that $B$ is a regular local ring. By Lemma 10.109.9 we conclude that $A$ is regular. $\square$ Lemma 10.158.7. Let $R \to S$ be a ring map. Assume that 1. $R \to S$ is smooth and surjective on spectra, and 2. $S$ is a Nagata ring. Then $R$ is a Nagata ring. Proof. Recall that a Nagata ring is the same thing as a Noetherian universally Japanese ring (Proposition 10.156.15). We have already seen that $R$ is Noetherian in Lemma 10.158.1. Let $R \to A$ be a finite type ring map into a domain. According to Lemma 10.156.3 it suffices to check that $A$ is N-1. It is clear that $B = A \otimes _ R S$ is a finite type $S$-algebra and hence Nagata (Proposition 10.156.15). Since $A \to B$ is smooth (Lemma 10.135.4) we see that $B$ is reduced (Lemma 10.157.7). Since $B$ is Noetherian it has only a finite number of minimal primes $\mathfrak q_1, \ldots , \mathfrak q_ t$ (see Lemma 10.30.6). As $A \to B$ is flat each of these lies over $(0) \subset A$ (by going down, see Lemma 10.38.18) The total ring of fractions $Q(B)$ is the product of the $L_ i = \kappa (\mathfrak q_ i)$ (Lemmas 10.24.4 and 10.24.1). Moreover, the integral closure $B'$ of $B$ in $Q(B)$ is the product of the integral closures $B_ i'$ of the $B/\mathfrak q_ i$ in the factors $L_ i$ (compare with Lemma 10.36.16). Since $B$ is universally Japanese the ring extensions $B/\mathfrak q_ i \subset B_ i'$ are finite and we conclude that $B' = \prod B_ i'$ is finite over $B$. Since $A \to B$ is flat we see that any nonzerodivisor on $A$ maps to a nonzerodivisor on $B$. The corresponding map $Q(A) \otimes _ A B = (A \setminus \{ 0\} )^{-1}A \otimes _ A B = (A \setminus \{ 0\} )^{-1}B \to Q(B)$ is injective (we used Lemma 10.11.15). Via this map $A'$ maps into $B'$. This induces a map $A' \otimes _ A B \longrightarrow B'$ which is injective (by the above and the flatness of $A \to B$). Since $B'$ is a finite $B$-module and $B$ is Noetherian we see that $A' \otimes _ A B$ is a finite $B$-module. Hence there exist finitely many elements $x_ i \in A'$ such that the elements $x_ i \otimes 1$ generate $A' \otimes _ A B$ as a $B$-module. Finally, by faithful flatness of $A \to B$ we conclude that the $x_ i$ also generated $A'$ as an $A$-module, and we win. $\square$ Remark 10.158.8. The property of being “universally catenary” does not descend; not even along étale ring maps. In Examples, Section 102.16 there is a construction of a finite ring map $A \to B$ with $A$ local Noetherian and not universally catenary, $B$ semi-local with two maximal ideals $\mathfrak m$, $\mathfrak n$ with $B_{\mathfrak m}$ and $B_{\mathfrak n}$ regular of dimension $2$ and $1$ respectively, and the same residue fields as that of $A$. Moreover, $\mathfrak m_ A$ generates the maximal ideal in both $B_{\mathfrak m}$ and $B_{\mathfrak n}$ (so $A \to B$ is unramified as well as finite). By Lemma 10.147.11 there exists a local étale ring map $A \to A'$ such that $B \otimes _ A A' = B_1 \times B_2$ decomposes with $A' \to B_ i$ surjective. This shows that $A'$ has two minimal primes $\mathfrak q_ i$ with $A'/\mathfrak q_ i \cong B_ i$. Since $B_ i$ is regular local (since it is étale over either $B_{\mathfrak m}$ or $B_{\mathfrak n}$) we conclude that $A'$ is universally catenary. In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9954267740249634, "perplexity": 184.38015883374197}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202588.97/warc/CC-MAIN-20190321234128-20190322020128-00123.warc.gz"}
https://www.kseebsolutions.com/kseeb-solutions-for-class-6-maths-chapter-5-ex-5-5/	KSEEB Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5 Students can Download Chapter 5 Understanding Elementary Shapes Ex 5.5 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 6 Maths helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka State Syllabus Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5 Question 1. Which of the following are models for perpendicular lines: Solution: a) The adjacent angles of a table top The adjacent edge of a table top are perpendicular to each other. b) The line of a railway track The lines of a railway track are parallel to each other. c) The line segments forming the letter ‘L’ The line segments forming the letter ‘L’ are perpendicular to each other. d) The letter V. The sides of letter V are inclined at some a cute angle on each other Hence (a) and (c) are the models for perpendicular lines. Question 2. Let $$\overline{\mathbf{P Q}}$$ be the perpendicular to the line segment $$\overline{\mathbf{X Y}}$$. Let $$\overline{\mathbf{P Q}}$$ and $$\overline{\mathbf{X Y}}$$ intersect in the point A. What is the measure of ∠PAY? Solution: From the figure if c be easily observed that the measure of ∠PAY is 90° Question 3. There are two set-squares in your box. What are the measures of the angles that are formed at their corners? Do they have any angle measure that is common? Solution: On has a measure of 90°, 45°, 45° other has a measure of 90°, 30°, 60° Therefore, the angle of 90° measure is common between them. Question 4. Study the diagram. The line l is perpendicular to line m Solution: a) Is CE = EG? Yes, As CE = EG = 2 units b) Does PE bisect CG? Yes, PE bisects CG since CE = EG c) Identify any two line segments for which PE is the perpendicular bisector. DF and BH d) Are these true? i) AC < EG True, As length of AC and FG are of 2 units and 1 unit respectively ii) CD = GH True, As both have 1 unit length iii) BC < EH True, As the length of BC and EH are of 1 unit and 3 units respectively. error: Content is protected !!	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9249478578567505, "perplexity": 1916.1480238442139}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039560245.87/warc/CC-MAIN-20210422013104-20210422043104-00135.warc.gz"}
https://jgaa.info/getPaper?id=562	An algorithm for embedding Turán graphs into incomplete hypercubes with minimum wirelength A. Arul Shantrinal, Sandi Klavžar, T.M. Rajalaxmi, and R. Sundara Rajan Vol. 25, no. 1, pp. 367-381, 2021. Regular paper. Abstract The wirelength is one of the key parameters of the quality of embedding graphs into host graphs. To our knowledge, no results for computing the wirelength of embedding irregular graphs into irregular graphs are known in the literature. We develop an algorithm that determines the wirelength of embedding of the Turán graph $T(\ell, 2^p)$, where $2^{n-1} \leq \ell < 2^{n}$ and $1\le p\le \lceil \log_2 \ell\rceil\leq n$, into the incomplete hypercube $I^{\ell}_{n}$. Incomplete hypercubes form an important generalization of hypercubes because they eliminate the restriction on the number of nodes in a system. This work is licensed under the terms of the CC-BY license. Submitted: March 2020. Reviewed: February 2021. Revised: March 2021. Reviewed: April 2021. Revised: May 2021. Accepted: June 2021. Final: June 2021. Published: June 2021. Communicated by Antonios Symvonis article (PDF) BibTeX	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8623157739639282, "perplexity": 1833.7284487256352}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151563.91/warc/CC-MAIN-20210725014052-20210725044052-00664.warc.gz"}
http://mymathforum.com/calculus/9480-water-tank-has-shape-inverted-circular-cone-altit.html	My Math Forum A water tank has shape of an inverted circular cone of altit Calculus Calculus Math Forum October 31st, 2009, 04:06 AM #1 Newbie Joined: Oct 2009 Posts: 7 Thanks: 0 A water tank has shape of an inverted circular cone of altit A water tank has shape of an inverted circular cone of altitude 12ft and base radius 6ft. if water is being pumped into the tank at a rate of 10lit/min, approximate the rate at which the water level is rising when it is 3 ft deep please solve this its answer is 1.89ft/min October 31st, 2009, 09:18 AM #2 Guest Joined: Posts: n/a Thanks: Re: A water tank has shape of an inverted circular cone of altit Perhaps I am in error, but I get dh/dt=$\frac{40}{9\pi}\approx 1.415$ $\frac{dh}{dt}=\frac{\frac{dv}{dt}}{A(t)}$ $A(t)=\text{area of surface of water when it is 3 feet deep}$ Area of water surface when 3 feet deep is $A={\pi}(\frac{3}{2})^{2}=\frac{9\pi}{4}$ November 1st, 2009, 04:06 AM #3 Global Moderator Joined: Dec 2006 Posts: 18,444 Thanks: 1462 Quote: Originally Posted by urduworld . . . if water is being pumped into the tank at a rate of 10lit/min, . . . Are you sure that the fill rate is being given in these units, when all the other measurements given use feet? If the fill rate is 10 ft³/min, I get 40/(9pi) ft/min = 1.41471... ft/min, as per galactus. If the fill rate is 10 l/min, you'd need to know that 10 l/min = 0.353146667 ft³/min, which gives a numerically much smaller answer (0.04996... ft/min). Tags altit, circular, cone, inverted, shape, tank, water , , , , , , , , , , , , , , # a water tank is in the shape of an inverted right circular cone of altitude 12 ft Click on a term to search for related topics. Thread Tools Display Modes Linear Mode Similar Threads Thread Thread Starter Forum Replies Last Post chuackl Calculus 2 December 27th, 2013 06:06 PM chuackl Calculus 11 November 4th, 2013 12:30 AM Chikis Elementary Math 2 May 12th, 2013 03:44 PM Decave Calculus 3 February 15th, 2012 06:50 PM urduworld Calculus 2 October 31st, 2009 06:31 AM Contact - Home - Forums - Cryptocurrency Forum - Top	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 4, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.856400191783905, "perplexity": 3045.092992458418}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891886.70/warc/CC-MAIN-20180123091931-20180123111931-00130.warc.gz"}
http://worldwidescience.org/topicpages/h/h-alpha+equivalent+width.html	1 Science.gov (United States) The near-infrared (NIR) wavelength range offers some unique spectral features, and it is less prone to the extinction than the optical one. Recently, the first flux calibrated NIR library of cool stars from the NASA Infrared Telescope Facility (IRTF) have become available, and it has not been fully exploited yet. We want to develop spectroscopic diagnostics for stellar physical parameters based on features in the wavelength range 1-5um. In this work we test the technique in the I and K bands. The study of the Y, J, H, and L bands will be presented in the following paper. An objective method for semi-empirical definition of spectral features sensitive to various physical parameters is applied to the spectra. It is based on sensitivity map - i.e., derivative of the flux in the spectra with respect to the stellar parameters at a fixed wavelength. New optimized indices are defined and their equivalent widths (EWs) are measured. (6 data files). Cesetti, M.; Pizzella, A.; Ivanov, V. D.; Morelli, L.; Corsini, E. M.; Dalla Bonta, E. 2013-04-01 2 Science.gov (United States) Table A1. reports the line list and atomic parameters adopted for the Palomar 1 giant Pal1-I and the Sun. For the Mn and Co lines we adopted the hyperfine structures (HFS) tabulated by Prochaska et al. (2000AJ....120.2513P). The measured equivalent width and the corresponding abundance obtained for each line are also reported. (1 data file). Monaco, L.; Saviane, I.; Correnti, M.; Bonifacio, P.; Geisler, D. 2010-11-01 3 Scientific Electronic Library Online (English) Full Text Available Abstract in spanish Implementamos un programa en Fortran que determina parámetros fundamentales de estrellas de tipo solar, a partir de anchos equivalentes del Fe. La solución debe verificar tres condiciones en el método estándar: equilibrio de ionización, equilibrio de excitación e independencia entre abundancias y anchos equivalentes. Calculamos modelos de atmósfera de Kurucz con opacidades NEWODF. Detalles como el parámetro de longitud de mezcla, el sobre impulso convectivo, etc. (more) se calculan con un programa independiente. FUNDPAR calcula las incertezas por dos métodos: el criterio de Gonzalez & Vanture (1998) y utilizando la función ?² . Los resultados derivados con FUNDPAR están de acuerdo con determinaciones previas en la literatura. En particular obtuvimos parámetros fundamentales de 58 estrellas con exoplanetas. El programa está disponible en la red1. Abstract in english We implemented a Fortran code that determines fundamental parameters of solar type stars from a list of Fe line equivalent widths. The solution should verify three conditions in the standard method: ionization equilibrium, excitation equilibrium and independence between metallicity and equivalent widths. Solarscaled Kurucz model atmospheres with NEWODF opacities are calculated with an independent program. Parameter files control different details, such as the mixinglength (more) parameter and the overshooting. FUNDPAR derives the uncertainties following two methods: the criterion of Gonzalez & Vanture (1998) and the dispersion using the ?2 function. The code uses the 2009 version of the MOOG program. The results derived with FUNDPAR are in agreement with previous determinations in the literature. The program is freely available from the web1. Saffe, C 2011-04-01 4 CERN Document Server We present a tool for measuring the equivalent width (EW) in high-resolution spectra. The Tool for Automatic Measurement of Equivalent width (TAME)provides the EWs of spectral lines by profile fitting in the automatic or the interactive mode, which can yield a more precise result through the adjustment of the local continuum and fitting parameters. The automatic EW results of TAME have been verified by comparing them with the manual EW measurements by IRAF splot task using the high-resolution spectrum of the Sun, and measuring EWs in the synthetic spectra with different spectral resolutions and S/N ratios. The EWs measured by TAME agree well with manually measured values, with a dispersion of less than 2 mA. By comparing the input EWs for synthetic spectra and EWs measured by TAME, we conclude that it is reliable for measuring the EWs in a spectrum with a spectral resolution, R > 20000 and find that the errors in EWs is less than 1 mA for a S/N ratio > 100. Kang, Wonseok 2012-01-01 5 CERN Document Server The extreme brightness of gamma-ray burst (GRB) afterglows and their simple spectral shape make them ideal beacons to study the interstellar medium of their host galaxies through absorption line spectroscopy. Using 69 low-resolution GRB afterglow spectra, we conduct a study of the rest-frame equivalent width (EW) distribution of features with an average rest-frame EW larger than 0.5 A. To compare an individual GRB with the sample, we develop EW diagrams as a graphical tool, and we give a catalogue with diagrams for the 69 spectra. We introduce a line strength parameter (LSP) that allows us to quantify the strength of the absorption features as compared to the sample by a single number. Using the distributions of EWs of single-species features, we derive the distribution of column densities by a curve of growth (CoG) fit. We find correlations between the LSP and the extinction of the GRB, the UV brightness of the host galaxies and the neutral hydrogen column density. However, we see no significant evolution of... Postigo, A de Ugarte; Thoene, C C; Christensen, L; Gorosabel, J; Milvang-Jensen, B; Schulze, S; Jakobsson, P; Wiersema, K; Sanchez-Ramirez, R; Leloudas, G; Zafar, T; Malesani, D; Hjorth, J 2012-01-01 6 CERN Multimedia The flux of the [OIII] line is considered to be a good indicator of the bolometric emission of quasars. The observed continuum emission from the accretion disc should instead be strongly dependent on the inclination angle theta between the disc axis and the line of sight. Based on this, the equivalent width (EW) of [OIII] should provide a direct measure of theta. Here we analyze the distribution of EW([OIII]) in a sample of ~6,000 SDSS quasars, and find that it can be accurately reproduced assuming a relatively small intrinsic scatter and a random distribution of inclination angles. This result has several implications: 1) it is a direct proof of the disc-like emission of the optical continuum of quasars; 2) the value of EW([OIII]) can be used as a proxy of the inclination, to correct the measured continuum emission and then estimate the bolometric luminosity of quasars; 3) the presence of almost edge-on discs among broad line quasars implies that the accretion disc is not aligned with the circumnuclear absor... Risaliti, G; Marconi, A 2010-01-01 7 Energy Technology Data Exchange (ETDEWEB) During routine monitoring of the Be star HR 4123 during the year 1987-1988, a burst of H-alpha emission was observed on May 11, 1987. The increase was observed on May 9 and lasted until June 7, peaking to an equivalent width of 31.6 A on May 11. This short-term burst is interpreted as due to the presence of a compact object in binary motion around the Be star, which accretes the matter ejected by the Be star to give out X-rays, which in turn produce ionization in the gas to give out the H-alpha emission. The broad line at 6577.5 A observed to accompany H-alpha emission during the burst is suggested to be emission from dielectronic recombination from C III ions in a C II region around the H II region formed by the X radiation. 18 refs. Ghosh, K.K.; Apparao, K.M.V.; Tarafdar, S.P. (Vainu Bappu Observatory, Kavalur (India); Tata Institute of Fundamental Research, Bombay (India)) 1989-09-01 8 CERN Document Server Aims: The precise determination of the stellar effective temperature of solar type stars is of extreme importance for Astrophysics. We present an effective temperature calibration for FGK dwarf stars using line equivalent width ratios of spectral absorption lines. Method: The ratios of spectral line equivalent width can be very sensitive to effective temperature variations for a well chosen combination of lines. We use the automatic code ARES to measure the equivalent width of several spectral lines, and use these to calibrate with the precise effective temperature derived from spectroscopy presented in a previous work. Results: We present the effective temperature calibration for 433 line equivalent width ratios built from 171 spectral lines of different chemical elements. We also make available a free code that uses this calibration and that can be used as an extension to ARES for the fast and automatic estimation of spectroscopic effective temperature of solar type stars. Sousa, S G; Israelian, G; Santos, N C 2009-01-01 9 UK PubMed Central (United Kingdom) The Calcium II triplet (Ca II T) lines in the near infrared spectral region is very important feature for late type stars, which serves as an important metallicity indicator for such stars. This is also true for stellar systems composed mainly of late type stars, such as old stellar clusters and galaxies. In this work, we made observations of the very famous spiral galaxy M31 and its dwarf elliptical companion M32, using the OMR spectrograph attached to the 2.16-meter telescope in Beijing Astronomical Observatory. Near-infrared spectra of the nuclear and disk regions on M31, as well as two slices along the major and the minor axis of M32, are derived. Equivalent widths of the Ca II triplet lines are measured using normal astrophysical spectrum analyzing techniques. The results are fundamental data for these two galaxies, which can be applied to researches for stellar population analysis of these galaxies. Li T; Deng L; Zhao G 2000-08-01 10 CERN Multimedia We present a new diagnostic diagram for mid-infrared spectra of infrared galaxies based on the equivalent width of the 6.2 micron PAH emission feature and the strength of the 9.7 micron silicate feature. Based on the position in this diagram we classify galaxies into 9 classes ranging from continuum-dominated AGN hot dust spectra and PAH-dominated starburst spectra to absorption-dominated spectra of deeply obscured galactic nuclei. We find that galaxies are systematically distributed along two distinct branches: one of AGN and starburst-dominated spectra and one of deeply obscured nuclei and starburst-dominated spectra. The separation into two branches likely reflects a fundamental difference in the dust geometry in the two sets of sources: clumpy versus non-clumpy obscuration. Spectra of ULIRGs are found along the full length of both branches, reflecting the diverse nature of the ULIRG family. Spoon, H W W; Houck, J R; Elitzur, M; Hao, L; Armus, L; Brandl, B R; Charmandaris, V 2006-01-01 11 Science.gov (United States) DAOSPEC is a Fortran code for measuring equivalent widths of absorption lines in stellar spectra with minimal human involvement. It works with standard FITS format files and it is designed for use with high resolution (R>15000) and high signal-to-noise-ratio (S/N>30) spectra that have been binned on a linear wavelength scale. First, we review the analysis procedures that are usually employed in the literature. Next, we discuss the principles underlying DAOSPEC and point out similarities and differences with respect to conventional measurement techniques. Then experiments with artificial and real spectra are discussed to illustrate the capabilities and limitations of DAOSPEC, with special attention given to the issues of continuum placement; radial velocities; and the effects of strong lines and line crowding. Finally, quantitative comparisons with other codes and with results from the literature are also presented. Stetson, P. B.; Pancino, E. 2010-11-01 12 CERN Document Server DAOSPEC is a Fortran code for measuring equivalent widths of absorption lines in stellar spectra with minimal human involvement. It works with standard FITS format files and it is designed for use with high resolution (R>15000) and high signal-to-noise-ratio (S/N>30) spectra that have been binned on a linear wavelength scale. First, we review the analysis procedures that are usually employed in the literature. Next, we discuss the principles underlying DAOSPEC and point out similarities and differences with respect to conventional measurement techniques. Then experiments with artificial and real spectra are discussed to illustrate the capabilities and limitations of DAOSPEC, with special attention given to the issues of continuum placement; radial velocities; and the effects of strong lines and line crowding. Finally, quantitative comparisons with other codes and with results from the literature are also presented. Stetson, P B 2008-01-01 13 DEFF Research Database (Denmark) It has been suggested that radiative transfer effects may explain the unusually high equivalent widths (EWs) of the Lya line, observed occasionally from starburst galaxies, especially at high redshifts. If the dust is locked up inside high-density clouds dispersed in an empty intercloud medium, the Lya photons could scatter off of the surfaces of the clouds, effectively having their journey confined to the dustless medium. The continuum radiation, on the other hand, does not scatter, and would thus be subject to absorption inside the clouds. This scenario is routinely invoked when Lya EWs higher than what is expected theoretically are observed, although the ideal conditions under which the results are derived usually are not considered. Here we systematically examine the relevant physical parameters in this idealized framework, testing whether any astrophysically realistic scenarios may lead to such an effect. It is found that although clumpiness indeed facilitates the escape of Lya, it is highly unlikely that any real interstellar media should result in a preferential escape of Lya over continuum radiation. Other possible causes are discussed, and it is concluded that the observed high EWs are more likely to be caused by cooling radiation from cold accretion and/or anisotropic escape of the Lya radiation. © 2013. The American Astronomical Society. All rights reserved. Laursen, P.; Duval, F. 2013-01-01 14 CERN Multimedia We consider the notion of bounded m-ary patch-width and its very close relative m-constructible. We show that the notions of m-constructibility all coincide for m>2, while 1-constructibility is a weaker notion. The same holds for bounded patch-width. The cace m=2 is left open. Shelah, S; Shelah, Saharon; Doron, Mor 2006-01-01 15 CERN Document Server We present and analyze epsilon Aurig\\ae\\ data concerning the evolution of the H{\\alpha} line on the occasion of the 2009 International observation campaign launched to cover the eclipse of this object. We visually inspect the dynamical spectrum constructed from the data and analyze the evolution with time of the EW (Equivalent Width) and of the radial velocity. The spectroscopic data reveal many details which confirm the complexity of the Aurig\\ae\\ system. The object is far from being understood. In particular, according to our measurements, the eclipse duration has been underestimated. A complete analysis of details revealed by our data would require much time and effort. Observers are encouraged to continue monitoring the H{\\alpha} line out of eclipse in the hope that it will provide further important information. Mauclaire, B; Garrel, T; Leadbeater, R; Lopez, A 2012-01-01 16 CERN Document Server We present the results of H-alpha monitoring of the BL Lac object OJ 287 with the VLT during seven epochs in 2005-08. We were able to detect five previously undetected narrow emission lines, 6548,6583[NII], 6563H-alpha$and 6716,6731[SII] during at least one of the epochs and a broad H-alpha feature during two epochs. The broad H-alpha luminosity was a factor ~10 lower in 2005-08 than in 1984 when the line was previously detected and a factor ~10 lower than what is observed in quasars and Seyfert galaxies at the same redshift. The data are consistent with no change in the position or luminosity of the H-alpha line in 2005-08. The width of the H-alpha line was 4200 +- 500 km/s, consistent with the width in 1984. Nilsson, K; Lehto, H J; Sillanpää, A 2010-01-01 17 CERN Document Server We report new follow-up spectroscopy of i-dropout galaxies with an NB921-band depression found in the Subaru Deep Field. The NB921-depressed i-dropout selection method is expected to select galaxies with large equivalent width Ly alpha emission over a wide redshift range, 6.0equivalent widths are 153A and 114A, which are lower limits on the intrinsic equivalent widths. Through our spectroscopic observations (including previous ones) of NB921-depressed i-dropout galaxies, we identified 5 galaxies in total with a rest-frame equivalent width larger than 100A at 6.0equivalent width, in a wider redshift range than usual narrow-band excess techniques. B... Nagao, T; Maiolino, R; Marconi, A; Kashikawa, N; Ajiki, M; Hattori, T; Ly, C; Malkan, M A; Motohara, K; Ohta, K; Sasaki, S S; Shioya, Y; Taniguchi, Y; Nagao, Tohru; Murayama, Takashi; Maiolino, Roberto; Marconi, Alessandro; Kashikawa, Nobunari; Ajiki, Masaru; Hattori, Takashi; Ly, Chun; Malkan, Matthew A.; Motohara, Kentaro; Ohta, Kouji; Sasaki, Shunji S.; Shioya, Yasuhiro; Taniguchi, Yoshiaki 2007-01-01 18 CERN Document Server This paper reports on the first results of the Suzaku observation in the Sgr C region. We detected four diffuse clumps with strong line emission at 6.4keV, Ka from neutral or low-ionized Fe. One of them, M359.38-0.00, is newly discovered with Suzaku. The X-ray spectra of the two bright clumps, M359.43-0.07 and M359.47-0.15, after subtracting the Galactic center diffuse X-ray emission (GCDX), exhibit strong Ka line from FeI with large equivalent widths (EWs) of 2.0-2.2keV and clear Kb of FeI. The GCDX in the Sgr C region is composed of the 6.4keV- and 6.7keV-associated components. These are phenomenologically decomposed by taking relations between EWs of the 6.4keV and 6.7keV lines. Then the former EWs against the associated continuum in the bright clump regions are estimated to be 2.4(+2.3_-0.7)keV. Since the two different approaches give similar large EWs of 2keV, we strongly suggest that the 6.4keV clumps in the Sgr C region are due to X-ray reflection/fluorescence (the X-ray reflection nebulae). Nakajima, Hiroshi; Nobukawa, Masayoshi; Matsumoto, Hironori; Koyama, Katsuji; Murakami, Hiroshi; Senda, Atsushi; Yamauchi, Shigeo 2008-01-01 19 CERN Multimedia We investigate the evolution of the Halpha equivalent width, EW(Halpha), with redshift and its dependence on stellar mass, taking advantage of the first data from the 3D-HST survey, a large spectroscopic Treasury program with the Hubble Space Telescope WFC3. Combining our Halpha measurements of 854 galaxies at 0.8 Fumagalli, Mattia; Franx, Marijn; Brammer, Gabriel; van Dokkum, Pieter; da Cunha, Elisabete; Kriek, Mariska; Lundgren, Britt; Momcheva, Ivelina; Rix, Hans-Walter; Schmidt, Kasper B; Skelton, Rosalind E; Whitaker, Katherine E; Labbe, Ivo; Nelson, Erica 2012-01-01 20 CERN Multimedia (Shortened) We consider the massive star formation properties, radial profiles, and atomic gas masses of those galaxies in our H alpha Galaxy Survey, a representative sample of the local Universe of 327 disk galaxies, that have close companion galaxies, in comparison with a matched control sample of galaxies without companions. We find that the presence of a close companion raises the star formation rate by a factor of just under two, while increasing hardly at all the equivalent width of the H alpha emission. This means that although statistically galaxies with close companions form stars at a higher rate, they do this over extended periods of time, and not as bursts. We find no significant increase in the central concentration of the star formation as a result of the presence of a close companion. The fraction of truly interacting or merging galaxies is very small in the local Universe, at around 2%, and possibly 4% of bright galaxies. Most of these interacting galaxies currently have unremarkable star form... Knapen, Johan H 2009-01-01 21 CERN Document Server We present here a study of the Halpha equivalent widths of the flocculent galaxy NGC 4395 and the grand design galaxy NGC 5457. A difference between the mean values of the Halpha equivalent widths for the two galaxies has been found. Several hypotheses are presented in order to explain this difference: differences in age, metallicity, star formation rate, photon leakage and initial mass function. Various tests and Monte Carlo models are used to find out the most probable cause of this difference. The resultsshow that the possible cause for the difference could be a variation in the initial mass function. This difference is such that it seems to favor a fraction of more massive stars in the grand design galaxy when compared with the flocculent galaxy. This could be due to a change of the environmental conditions due to a density wave. Cedres, B; Tomita, A; Cedres, Bernabe; Cepa, Jordi; Tomita, Akihiko 2005-01-01 22 CERN Document Server We present H${\\alpha}$emission line measurements of the W80 nebular complex. A total of 26 regions have been observed inside the nebula with the Dual Etalon Fabry-Perot Optical Spectrometer (DEFPOS) system at the f/48 Coude focus of 150 cm RTT150 telescope located at TUBITAK National Observatory (TUG) in Antalya/Turkey. The intensities, the local standard of rest (LSR) velocities ($V_{LSR}$), heliocentric radial velocities ($V_{HEL}$) and the linewidths at Full Width at Half Maximum (FWHM) of the H${\\alpha}$emission lines have been determined from these observations. They lie in the range of 259 to 1159 Rayleigh {1R = 10$^{6}/4\\pi$photons cm$^{-2}$sr$^{-1}$s$^{-1}$= 2.4110$^{-7}$erg cm$^{-2}$sr$^{-1}$s$^{-1}$at H${\\alpha}$.} (R), 4 to 12 km s$^{-1}$and 44 to 55 km s$^{-1}$, respectively. The radial velocity measurements show that there are several maxima and minima inside the W80. The new results confirm the literature that complex seems to be rather a uniform in radial velocity and no seen turbule... Aksaker, Naz\\im 2012-01-01 23 International Nuclear Information System (INIS) Variations of equivalen widths of absorption lines and of the radial velocities with the phase of the orbital period have been calculated for stars in a binary system with an account of the absorption component originating in a common spherically symmetric envelope having the radial opacity gradient. It is shown that a general expansion or contraction of the envelope may give rise to the distortion of the sinusoidal shape of radial velocity curves which is conventionally interpreted in terms of gas streams or is ascribed to the effect of elliptical orbit. 1985-01-01 24 CERN Multimedia We investigate a region of the Galactic plane, between 120 <= l <= 140 and -1 <= b <= +4, and uncover a population of moderately reddened (E(B-V) \\sim 1) classical Be stars within and beyond the Perseus and Outer Arms. 370 candidate emission line stars (13 <= r <= 16) selected from the INT Photometric H-alpha Survey of the Northern Galactic plane (IPHAS) have been followed up spectroscopically. A subset of these, 67 stars with properties consistent with those of classical Be stars, have been observed at sufficient spectral resolution (Delta_lambda \\sim 2 - 4 Angstrom) at blue wavelengths to narrow down their spectral types. We determine these to a precision estimated to be +/- 1 sub-type and then we measure reddenings via SED fitting with reference to appropriate model atmospheres. Corrections for contribution to colour excess from circumstellar discs are made using an established scaling to H-alpha emission equivalent width. Spectroscopic parallaxes are obtained after luminosity class has b... Raddi, R; Fabregat, J; Steeghs, D; Wright, N J; Sale, S E; Farnhill, H J; Barlow, M J; Greimel, R; Sabin, L; Corradi, R M L; Drake, J J 2013-01-01 25 CERN Multimedia In this work we present scanning Fabry-Perot H$\\alpha$observations of the isolated interacting galaxy pair NGC 5278/79 obtained with the PUMA Fabry-Perot interferometer. We derived velocity fields, various kinematic parameters and rotation curves for both galaxies. Our kinematical results together with the fact that dust lanes have been detected in both galaxies, as well as the analysis of surface brightness profiles along the minor axis, allowed us to determine that both components of the interacting pair are trailing spirals. Repetto, P; Fuentes-Carrera, R Gabbasov I 2009-01-01 26 CERN Document Server We report on the finding of the strongest H(alpha) emission -pseudoequivalent width of 705 Angstrom- known so far in a young, late type dwarf. This object, named as SOri71, is a substellar candidate member of the 1-8 Myr star cluster sigma Orionis. Due to its overluminous location in color-magnitude diagrams, SOri71 might be younger than other cluster members, or a binary of similar components. Its mass is in the range 0.021-0.012 M(sun), depending on evolutionary models and possible binarity. The broad H(alpha) line of SOri71 appears asymmetric, indicative of high velocity mass motions in the H(alpha) forming region. The origin of this emission is unclear at the present time. We discuss three possible scenarios: accretion from a disk, mass exchange between the components of a binary system, and emission from a chromosphere. Barrado y Navascués, D; Martín, E L; Béjar, V J S; Rebolo, R; Mundt, R; Navascues, David Barrado y; Osorio, Maria Rosa Zapatero; Martin, Eduardo L.; Bejar, Victor J.S.; Rebolo, Rafael; Mundt, Reinhard 2002-01-01 27 Science.gov (United States) The Universidad Complutense de Madrid survey is a long project with the aim of finding and analyzing star formation galaxies using the H-alpha line as the tracer for the massive star formation processes. In order to obtain a representative complete sample of such a technique, several objective prism plates were taken with the Schmidt telescope at Calar Alto Almeria (Spain). The combination of IIIaF Kodak emulsion and a RG630 filter was used for covering the red spectral region, from 6400A to a redshift of 0.045 for the H-alpha line. A compilation of descriptions and positions is presented for 272 emission-line candidates from 545 square degrees of the sky. Also apparent magnitude and equivalent width estimators are given. Spectroscopical observations were carried out for the full sample of H-alpha emission--line galaxy (ELGs) candidates. All the spectroscopic information is presented in the form of an appendix. Each ELG was classified into one of eight natural groups of star forming galaxies. The ELG types most commonly found (47%) are intermediate to low-luminosity objects with a very intense star-formation region which dominates the optical output of the galaxy. This kind of ELGs is similar to the galaxy population detected in the blue objective prism surveys, but what is more important, it was found a second population (43%) of star-forming galaxies with low ionization or high extinction properties. This ELGs group are not detected nor in the blue (University of Michigan survey) neither in other surveys (Kiso, IRAS, Markarian) using other selection techniques. Emission-line ratio diagnostic diagrams reveal that the ELGs in the different natural groups tend to have distinctly different line ratios. This suggests that the various ELGs types differ from one another in terms of metal abundance of their ionized gas, the ionization parameter and the relative importance of the starburst process in the galaxy, confirming a previous similar result found for the UM survey. There is present a trend for lower metallicities at lower luminosities. It has not been found any galaxy with metallicity lower than I Zw 18. >From the original IRAS data it was obtained for the whole sample the far-infrared fluxes. In the one hand it is necessary to apply a two-component model for reproducing the general behaviour of the UCM sample at that spectral range. In the other hand the FIR properties of a H-alpha selected sample are well differentiated against FIR-selected samples. The line+continuum flux is the main selection parameter for the UCM survey, but other secondary effects are discussed. An study of the luminosity and spatial distribution of the UCM galaxies is presented. The ELGs follow at great scale the distribution of the catalog galaxies. Using the UCM ELGs as SFR tracers a luminosity function for the SFR at the local Universe is computed. These result has important implications for our understanding of the origin of the star formation phenomena as well as the evolution of the galaxies. In the future, we propose to extend the survey to new sky regions and deeper redshifts and to quantify the SFR at the Local Universe by means of the UCM sample. The original is written in spanish. (SECTION: Dissertation Summary) Gallego Maestro, Jesus 1995-07-01 28 CERN Document Server The AAO/UKST SuperCOSMOS H-alpha Survey (SHS) of the southern Galactic plane was, when completed in 2003, a powerful new addition to wide-field surveys. It has a combination of areal coverage, spatial resolution and flux sensitivity in a narrow imaging band which still marks it out today as an excellent resource for the astronomical community. The 233 separate fields are available online in digital form, with each field covering 25 square degrees. The SHS has been the motivation for equivalent surveys in the north, and new digital H-alpha surveys now beginning in the south such as VPHAS+. The SHS has been the foundation of many important follow-up discovery projects in the southern sky with the Macquarie/AAO/Strasbourg H-alpha (MASH) planetary nebula project being a particularly successful example. However, the full astrophysical potential of the SHS has been hampered by lack of a clear route to acceptable flux calibration from the base photographic data. We have determined the calibration factors for 170 sep... Frew, David J; Parker, Quentin A; Pierce, Mark J; Gunawardhana, M L P; Reid, W A 2013-01-01 29 Energy Technology Data Exchange (ETDEWEB) The Fabry-Perot interferometer is an effective dispersing element for studying H-alpha emission from solar limb prominences. Having a reflecting coefficient in the range 0.85-0.95, the Fabry-Perot multiple beam interferometer behaves as an angular filter, forming circular interference fringes. Results from an investigation performed at the solar installation at Boyden Observatory in South Africa are presented, where a photographic Fabry-Perot interferometer was used to obtain fringes from the 656.3-nm H-alpha emission during April and May 1980. Successful scans were made with air admitted to the interferometer pressure chamber, and reduction of the data on photon count and chamber pressure was made by a UNIVAC 1108 computer. Sketches and profiles from the limb prominences are shown a table of fringe half-widths, corrected for the instrumental width of the interferometer, were obtained by matching a Voigt function by a least-squares computer fit to the observed scanned Fabry-Perot fringe profiles. Jarrett, A.H. (Boyden Observatory, Bloemfontein, Republic of South Africa); Stapelberg, J. (Orange Free State, University, Bloemfontein, Republic of South Africa) 1981-02-01 30 CERN Multimedia Solar storms can have a major impact on the infrastructure of the earth. Some of the causing events are observable from ground in the H{\\alpha} spectral line. In this paper we propose a new method for the simultaneous detection of flares and filaments in H{\\alpha} image sequences. Therefore we perform several preprocessing steps to enhance and normalize the images. Based on the intensity values we segment the image by a variational approach. In a final postprecessing step we derive essential properties to classify the events and further demonstrate the performance by comparing our obtained results to the data annotated by an expert. The information produced by our method can be used for near real-time alerts and the statistical analysis of existing data by solar physicists. Riegler, Gernot; Pötzi, Werner; Veronig, Astrid 2013-01-01 31 Science.gov (United States) A wide-field H-alpha survey of the Galactic Plane has been initiated by Mount Stromlo & Siding Spring Observatories in collaboration with the University of Sydney. The primary aim of the survey is to obtain images of the Galactic Plane in H-alpha and red continuum filters which will be compared with radio continuum images at 843 MHz from the Molonglo Observatory Synthesis Telescope (MOST). The secondary aim is to obtain images in [OIII] and [SII] to provide additional information on the nature of excitation in HII regions. Thirdly, additional images will be taken in B, V and I of interesting areas suitable for general publications as coloured reproductions. The images are taken with a 400 mm f/4.5 Nikkor-Q lens in conjunction with a 2K x 2K SITe thinned CCD. The resolution is 12'' per pixel and the pixel size is 24 microns giving a 7 x 7 sq. deg. field of view. H-alpha and red continuum observations are expected to be completed by the end of 1997. It is planned to make the results from the survey available on CD ROM and possibly video. Buxton, M.; Bessell, M.; Watson, B. 1998-04-01 32 CERN Multimedia Aims: We attempt to constrain progenitors of the different types of supernovae from their spatial distributions relative to star formation regions in their host galaxies, as traced by H alpha + NII line emission. Methods: We analyse 63 supernovae which have occurred within galaxies from our H alpha survey of the local Universe. Three statistical tests are used, based on pixel statistics, H alpha radial growth curves, and total galaxy emission-line fluxes. Results: Many more type II supernovae come from regions of low or zero emission line flux than would be expected if the latter accurately traces high-mass star formation. We interpret this excess as a 40% Runaway' fraction in the progenitor stars. Supernovae of types Ib and Ic do appear to trace star formation activity, with a much higher fraction coming from the centres of bright star formation regions than is the case for the type II supernovae. Type Ia supernovae overall show a weak correlation with locations of current star formation, but there is evide... James, P A 2006-01-01 33 Science.gov (United States) We have developed a procedure for the automatic selection of emission-line galaxies candidates from the digitization of objective prism plates. This procedure has been applied over two pair of direct and prism plates of the Universidad Complutense de Madrid (UCM) survey, digitized by the fast and high performance microdensitometer MAMA (Machine Automatique a Mesurer pour l'Astronomie) located at the Observatoire de Paris. The plates where obtained with the Schmidt Telescope at Calar Alto Observatory in Almeria (Spain). The instrumental setup used for the acquisition of the prism plates (IIIa-F emulsion and RG630 filter) allows to register the H-alpha +[NII] emission for galaxies up to z <= 0.045. Therefore the criteria developed for the automatic selection of ELGs candidates consist in identifying the H-alpha emission feature in the extracted monodimensional prism spectra. We have noted that there is not a nitid edge to distinguish between the spectra showing the H-alpha line in emission and the rest. Consequently we have studied the residual obtained after the estimation of the continuum and the variation of the slopes calculated over each spectrum in order to identify the line feature. The efficiency of this technique has been tested by comparing the results obtained applying the automatic procedure with those achieved after a careful visual search for the candidates, as performed up to date in the UCM and similar surveys. The results show us that the automatic procedure only ignore very extended and near saturated known galaxies with well resolved emitting regions located at the external regions. Spectroscopic observations of moderate dispersion for the whole set of candidates selected both automatic and visually show that the former has been able, not only to select the 100% of candidates with confirmed emission recognized also by visual means, but also, and what is more important, to identify a 29% more of confirmed ELGs, without lost of efficiency by the increase of spurious identifications. The digitization of the plates has allowed us to measure a set of accurate observational parameters as positions, magnitudes, sizes and redshifts that will permit to perform statistical analysis of this kind of objects before carrying out specific observations with larger telescopes. Since our plates have not sensitometric spots to calculate its characteristic curve, it has been necessary to obtain external calibrations by comparing with calibrated data offered by several catalogs. We have tested that the precision achieved using this method is mainly limited by the accuracy of the different catalog employed. The redshift of the candidates can be derived from the location of the H-alpha line on the prism spectra. Since they have no spectral features to refer the position of the H$\\alpha$line, the positions of the objects in the direct plate and their transformations to the prism one have been used to provide a reference point which is dependent neither on magnitude, nor on color, nor spatial light distribution. A precision of 0.003 is reached when measuring redshifts by this method. Finally, the comparison of the candidate samples obtained from two plates of our survey covering the same area on the sky allows the study of the selection effects that affects the identification of the H-alpha line in photographic prism plates. The parameter EW X F of the emission H-alpha +[NII] can be used as a threshold that inform us about the unambiguous identification of the emission in the prism spectra, being 10^-13 erg s^-1 cm^-2A the mean value of this parameter for the whole sample of the UCM survey. We have also developed an algorithm to simulate the expected objective-prism spectra for an object by using different instrumental setups. The simulation permits to investigate the different combinations of EW, fluxes and magnitude that allow the detection of the H$\\alpha$line in the plates and will be used in the near future to predict the expected spectra by the substitution of the photographic emulsion with CCD detectors. (SECTION: D Lasheras, Oscar Alonso 1996-06-01 34 Energy Technology Data Exchange (ETDEWEB) [alpha]-Farnesene deuterated at C1 or C4 was synthesised by regiospecific deuteration of 2-geranyl-3-methylsulpholene (2). Treatment of (2) with butyl lithium in dimethylpropenylurea (DMPU) mediated THF resulted in deprotonation at C2. Quenching with D[sub 2]O/CH[sub 3]CO[sub 2]D gave a mixture of deuterated sulpholenes (43-68%). Thermal elimination of sulphur dioxide gave 4-[sup 2]H-[alpha]-farnesene (85%) but with low deuterium incorporation (60%) and poor regiospecificity. Treatment of (2) with butyl lithium in TMEDA mediated THF resulted in deprotonation at C5 with minimal bond migration (1%). Quenching with D[sub 2]O/CH[sub 3]CO[sub 2]D yielded 5-[sup 2]H-2-geranyl-3-methylsulpholene (75%) which on thermolysis gave 1-[sup 2]H-[alpha]-farnesene (86%) with high regiospecificity and improved deuteration (85%). Some mechanistic aspects of the alkylation of 3-methylsulpholenes are discussed. (Author). Fielder, S.; Rowan, D.D.; Reay, P.F. (Horticulture and Food Research Inst. of New Zealand Ltd., Palmerston North (New Zealand)) 1993-10-01 35 CERN Multimedia In this work we present scanning Fabry-Perot H$\\alpha$observations of the isolated interacting galaxy pair NGC 5278/79 obtained with the PUMA Fabry-Perot interferometer. We derived velocity fields and rotation curves for both galaxies. For NGC 5278 we also obtained the residual velocity map to investigate the non-circular motions, and estimated its mass by fitting the rotation curve with a disk+halo components. We test three different types of halo (pseudo-isothermal, Hernquist and Navarro Frenk White) and obtain satisfactory fits to the rotation curve for all profiles. The amount of dark matter required by pseudo-isothermal profile is about ten times smaller than, that for the other two halo distributions. Finally, our kinematical results together with the analysis of dust lanes distribution and of surface brightness profiles along the minor axis allowed us to determine univocally that both components of the interacting pair are trailing spirals. Repetto, P; Gabbasov, R; Fuentes-Carrera, I 2010-01-01 36 CERN Multimedia It is now apparent that classical T Tauri-like outflows commonly accompany the formation of young brown dwarfs. To date two optical outflows have been discovered and results presented in this paper increase this number to three. Using spectro-astrometry the origin of the LS-RCrA 1 forbidden emission lines in a blue-shifted outflow is confirmed. The non-detection of the red-shifted component of the outflow in forbidden lines, along with evidence for some separation between low and high velocity outflow components, do not support the hypothesis that LS-RCrA 1 has an edge-on accretion disk. The key result of this analysis is the discovery of an outflow component to the H-alpha line. The H-alpha line profile has blue and red-shifted features in the wings which spectro-astrometry reveals to also originate in the outflow. The discovery that H-alpha emission in BDs can have a significant contribution from an outflow suggests the use of H-alpha line widths as a proxy of mass accretion in BDs is not clear-cut. This me... Whelan, E T; Bacciotti, F 2009-01-01 37 Energy Technology Data Exchange (ETDEWEB) A study of type II solar radio bursts recorded at 160 MHz by the Culgoora radioheliograph during 1980 to 1982 shows that the radio emission occurs above H-alpha filaments rather than above H-alpha flares. This suggests that the type II radio emission most probably originates from within a coronal helmet streamer overlying the filament channel. 9 references. Stewart, R.T. 1984-09-01 38 CERN Multimedia [Abridged] We present new measurements of the H-alpha luminosity function (LF) and SFR volume density for galaxies at z~0.8. Our analysis is based on 1.18$\\mu$m narrowband data from the NEWFIRM H-alpha Survey, a comprehensive program designed to capture deep samples of intermediate redshift emission-line galaxies using narrowband imaging in the near-infrared. The combination of depth ($\\approx1.9\\times10^{-17}$erg s$^{-1}$cm$^{-2}$in H-alpha at 3$\\sigma$) and areal coverage (0.82 deg$^2$) complements other recent H-alpha studies at similar redshifts, and enables us to minimize the impact of cosmic variance and place robust constraints on the shape of the LF. The present sample contains 818 NB118 excess objects, 394 of which are selected as H-alpha emitters. Optical spectroscopy has been obtained for 62% of the NB118 excess objects. Empirical optical broadband color classification is used to sort the remainder of the sample. A comparison of the LFs constructed for the four individual fields reveals signific... Ly, Chun; Dale, Daniel A; Momcheva, Ivelina; Salim, Samir; Staudaher, Shawn; Moore, Carolynn A; Finn, Rose 2010-01-01 39 CERN Document Server From H alpha images of a carefully selected sample of 57 relatively large, Northern spiral galaxies with low inclination, we study the distribution of the H alpha emission in the circumnuclear and nuclear regions. At a resolution of around 100 parsec, we find that the nuclear H alpha emission in the sample galaxies is often peaked, and significantly more often so among AGN host galaxies. The circumnuclear H alpha emission, within a radius of two kpc, is often patchy in late-type, and absent or in the form of a nuclear ring in early-type galaxies. There is no clear correlation of nuclear or circumnuclear H alpha morphology with the presence or absence of a bar in the host galaxy, except for the nuclear rings which occur in barred hosts. The presence or absence of close bright companion galaxies does not affect the circumnuclear H alpha morphology, but their presence does correlate with a higher fraction of nuclear H alpha peaks. Nuclear rings occur in at least 21% (+-5%) of spiral galaxies, and occur predomina... Knapen, J H 2004-01-01 40 CERN Document Server The clustering properties of a well-defined sample of 734 H-alpha emitters at z=0.84 obtained as part of the Hi-z Emission Line Survey (HiZELS) are investigated. The spatial correlation function is very well-described by (r/r_0)^-1.8, with r_0=2.7+-0.3Mpc/h. The correlation length r_0 increases strongly with H-alpha luminosity, L_H-alpha, from r_0~2Mpc/h for the most quiescent galaxies (star-formation rates of ~4M_sun/yr), up to r_0>5Mpc/h for the brightest galaxies in H-alpha. The correlation length also increases with increasing rest-frame K-band luminosity (M_K), but the r_0-L_H-alpha correlation maintains its full statistical significance at fixed M_K. At z=0.84, star-forming galaxies classified as irregulars or mergers are much more clustered than discs and non-mergers, but once the samples are matched in L_H-alpha and M_K, the differences vanish, implying that the clustering is independent of morphological type at z~1. The typical H-alpha emitters found at z=0.84 reside in dark-matter haloes of ~10^12M_... Sobral, David; Geach, James E; Smail, Ian; Cirasuolo, Michele; Garn, Timothy; Dalton, Gavin B; Kurk, Jaron 2009-01-01 41 CERN Multimedia We present observations of the HI tidal arm near dwarf galaxy NGC 3077 (member of the M81 galaxy group) in narrow band [SII] and H_alpha filters. Observations were carried out in March 2011 with the 2m RCC telescope at NAO Rozhen, Bulgaria. Our search for possible supernova remnant candidates (identified as sources with enhanced [SII] emission relative to their H_alpha emission) in this region yielded no sources of this kind. Nevertheless, we found a number of objects with significant H_alpha emission that probably represent uncatalogued, low brightness HII regions. Andjelic, M; Arbutina, B; Ilic, D; Urosevic, D 2011-01-01 42 CERN Document Server e present and analyze the correlations between mid-infrared (MIR), far-infrared (FIR), total-infrared (TIR), H$\\alpha$, and FUV luminosities for star-forming galaxies, composite galaxies and AGNs, based on a large sample of galaxies selected from the$Spitzer$SWIRE fields. The MIR luminosities of star-forming galaxies are well correlated with their H$\\alpha$, TIR and FUV luminosities, and we re-scaled the MIR-derived SFR formulae according to the above correlations with differences less than 15%. We confirm the recent result by calzetti et al. (2007) that the combined observed H$\\alpha$+ 24$\\mu$m luminosities L(H$\\alpha IR and TIR luminosities are completely following those of star-forming galaxies. Zhu, Yi-Nan; Cao, Chen; Li, Hai-Ning 2008-01-01 43 CERN Multimedia A particularly interesting line for exploring the physical conditions of the quiet solar chromosphere is H$\\alpha$, but its intensity profile is magnetically insensitive and the small circular polarization signatures produced by the longitudinal Zeeman effect come mainly from the underlying photosphere. Here we show that the Hanle effect in H$\\alpha$ provides quantitative information on the magnetism of the quiet chromosphere. To this end, we calculate the response function of the emergent scattering polarization to perturbations in the magnetic field. Stepan, Jiri 2010-01-01 44 CERN Multimedia We analyze H-alpha observations of the recurrent nova T CrB obtained during the last decade. For the first time the H-alpha emission profile is analyzed after subtraction of the red giant contribution. Based on our new radial velocity measurements of the H-alpha emission line we estimate the component masses of T CrB. It is found that the hot component is most likely a massive white dwarf. We estimate the inclination and the component masses to be i~67 deg, Mwd = 1.37 +/-0.13 Msun and Msec=1.12 +/-0.23 Msun, respectively. The radial velocity of the central dip in the H-alpha profile changes nearly in phase with that of the red giant's absorption lines. This suggests that the dip is most likely produced by absorption in the giant's wind. Our observations cover an interval when the H-alpha and the U-band flux vary by a factor of ~6, while the variability in B and V is much smaller. Based on our observations, and archival ultraviolet and optical data we show that the optical, ultraviolet and H-alpha fluxes stron... Stanishev, V; Tomov, N; Marziani, P 2003-01-01 45 CERN Document Server In a first of a series of studies of the H-alpha + [NII] emission from nearby spiral galaxies, we present measurements of H-alpha + [NII] emission from HII regions in M81. Our method uses large-field-CCD images and long-slit spectra, and is part of the ongoing Beijing-Arizona-Taipei-Connecticut Sky Survey. The CCD images are taken with the NAOC 0.6/0.9m f/3 Schmidt telescope at the Xinglong Observing Station, using a multicolor filter set. Spectra of 10 of the brightest HII regions are obtained using the NAOC 2.16m telescope with a Tek 1024 X 1024 CCD. The continua of the spectra are calibrated by flux-calibrated images taken from the Schmidt observations. We determine the continuum component of our H-alpha + [NII] image via interpolation from the more accurately-measured backgrounds (M81 starlight) obtained from the two neighboring (in wavelength) BATC filter images. We use the calibrated fluxes of H-alpha + [NII] emission from the spectra to normalize this interpolated, continuum-subtracted H-alpha + [NII] ... Lin, W P; Burstein, D; Windhorst, R A; Chen, J S 2003-01-01 46 CERN Document Server H-alpha and continuum images are presented for 27 nearby early-type(Sa-Sab) spiral galaxies. Contrary to popular perception, the images reveal copious massive star formation in some of these galaxies. A determination of the H-alpha morphology and a measure of the H-alpha luminosity suggests that early-type spirals can be classified into two broad categories based on the luminosity of largest HII region in the disk. The first category includes galaxies for which the individual HII regions have L(H-alpha) 10^(39) erg/s. All category 2 galaxies show either prominent dust lanes or other morphological peculiarities such as tidal tails which suggests that the anomalously luminous HII regions in category 2 galaxies may have formed as a result of a recent interaction. The observations, which are part of an on-going H-alpha survey, reveal early-type spirals to be a heterogeneous class of galaxies that are evolving in the current epoch. We have also identified some systematic differences between the classifications of... Hameed, S A; Hameed, Salman; Devereux, Nick 1999-01-01 47 CERN Multimedia We present Monte Carlo simulations of the Diffuse H$\\alpha$ Galactic Background. Our models comprise direct and multiply scattered H$\\alpha$ radiation from the kpc scaleheight Warm Ionized Medium and midplane H II regions. The scattering is off dust that is assumed to be well mixed with the gas, with an axisymmetric density distribution taken from the literature. The results of our simulations are all-sky H$\\alpha$ images that enable us to separate out the contributions of direct and scattered radiation. We also determine how far the model H$\\alpha$ photons have traveled, i.e., how far we see into the Galaxy at H$\\alpha$. Our models reproduce the overall characteristics of the observed H$\\alpha$ background and predict the scattered H$\\alpha$ intensity at high latitudes is in the range 5% to 20% of the total intensity, in agreement with estimations based on [S II]/H$\\alpha$ and [O III]/H$\\alpha$ line ratio measurements. The polarization arising from dust scattering of H$\\alpha$ from midplane H II regions is pr... Wood, K; Wood, Kenneth; Reynolds, Ron 1999-01-01 48 International Nuclear Information System (INIS) A high-sensitivity search for H-alpha emission from a -300 km/s H-I cloud in Cetus was performed using a large-aperture Fabry-Perot spectrometer. Weak emission features were noted in the H-alpha spectra at radial velocities coinciding with the 21-cm emission. The H-alpha surface brightness of the cloud is found to be 2.0 + or - 0.5 x 10 to the -8th ergs/sq cm per s per sr. The results are used to set an upper limit of 200,000/sq cm per s on the flux of Lyman-continuum photons in the vicinity of the cloud, almost a factor of 10 lower than the flux estimated to be present within the Galactic halo and comparable to some estimates for the intergalactic EUV radiation field. 17 refs. 1989-01-01 49 Science.gov (United States) The isobaric multiplet width equation is verified in the light of recent experimental information on masses and widths. The verification is carried out for the known level widths and the results came in support of the isobaric width equation removing all ... A. M. Awin 1991-01-01 50 CERN Multimedia We present our H-alpha observations of 11 isolated southern galaxies: SDIG, PGC 51659, E 222-010, E 272-025, E 137-018, IC 4662, Sag DIG, IC 5052, IC 5152, UGCA 438, and E149-003, with distances from 1 to 7 Mpc. We have determined the total H-alpha fluxes from these galaxies. The star formation rates in these galaxies range from 10^{-1} (IC 4662) to 10^{-4}_{\\odot}/yr (SDIG) and the gas depletion time at the observed star formation rates lies within the range from 1/6 to 24 Hubble times H_0^{-1} . Kaisin, S S; Knyazev, A Yu; Karachentsev, I D 2007-01-01 51 International Nuclear Information System (INIS) The narrow hydrogen Balmer alpha profiles observed in tokamaks are explained in terms of the slow (approx. 0.3 eV) and fast (2 to 6 eV) excited atoms formed by dissociation of molecular hydrogen at the plasma edge. Extra widening of the spectrum in the wings can be explaind by Zeeman split H-alpha that is reflected from the vacuum vessel. This interpretation is consistent with available high-resolution data. The use of H-alpha as a diagnostic is discussed briefly 1981-01-01 52 Energy Technology Data Exchange (ETDEWEB) The narrow hydrogen Balmer alpha profiles observed in tokamaks are explained in terms of the slow (approx. 0.3 eV) and fast (2 to 6 eV) excited atoms formed by dissociation of molecular hydrogen at the plasma edge. Extra widening of the spectrum in the wings can be explaind by Zeeman split H-alpha that is reflected from the vacuum vessel. This interpretation is consistent with available high-resolution data. The use of H-alpha as a diagnostic is discussed briefly. McNeill, D.H. 1981-04-01 53 CERN Multimedia We report on the first simultaneous observation of an H-alpha Moreton wave, the corresponding EUV fast coronal waves, and a slow and bright EUV wave (typical EIT wave). Associated with an X6.9 flare that occurred on 2011 August 9 at the active region NOAA 11263, we observed a Moreton wave in the H-alpha images taken by the Solar Magnetic Activity Research Telescope (SMART) at Hida Observatory of Kyoto University. In the EUV images obtained by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO) we found not only the corresponding EUV fast "bright" coronal wave, but also the EUV fast "faint" wave that is not associated with the H-alpha Moreton wave. We also found a slow EUV wave, which corresponds to a typical EIT wave. Furthermore, we observed, for the first time, the oscillations of a prominence and a filament, simultaneously, both in the H-alpha and EUV images. To trigger the oscillations by the flare-associated coronal disturbance, we expect a coronal wave as fast as the fast... Asai, Ayumi; Isobe, Hiroaki; Kitai, Reizaburo; UeNo, Satoru; Nagata, Shin'ichi; Morita, Satoshi; Nishida, Keisuke; Shiota, Daikou; Oi, Akihito; Akioka, Maki; Shibata, Kazunari 2011-01-01 54 CERN Document Server After a successful eleven-year campaign at Kitt Peak, we moved the Wisconsin H-Alpha Mapper (WHAM) to Cerro Tololo in early 2009. Here we present some of the early data after a few months under southern skies. These maps begin to complete the first all-sky, kinematic survey of the diffuse H-alpha emission from the Milky Way. Much of this emission arises from the Warm Ionized Medium (WIM), a significant component of the ISM that extends a few kiloparsecs above the Galactic disk. While this first look at the data focuses on the H-alpha survey, WHAM is also capable of observing many other optical emission lines, revealing fascinating trends in the temperature and ionization state of the WIM. Our ongoing studies of the physical conditions of diffuse ionized gas will continue from the southern hemisphere following the H-alpha survey. In addition, future observations will cover the full velocity range of the Magellanic Stream, Bridge, and Clouds to trace the ionized gas associated with these neighboring systems. Haffner, L M; Madsen, G J; Hill, A S; Barger, K A; Jaehnig, K P; Mierkiewicz, E J; Percival, J W; Chopra, N 2010-01-01 55 CERN Document Server We study an undocumented large translucent cloud, detected by means of its enhanced radiation on the SHASSA (Southern H-Alpha Sky Survey Atlas) survey. We consider whether its excess surface brightness can be explained by light scattered off the dust grains in the cloud, or whether emission from in situ ionized gas is required. In addition, we aim to determine the temperature of dust, the mass of the cloud, and its possible star formation activity. We compare the observed H-alpha surface brightness of the cloud with predictions of a radiative transfer model. We use the WHAM (Wisconsin H-Alpha Mapper) survey as a source for the Galactic H-alpha interstellar radiation field illuminating the cloud. Visual extinction through the cloud is derived using 2MASS J, H, and K band photometry. We use far-IR ISOSS (ISO Serendipitous Survey), IRAS, and DIRBE data to study the thermal emission of dust. The LAB (The Leiden/Argentine/Bonn Galactic HI Survey) is used to study 21cm HI emission associated with the cloud. Radiati... Lehtinen, K; Mattila, K 2010-01-01 56 International Nuclear Information System (INIS) The radial velocity and linewidth of H-alpha emission from 284 objects listed in Galactic H II region catalogs were observed using a Fabry-Perot spectrometer. A few of these objects are supernova remnants or planetary nebula. The rest of this sample encompasses most of the H II regions that are visible optically from the Northern Hemisphere. These observations are compared to previous H-alpha observations as well as to radio recombination line and CO observations. The average radial-velocity difference V(CO) - V(H-alpha) is 0.50 + or - 0.48 km/s and the (1-sigma) dispersion is 6.44 km/s. The implications of these values are discussed in terms of a very simple kinematic and extinction H II region model. Total H-alpha luminosities for the sample are estimated, and the Galactic H II region luminosity function is compared to that recently found for other galaxies. 18 refs. 1990-01-01 57 CERN Multimedia Recent papers published in the last years contributed to resolve the enigma on the hypothetical Be nature of the hot pulsating star $\\beta$ Cep. This star shows variable emission in the H$\\alpha$ line, typical for Be stars, but its projected rotational velocity is very much lower than the critical limit, contrary to what is expected for a typical Be star. The emission has been attributed to the secondary component of the $\\beta$ Cep spectroscopic binary system. In this paper, using both ours and archived spectra, we attempted to recover the H$\\alpha$ profile of the secondary component and to analyze its behavior with time for a long period. To accomplish this task, we first derived the atmospheric parameters of the primary: T$_{\\rm eff}$ = 24000 $\\pm$ 250 K and $\\log g$ = 3.91 $\\pm$ 0.10, then we used these values to compute its synthetic H$\\alpha$ profile and finally we reconstructed the secondary's profile disentangling the observed one. The secondary's H$\\alpha$ profile shows the typical two peaks emission... Catanzaro, G 2008-01-01 58 International Nuclear Information System (INIS) The results of high-resolution observations of the solar preflare activity of June 25, 1980 are analyzed. The observations were carried out simultaneously in the UV microwave, and H-alpha wavelengths using the VLA, the Ottawa River photoheliograph, and the Solar Max spectrometer and polarimeter instruments. Increases were observed in the intensitiy and polarization of compact sources at a wavelength of 6-cm during the preflare hour. The increases were associated with rising and twisting motions in the magnetic loops near the sight of the subsequent flare. Consistent with this process, analysis of the transverse and Doppler motions observed in the H-alpha filament before disruption showed that the filament was activated internally by the motions of evolving magnetic flux patterns. Ultraviolet data for C IV brightenings and upflows at the first appearance of the H-alpha filament indicated the presence of rising magnetic loops and material rising within the loops. The complete VLA, microwave and H-alpha data sets are given. 30 references. 1985-01-01 59 Science.gov (United States) The results of high-resolution observations of the solar preflare activity of June 25, 1980 are analyzed. The observations were carried out simultaneously in the UV microwave, and H-alpha wavelengths using the VLA, the Ottawa River photoheliograph, and the Solar Max spectrometer and polarimeter instruments. Increases were observed in the intensitiy and polarization of compact sources at a wavelength of 6-cm during the preflare hour. The increases were associated with rising and twisting motions in the magnetic loops near the sight of the subsequent flare. Consistent with this process, analysis of the transverse and Doppler motions observed in the H-alpha filament before disruption showed that the filament was activated internally by the motions of evolving magnetic flux patterns. Ultraviolet data for C IV brightenings and upflows at the first appearance of the H-alpha filament indicated the presence of rising magnetic loops and material rising within the loops. The complete VLA, microwave and H-alpha data sets are given. Kundu, M. R.; Gaizauskas, V.; Woodgate, B. E.; Schmahl, E. J.; Shine, R.; Jones, H. P. 1985-03-01 60 CERN Multimedia We present a near-infrared spectroscopic study of a stellar mass selected sample of galaxies at z~1 utilising the LIRIS multi-object spectrograph on the WHT. We detect continuum, and the H alpha line for our sample, which is one of the better direct tracers of star formation in external galaxies. We spectroscopically measure the H alpha emission from 41 massive (M_{}>10^{10.5} Msol) galaxies taken from the POWIR Survey with spectroscopic redshifts 0.410^{11} Msol which are detected in H alpha emission at z<0.9. We furthermore find that the fraction of galaxies with H alpha emission drops steadily and significantly with redder (U-B) colours at z~1, and that the SSFR drops with increasing (U-B) colour for galaxies at all masses. By investigating the SFR-mass relation we find that the SFR is roughly constant with mass, in possible contrast to previous work, and that the specific star formation rate (SSFR) is lower in the most massive galaxies. The scatter in the SFR vs. mass relationship is very small for th... Twite, Jonathan W; Buitrago, Fernando; Noeske, Kai; Weiner, Benjamin J; Acosta-Pulido, Jose A; Bauer, Amanda E 2011-01-01 61 CERN Multimedia The $R_h^{j_1;j_2}$ matrices of the Jordanian U$_h$(sl(2)) algebra at arbitrary dimensions may be obtained from the corresponding $R_q^{j_1;j_2}$ matrices of the standard $q$-deformed U$_q$(sl(2)) algebra through a contraction technique. By extending this method, the coloured two-parametric ($h, \\alpha$) Jordanian $R_{h,\\alpha}^{j_1,z_1;j_2,z_2}$ matrices of the U$_{h,\\alpha}$(gl(2)) algebra may be derived from the corresponding coloured $R_{q,\\lambda}^{j_1,z_1;j_2,z_2}$ matrices of the standard ($q, contraction process as a tool, the coloured$T_{h,\\alpha}^{j,z}$matrices for arbitrary ($j, z$) representations of the Jordanian Fun$_{h,\\alpha}$(GL(2)) algebra may be extracted from the corresponding$T_{q,\\lambda}^{j,z}$matrices of the standard Fun$_{q,\\lambda}$(GL(2)) algebra. Chakrabarti, R 1999-01-01 62 CERN Multimedia The Tremaine-Weinberg method is a well-known model independent technique for measuring density wave pattern speeds in spiral galaxies. Here we show how it can be applied to the data cubes (maps of surface brightness and velocity) obtained in H-alpha emission using a Fabry-Perot spectrometer. One of the main difficulties, the discontinuity of the H-alpha emission, is resolved using the neighbouring stellar continuum delivered by the data cube. We argue from symmetry that the motions not associated with the density wave should cancel. We show that our pattern speeds are reasonable by computing corotation radii, and comparing them to measured bar lengths. Simulations including star forming gas also add credibility to our results. Nevertheless it will be necessary to compare them with results using the spectra of the stellar components to quantify any systematic deviations from valid pattern speed values. Beckman, John; Piñol, Nuria; Hernandez, Olivier; Carignan, Claude; Pérez, Isabel 2008-01-01 63 CERN Multimedia A new algorithm is developed that automatically detects filaments on the solar disc in H-alpha images. Preprocessing of H-alpha images include corrections for limb darkening and foreshortening. Further, by applying suitable intensity and size thresholds, filaments are extracted, while other solar features e.g. sunspots and plages are removed. Filaments attributes such as their position on the solar disc, total area, length, and number of fragments are determined. In addition, every filament is also labelled with a unique number. The algorithm is capable of following a particular filament through successive images which allows us to detect the changes and disappearance of the same, and thus provides a real-time warning of eruptive filaments. This aspect would prove to be of particular importance in studies pertaining to space weather. The algorithm will eventually be integrated with an upcoming telescope at Udaipur Solar Observatory for real time monitoring of activated/eruptive filaments. Joshi, Anand D; Mathew, Shibu K 2009-01-01 64 CERN Document Server We have attempted to constrain the progenitors of all supernova types, through correlations of the positions of historical supernovae with recent star formation, as traced by H-alpha emission. Through pixel statistics we have found that a large fraction of the SNII population do not show any association with current star formation, which we put down to a 'runaway' fraction of these progenitors. The SNIb/c population accurately traces the H-alpha emission, with some suggestion that the SNIc progenitors show a higher degree of correlation than the SNIb, suggesting higher mass progenitors for the former. Overall the SNIa population only show a weak correlation to the positions of HII regions, but as many as a half may be associated with a young stellar population. Anderson, J P; Salaris, M; Percival, S M 2007-01-01 65 International Nuclear Information System (INIS) This paper discusses that optically fast multichannel Thomson scattering optics that can be used for H-alpha emission profile measurement. A technique based on the fact that a particular volume element of the overall field of view can be seen by many channels, depending on its location, is discussed. It is applied to measurement made on PDX with the vertically viewing TVTS collecting optics (56 channels). The authors found that for this case, about 28 Fourier modes are optimum to represent the spatial behavior of the plasma emissivity. The coefficients for these modes are obtained by doing a least-square-fit to the data subjet to certain constraints. The important constraints are non-negative emissivity, the assumed up and down symmetry and zero emissivity beyond the liners. H-alpha deconvolutions are presented for diverted and circular discharges. 1986-01-01 66 CERN Document Server The gamma-ray binary LS I +61 303 is one of the brightest Fermi sources, with orbitally modulated emission across the electromagnetic spectrum. Here we present H-alpha spectra of LS I +61 303 that exhibit a dramatic emission burst shortly before apastron, observed as a redshifted shoulder in the line profile. A correlated burst in radio, X-ray, and GeV emission is observed at the same orbital phase. We interpret the source of the emission as a compact pulsar wind nebula that forms when a tidal mass stream from the Be circumstellar disk interacts with the relativistic pulsar wind. The H-alpha emission offers an important probe of the high energy emission morphology in this system. McSwain, M Virginia 2011-01-01 67 CERN Multimedia We analyze the temporal variations of the sizes and emission intensities of thirtyone flaring kernels in various parts of the H{\\alpha} line profile. We have found that the areas of all kernels decrease systematically when observed in consecutive wavelengths toward the wings of the H{\\alpha} line, but their areas and emission intensity vary in time. Our results are in agreement with the commonly accepted model of the glass-shaped lower parts of the magnetic flaring loops channelling high energy variable particle beams toward the chromospheric plasma. High time resolution spectral-imaging data used in our work were collected using the Large Coronagraph and Horizontal Telescope equipped with the Multi-channel Subtractive Double Pass Spectrograph and the Solar Eclipse Coronal Imaging System (MSDP-SECIS) at the Bia{\\l}k\\'ow Observatory of the University of Wroc{\\l}aw, Poland. Radziszewski, K 2012-01-01 68 CERN Document Server We searched for narrow H\\alpha in a high-resolution spectrum of SN 1994D taken 10 days before maximum, and found none. We estimate the limit this places on the progenitor mass loss, and find that it is competitive with recent radio limits, and excludes the highest-mass-loss-rate symbiotic systems as possible progenitors of the normal Type Ia SN 1994D. Cumming, R J; Smith, L J; Pettini, M; King, D L 1995-01-01 69 Science.gov (United States) We obtained a set of 11x180s, 11x120s, and 11x60s dithered stacked CCD images of M 31, respectively, using Baader broad (7nm wide) H-alpha, Baader R and Baader clear (Cl) filters on 2011 July 5 with the Open University PIRATE Planewave CDK17 0.43m Dall-Kirkham f/6.7 telescope at the Observatorio Astronomico de Mallorca, Costitx, Spain, using an SBIG STX 16803 CCD Camera. Burwitz, V.; Henze, M.; Pietsch, W.; Holmes, S.; Kolb, U.; Rodriguez, C. A. Haswell J. 2011-07-01 70 CERN Document Server We report the discovery of a two-armed mini-spiral structure within the inner kiloparsec of the E0 LINER/Seyfert 1 galaxy Arp102B. The arms are observed in H-alpha emission and located East and West of the nucleus, extending up to about 1 kpc from it. We use narrow-band imaging from the Hubble Space Telescope Advanced Camera for Surveys, in combination with archival VLA radio images at 3.6 and 6 cm to investigate the origin of the nuclear spiral. From the H-alpha luminosity of the spiral, we obtain an ionized gas mass of the order of one million solar masses. One possibility is that the nuclear spiral represents a gas inflow triggered by a recent accretion event which has replenished the accretion disk, giving rise to the double-peaked emission-line profiles characteristic of Arp102B. However, the radio images show a one-sided curved jet which correlates with the eastern spiral arm observed in the H-alpha image. A published milliarcsecond radio image also shows one-sided structure at position angle about 40 d... Fathi, Kambiz; Storchi-Bergmann, Thaisa; Kharb, Preeti; Robinson, Andrew; Marconi, Alessandro; Maciejewski, Witold; Capetti, Alessandro 2011-01-01 71 CERN Multimedia Be stars, which are characterised by intermittent emission in their hydrogen lines, are known to be fast rotators. This fast rotation is a requirement for the formation of a Keplerian disk, which in turn gives rise to the emission. However, the pulsating, magnetic B1IV star$\\beta$Cephei is a very slow rotator that still shows H$\\alpha$emission episodes like in other Be stars, contradicting current theories. We investigate the hypothesis that the H$\\alpha$emission stems from the spectroscopically unresolved companion of$\\beta$Cep. Spectra of the two unresolved components have been separated in the 6350-6850\\AA range with spectro-astrometric techniques, using 11 longslit spectra obtained with ALFOSC at the Nordic Optical Telescope, La Palma. We find that the H$\\alpha$emission is not related to the primary in$\\beta$Cep, but is due to its 3.4 magnitudes fainter companion. This companion has been resolved by speckle techniques, but it remains unresolved by traditional spectroscopy. The emission extends fr... Schnerr, R S; Oudmaijer, R D; Telting, J H 2006-01-01 72 CERN Multimedia We present integrated H alpha measurements obtained from imaging observations of 98 late-type galaxies, primarily selected in the Coma supercluster. These data, combined with H alpha photometry from the literature, include a magnitude selected sample of spiral (Sa to Irr) galaxies belonging to the "Great Wall" complete up to mp=15.4, thus composed of galaxies brighter than Mp=-18.8 (H0=100 km Mpc^-1 s^-1). The frequency distribution of the H alpha E.W., determined for the first time from an optically complete sample, is approximately gaussian peaking at E.W. ~25 A. We find that, at the present limiting luminosity, the star formation properties of spiral+Irr galaxies members of the Coma and A1367 clusters do not differ significantly from those of the isolated ones belonging to the Great Wall. The present analysis confirms the well known increase of the current massive star formation rate (SFR) with Hubble type. Moreover perhaps a more fundamental anticorrelation exists between the SFR and the mass of disk gala... Gavazzi, G; Carrasco, L; Boselli, A; Contursi, A 1998-01-01 73 CERN Multimedia High signal-to-noise, representative spectra of star-forming galaxies at z~2, obtained via stacking of the galaxies observed in the context of the SINS survey, reveal broad (FWHM > 1500 km/s) H-alpha emission. This feature is preferentially found in the more massive and more rapidly star-forming systems, which also tend to be older and larger galaxies. We interpret this feature as evidence of either powerful starburst-driven galactic winds or active supermassive black holes. If galactic winds are responsible for the broad H-alpha emission, the high velocities of this ionized gas indicate that much of it will be expelled from the host galaxy and its dark matter halo. On the other hand, if the broad line regions of active black holes account for the broad H-alpha feature, the corresponding black holes masses are estimated to be an order of magnitude lower than those predicted by local scaling relations, suggesting a delayed assembly of supermassive black holes with respect to their host bulges. Shapiro, Kristen L; Quataert, Eliot; Schreiber, Natascha M Förster; Davies, Richard; Tacconi, Linda; Armus, Lee; Bouché, Nicolas; Buschkamp, Peter; Cimatti, Andrea; Cresci, Giovanni; Daddi, Emanuele; Eisenhauer, Frank; Erb, Dawn K; Genel, Shy; Hicks, Erin K S; Lilly, Simon J; Lutz, Dieter; Renzini, Alvio; Shapley, Alice; Steidel, Charles C; Sternberg, Amiel 2009-01-01 74 CERN Multimedia We present a supplement to the Macquarie/AAO/Strasbourg H$\\alpha$planetary nebulae (PNe) catalogue (MASH), which we denote MASH-II. The supplement consists of over 300 true, likely and possible new Galactic PNe found after re-examination of the entire AAO/UKST H$\\alpha$survey of the southern Galactic Plane in digital form. We have spectroscopically confirmed over 240 of these new candidates as bona-fide PNe and we include other high quality candidates awaiting spectroscopic confirmation as possible PNe. These latest discoveries largely comprise two distinct groups: small, star-like or moderately resolved PNe at one end and mostly large, extremely low surface brightness PNe at the other. Neither group were easy to discover from simple visual scrutiny of the original survey exposures as for MASH but were relatively straightforward to uncover from the digital images via application of semi-automated discovery techniques. We suspect the few PNe still hidden in the H$\\alpha$survey will lie outside our search cr... Miszalski, B; Acker, A; Birkby, J L; Frew, D J; Kovacevic, A 2007-01-01 75 CERN Document Server We use the catalogue of HII regions obtained from a high quality continuum-subtracted H$\\alpha$image of the grand design spiral galaxy NGC 7479, to construct the luminosity function (LF) for the HII regions (over 1000) of the whole galaxy. Although its slope is within the published range for spirals of the same morphological type, the unusually strong star formation along the intense bar of NGC 7479 prompted us to analyze separately the HII regions in the bar and in the disc. We have calculated the physical properties of a group of HII regions in the bar and in the disc selected for their regular shapes and absence of blending. We have obtained galaxy-wide relations for the HII region set: diameter distribution function and also the global H$\\alpha$surface density distribution. As found previously for late-type spirals, the disc LF shows clear double-linear behaviour with a break at log L$_{H\\alpha}$=38.6 (in erg/s). The bar LF is less regular. This reflects a physical difference between the bar and the dis... Zurita, A; Beckman, J E; Zurita, Almudena; Rozas, Maite; Beckman, John E. 1999-01-01 76 CERN Document Server We searched for a fast moving H$\\alpha$shell around the Crab nebula. Such a shell could account for this supernova remnant's missing mass, and carry enough kinetic energy to make SN 1054 a normal Type II event. Deep H$\\alpha$images were obtained with WFI at the 2.2m MPG/ESO telescope and with MOSCA at the 2.56m NOT. The data are compared with theoretical expectations derived from shell models with ballistic gas motion, constant temperature, constant degree of ionisation and a power law for the density profile. We reach a surface brightness limit of$5\\times10^{-8} ergs s^{-1} cm^{-2} sr^{-1}$. A halo is detected, but at a much higher surface brightness than our models of recombination emission and dust scattering predict. Only collisional excitation of Ly$\\beta$with partial de-excitation to H$\\alpha$could explain such amplitudes. We show that the halo seen is due to PSF scattering and thus not related to a real shell. We also investigated the feasibility of a spectroscopic detection of high-velocity H$\\al... Tziamtzis, A; Lundqvist, P; Sollerman, J 2009-01-01 77 CERN Multimedia We report on H-alpha spectroscopy of the 2009.0 spectroscopic event of eta Carinae collected via SMARTS observations using the CTIO 1.5 m telescope and echelle spectrograph. Our observations were made almost every night over a two month interval around the predicted minimum of eta Car. We observed a significant fading of the line emission that reached a minimum seven days after the X-ray minimum. About 17 d prior to the H-alpha flux minimum, the H-alpha profile exhibited the emergence of a broad, P Cygni type, absorption component (near a Doppler shift of -500 km/s) and a narrow absorption component (near -144 km/s and probably associated with intervening gas from the Little Homunculus Nebula). All these features were observed during the last event in 2003.5 and are probably related to the close periastron passage of the companion. We argue that these variations are consistent with qualitative expectations about changes in the primary star's stellar wind that result from the wind-wind collision with a massive... Richardson, N D; Henry, T J; Fernandez-Lajus, E; Okazaki, A T 2010-01-01 78 CERN Multimedia The origin and configuration of the gas which emits broad lines in Type I active galactic nuclei is not established yet. The lack of small-scale structure in the broad emission-line profiles is consistent with a smooth gas flow, or a clumped flow with many small clouds. An attractive possibility for the origin of many small clouds is the atmospheres of bloated stars, an origin which also provides a natural mechanism for the cloud confinement. Earlier studies of the broad-line profiles have already put strong lower limits on the minimum number of such stars, but these limits are sensitive to the assumed width of the lines produced by each cloud. Here we revisit this problem using high-resolution Keck spectra of the H alpha line in NGC 4395, which has the smallest known broad-line region (~10^14 cm). Only a handful of the required bloated stars (each having r~10^14 cm) could fit into the broad-line region of NGC 4395, yet the observed smoothness of the H alpha line implies a lower limit of ~10^4-10^5 on the num... Laor, A; Ho, L C; Filippenko, A V; Laor, Ari; Barth, Aaron J.; Ho, Luis C.; Filippenko, Alexei V. 2005-01-01 79 Science.gov (United States) High-resolution spectra of six core helium-burning clump' stars and three giants in the open cluster M 67 have been obtained with the SOFIN spectrograph on the Nordic Optical Telescope to investigate abundances of up to 25 chemical elements. Abundances of carbon were studied using the C2 Swan (0,1) band head at 5635.5Å. The wavelength interval 7980-8130Å with strong CN features was analysed in order to determine nitrogen abundances and 12C/13C isotope ratios. The oxygen abundances were determined from the [O I] line at 6300Å. The overall metallicity of the cluster stars was found to be close to solar ([Fe/H]=-0.03+/-0.03). Compared with the Sun and other dwarf stars of the Galactic disk, as well as with dwarf stars of M 67 itself, abundances in the investigated stars suggest that carbon is depleted by about 0.2dex, nitrogen is enhanced by about 0.2dex and oxygen is unaltered. Among other mixing-sensitive chemical elements an overabundance of sodium may be suspected. The mean C/N and 12C/13C ratios are lowered to the values of 1.7+/-0.2 and 24+/-4 in the giants and to the values of 1.4+/-0.2 and 16+/-4 in the clump stars. These results suggest that extra mixing of CN-cycled material to the stellar surface takes place after the He-core flash. Abundances of heavy chemical elements in all nine stars were found to be almost identical and close to solar. (2 data files). Tautvaisiene, G.; Edvardsson, B.; Tuominen, I.; Ilyin, I. 2000-08-01 80 Science.gov (United States) The spectra were acquired in January 2000 at the ESO 1.52-m telescope (La Silla, Chile) with the fiber-fed, cross-dispersed echelle spectrograph FEROS in the object+sky configuration. The atomic data have been calibrated using a high S/N moonlight spectrum extracted from the archive of the first FEROS commissioning period (fall 1998). (1 data file). Morel, T.; Micela, G.; Favata, F.; Katz, D.; Pillitteri, I. 2003-11-01 81 Directory of Open Access Journals (Sweden) Full Text Available We present observations of the nearby tidal dwarf galaxy Holmberg IX in M81 galaxy group in narrow band [SII] and H$alpha$ filters, carried out in March and November 2008 with the 2m RCC telescope at NAO Rozhen, Bulgaria. Our search for resident supernova remnants (identified as sources with enhanced [SII] emission relative to their H$alpha$ emission) in this galaxy yielded no sources of this kind, besides M&H 10-11 or HoIX X-1. Nevertheless, we found a number of objects with significant H$alpha$ emission that probably represent uncatalogued HII regions. Arbutina, B.; Ili?, D.; Stavrev, K.; Uroševi?, D.; Vukoti?, B.; Oni?, D. 2009-01-01 82 Energy Technology Data Exchange (ETDEWEB) The partial Auger width corresponding to the transitions from the considered level to all levels of particular configuration is presented in the form of the diagonal matrix element of an effective operator. The general expressions for such an operator in the case of two main types of Auger transitions are obtained. They are used to derive the explicit formulae in some special cases as well as to investigate the term-dependence of the Auger width. The types of configurations which levels have equal Auger width or, on the contrary, strongly depend on many-electron quantum numbers, are indicated. Merkelis, G. E-mail: [email protected]; Karazija, R 2003-11-01 83 CERN Document Server We present high-resolution ($0\\farcs2$) near-infrared images of the area surrounding the Herbig Be star LkH$\\alpha$ 234 taken with the Coronagraphic Imager with Adaptive Optics (CIAO) and the adaptive optics on the Subaru Telescope. The near-infrared ($J$, $H$, $K$, $L'$ and $M'$ bands) images reveal circumstellar structures around LkH$\\alpha$ 234 in detail. Eight young stellar object (YSO) candidates (Object B, C, D, E, F, G, NW1, and NW2) were detected at 2$\\arcsec$--11$\\arcsec$ from LkH$\\alpha$ 234. Objects B and C are likely variable stars, which is consistent with a young evolutionary status. Three objects (LkH$\\alpha$ 234, NW1, and NW2) were identified in the 11.8 $\\micron$ (SiC) and 17.65 $\\micron$ images obtained with the Long Wavelength Spectrometer (LWS) on the Keck Telescope. NW1 and NW2 are thought to be embedded young stars. We suggest that NW1 and not LkH$\\alpha$ 234 is the source illuminating the reflection nebula west of LkH$\\alpha$ 234, although Object G may be another candidate. In our image... Kato, Eri; Perrin, Marshall D; Shibai, Hiroshi; Itoh, Yusuke; Ootsubo, Takafumi 2011-01-01 84 CERN Document Server We prove that every graph of rank-width $k$ is a pivot-minor of a graph of tree-width at most $2k$. We also prove that graphs of rank-width at most 1, equivalently distance-hereditary graphs, are exactly vertex-minors of trees, and graphs of linear rank-width at most 1 are precisely vertex-minors of paths. In addition, we show that bipartite graphs of rank-width at most 1 are exactly pivot-minors of trees and bipartite graphs of linear rank-width at most 1 are precisely pivot-minors of paths. Kwon, O-joung 2012-01-01 85 CERN Multimedia We present a study of the kinematics of the isolated spiral galaxy NGC 864, using H{\\alpha} Fabry-Perot data obtained with the GH{\\alpha}FaS instrument at the William Herschel Telescope in La Palma, complemented with images at 3.6 {\\mu}m, in the R band and in H{\\alpha} filter, and integral field spectroscopic data. The resulting data cubes and velocity maps allow the study of the kinematics of the galaxy, including in-depth investigations of the rotation curve, velocity moment maps, velocity residual maps, gradient maps and position-velocity diagrams. We find asymmetries in the velocity field in the bar zone, caused by non-circular motions, probably in response to the potential of the bar. We also find a flat-profile bar, in agreement with the strong bar, with the grand design spiral pattern, and with the gap between the ends of the bar and the start of the spiral arms. We quantify the rate of massive star formation, which is concentrated in the two spiral arms. Erroz-Ferrer, Santiago; Font, Joan; Beckman, John E; Falcón-Barroso, Jesús; Sánchez-Gallego, José Ramón; Athanassoula, E; Bosma, Albert; Gadotti, Dimitri A; Muñoz-Mateos, Juan Carlos; Sheth, Kartik; Buta, Ronald J; Comerón, Sébastien; de Paz, Armando Gil; Hinz, Joannah L; Ho, Luis C; Kim, Taehyun; Laine, Jarkko; Laurikainen, Eija; Madore, Barry F; Menéndez-Delmestre, Karín; Mizusawa, Trisha; Regan, Michael W; Salo, Heikki; Seibert, Mark 2012-01-01 86 CERN Multimedia We present an analysis of the star formation properties of field galaxies within the local volume out to a recession velocity limit of 3000 km/s. A parent sample of 863 star-forming galaxies is used to calculate a B-band luminosity function. This is then populated with star formation information from a subsample of 327 galaxies, for which we have H alpha imaging, firstly by calibrating a relationship between galaxy B-band luminosity and star formation rate, and secondly by a Monte Carlo simulation of a representative sample of galaxies, in which star formation information is randomly sampled from the observed subset. The total star formation rate density of the local Universe is found to be between 0.016 and 0.023 MSun/yr/cubic Mpc, with the uncertainties being dominated by the internal extinction correction used in converting measured H alpha fluxes to star formation rates. If our internally derived B-band luminosity function is replaced by one from the Sloan Digital Sky Survey blue sequence, the star format... James, P A; Shane, N S; Baldry, I K; De Jong, R S 2008-01-01 87 CERN Multimedia This study presents a deep H{\\alpha} kinematical analysis of the Sculptor Group galaxy NGC253. The Fabry-Perot data were taken with the 36-cm Marseille Telescope in La Silla, Chile, using an EMCCD detector. Typical emission measures of ~0.1 cm^-6 pc are reached. The observations allow the detection of the Diffuse Ionized Gas component through [N II] emission at very large radii of 11.5', 12.8' and 19.0', on the receding side of the galaxy. No H{\\alpha} emission is observed at radii larger than the neutral component (11.5'). The very extended rotation curve confirms previous results and shows signs of a significant decline, on the order of 30 per cent vmax . Using the rotation data, mass models are constructed with and without the outer [N II] data points, and similar results are found. The declining part of the rotation curve is very well modeled, and seems to be truly declining. Hlavacek-Larrondo, J; Daigle, O; de Denus-Baillargeon, M -M; Marcelin, M; Epinat, B; Hernandez, O 2010-01-01 88 CERN Document Server We present two-dimensional H_alpha velocity fields for 20 late-type, disk-dominated spiral galaxies, the largest sample to date with high-resolution H_alpha velocity fields for bulgeless disks. From these data we derive rotation curves and the location of the kinematic centers. The galaxy sample was selected to contain nucleated and non-nucleated galaxies, which allows us to investigate what impact the gas kinematics in the host disk have on the presence (or absence) of a nuclear star cluster. In general, we find that the velocity fields span a broad range of morphologies. While some galaxies show regular rotation, most have some degree of irregular gas motions. There appears to be no systematic difference in the kinematics of nucleated and non-nucleated disks. Due to the large fields of view of the integral field units we use, we are able to observe the flattening of the rotation curve in almost all of our sample galaxies. This makes modeling of the velocity fields relatively straight-forward. Due to the com... Neumayer, Nadine; Andersen, David; Sanchez, Sebastian F; Boeker, Torsten; Rix, Hans-Walter 2011-01-01 89 CERN Multimedia We present the results of a narrow-band (H2S1, 2.121/0.021um) imaging search with WFCAM/UKIRT for H-alpha emitters around several potential signposts of rare (10^-7-10^-8 Mpc^-3) over-dense regions at z=2.23: an over-density of QSOs (2QZ cluster), a powerful, high-redshift radio galaxy (HzRG), and a concentration of submillimetre galaxies (SMGs) and optically faint radio galaxies (OFRGs). In total, we detect 137 narrow-band emitter candidates down to emission-line fluxes of 0.5-1 x 10^-16 erg s^-1 cm^-2, across a total area of 0.56 sq. degrees (2.1 x 10^5 comoving Mpc at z=2.23) in these fields. The BzK colours of the emitters suggest that at least 80% of our sample are likely to be H-alpha emitters (HAEs) at z=2.23. This is one of the largest HAE samples known at z>2. We find modest (~3-sigma) local over-densities of emitters associated with all the three targets. In the 2QZ cluster field, the emitters show a striking filamentary structure connecting four of the z=2.23 QSOs extending over 30Mpc (comoving). I... Matsuda, Y; Geach, J E; Best, P N; Sobral, D; Tanaka, I; Ohta, K; Kurk, J; Iwata, I; Bielby, Rich; Wardlow, J L; Bower, R G; Fanidakis, N; Ivison, R J; Kodama, T; Yamada, T; Mawatari, K; Casali, M 2011-01-01 90 CERN Document Server We present the first successful demonstration of multi-object near-infrared spectroscopy on high redshift galaxies. Our objective is to address the true star formation history of the universe at z~1, a crucial epoch which some have suggested is the peak of star formation activity. By using H-alpha -the same robust star formation indicator used at low-z - redshifted into the J- and H-bands, we can trace star formation without the systematic uncertainties of different calibrators, or the extreme dust extinction in the rest-UV, which have plagued previous efforts. We are using the instrument CIRPASS (the Cambridge Infra-Red PAnoramic Survey Spectrograph), in multi-object mode, which has been successfully demonstrated on the Anglo-Australian Telescope (AAT) and the William Herschel Telescope (WHT). CIRPASS has 150 fibres deployable over \\~40arcmin on the AAT and ~15arcmin on the WHT. Here we present preliminary results from one of our fields observed with the WHT: H-alpha detections of z~1 galaxies in the Hubble ... Doherty, M; Sharp, R; Dalton, G B; Parry, I; Lewis, I; McDonald, E; Wolf, C 2004-01-01 91 International Nuclear Information System (INIS) The temporal evolution of the ratio between H-alpha to nonthermal hard X-ray emission was investigated using coordinated H-alpha and hard- and soft-X-ray observations of five solar flares (on May 7, June 23, June 24, and June 25, 1980 and on April 30, 1985). These observations were used to estimate the emitted flare energy flux F(H-alpha) in H-alpha, the flux of F(2O) energy deposited by nonthermal electrons with energies above 20 keV, and the pressure p(c) of soft X-ray-emitting plasma as functions of time during the impulsive phase of each flare. It was found that the F(H-alpha)/F(2O) ratio shows a power-law dependence on F(2O), with a slope that differs slightly from that predicted by the static thick-target model of solar transport. Results also indicate that the power-law dependence is modified by hydrostatic pressure effects. 25 refs. 1991-01-01 92 CERN Document Server We present a panoramic narrow-band study of H-alpha emitters in the field of the z=2.16 proto-cluster around PKS1138-262 using MOIRCS on the Subaru Telescope. We find 83 H-alpha emitters down to a SFR(Ha)~10Msun/yr across a ~7'x7' region centered on the radio galaxy, and identify ~10-Mpc scale filaments of emitters running across this region. By examining the properties of H-alpha emitters within the large-scale structure, we find that galaxies in the higher-density environments at z=2.16 tend to have redder colours and higher stellar masses compared to galaxies in more underdense regions. We also find a population of H-alpha emitters with red colours ((J-Ks)>1), which are much more frequent in the denser environments and which have apparently very high stellar masses with M>~10^11Msun, implying that these cluster galaxies have already formed a large part of their stellar mass before z~2. Spitzer Space Telescope 24-micron data suggests that many of these red H-alpha emitters are bright, dusty starbursts (rat... Koyama, Yusei; Tadaki, Ken-ichi; Hayashi, Masao; Tanaka, Masayuki; Smail, Ian; Tanaka, Ichi; Kurk, Jaron 2012-01-01 93 Science.gov (United States) Using the instrumental of the Observatorio Astronómico Municipal de Rosario (OAMR), we analyze the solar chromospheric activity during an approximate period of 11 years. The instrument is a Carl Zeiss refractor telescope of 150 mm aperture and 2250 mm of focal distance with monochromatic filter in the H-alpha line. We take as proxy for the solar activity the area covered by chromospheric plages. Simultaneously, we determine the relative wolf number from observations of the solar photosphere. We describe our technique and the results obtained. We observe 2 maxima of solar activity in the years 2000 and 2001 respectively, and a later decrease of this activity with low average values starting around 2006 that corresponds to the end of cycle 23. FULL TEXT IN SPANISH Davoli, D.; Aquilano, R.; Missio, H. 94 CERN Multimedia We present the first results of an ongoing spectroscopic follow-up program of blue H-alpha excess sources within the Kepler field-of-view, in order to identify new cataclysmic variables. Kepler observations of the identified targets in this work will then provide detailed, time-resolved, studies of accretion. Candidates selected from the Kepler-INT Survey were observed with the 4.2 meter William Herschel Telescope. Out of 38 observed candidates, we found 11 new cataclysmic variables reported here for the first time, as well as 13 new quasars. Our target selection has a success rate of 29% when searching for cataclysmic variables, and we show how this can be improved by including photometry obtained with the Wide-field Infrared Survey Explorer. Scaringi, S; Verbeek, K; Greiss, S; Knigge, C; Koerding, E 2012-01-01 95 Science.gov (United States) We report the detection of seven recent nova candidates in M 31 on two sets of three 300 s dithered stacked CCD images obtained on 2010 Oct 4 with the 1.3m Ritchey Chretien f/7.5 telescope at Skinakas Observatory, Crete, Greece, using an Andor DZ436-BV CCD Camera (with a Marconi 2k x 2k chip with 13.5 microns sq. pixels) and a broad (75 Angstrom wide) H-alpha filter. Only novae M31N 2010-07a and M31N 2010-10a were also detected on four 100 s dithered stacked CCD images obtained on 2010 Oct 5 with the same telescope and camera using a R filter. Pietsch, W.; Lloyd, J.; Henze, M.; Burwitz, V.; Liakos, A.; Hatzidimitriou, D. 2010-10-01 96 CERN Document Server We have conducted an H-alpha survey of 38 0.77 Doherty, M; Dalton, G; Lewis, I; Parry, I; Sharp, R; Bunker, Andrew; Dalton, Gavin; Doherty, Michelle; Lewis, Ian; Parry, Ian; Sharp, Robert 2006-01-01 97 CERN Multimedia We study chromospheric oscillations including umbral flashes and running penumbral waves in a sunspot of active region (AR) using scanning spectroscopy in H-alpha and Ca II 8542A, with the Fast Imaging Solar Spectrograph (FISS) at the 1.6 meter New Solar Telescope at Big Bear Solar Observatory. A bisector method is applied to spectral observations to construct chromospheric Doppler velocity maps. Temporal sequence analysis of these shows enhanced high-frequency oscillations inside the sunspot umbra in both lines. Their peak frequency gradually decreases outward from the umbra. The oscillation power is found to be associated with magnetic-field strength and inclination, with different relationships in different frequency bands. Maurya, Ram Ajor; Park, Hyungmin; Yang, Heesu; Song, Donguk; Cho, Kyuhyoun 2013-01-01 98 Energy Technology Data Exchange (ETDEWEB) Observations of very metal poor stars have yielded evidence for the less abundant lithium isotope {sup 6}Li in several cases. These findings prompt the question whether there is a non-negligible primordial contribution to the observed {sup 6}Li abundances. Network calculations show that the {sup 2}H({alpha},{gamma}){sup 6}Li reaction dominates {sup 6}Li production in the Big Bang. A recent Coulomb dissociation work on this reaction produced only an upper limit for the astrophysical S-factor. At the 400 kV underground accelerator LUNA in Gran Sasso/Italy, an experiment is underway to gain direct cross section data, but the background is formidable. Preliminary data of the first phase of the LUNA experiment will be shown, and an outlook will be given. Anders, Michael; Bemmerer, Daniel [Forschungszentrum Dresden-Rossendorf (FZD), Dresden (Germany); Collaboration: LUNA-Collaboration 2011-07-01 99 CERN Multimedia (abridged) Using a complete sample of ~300 star-forming galaxies within 11 Mpc, we evaluate the consistency between star formation rates (SFRs) inferred from the far ultraviolet (FUV) non-ionizing continuum and H-alpha nebular emission, assuming standard conversion recipes in which the SFR scales linearly with luminosity at a given wavelength. Our analysis probes SFRs over 5 orders of magnitude, down to ultra-low activities on the order of ~0.0001 M_sun/yr. The data are drawn from the 11 Mpc H-alpha and Ultraviolet Galaxy Survey (11HUGS), which has obtained H-alpha fluxes from ground-based narrowband imaging, and UV fluxes from imaging with GALEX. For normal spiral galaxies (SFR~1 M_sun/yr), our results are consistent with previous work which has shown that FUV SFRs tend to be lower than H-alpha SFRs before accounting for internal dust attenuation, but that there is relative consistency between the two tracers after proper corrections are applied. However, a puzzle is encountered at the faint end of the lumin... Lee, Janice C; Tremonti, Christy; Kennicutt, Robert C; Salim, Samir; Bothwell, Matthew; Calzetti, Daniela; Dalcanton, Julianne; Dale, Daniel; Engelbracht, Chad; J., Jose G Funes S; Johnson, Benjamin; Sakai, Shoko; Skillman, Evan; van Zee, Liese; Walter, Fabian; Weisz, Daniel 2009-01-01 100 Energy Technology Data Exchange (ETDEWEB) We report on the first simultaneous observation of an H{alpha} Moreton wave, the corresponding EUV fast coronal waves, and a slow and bright EUV wave (typical EIT wave). We observed a Moreton wave, associated with an X6.9 flare that occurred on 2011 August 9 at the active region NOAA 11263, in the H{alpha} images taken by the Solar Magnetic Activity Research Telescope at Hida Observatory of Kyoto University. In the EUV images obtained by the Atmospheric Imaging Assembly on board the Solar Dynamic Observatory we found not only the corresponding EUV fast 'bright' coronal wave, but also the EUV fast 'faint' wave that is not associated with the H{alpha} Moreton wave. We also found a slow EUV wave, which corresponds to a typical EIT wave. Furthermore, we observed, for the first time, the oscillations of a prominence and a filament, simultaneously, both in the H{alpha} and EUV images. To trigger the oscillations by the flare-associated coronal disturbance, we expect a coronal wave as fast as the fast-mode MHD wave with the velocity of about 570-800 km s{sup -1}. These velocities are consistent with those of the observed Moreton wave and the EUV fast coronal wave. Asai, Ayumi; Isobe, Hiroaki [Unit of Synergetic Studies for Space, Kyoto University, Yamashina, Kyoto 607-8471 (Japan); Ishii, Takako T.; Kitai, Reizaburo; Ichimoto, Kiyoshi; UeNo, Satoru; Nagata, Shin' ichi; Morita, Satoshi; Nishida, Keisuke; Shibata, Kazunari [Kwasan and Hida Observatories, Kyoto University, Yamashina, Kyoto 607-8471 (Japan); Shiota, Daikou [Advanced Science Institute, RIKEN, Wako, Saitama 351-0198 (Japan); Oi, Akihito [College of Science, Ibaraki University, Mito, Ibaraki 310-8512 (Japan); Akioka, Maki, E-mail: [email protected] [Hiraiso Solar Observatory, National Institute of Information and Communications Technology, Hitachinaka, Ibaraki 311-1202 (Japan) 2012-02-15 101 CERN Multimedia We present tentative H-alpha emission line detections of four submillimetre-detected galaxies at z>3.5: the radio galaxies 8C1909+722 and 4C60.07 at signal-to-noise ratios (SNRs) of 3.1 and 2.5, and two submillimetre-selected galaxies (SMGs) near the first of these at SNRs of 10.0 and 2.4, made with the AKARI Space Telescope as part of the FUHYU mission program. These are the highest-redshift H-alpha detections in such galaxies, made possible by AKARI's unique near-infrared spectroscopic capability. The two radio galaxies had known redshifts and surrounding structure, and we have detected broad H-alpha components indicating the presence of dust-shrouded quasars. We conclude that powerful AGNs at z>3.5 occur in peaks of the star-formation density fields, supporting a close connection between stellar mass build-up and black hole mass assembly at this redshift. We also show that 4C60.07 is a binary AGN. The H-alpha detections of the two SMGs are the first redshift determinations for these sources, confirming the... Sedgwick, Chris; Pearson, Chris; Smail, Ian; Im, Myungshin; Oyabu, Shinki; Takagi, Toshinobu; Matsuhara, Hideo; Wada, Takehiko; Lee, Hyung Mok; Jeong, Woong-Seob; White, Glenn J 2013-01-01 102 CERN Document Server GH$\\alpha$FaS a new Fabry-Perot system, is now available at the William Herschel Telescope. It was mounted, for the first time, at the Nasmyth focus of the 4.2 meter WHT on La Palma in July 2007. Using modern technology, with a spectral resolution of the order R$\\sim$15000, and with a seeing limited spatial resolution, GH$\\alpha$FaS will provide a new look at the H$\\alpha$ -emitting gas over a 4.8 arcminutes circular field in the nearby universe. Many science programs can be done on a 4.2 metre class telescope in world class seeing conditions with a scanning Fabry-Perot. Not only galaxies but HII regions, planetary nebulae, supernova remnants and the diffuse interstellar medium are subjects for which unique data can be aquired rapidly. Astronomers from the Laboratoire d'Astrophysique Exp\\'erimentale (LAE) in Montr\\'eal, the Laboratoire d'Astrophysique de Marseille (LAM-OAMP), and the Instituto de Astrof\\'isica de Canarias (IAC), have inaugurated GH$\\alpha$FaS by studying in detail the dynamics of some nearby ... Hernández, O; Carignan, C; Beckman, J; Gach, J L; Balard, P; Amram, P; Boulesteix, J; Corradi, R L M; de Denus-Baillargeon, M-M; Epinat, B; Relaño, M; Thibault, S; Vallée, P 2008-01-01 103 CERN Document Server We have applied the Tremaine-Weinberg method to 10 late-type barred spiral galaxies using data cubes, in H-alpha emission, from the GHAFAS and FANTOMM Fabry-Perot spectrometers. We have combined the derived bar (and/or spiral) pattern speeds with angular frequency plots to measure the corotation radii for the bars in these galaxies. We base our results on a combination of this method with a morphological analysis designed to estimate the corotation radius to bar-length ratio using two independent techniques on archival near infrared images, and although we are aware of the limitation of the application of the Tremaine-Weinberg method using ionised gas observations, we find consistently excellent agreement between bar and spiral arm parameters derived using different methods. In general, the corotation radius, measured using the Tremaine-Weinberg method, is closely related to the bar length, measured independently from photometry and consistent with previous studies. Our corotation/bar-length ratios and patter... Fathi, Kambiz; Piñol-Ferrer, Nuria; Hernandez, Olivier; Martinez-Valpuesta, Inma; Carignan, Claude 2009-01-01 104 CERN Multimedia The Fabry-Perot interferometer FaNTOmM was used at the 3.6m Canada France Hawaii Telescope and the 1.6m Mont Megantic Telescope to obtain data cubes in H-alpha of 9 nearby spiral galaxies from which maps in integrated intensity, velocity, and velocity dispersion were derived. We then applied the Tremaine-Weinberg method, in which the pattern speed can be deduced from its velocity field, by finding the integrated value of the mean velocity along a slit parallel to the major axis weighted by the intensity and divided by the weighted mean distance of the velocity points from the tangent point measured along the slit. The measured variables can be used either to make separate calculations of the pattern speed and derive a mean, or in a plot of one against the other for all the points on all slits, from which a best fit value can be derived. Linear fits were found for all the galaxies in the sample. For two galaxies a clearly separate inner pattern speed with a higher value, was also identified and measured. Beckman, John E; Piñol, Núria; Toonen, Silvia; Hernandez, Olivier; Carignan, Claude 2007-01-01 105 CERN Document Server This is the second part of an H-alpha kinematics follow-up survey of the Spitzer Infrared Nearby Galaxies Survey (SINGS) sample. The aim of this program is to shed new light on the role of baryons and their kinematics and on the dark/luminous matter relation in the star forming regions of galaxies, in relation with studies at other wavelengths. The data for 37 galaxies are presented. The observations were made using Fabry-Perot interferometry with the photon-counting camera FaNTOmM on 4 different telescopes, namely the Canada-France-Hawaii 3.6m, the ESO La Silla 3.6m, the William Herschel 4.2m, and the Observatoire du mont Megantic 1.6m telescopes. The velocity fields are computed using custom IDL routines designed for an optimal use of the data. The kinematical parameters and rotation curves are derived using the GIPSY software. It is shown that non-circular motions associated with galactic bars affect the kinematical parameters fitting and the velocity gradient of the rotation curves. This leads to incorrec... Dicaire, I; Amram, P; Hernández, O; Chemin, L; Daigle, O; de Denus-Baillargeon, M -M; Balkowski, C; Boselli, A; Fathi, K; Kennicutt, R C 2008-01-01 106 CERN Multimedia We present a proper motion study of the eastern shock-region of the supernova remnant RCW 86 (MSH 14-63, G315.4-2.3), based on optical observations carried out with VLT/FORS2 in 2007 and 2010. For both the northeastern and southeastern regions, we measure an average proper motion of H-alpha filaments of 0.10 +/- 0.02 arcsec/yr, corresponding to 1200 +/- 200 km/s at 2.5kpc. There is substantial variation in the derived proper motions, indicating shock velocities ranging from just below 700 km/s to above 2200 km/s. The optical proper motion is lower than the previously measured X-ray proper motion of northeastern region. The new measurements are consistent with the previously measured proton temperature of 2.3 +/- 0.3 keV, assuming no cosmic-ray acceleration. However, within the uncertainties, moderately efficient (< 27 per cent) shock acceleration is still possible. The combination of optical proper motion and proton temperature rule out the possibility that RCW 86 has a distance less than 1.5kpc. The simil... Helder, E A; Bamba, A; Bleeker, J A M; Burrows, D N; Ghavamian, P; Yamazaki, R 2013-01-01 107 CERN Document Server The KPNO International Spectroscopic Survey (KISS) is an objective-prism survey designed to detect extragalactic emission-line objects. It combines many of the features of previous slitless spectroscopic surveys with the advantages of modern CCD detectors, and is the first purely digital objective-prism survey for emission-line galaxies (ELGs). Here we present the third list of ELG candidates selected from our red spectral data, which cover the wavelength range 6400 to 7200 A. In most cases, the detected emission line is H-alpha. The current survey list covers the region of the NOAO Deep Wide-Field Survey (NDWFS). This survey covers two fields; the first is 3 x 3 degrees square and located at RA = 14h 30m, DEC = 34.5 deg (B1950), the second is 2.3 x 4.0 degrees and centered at RA = 2h 7.5m, DEC = -4.75 deg. A total area of 19.65 deg^2 is covered by the KISS data. A total of 261 candidate emission-line objects have been selected for inclusion in the survey list (13.3 per deg^2). We tabulate accurate coordinate... Jangren, A; Sarajedini, V L; Gronwall, C; Werk, J K; Chomiuk, L; Moody, J W; Boroson, T A; Jangren, Anna; Salzer, John J.; Sarajedini, Vicki L.; Gronwall, Caryl; Werk, Jessica K.; Chomiuk, Laura; Boroson, Todd A. 2005-01-01 108 Science.gov (United States) Analysis of EUV, UV, and H-alpha Emission from Two Very Different Prominences T. Kucera (NASA/GSFC), E. Landi (Artep Inc.) We analyze the properties of a pair of prominences observed the UV and EUV in April 2004. One was a generally quiet prominence which exhibited a period of activation. Another was a large "coronal cloud" type prominence. Both were observed in by SOHO/SUMER, TRACE, and in H? by BBSO and MLSO. The quiet promince was also observed by the SOHO/CDS instrument. TRACE and H? data provide 2D images on with time cadences on the order of 1 minute. The SUMER data was taken from a single slit location with a 90 second cadence and included a number of lines spanning the temperature range 80,000 to 1.6 million K. This observing program was designed to allow us to study prominence dynamics. CDS raster data was taken with a slower cadence, in lines formed at temperatures from 20,000 - 1 million K. We combine these different data sets to analyze the thermal properties, including differential emission measures (DEMs), of these very different prominences, and compare the results to those of prominences previously analyzed by ourselves and others. This work was partly funded through a NASA Heliophysics GI RTOP and NASA award NNH04AA12 Kucera, T. A.; Landi, E. 2008-05-01 109 CERN Document Server A distance-limited sample of 869 objects from the Updated Nearby Galaxy Catalog is used to characterize the star formation status of the Local Volume population. We present a compiled list of 1217 star formation rate (SFR) estimates for 802 galaxies within 11 Mpc from us, derived from the H-alpha imaging surveys and GALEX far-ultraviolet survey. We briefly discuss some basic scaling relations between SFR and luminosity, morphology, HI-mass, surface brightness, as well as environment of the galaxies. About 3/4 of our sample consist of dwarf galaxies, for which we offer a more refined classification. We note that the specific star formation rate of nearly all luminous and dwarf galaxies does not exceed the maximum value: $\\log(SFR/L_K) = -9.4$ [yr$^{-1}$]. The bulk of spiral and blue dwarf galaxies have enough time to generate their stellar mass during the cosmological time, $T_0$, with the observed SFRs. They dispose of a sufficient amount of gas to support their present SFRs over the next $T_0$ term. We note ... Karachentsev, Igor D 2013-01-01 110 Science.gov (United States) Free-space Quantum key distribution (QKD) has shown the potential for the practical production of cryptographic key for ultra-secure communications. The performance of any QKD system is ultimately limited by the signal to noise ratio on the single-photon channel, and over most useful communications links the resulting key rates are impractical for performing continuous one-time-pad encryption of today's broadband communications. We have adapted clock and data recovery techniques from modern telecommunications practice, combined with a synchronous classical free-space optical communications link operating in parallel, to increase the repetition rate of a free-space QKD system by roughly 2 orders of magnitude over previous demonstrations. We have also designed the system to operate in the H-alpha Fraunhofer window at 656.28 nm, where the solar background is reduced by roughly 7 dB. This system takes advantage of high efficiency silicon single-photon avalanche photodiodes with <50ps timing resolution that are expected to enable operation at a repetition rate of 2.5 GHz. We have identified scalable solutions for delivering sustained one-time-pad encryption at 10 Mbps, thus making it possible to integrate quantum cryptography into first-generation Ethernet protocols. Rogers, D. J.; Bienfang, J. C.; Mink, A.; Hershman, B. J.; Nakassis, A.; Tang, X.; Ma, L.; Su, D. H.; Williams, Carl J.; Clark, Charles W. 2006-09-01 111 CERN Document Server We introduce a new width parameter for matroids called decomposition width and prove that every matroid property expressible in the monadic second order logic can be computed in linear time for matroids with bounded decomposition width if their decomposition is given. Since decompositions of small width for our new notion can be computed in polynomial time for matroids of bounded branch-width represented over finite fields, our results include recent algorithmic results of Hlineny [J. Combin. Theory Ser. B 96 (2006), 325-351] in this area and extend his results to matroids not necessarily representable over finite fields. Kral, Daniel 2009-01-01 112 CERN Document Server Context. SuperclusterA in the extragalactic HII region NGC2363 is remarkable for the hypersonic gas seen as faint extended broad emission lines with a full width zero intensity of 7000km/s. Aims. We explore the possibility that the observed broad profiles are the result of the interaction of a high velocity cluster wind with dense photoionized clumps. Methods. The geometry considered is that of near static photoionized condensations at the surface of which turbulent mixing layers arise as a result of the interaction with the hot wind. The approximative treatment of turbulence is carried out using the mixing length approach of Canto & Raga. The code mappings Ic is used to derive the mean quantities describing the flow and to compute the line emissivities within the turbulent layers. The velocity projection in three dimensions of the line sources is carried out analytically. Results. A fast entraining wind of up to ~4300km/s appears to be required to reproduce the faint wings of the broad H-alpha and [O III... Binette, Luc; Ubeda, Leonardo; Raga, Alejandro C; Robert, Carmelle; Krongold, Yair 2009-01-01 113 CERN Document Server For solar activity cycles 20 and 21 (1966-1985) the solar differential rotation has been investigated using H{\\alpha} filaments and relatively small-scale long-lived magnetic features with negative and positive polarities. We used annual averaged angular velocities of quiescent H{\\alpha} filaments from H{\\alpha} photoheliograms of the Abastumani Astrophysical Observatory film collection and selected long-lived magnetic features from the McIntosh atlas (McIntosh, Willock, and Thompson, Atlas of Stackplots, NGDC, 1991). We have determined coefficients of Faye's formulas for H{\\alpha} filaments as well as for long-lived magnetic features and have found that for solar cycles 20 and 21 the H{\\alpha} filaments have lower rotation rates and rotated more differentially than the long-lived magnetic features. Gigolashvili, M Sh; Kukhianidze, V J 2012-01-01 114 Energy Technology Data Exchange (ETDEWEB) High specific activity N-Acetyl-3{sup H}- {alpha} -Aspartyl-I-Glutamic acid at micro mole scale in prepared acetylating L- {alpha} -Aspartyl-L-glutamic with 3{sup H}-acetic anhydride in re distilled toluene. The product le purified through cationic and anionic columns. The radiochemical purity as determined by thin-layer chromatography is greater then 99% at the time preparation. (Author) 5 refs. Suarez, C. 1984-07-01 115 CERN Document Server This paper presents optical and H-alpha imaging for a large sample of LSB galaxies selected from the PSS-II catalogs (Schombert et. al 1992). As noted in previous work, LSB galaxies span a range of luminosities (-10 > M_V > -20) and sizes (0.3 kpc < R_V25 < 10 kpc), although they are consistent in their irregular morphology. Their H-alpha luminosities (L(H-alpha) range from 10^36 to 10^41 ergs s^-1 (corresponding to a range in star formation, using canonical prescriptions, from 10^-5 to 1 M_solar yr^-1). Although their optical colors are at the extreme blue edge for galaxies, they are similar to the colors of dwarf galaxies (van Zee 2001) and gas-rich irregulars (Hunter & Elmegreen 2006). However, their star formation rates per unit stellar mass are a factor of ten less than other galaxies of the same baryonic mass, indicating that they are not simply quiescent versions of more active star forming galaxies. This paper presents the data, reduction techniques and new philosophy of data storage and pre... Schombert, James; McGaugh, Stacy 2011-01-01 116 Energy Technology Data Exchange (ETDEWEB) We utilize the new Magellan adaptive optics system (MagAO) to image the binary proplyd LV 1 in the Orion Trapezium at H{alpha}. This is among the first AO results in visible wavelengths. The H{alpha} image clearly shows the ionization fronts, the interproplyd shell, and the cometary tails. Our astrometric measurements find no significant relative motion between components over {approx}18 yr, implying that LV 1 is a low-mass system. We also analyze Large Binocular Telescope AO observations, and find a point source which may be the embedded protostar's photosphere in the continuum. Converting the H magnitudes to mass, we show that the LV 1 binary may consist of one very-low-mass star with a likely brown dwarf secondary, or even plausibly a double brown dwarf. Finally, the magnetopause of the minor proplyd is estimated to have a radius of 110 AU, consistent with the location of the bow shock seen in H{alpha}. Wu, Y.-L.; Close, L. M.; Males, J. R.; Follette, K.; Morzinski, K.; Kopon, D.; Rodigas, T. J.; Hinz, P. [Steward Observatory, University of Arizona, Tucson, AZ 85721 (United States); Puglisi, A.; Esposito, S.; Pinna, E.; Riccardi, A.; Xompero, M.; Briguglio, R., E-mail: [email protected] [INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze (Italy) 2013-09-01 117 CERN Document Server (Abridged) We study the host galaxy regions in close proximity to Type Ia supernovae (SNe Ia) to analyze relations between the properties of SN Ia events and environments most similar to where their progenitors formed. We focus on local H\\alpha\\ emission as an indicator of young environments. The Nearby Supernova Factory has obtained flux-calibrated spectral timeseries for SNe Ia using integral field spectroscopy, allowing the simultaneous measurement of the SN and its immediate vicinity. For 89 SNe Ia we measure H\\alpha\\ emission tracing ongoing star formation within a 1 kpc radius around each SN. This constitutes the first direct study of the local environment for a large sample of SNe Ia also having accurate luminosity, color and stretch measurements. We find that SNe Ia with local H\\alpha\\ emission are redder by 0.036+/-0.017 mag, and that the previously-noted correlation between stretch and host mass is entirely driven by the SNe Ia coming from passive regions. Most importantly, the mean standardized bri... Rigault, M; Aldering, G; Antilogus, P; Aragon, C; Bailey, S; Baltay, C; Bongard, S; Buton, C; Canto, A; Cellier-Holzem, F; Childress, M; Chotard, N; Fakhouri, H K; Feindt, U; Fleury, M; Gangler, E; Greskovic, P; Guy, J; Kim, A G; Kowalski, M; Lombardo, S; Nordin, J; Nugent, P; Pain, R; Pécontal, E; Pereira, R; Perlmutter, S; Rabinowitz, D; Runge, K; Saunders, C; Scalzo, R; Smadja, G; Tao, C; Thomas, R C; Weaver, B A 2013-01-01 118 CERN Multimedia We study disparity between H\\alpha\\ and H\\beta\\ in early spectra of the type IIP supernova SN 2008in. The point is that these lines cannot be described simultaneously in a spherically-symmetric model with the smooth density distribution. It is shown that an assumption of a clumpy structure of external layers of the envelope resolves the problem. We obtain estimates of the velocity at the inner border of the inhomogeneous zone (\\approx6100 km s^{-1}), the filing factor of inhomogeneities (\\leq0.5), and the mass of the inhomogeneous layers (~ 0.03 M_{\\odot}). The amplitude of flux fluctuations in the early spectrum of H\\alpha\\ (\\Delta F/F ~ 10^{-2}) imposes a constraint on the size of inhomogeneities (\\leq 200 km s^{-1}). A detection of fluctuations in the early H\\alpha\\ of type IIP supernovae might become an observational test of the inhomogeneous structure of their envelopes. We propose also the indirect test of the clumpy structure of external layers: the study of properties of the initial radiation outburst... Chugai, N N 2013-01-01 119 CERN Document Server We present a pilot narrow-band survey of H-alpha emitters at z=2.2 in the Great Observatories Origins Deep Survey North (GOODS-N) field with MOIRCS instrument on the Subaru telescope. The survey reached a 3 sigma limiting magnitude of 23.6 (NB209) which corresponds to a 3 sigma limiting line flux of 2.5 x 10^-17 erg s^-1 cm^-2 over a 56 arcmnin^2 contiguous area (excluding a shallower area). From this survey, we have identified 11 H-alpha emitters and one AGN at z=2.2 on the basis of narrow-band excesses and photometric redshifts. We obtained spectra for seven new objects among them, including one AGN, and an emission line above 3 sigma is detected from all of them. We have estimated star formation rates (SFR) and stellar masses (M_star) for individual galaxies. The average SFR and M_star is 27.8M_solar yr^-1 and 4.0 x 10^10M_solar, respectivly. Their specific star formation rates are inversely correlated with their stellar masses. Fitting to a Schechter function yields the H-alpha luminosity function with lo... Tadaki, Ken-ichi; Koyama, Yusei; Hayashi, Masao; Tanaka, Ichi; Tokoku, Chihiro 2010-01-01 120 CERN Multimedia We present the results of a long-term monitoring campaign of the H\\alpha line in a sample of bright OB-supergiants (O7.5-B9) that aims at detecting rotationally modulated changes potentially related to the existence of large-scale wind structures. A total of 22 objects were monitor ed during 36 nights spread over 6 months in 2001-2002. Coordinated broad-band photometric observations were also obtained for some targets. Conspicuous evidence for variability in H\\alpha is found for the stars displaying a feature contaminated by wind emission. Most changes take place on a daily time-scale, although hourly variations are also occasionally detected. Convincing evidence for a cyclical pattern of variability in H\\alpha has been found in 2 stars: HD 14134 and HD 42087 (periodic signals are also detected in other stars, but independent confirmation is required). Rotational modulation is suggested from the similarity between the observed recurrence time-scales (in the range 13-25 days) and estimated periods of stellar r... Morel, T; Pati, A K; Kuppuswamy, K; Carini, M T; Wood, E; Zimmerman, R 2004-01-01 121 CERN Document Server Radio and optical observations of the evolution of flare-associated phenomena have shown an initial and rapid burst at 0.4 THz only followed subsequently by a localized chromospheric heating producing an H{\\alpha} brightening with later heating of the whole active region. A major instability occurred several minutes later producing one impulsive burst at microwaves only, associated with an M2.0 GOES X-ray flare that exhibited the main H{\\alpha} brightening at the same site as the first flash. The possible association between long-enduring time profiles at soft X-rays, microwaves, H{\\alpha} and sub-THz wavelengths is discussed. In the decay phase the H{\\alpha} movie shows a disrupting magnetic arch structure ejecting dark, presumably chromospheric, material upwards. The time sequence of events suggests genuine interdependent and possibly non-thermal instabilities triggering phenomena, with concurrent active region plasma heating and material ejection. Kaufmann, Pierre; de Castro, C Guillermo Giménez; White, Stephen M; Raulin, Jean-Pierre; Correia, Emilia; Fernandes, Luis Olavo; de Souza, Rodney V; Godoy, Rodolfo; Marun, Adolfo; Pereyra, Pablo 2011-01-01 122 CERN Multimedia The Hanle effect in strong spectral lines is the physical mechanism that should be increasingly exploited for quantitative explorations of the magnetism of the quiet solar chromospheric plasma. Here we show, by means of multilevel radiative transfer calculations and new spectropolarimetric observations, that the amplitude and shape of the scattering polarization profiles of the H-alpha line is very sensitive to the strength and structure of the chromospheric magnetic field. The interpretation of the observations in terms of one-dimensional radiative transfer modeling suggests that there is an abrupt magnetization in the upper chromosphere of the quiet Sun. Stepan, Jiri; Ramelli, Renzo; Bianda, Michele 2011-01-01 123 CERN Document Server Recent data on neutron resonance widths indicate disagreement with the Porter-Thomas distribution (PTD). I discuss the theoretical arguments for the PTD, possible theoretical modifications, and I summarize the experimantal evidence. Weidenmueller, Hans A 2011-01-01 124 CERN Multimedia We present the results of a statistical study of the star formation rates (SFR) derived from the Galaxy Evolution Explorer (GALEX) observations in the ultraviolet continuum and in the H\\alpha emission line for a sample of about 800 luminous compact galaxies (LCGs). Galaxies in this sample have a compact structure and include one or several regions of active star formation. Global galaxy characteristics (metallicity, luminosity, stellar mass) are intermediate between ones of the nearby blue compact dwarf (BCD) galaxies and Lyman-break galaxies (LBGs) at high redshifts z > 2 - 3. SFRs were corrected for interstellar extinction which was derived from the optical Sloan Digital Sky Survey (SDSS) spectra. We find that SFRs derived from the galaxy luminosities in the far ultraviolet (FUV) and near ultraviolet (NUV) ranges vary in a wide range from 0.18 M_Sun/yr to 113 M_Sun/yr with median values of 3.8 M_Sun/yr and 5.2 M_Sun/yr, respectively. Simple regression relations are found for luminosities L(H\\alpha) and L(UV... Parnovsky, S L; Izotov, Y I 2012-01-01 125 CERN Document Server We aim to place new, strengthened constraints on the luminosity function (LF) of H-alpha emitting galaxies at redshift z=2.2, and to further constrain the instantaneous star-formation rate density of the universe (rho). We have used the new HAWK-I instrument at ESO-VLT to obtain extremely deep narrow-band (line; NB2090) and broad-band (continuum; Ks) imaging observations. The target field is in the GOODS-South, providing us with a rich multi-wavelength auxiliary data set, which we utilise for redshift confirmation and to estimate dust content. We use this new data to measure the faint-end slope (alpha) of LF(H-alpha) with unprecedented precision. The data are well fit by a Schechter function and also a single power-law, yielding alpha=(-1.72 +/- 0.20) and (-1.77 +/- 0.21), respectively. Thus we are able to confirm the steepening of alpha from low- to high-z predicted by a number of authors and observed at other wavelengths. We combine our LF data-points with those from a much shallower but wider survey at z=... Hayes, Matthew; Ostlin, Goran 2009-01-01 126 CERN Multimedia Efficient selection of emission line galaxies at z > 1 by photometric information in wide field surveys is one of the keys for future spectroscopic surveys to constrain dark energy using the baryon acoustic oscillation (BAO) signature. Here we estimate the H alpha and [O II] line luminosity functions of galaxies at z = 0.5-1.7 using a novel approach where multi-wavelength imaging data is used to jointly estimate both photometric redshifts and star-formation rates. These photometric estimates of line luminosities at high-redshift use the large data sets of the Subaru Deep Field and Subaru XMM-Newton Deep Field (covering \\sim 1 deg^2) and are calibrated with the spectroscopic data of the local Sloan Digital Sky Survey galaxies. The derived luminosity functions (especially H alpha) are in reasonable agreement with the past estimates based on spectroscopic or narrow-band-filter surveys. This dataset is useful for examining the photometric selection of target galaxies for BAO surveys because of the large cosmologi... Sumiyoshi, Masanao; Oshige, Shunsuke; Glazebrook, Karl; Akiyama, Masayuki; Morokuma, Tomoki; Motohara, Kentaro; Shimasaku, Kazuhiro; Hayashi, Masao; Yoshida, Makiko; Kashikawa, Nobunari; Kodama, Tadayuki 2009-01-01 127 CERN Document Server The INT/WFC Photometric H-alpha Survey of the Northern Galactic Plane (IPHAS) is an imaging survey being carried out in H-alpha, r' and i' filters, with the Wide Field Camera (WFC) on the 2.5-metre Isaac Newton Telescope (INT) to a depth of r'=20 (10 sigma). The survey is aimed at revealing large scale structure in our local galaxy, and also the properties of key early and late populations making up the Milky Way. Mapping emission line objects enables a particular focus on objects in the young and old stages of stellar evolution ranging from early T-Tauri stars to late planetary nebulae. In this paper we present the IPHAS Initial Data Release, primarily a photometric catalogue of about 200 million unique objects, coupled with associated image data covering about 1600 square degrees in three passbands. We note how access to the primary data products has been implemented through use of standard virtual observatory publishing interfaces. Simple traditional web access is provided to the main IPHAS photometric cat... González-Solares, E A; Greimel, R; Drew, J E; Irwin, M J; Sale, S E; Andrews, K; Aungwerojwit, A; Barlow, M J; Besselaar, E van den; Corradi, R L M; Gänsicke, B T; Groot, P J; Hales, A S; Hopewell, E C; Hu, H; Irwin, J; Knigge, C; Lagadec, E; Leisy, P; Lewis, J R; Mampaso, A; Matsuura, M; Moont, B; Morales-Rueda, L; Morris, R A H; Naylor, T; Parker, Q A; Prema, P; Pyrzas, S; Rixon, G T; Rodríguez-Gil, P; Roelofs, G; Sabin, L; Skillen, I; Suso, J; Tata, R; Viironen, K; Vink, J S; Witham, A; Wright, N J; Zijlstra, A A; Zurita, A; Drake, J; Fabregat, J; Lennon, D J; Lucas, P W; Martín, E L; Steeghs, D; Unruh, Y C 2007-01-01 128 Energy Technology Data Exchange (ETDEWEB) Tritium-{alpha}-fluoromethyl histidine ({sup 3}H-{alpha}-FMH), designed as a K{sub cat}-inhibitor of mammalian histidine decarboxylase (EC 4.1.1.22), was administered intravenously in male and pregnant female mice of the NMRI strain and the distribution of tritium in the body recorded by whole-body and microautoradiography. The results showed penetration of radioactivity into most tissues within 5 min. after the injection. After 4 hrs the highest levels of radioactivity were present in the intestinal content and in the kidneys. In the pregnant animal there was also a high labelling of the foetal tissues. When whole-body sections were washed in TCA prior to the autoradiographic exposure to retain only protein-bound radioactivity, a distinct labelling pattern was seen in the kidneys of the pregnant female mice ebut not in those of the male mice. Microautoradiography of the kidneys showed that the cells involved were located within the proximal convoluted tubuli. In several mouse strains, including the NMRI, the activity of kidney histidine decarboxylase is low in the males but high in females during a transient period of pregnancy. Incorporation of tritium into kidney protein after treatment with {sup 3}H-{alpha}-FMH, was correlated to a loss in histidine decarboxylase activity. The isotopic labelling was confined mainly to a component which cofractionated with histidine decarboxylase in polyacrylamidegel electrophoresis (PAGE) under nondenaturing conditions. Our data indicate that the cells described above represent the location of kidney histidine decarboxylase. (author). Hammar, L. (Department of Veterinary Virology, Biomedical Center, Uppsala (Sweden)); Henningsson, S. (Division of Clinical Pharmacology, University Hospital, Uppsala (Sweden)); Henningsson, A.-C. (Department of Obstetrics and Gynaecology, Univ. Hospital, Uppsala (Sweden)); Appelgreen, L.-E.; Tjaelve, H. (Department of Pharmacology and Toxicology, Biomedical Center, Uppsala (Sweden)); Kollonitsch, J. (Merck, Sharp and Dohme Research Laboratories, Rahway, New Jersey (USA)) 1990-01-01 129 CERN Multimedia We present the results of deep multicolour CCD imaging with the 6-m telescope of the pair of extremely metal-deficient gas-rich dwarf galaxies SBS 0335-052 E and W. The total magnitudes in U,B,V,R,I bands and the integrated fluxes of H-alpha emission are measured for both galaxies, and their integrated colours are derived. The analysis of their surface brightness (SB) distributions is performed with the use of the azimuthally-averaged SB profiles. The latter were modeled by the central Gaussian component and the underlying exponential disk', mainly contributing in the outermost, very low SB regions. The colours of these LSB components are used to estimate the age of the oldest visible stellar population. For the interpretation of the observed LSB colours their contamination by the nebular emission of ionized gas is accounted for by the use of the distribution of H-alpha flux. We compare the derived gas-free' colours with the colours predicted by the evolution synthesis models from the PEGASE.2 package, cons... Pustilnik, S A; Kniazev, A Yu 2004-01-01 130 CERN Document Server I describe a novel covariant formulation of massive gauge theories in which the longitudinal polarization vectors do not grow with the energy. Therefore in the present formalism, differently from the ordinary one, the energy and coupling power-counting is completely transparent at the level of individual Feynman diagrams, with obvious advantages both at the conceptual and practical level. Since power-counting is transparent, the high-energy limit of the amplitudes involving longitudinal particles is immediately taken, and the Equivalence Theorem is easily demonstrated at all orders in perturbation theory. Since the formalism makes the Equivalence Theorem self-evident, and because it is based on a suitable choice of the gauge, we can call it an "Equivalent Gauge". Wulzer, Andrea 2013-01-01 131 CERN Document Server We report a discovery of a proto-cluster in vigorous assembly and hosting strong star forming activities, associated to a radio galaxy USS 1558-003 at z=2.53, as traced by a wide-field narrow-band H_alpha imaging with MOIRCS on Subaru Telescope. We find 68 H_alpha emitters with dust-uncorrected SFRs down to 8.6 Msun/yr. Their spatial distribution indicates that there are three prominent clumps of H_alpha emitters, one surrounding the radio galaxy and another located at ~1.5 Mpc away to the south-west, and the other located in between the two. These contiguous three systems are very likely to merge together in the near future and may grow to a single more massive cluster at later times. Whilst most H_alpha emitters reside in the "blue cloud" on the color--magnitude diagram, some emitters have very red colors with J-Ks>1.38(AB). Interestingly, such red H_alpha emitters are located towards the faint end of the red sequence, and they tend to be located in the high density clumps. We do not see any statistically s... Hayashi, Masao; Tadaki, Ken-ichi; Koyama, Yusei; Tanaka, Ichi 2012-01-01 132 International Nuclear Information System (INIS) During the SERF interval of the SMY, October 4 to 9, 1979, the observations of regions Bou 2030 and 2032 were coordinated. An analysis of H-alpha observations indicates that, contrary to expectations, flares initiated in the magnetically simpler sunspot group Bou 2030 (Hale 16 341) occurred north off Bou 2032. The enhanced occurrence of flares in Bou 2030 on October 6, 1979 was located in an area with pronounced changes in polarity and structure of the background field in the neighbourhood of Bou 2030. The new positive large-scale field interacted with the negative field of the following spot B. Emission flare structures developed homologously along the new neutral line of the large-scale field. In analysing the pre-flare situation in a particular active region, it is therefore also necessary to know the characteristics of the large-scale field. (author). 2030-01-00 133 Science.gov (United States) This interactive Java applet helps users explore equivalent fractions through partitioning circles and squares. The applet provides a random fraction and the user creates one or two equivalent representations of that fraction by partitioning and coloring a square (or circle). The applet also plots the fraction on a number line and points from the shape to the number line displaying its equivalent value while the fraction is being built. Options include choice of circles or squares, one or two equivalent fractions, and a scoring feature allows users to keep track of the number correct. 2006-01-01 134 Science.gov (United States) This interactive Java applet helps users explore equivalent fractions through partitioning circles and squares. The applet provides a random fraction and the user creates one or two equivalent representations of that fraction by partitioning and coloring a square (or circle). The applet also plots the fraction on a number line and points from the shape to the number line displaying its equivalent value after the fraction is built. Options include choice of circles or squares, one or two equivalent fractions, and a scoring feature allows users to keep track of the number correct. 2006-01-01 135 CERN Multimedia We report the detection of an H-alpha emission line in the low resolution spectrum of a quasar, RX J1759.4+6638, at a redshift of 4.3 with the InfraRed Camera (IRC) onboard the AKARI. This is the first spectroscopic detection of an H-alpha emission line in a quasar beyond z=4. The overall spectral energy distribution (SED) of RX J1759.4+6638 in the near- and mid-infrared wavelengths agrees with a median SED of the nearby quasars and the flux ratio of F(Ly-alpha)/F(H-alpha) is consistent with those of previous reports for lower-redshift quasars. Oyabu, Shinki; Ohyama, Youichi; Matsuhara, Hideo; Takagi, Toshinobu; Nakagawa, Takao; Onaka, Takashi; Fujishiro, Naofumi; Ishihara, Daisuke; Ita, Yoshifusa; Kataza, Hirokazu; Kim, Woojung; Matsumoto, Toshio; Murakami, Hiroshi; Sakon, Itsuki; Tanabe, Toshihiko; Uemizu, Kazunori; Ueno, Munetaka; Usui, Fumihiko; Watarai, Hidenori; Haze, Kanae 2007-01-01 136 International Nuclear Information System (INIS) The widths of the isovector monopole ?Tsub(z) = 1 component in 208Tl, 140La, 120In and 90Y are evaluated within the self-consistent Hartree-Fock + charge-exchange RPA using the Skyrme interaction. The coupling of 1p-1h states to 2p-2h configurations is microscopically calculated. The results are compared with those of recent pion charge-exchange reactions. (author). 1983-01-01 137 International Nuclear Information System (INIS) The radiative decay ?(1520) ? ?? was recorded in the exclusive reaction p + N ? ?(1520)K+ + N at the SPHINX facility. The branching ratio for this decay and the corresponding partial width were found to be, respectively, Br[?(1520) ? ??] = (1.02 ± 0.21) x 10-2 and ?[?(1520) ? ??] = 159 ± 35 keV (the quoted errors are purely statistical, the systematic errors being within 15%). 2005-01-01 138 UK PubMed Central (United Kingdom) A viscous fluid flowing over plastic grains spontaneously generates single-thread channels. With time, these laminar analogues of alluvial rivers reach a reproducible steady state, showing a well-defined width and cross section. In the absence of sediment transport, their shape conforms with the threshold hypothesis which states that, at equilibrium, the combined effects of gravity and flow-induced stress maintain the bed surface at the threshold of motion. This theory explains how the channel selects its size and slope for a given discharge. In this light, laboratory rivers illustrate the similarity between the avalanche angle of granular materials and Shields's criterion for sediment transport. Seizilles G; Devauchelle O; Lajeunesse E; Métivier F 2013-05-01 139 CERN Multimedia As a function of energy E, the average strength function S(E) of a doorway state is commonly assumed to be Lorentzian in shape and characterized by two parameters, the peak energy E_0 and the spreading width Gamma. The simple picture is modified when the density of background states that couple to the doorway state changes significantly in an energy interval of size Gamma. For that case we derive an approximate analytical expression for S(E). We test our result successfully against numerical simulations. Our result may have important implications for shell--model calculations. De Pace, A; Weidenmueller, H A 2010-01-01 140 CERN Document Server We report results from the Wyoming Survey for H-alpha (WySH), a comprehensive four-square degree survey to probe the evolution of star-forming galaxies over the latter half of the age of the Universe. We have supplemented the H-alpha data from WySH with infrared data from the Spitzer Wide-area Infrared Extragalactic (SWIRE) Survey and ultraviolet data from the Galaxy Evolution Explorer (GALEX) Deep Imaging Survey. This dataset provides a multi-wavelength look at the evolution of the attenuation by dust, and here we compare a traditional measure of dust attenuation (L(TIR)/L(FUV)) to a diagnostic based on a recently-developed robust star formation rate (SFR) indicator, [H-alpha_obs+24-micron]/H-alpha_obs. With such data over multiple epochs, the evolution in the attenuation by dust with redshift can be assessed. We present results from the ELAIS-N1 and Lockman Hole regions at z~0.16, 0.24, 0.32 and 0.40. While the ensemble averages of both diagnostics are relatively constant from epoch to epoch, each epoch ind... Moore, Carolynn A; Barlow, Rebecca J; Cohen, Seth A; Cook, David O; Johnson, L C; Kattner, ShiAnne M; Lee, Janice C; Staudaher, Shawn M 2010-01-01 141 Science.gov (United States) Observations of the central region of the galaxy cluster associated with 2A 0335+096, obtained in H-alpha, R, I, and b45 (4506 A with FWHM 355 A) using an 800 x 800-pixel CCD detector on the 4-m telescope at KPNO on December 27 and 30, 1986, are reported. The data are presented graphically and analyzed. Features discussed include a 17-kpc-long bar of H-alpha emission surrounded by filaments, a smaller elongated H-alpha structure (possibly an accretion disk) centered on the nucleus of the central galaxy, a secondary galaxy with a red H-alpha-bright nucleus located within the 17-kpc bar about 6 arcsec from the central-galaxy nucleus, and evidence for excess blue emission (indicating star formation at about 8 solar mass/yr in the cooling flow). From the presence of dust in the emission-line gas it is inferred that theoretical models based on preferential formation of low-mass stars may not be applicable to this object. Romanishin, W.; Hintzen, Paul 1988-01-01 142 International Nuclear Information System (INIS) Observations of the central region of the galaxy cluster associated with 2A 0335+096, obtained in H-alpha, R, I, and b45 (4506 A with FWHM 355 A) using an 800 x 800-pixel CCD detector on the 4-m telescope at KPNO on December 27 and 30, 1986, are reported. The data are presented graphically and analyzed. Features discussed include a 17-kpc-long bar of H-alpha emission surrounded by filaments, a smaller elongated H-alpha structure (possibly an accretion disk) centered on the nucleus of the central galaxy, a secondary galaxy with a red H-alpha-bright nucleus located within the 17-kpc bar about 6 arcsec from the central-galaxy nucleus, and evidence for excess blue emission (indicating star formation at about 8 solar mass/yr in the cooling flow). From the presence of dust in the emission-line gas it is inferred that theoretical models based on preferential formation of low-mass stars may not be applicable to this object. 17 references. 1988-01-01 143 Energy Technology Data Exchange (ETDEWEB) Observations of the central region of the galaxy cluster associated with 2A 0335+096, obtained in H-alpha, R, I, and b45 (4506 A with FWHM 355 A) using an 800 x 800-pixel CCD detector on the 4-m telescope at KPNO on December 27 and 30, 1986, are reported. The data are presented graphically and analyzed. Features discussed include a 17-kpc-long bar of H-alpha emission surrounded by filaments, a smaller elongated H-alpha structure (possibly an accretion disk) centered on the nucleus of the central galaxy, a secondary galaxy with a red H-alpha-bright nucleus located within the 17-kpc bar about 6 arcsec from the central-galaxy nucleus, and evidence for excess blue emission (indicating star formation at about 8 solar mass/yr in the cooling flow). From the presence of dust in the emission-line gas it is inferred that theoretical models based on preferential formation of low-mass stars may not be applicable to this object. 17 references. Romanishin, W.; Hintzen, P. 1988-01-01 144 CERN Document Server New results from a large survey of H-alpha emission-line galaxies at z=0.84 using WFCAM/UKIRT and a custom narrow-band filter in the J band are presented as part of the HiZELS survey. Reaching an effective flux limit of 1e-16 erg/s/cm^2 in a comoving volume of 1.8e5 Mpc^3, this represents the largest and deepest survey of its kind ever done at z~1. There are 1517 potential line emitters detected across 1.4 sq.deg of the COSMOS and UKIDSS UDS fields, of which 743 are selected as H-alpha emitters. These are used to calculate the H-alpha luminosity function, which is well-fitted by a Schechter function with phi=10^(-1.92+-0.10) Mpc^-3, L=10^(42.26+-0.05)erg/s, and alpha=-1.65+-0.15. The integrated star formation rate density (SFRD) at z=0.845 is 0.15+-0.01 M_sun/yr/Mpc^3. The results robustly confirm a strong evolution of SFRD from the present day out to z~1 and then flattening to z~2, using a single star-formation indicator. Out to z~1, both the characteristic luminosity and space density of the H-alpha emitt... Sobral, D; Geach, J E; Smail, Ian; Kurk, J; Cirasuolo, M; Casali, M; Ivison, R J; Coppin, K; Dalton, G B 2009-01-01 145 CERN Document Server [Abridged] We compare H-alpha, ultraviolet (UV) and infrared (IR) indicators of star formation rate (SFR) for a sample of z = 0.84 galaxies from the High-z Emission Line Survey (HiZELS). Using multi-wavelength diagnostics, we estimate that 5 - 11 per cent of H-alpha emitters at this redshift are active galactic nuclei. We detect 35 per cent of the H-alpha emitters individually at 24 microns, and stack the star-forming emitters on deep 24-micron images in order to calculate the typical SFRs of our galaxies. These are compared to the observed H-alpha line fluxes in order to estimate the extinction at z = 0.84, and we find a significant increase in dust extinction for galaxies with higher SFRs. We demonstrate that the local relationship between SFR and extinction is suitable for our sample, and attribute the overall increase in dust extinction for z = 0.84 galaxies to an increase in the average SFR, rather than to a change in dust properties. We calculate the UV extinction, and find a similar dependence on SFR, ... Garn, Timothy; Best, Philip N; Geach, James E; Smail, Ian; Cirasuolo, Michele; Dalton, Gavin B; Dunlop, James S; McLure, Ross J; Farrah, Duncan 2009-01-01 146 CERN Multimedia We present first results from a near-infrared spectroscopic survey of the COSMOS field, using the Fiber Multi-Object Spectrograph (FMOS) on the Subaru telescope, designed to characterize the star-forming galaxy population at 1.4H\\alpha\\ in emission between 1.6-1.8\\mu m with $f_H\\alpha\\ \\gtrsim 4 \\times 10^{-17} ergs cm^{-2} s^{-1}$. Here, we specifically focus on 271 sBzK-selected galaxies that yield a H\\alpha\\ detection thus providing a redshift and emission-line luminosity to establish the relation between star formation rate (SFR) and stellar mass. With further J-band spectroscopy for 89 of these, the level of dust extinction is assessed by measuring the Balmer decrement using co-added spectra. We find that the extinction (0.6\\lesssim A_H\\alpha\\ \\lesssim 2.5) rises with stellar mass and is elevated at high masses compared to low-redshift galaxies. Using this subset of the spectroscopic sample, we further find that the differential extinction b... Kashino, D; Rodighiero, G; Renzini, A; Arimoto, N; Daddi, E; Lilly, S J; Sanders, D B; Kartaltepe, J; Zahid, H J; Nagao, T; Sugiyama, N; Capak, P; Carollo, C M; Chu, J; Hasinger, G; Ilbert, O; Kajisawa, M; Kewley, L J; Koekemoer, A M; Kova?, K; Fèvre, O Le; Masters, D; McCracken, H J; Onodera, M; Scoville, N; Strazzullo, V; Symeonidis, M; Taniguchi, Y 2013-01-01 147 CERN Document Server We compute population synthesis models for the variation of H-alpha absorption indices (HaA and HaF), as a function of age and metallicity in old stellar systems. The models are based on the STELIB spectral library, and defined at resolution of 3 Angstrom FWHM. The indices are found to be highly sensitive to age variation, with only moderate response to metallicity. For galaxies uncontaminated by nebular emission, our HaA index is more powerful in breaking the age/metallicity degeneracy than H-beta or H-gamma_F. Using a sample of red cluster galaxies carefully selected to exclude objects with emission, we find a steep decline of HaA with velocity dispersion (slope -0.75 +/- 0.07 Angstrom/dex). The slope can be translated to constraints on age and metallicity scaling relations, incorporating measurement and model errors. If the HaA-sigma slope is due only to age, we obtain Age proportional to sigma^{0.95 +/- 0.12}. Because HaA depends quite weakly on [Fe/H], a metallicity interpretation would require Fe/H prop... Smith, R J 2005-01-01 148 CERN Multimedia [abridged] We describe the results of our multi-wavelength observing campaign on the young stellar objects in the LkH$\\alpha$101 cluster. Our simultaneous X-ray and multi-frequency radio observations are unique in providing simultaneous constraints on short-timescale variability at both wavelengths as well as constraints on the thermal or nonthermal nature of radio emission from young stars. Focussing in on radio-emitting objects and the multi-wavelength data obtained for them, we find that multi-frequency radio data indicate nonthermal emission even in objects with infrared evidence for disks. We find radio variability on timescales of decades, days and hours. About half of the objects with X-ray and radio detections were variable at X-ray wavelengths, despite lacking large-scale flares or large variations. Variability appears to be a bigger factor affecting radio emission than X-ray emission. A star with infrared evidence for a disk, [BW88]~3, was observed in the decay phase of a radio flare. In this object... Osten, R A 2008-01-01 149 CERN Document Server Searching for the presence of circumstellar material is currently the only direct way to discriminate between the different types of possible progenitor systems for Type Ia supernovae. We have therefore looked for narrow H-alpha in a high-resolution spectrum of the normal Type Ia supernova 1994D taken 10 days before maximum and only 6.5 days after explosion. We derive an upper limit of 2.0E-16 erg cm^{-2} s^{-1} for an unresolved emission line at the local H II region velocity. To estimate the limit this puts on wind density, we have made time-dependent photoionization calculations. Assuming spherical symmetry we find an upper limit of the mass loss rate which is roughly 1.5E-5 solar masses per year for a wind speed of 10 km s^{-1}. This limit can exclude only the highest-mass-loss-rate symbiotic systems as progenitors. We discuss the effect of asymmetry and assess the relative merits of early optical, radio and X-ray limits in constraining mass loss from Type Ia progenitors. We find that X-ray observations c... Cumming, R J; Smith, L J; Pettini, M; King, D L 1996-01-01 150 Energy Technology Data Exchange (ETDEWEB) A distance-limited sample of 869 objects from the Updated Nearby Galaxy Catalog is used to characterize the star formation status of the Local Volume population. We present a compiled list of 1217 star formation rate (SFR) estimates for 802 galaxies within 11 Mpc, derived from the H{alpha} imaging surveys and the GALEX far-ultraviolet survey. We briefly discuss some basic scaling relations between SFR and luminosity, morphology, H I mass, surface brightness, and the environment of the galaxies. About 3/4 of our sample consist of dwarf galaxies, for which we offer a more refined classification. We note that the specific SFR of nearly all luminous and dwarf galaxies does not exceed the maximum value: log (SFR/L{sub K} ) = -9.4 [yr{sup -1}]. Most spiral and blue dwarf galaxies have enough time to generate their stellar mass during the cosmological time, T{sub 0}, with the observed SFRs. They dispose of a sufficient amount of gas to support their present SFRs over the next T{sub 0} term. We note that only a small fraction of BCD, Im, and Ir galaxies (about 1/20) proceed in a mode of vigorous starburst activity. In general, the star formation history of spiral and blue dwarf galaxies is mainly driven by their internal processes. The present SFRs of E, S0, and dSph galaxies typically have 1/30-1/300 of their former activity. Karachentsev, Igor D.; Kaisina, Elena I., E-mail: [email protected], E-mail: [email protected] [Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Karachai-Cherkessian Republic 369167 (Russian Federation) 2013-09-15 151 CERN Multimedia We report on a high-resolution, spectroscopic stellar parameter and abundance analysis of a d' symbiotic star: the yellow component of StH\\alpha190. This star has recently been discovered, and confirmed here, to be a rapidly rotating (vsini=100 km/s) subgiant, or giant, that exhibits radial-velocity variations of probably at least 40 km/s, indicating the presence of a companion (a white dwarf star). It is found that the cool stellar component has Teff=5300K and log g=3.0. The iron and calcium abundances are close to solar, however, barium is overabundant, relative to Fe and Ca, by about +0.5 dex. The barium enhancement reflects mass-transfer of s-process enriched material when the current white dwarf was an asymptotic giant branch (AGB) star. The past and future evolution of this binary system depends critically on its current orbital period, which is not yet known. Concerted and frequent radial-velocity measurements are needed to provide crucial physical constraints to this d' symbiotic system. Smith, V V; Cunha, K; Smith, Verne V.; Pereira, Claudio B.; Cunha, Katia 2001-01-01 152 CERN Multimedia We present multiwavelength observations of a large-amplitude oscillation of a polar crown filament on 15 October 2002. The oscillation occurred during the slow rise (about 1 km/s) of the filament. It completed three cycles before sudden acceleration and eruption. The oscillation and following eruption were clearly seen in observations recorded by the Extreme-Ultraviolet Imaging Telescope onboard SOHO. The oscillation was seen only in a part of the filament, and it appears to be a standing oscillation rather than a propagating wave. The period of oscillation was about two hours and did not change significantly during the oscillation. We also identified the oscillation as a "winking filament" in the H-alpha images taken by the Flare Monitoring Telescope, and as a spatial displacement in 17 GHz microwave images from Nobeyama Radio Heliograph (NoRH). The filament oscillation seems to be triggered by magnetic reconnection between a filament barb and nearby emerging magnetic flux as was evident from the MDI magneto... Isobe, H; Asai, A; Jain, R 2007-01-01 153 Directory of Open Access Journals (Sweden) Full Text Available Mobile apps are often developed and then evolved on more than one mobile operating system. For the publisher of such apps, the problem is how to ensure equivalence of the product on the various platforms, in the sense of acting equivalently with respect to a test set. In this paper we present an approach that tackles this problem from two directions: architecture and testing. First we will explain the role and pitfalls of reference architectures. Then we will present our equivalence testing framework. It is based on mocking components of the target implementation. Instead of implementing mock components for all platforms, our approach is to implement these mocks only once and run them on a central server. On the tested target device, stub components are injected that forward to their server-based counterparts. Thus the exactly same test code is applied to all platform specific implementations. Denzler Christoph; Kröni Daniel; Moschko Maxim 2012-01-01 154 Digital Repository Infrastructure Vision for European Research (DRIVER) In earlier work, we described an equivalence result for network capacity. Roughly, that result is as follows. Given a network of noisy, memoryless, point-to-point channels, replace each channel by a noiseless, memoryless bit pipe of the same capacity yields a new network such that any collection of ... Koetter, Ralf; Effros, Michelle; Medard, Muriel 155 International Nuclear Information System (INIS) The report reviews, for the Member States of the European Community, possible situations in which an equivalence concept for radioactive waste may be used, analyses the various factors involved, and suggests guidelines for the implementation of such a concept. Only safety and technical aspects are covered. Other aspects such as commercial ones are excluded. Situations where the need for an equivalence concept has been identified are processes where impurities are added as a consequence of the treatment and conditioning process, the substitution of wastes from similar waste streams due to the treatment process, and exchange of waste belonging to different waste categories. The analysis of factors involved and possible ways for equivalence evaluation, taking into account in particular the chemical, physical and radiological characteristics of the waste package, and the potential risks of the waste form, shows that no simple all-encompassing equivalence formula may be derived. Consequently, a step-by-step approach is suggested, which avoids complex evaluations in the case of simple exchanges 1990-01-01 156 Science.gov (United States) The U.S. Environmental Protection Agency created the PEC in 1985 to make recommendations to EPA and State managers on the equivalency of unproven sewage sludge disinfection technologies/processes to either a Process to Significantly Reduce Pathogens (PSRP) or a Process to Further... 157 CERN Multimedia Recent measurements of resonance widths for low-energy neutron scattering off heavy nuclei show large deviations from the standard Porter-Thomas distribution. We propose a new resonance width distribution based on the random matrix theory for an open quantum system. Two methods of derivation lead to a single analytical expression; in the limit of vanishing continuum coupling, we recover the Porter-Thomas distribution. The result depends on the ratio of typical widths $\\Gamma$ to the energy level spacing $D$ via the dimensionless parameter $\\kappa=(\\pi\\Gamma/2D)$. The new distribution suppresses small widths and increases the probabilities of larger widths. Shchedrin, Gavriil 2011-01-01 158 CERN Multimedia Using H-alpha spectra of 114 rest-frame UV-selected galaxies at z~2, we compare inferred star formation rates (SFRs) with those determined from the UV continuum luminosity. After correcting for extinction using standard techniques based on the UV continuum slope, we find excellent agreement between the indicators, with = 31 Msun/yr and = 29 Msun/yr. The agreement between the indicators suggests that the UV luminosity is attenuated by an typical factor of ~4.5 (with a range from no attenuation to a factor of ~100 for the most obscured object in the sample), in good agreement with estimates of obscuration from X-ray, radio and mid-IR data. The H-alpha luminosity is attenuated by a factor of ~1.7 on average, and the maximum H-alpha attenuation is a factor of ~5. In agreement with X-ray and mid-IR studies, we find that the SFR increases with increasing stellar mass and at brighter K magnitudes, to ~ 60 Msun/yr for galaxies with K10^11 Msun) have had higher SFRs in the past. Erb, D K; Shapley, A E; Pettini, M; Reddy, N A; Adelberger, K L; Erb, Dawn K.; Steidel, Charles C.; Shapley, Alice E.; Pettini, Max; Reddy, Naveen A.; Adelberger, Kurt L. 2006-01-01 159 CERN Multimedia We compare H-alpha, radio continuum, and Spitzer Space Telescope (SST) images of 58 planetary nebulae (PNe) recently discovered by the Macquarie-AAO-Strasbo- urg H-alpha PN Project (MASH) of the SuperCOSMOS H-alpha Survey. Using InfraRed Array Camera (IRAC) data we define the IR colors of PNe and demonstrate good isolation between these colors and those of many other types of astronomical object. The only substantive contamination of PNe in the color-color plane we illustrate is due to YSOs. However, this ambiguity is readily resolved by the unique optical characteristics of PNe and their environs. We also examine the relationships between optical and MIR morphologies from 3.6 to 8.0um and explore the ratio of mid-infrared (MIR) to radio nebular fluxes, which is a valuable discriminant between thermal and nonthermal emission. MASH emphasizes late evolutionary stages of PNe compared with previous catalogs, enabling study of the changes in MIR and radio flux that attend the aging process. Spatially integrated M... Cohen, Martin; Green, Anne J; Murphy, Tara; Miszalski, Brent; Frew, David J; Meade, Marilyn R; Babler, Brian; Indebetouw, Remy; Whitney, Barbara A; Watson, Christer; Churchwell, Edward B; Watson, Douglas F 2007-01-01 160 CERN Document Server We present preliminary results from a programme to obtain multi-object near-infrared spectroscopy of galaxies at redshifts $0.7H-alpha in galaxies at$z\\sim1$. We aim to address the true star formation history of the universe at this epoch: potentially the peak period of star formation activity. H-alpha is the same star formation measure used at low redshift, and hence we can trace star formation without the systematic uncertainties of using different calibrators in different redshift bins, or the extreme dust extinction in the rest-UV. CIRPASS has been successfully demonstrated in multi-object mode on the AAT and WHT. Here we present preliminary results from one of our fields, the Hubble Deep Field North, observed with the WHT. With 150 fibres deployed over an unvignetted field of$\\sim15$arcmin, we have several detections of H-alpha from star forming galaxies at$0.8<... Doherty, M; Sharp, R; Dalton, G B; Parry, I; Lewis, I; MacDonald, E; Wolf, C; Hippelein, H; Doherty, Michelle; Bunker, Andrew; Sharp, Robert; Dalton, Gavin; Parry, Ian; Lewis, Ian; Donald, Emily Mac; Wolf, Christian; Hippelein, Hans 2004-01-01 161 UK PubMed Central (United Kingdom) CHAMBERS KENITH W; BUTTER MARY; BISH SUZANNE M 162 International Nuclear Information System (INIS) In this paper I report on the influence of steam and carbon dioxide on the detonability of hydrogen-air mixtures. Data were obtained on the detonation cell width in a heated detonation tube that is 0.43 m in diameter and 13.1 m long. The detonation cell widths were correlated using a characteristic length calculated from a chemical kinetic model. The addition of either diluent to a hydrogen-air mixture increased the cell width for all equivalence ratios. For equal diluent concentrations, however, carbon dioxide not only yielded larger increases in the cell width than steam, but its efficacy relative to steam was predicted to increase with increasing concentration. The range of detonable hydrogen concentrations in a hydrogen-air mixture initially at 1 atm pressure was found to be between 11.6 percent and 74.9 percent for mixtures at 20 degree C and 9.4 percent and 76.9 percent for mixtures at 100 degree C. The detonation limit was between 38.8 percent and 40.5 percent steam for a stoichiometric hydrogen-air-steam mixture initially at 100 degree C and 1 atm. 10 refs., 4 figs., 1 tab 1990-01-01 163 Energy Technology Data Exchange (ETDEWEB) In this paper I report on the influence of steam and carbon dioxide on the detonability of hydrogen-air mixtures. Data were obtained on the detonation cell width in a heated detonation tube that is 0.43 m in diameter and 13.1 m long. The detonation cell widths were correlated using a characteristic length calculated from a chemical kinetic model. The addition of either diluent to a hydrogen-air mixture increased the cell width for all equivalence ratios. For equal diluent concentrations, however, carbon dioxide not only yielded larger increases in the cell width than steam, but its efficacy relative to steam was predicted to increase with increasing concentration. The range of detonable hydrogen concentrations in a hydrogen-air mixture initially at 1 atm pressure was found to be between 11.6 percent and 74.9 percent for mixtures at 20{degree}C and 9.4 percent and 76.9 percent for mixtures at 100{degree}C. The detonation limit was between 38.8 percent and 40.5 percent steam for a stoichiometric hydrogen-air-steam mixture initially at 100{degree}C and 1 atm. 10 refs., 4 figs., 1 tab. Stamps, D.W. 1990-01-01 164 CERN Document Server We analyse the Einstein equivalence principle (EEP) for a Hubble observer in Friedmann-Lemaitre-Robertson-Walker spacetime. We show that the affine structure of light cone in the FLRW spacetime should be treated locally in terms of the optical metric which is not reduced to the Minkowski metric due to the non-uniform parametrization of the local equations of light propagation with the proper time of the observer's clock. The physical consequence of this difference is that the Doppler shift of radio waves measured locally, is affected by the Hubble expansion. Kopeikin, Sergei 2013-01-01 165 International Nuclear Information System (INIS) In this paper the nanosecond pulse signal generator with regulable pulse width as well as its apparatus structure, operating principle, circuit design, technica index and measure of anti-jamming will be introduced in brief. By combine digital integrate circuits with analog circuit, nanosecond pulse signal of two kinds of different pulse width and regulable pulse width at the same time is accomplished in the apparatus 2003-01-01 166 CERN Multimedia We present an alternative proof of the following fact: the hyperspace of compact closed subsets of constant width in $\\mathbb R^n$ is a contractible Hilbert cube manifold. The proof also works for certain subspaces of compact convex sets of constant width as well as for the pairs of compact convex sets of constant relative width. Besides, it is proved that the projection map of compact closed subsets of constant width is not 0-soft in the sense of Shchepin, in particular, is not open. Bazylevych, L E 2004-01-01 167 International Nuclear Information System (INIS) Method and results of calculation of the partial nucleon escape widths of various giant resonances are presented. The comparison with relevant experimental data and the results of other theoretical approaches is given where it is possible. The partial widths for the direct proton decay of the Gamow-Teller resonance in Sn isotopes are given special attention. (orig.) 1994-03-07 168 International Nuclear Information System (INIS) This Letter describes a direct measurement of the W boson decay width, ?(W), using the high-mass tail of the transverse mass spectrum of W?e? decays recorded by the Collider Detector at Fermilab. We find ?(W)=2.11±0.28(stat) ± 0.16(syst) GeV and compare this direct measurement with indirect means of obtaining the width. 1995-01-01 169 Directory of Open Access Journals (Sweden) Full Text Available Sun Pharmaceutical Advanced research Centre (SPARC),17/B, Off Mahakali caves road, Mahal Indl. Estate,Andheri (E), Mumbai-400 093,INDIA,email : [email protected] assess the role of genes required for skin organogenesis, tissue regeneration and homeostasis, in vitro skin equivalents composed of primary cells or cell lines, respectively. In these organotypic cocultures keratinocytes generate a normal epidermis irrespective of the species and tissue origin of fibroblasts. The combination of cells derived from mouse and human tissues facilitates the identification of the origin of compounds involved in epidermal tissue reconstitution and thus the precise analysis of growth regulatory mechanisms.Keywords: In vitro models, keratinocytes, fibroblasts, skin re-epithelialization, in situ hybridization, cadaver skin Hemant P. Joshi 2006-01-01 170 CERN Document Server For several semirings S, two weighted finite automata with multiplicities in S are equivalent if and only if they can be connected by a chain of simulations. Such a semiring S is called "proper". It is known that the Boolean semiring, the semiring of natural numbers, the ring of integers, all finite commutative positively ordered semirings and all fields are proper. The semiring S is Noetherian if every subsemimodule of a finitely generated S-semimodule is finitely generated. First, it is shown that all Noetherian semirings and thus all commutative rings and all finite semirings are proper. Second, the tropical semiring is shown not to be proper. So far there has not been any example of a semiring that is not proper. Esik, Zoltan 2010-01-01 171 Energy Technology Data Exchange (ETDEWEB) During recent decades the worldwide accepted standard for coke oven width has been 450 mm. Two new coke ovens constructed with widths of 450 and 600 mm were used to investigate the exponential relationship between coking time and chamber width. A relationship was found between coking time and flue temperature as a function of oven width. Extended residence times in the wider oven led to improved shrinkage of the coke cake, to lower power demand of the coke pushing machine, and to improved strength of the coke. The exponential function expressing the interdependence of chamber width and coking time was found to have an exponent power of 1.35 shifting to 1.20 as flue temperature increased. (CKK) Rohde, W.; Habermehl, D.; Flockenhaus, C. 1982-01-01 172 CERN Multimedia The significance of having finite widths of action potentials in integrate and fire neural networks is investigated. Models suggested by Hopfield and Herz [1] with zero action potential has been generalized to include pulse shapes of arbitrary widths and shapes. The convergence to limit cycle is examined both analytically and in simulation experiments. Hopfield's proof for nonleaking models has been extended nontrivially to the case of finite widths. It is pointed out that the concept of simultaneity in such networks maybe subject to bin widths in simulation experiments. The effects of varying the shape of the action potential and its width are examined. The roles of the magnitude of a leaking resistance connected to the neurons, a common external current and synaptic currents between neighbors are also examined and found to bear important consequences to the dynamical development of the network. Shafee, F 2001-01-01 173 CERN Multimedia We study the process theoretic notion of stuttering equivalence in the setting of parity games. We demonstrate that stuttering equivalent vertices have the same winner in the parity game. This means that solving a parity game can be accelerated by minimising the game graph with respect to stuttering equivalence. While, at the outset, it might not be clear that this strategy should pay off, our experiments using typical verification problems illustrate that stuttering equivalence speeds up solving parity games in many cases. Cranen, Sjoerd; Willemse, Tim A C 2011-01-01 174 UK PubMed Central (United Kingdom) BACKGROUND: Consideration of the biologic width in restorative dentistry seems to be important for maintaining periodontal health. OBJECTIVE: To evaluate the dimensions of the biologic width in humans. MATERIALS AND METHODS: A systematic literature search was performed for publications published by 28 September 2012 using five different electronic databases; this search was complemented by a manual search. Two reviewers conducted the study selection, data collection, and validity assessment. The PRISMA criteria were applied. From 615 titles identified by the search strategy, 14 publications were included and six were suitable for meta-analyses. RESULTS: Included studies were published from the years 1924 to 2012. They differed with regard to measurements of the biologic width. Mean values of the biologic width obtained from two meta-analyses ranged from 2.15 to 2.30 mm, but large intra- and inter-individual variances (subject sample range: 0.2 - 6.73 mm) were observed. The tooth type and site, the presence of a restoration and periodontal diseases/surgery affected the dimensions of the biologic width. Pronounced heterogeneity among studies regarding methods and outcome measures exists. CONCLUSIONS: No universal dimension of the biologic width appears to exist. Establishment of periodontal health is suggested prior to the assessment of the biologic width within reconstructive dentistry. Schmidt JC; Sahrmann P; Weiger R; Schmidlin PR; Walter C 2013-05-01 175 UK PubMed Central (United Kingdom) An algorithm is presented which determines the equivalence of two settings of a (3 + d)-dimensional superspace group (d = 1, 2, 3). The algorithm has been implemented as a web tool findssg on SSG(3+d)D, providing the transformation of any user-given superspace group to the standard setting of this superspace group in SSG(3+d)D. It is shown how the standard setting of a superspace group can be directly obtained by an appropriate transformation of the external-space lattice vectors (the basic structure unit cell) and a transformation of the internal-space lattice vectors (new modulation wavevectors are linear combinations of old modulation wavevectors plus a three-dimensional reciprocal-lattice vector). The need for non-standard settings in some cases and the desirability of employing standard settings of superspace groups in other cases are illustrated by an analysis of the symmetries of a series of compounds, comparing published and standard settings and the transformations between them. A compilation is provided of standard settings of compounds with two- and three-dimensional modulations. The problem of settings of superspace groups is discussed for incommensurate composite crystals and for chiral superspace groups. van Smaalen S; Campbell BJ; Stokes HT 2013-01-01 176 CERN Document Server Recently the theory of widths of Kolmogorov-Gelfand has received a great deal of interest due to its close relationship with the newly born area of Compressive Sensing in Signal Processing. However fundamental problems of the theory of widths in multidimensional Theory of Functions remain untouched, as well as analogous problems in the theory of multidimensional Signal Analysis. In the present paper we provide a multidimensional generalization of the original result of Kolmogorov about the widths of an "ellipsoidal sets" consisting of functions defined on an interval. Kounchev, Ognyan 2011-01-01 177 International Nuclear Information System (INIS) [en] In its report 39, the International Commission on Radiation Units and Measurements (ICRU), has defined four new quantities for the determination of dose equivalents from external sources: the ambient dose equivalent, the directional dose equivalent, the individual dose equivalent, penetrating and the individual dose equivalent, superficial. The rationale behind these concepts and their practical application are discussed. Reference is made to numerical values of these quantities which will be the subject of a coming publication from the International Commission on Radiological Protection, ICRP. (Author) 1985-01-01 178 CERN Document Server Recent studies of O-type stars demonstrated that discrepant mass-loss rates are obtained when different diagnostic methods are employed - fitting the unsaturated UV resonance lines (e.g. P v) gives drastically lower values than obtained from the H{\\alpha} emission. Wind clumping may be the main cause for this discrepancy. In a previous paper, we have presented 3-D Monte-Carlo calculations for the formation of scattering lines in a clumped stellar wind. In the present paper we select five O-type supergiants (from O4 to O7) and test whether the reported discrepancies can be resolved this way. In the first step, the analyses start with simulating the observed spectra with Potsdam Wolf-Rayet (PoWR) non-LTE model atmospheres. The mass-loss rates are adjusted to fit best to the observed H{\\alpha} emission lines. For the unsaturated UV resonance lines (i.e. P v) we then apply our 3-D Monte-Carlo code, which can account for wind clumps of any optical depths, a non-void inter-clump medium, and a velocity dispersion in... Šurlan, B; Aret, A; Kubát, J; Oskinova, L M; Torres, A F 2013-01-01 179 CERN Document Server A crucial issue in star formation is to understand the physical mechanism by which mass is accreted onto and ejected by a young star. The visible spectrometer VEGA on the CHARA array can be an efficient means of probing the structure and the kinematics of the hot circumstellar gas at sub-AU. For the first time, we observed the Herbig Ae star AB Aur in the H$\\alpha$ emission line, using the VEGA low spectral resolution on two baselines of the array. We computed and calibrated the spectral visibilities between 610 nm and 700 nm. To simultaneously reproduce the line profile and the visibility, we used a 1-D radiative transfer code that calculates level populations for hydrogen atoms in a spherical geometry and synthetic spectro-interferometric observables. We clearly resolved AB Aur in the H$\\alpha$ line and in a part of the continuum, even at the smallest baseline of 34 m. The small P-Cygni absorption feature is indicative of an outflow but could not be explained by a spherical stellar wind model. Instead, it f... Perraut, K; Mourard, D; Rajabi, S; Bacciotti, F; Bério, Ph; Bonneau, D; Chesneau, O; Clausse, J M; Delaa, O; Marcotto, A; Roussel, A; Spang, A; Stee, Ph; Tallon-Bosc, I; McAlister, H; Brummelaar, T ten; Sturmann, J; Sturmann, L; Turner, N; Farrington, C; Goldfinger, P J 2010-01-01 180 CERN Document Server The recently claimed observations of non-negligible amounts of 6Li in old halo stars have renewed interest in the Big-Bang Nucleosynthesis (BBN) of 6Li. One important ingredient in the predicted BBN abundance of 6Li is the low-energy 2H(alpha,gamma)6Li cross section. Up to now, the only available experimental result for this cross section showed an almost constant astrophysical S-factor below 400 keV, contrary to theoretical expectations. We report on a new measurement of the 2H(alpha,gamma)6Li reaction using the break-up of 6Li at 150 A MeV. Even though we cannot separate experimentally the Coulomb contribution from the nuclear one, we find clear evidence for Coulomb-nuclear interference by analyzing the scattering-angular distributions. This is in-line with our theoretical description which indicates a drop of the S_24-factor at low energies as predicted also by most other models. Consequently, we find even lower upper limits for the calculated primordial 6Li abundance than before. Hammache, F; Typel, S; Galaviz, D; Sümmerer, K; Coc, A; Uhlig, F; Attallah, F; Caamano, M; Cortina, D; Geissel, H; Hellström, M; Iwasa, N; Kiener, J; Koczon, P; Kohlmeyer, B; Mohr, P; Schwab, E; Schwarz, K; Schümann, F; Senger, P; Sorlin, O; Tatischeff, V; Thibaud, J P; Vangioni, E; Wagner, A; Walus, W 2010-01-01 181 International Nuclear Information System (INIS) In the context of intensity and resolution optimization of a neutron time-of-flight spectrometer several methods of beam width reduction at the chopper are considered aiming at a reduction of the neutron pulse width at minimum loss of intensity. The most advantageous technique discussed uses a double-trumpet arrangement in which the chopper is placed in between converging and diverging neutron guide sections. 7 refs., 1 fig 1989-01-01 182 Directory of Open Access Journals (Sweden) Full Text Available Introduction: Scatter radiation is one of the major sources of error in nuclear medicine data processing. Different methods of scatter correction have been introduced in order to improve the quality of data. However the best method is to avoid recording of scatter photons in acquisition. The only difference between scattered and non-scattered photons is the energy. Pulse height analyzer is the only option available to discriminate primary photons from scattered ones. Energy resolution of the gamma camera is gradually improving consequently the energy window width has to be decreased accordingly. In this study we tried to determine the most appropriate energy window width for present gamma camera systems. Methods and Materials: Since it is not possible to retrieve the data spectrum from the most of the gamma camera systems, a simple method was developed to extract the data from the image of the energy spectrum. Using a scatter phantom different level of scatter and count rate were generated and corresponding energy spectrum data were analyzed. It was assumed that around the peak of the spectrum, the primary photons obey a Gaussian distribution. Results: The data were analyzed using three different methods. All methods prove that the optimum window width regarding the present gamma camera energy resolution is 15%. At this level, the scattered radiation is decreased to 5%. In comparison to the conventional widow width of 20%, the sensitivity does not change dramatically. Conclusion: At the present, for most gamma camera, the energy window width of 20% is recommended. However occasionally energy window width of 15% and 25% are also used. In this study the energy spectrum at different levels of scatter were analyzed and the most suitable energy window width was found to be 15% for the gamma camera having approximate energy resolution of 11%. At this window setting the scatter decreases to 5% of the total counts recorded. Visually the quality of the images dose not improves significantly. However accuracy of data quantification improve significantly. Jabbari N; Rajabi H; Firouzabadi SH; Rastgoo F; Yaghoubi N; Bitarafan Rajabi A; Hashemi Malayeri B 2004-01-01 183 International Nuclear Information System (INIS) Introduction: scatter radiation is one of the major sources of error in nuclear medicine data processing. Different methods of scatter correction have been introduced in order to improve the quality of data. However the best method is to avoid recording of scatter photons in acquisition. The only difference between scattered and non-scattered photon is the energy. Pulse height analyzer is the only option available to discriminate primary photons from scattered ones. Energy resolutions of the gamma camera is gradually improving consequently the energy window width has to be decreased accordingly. In this study we tried to determine the most appropriate energy window width for present gamma camera systems. Methods and materials: since it is not possible to retrieve the data spectrum from the most of the gamma camera systems a simple method was developed to extract the data from the image of the energy spectrum. Using a scattered phantom different level of scatter and count rate were generated and corresponding energy spectrum data were analyzed. It was assumed that around the peak of the spectrum the primary photons obey a Gaussian distribution. Results: the data were analyzed using three different methods. All methods proved that the optimum window width regarding the present gamma camera energy resolution is 15%. At this level the scattered radiation is decreased to 5%. In comparison to the conventional window width of 20% the sensitivity does not change dramatically. Conclusion: at the present, for the most gamma camera the energy window width of 20% is recommended. However occasionally energy window width of 15 % and 25% are also used. In this study the energy spectrum at different levels of scatter were analyzed and the most suitable energy window width was found to be 15% for the gamma camera having approximate energy resolution of 11%. At this window setting the scatter decreases to 5% of the total counts recorded. Visually the quality of images does not improves significantly. However accuracy of data quantification improve significantly. 2004-01-01 184 International Nuclear Information System (INIS) According to definitions of the new operational radiation quantities for environmental (area) monitoring recommended by the International Commission of Radiation Units and Measurements (ICRU) report 39, a spherical ambient dose equivalent meter and a parallel-plane directional dose equivalent meter were designed and developed. Experimental measurements for main performances and calibrations for response factors were made. 1991-01-01 185 Science.gov (United States) Along the Dutch coastline, sand dunes form a natural defence against the sea. Together with the size of the beach, dune dimensions determine whether coastal safety requirements are met. Dunes grow via onshore transport of sediment by wind and erode mainly through the impact of sea waves during storms. Previous studies show that both dune growth and erosion are influenced by beach dimensions. A wide beach (500 m) is expected to provide more sediment for onshore transport and to dissipate more wave energy than a narrow beach (50 m). Hence, all other factors being equal, dune growth is likely to be higher on wide beaches than on narrow beaches. This study quantifies the relation between dune behaviour and beach width. Results will be used to improve and test predictive modelling of shoreline development. The combined effect of beach dimensions on dune behaviour was studied by comparing changes in dune volume at beaches of different widths. These volume changes represent the net effect of sediment accumulation and sediment loss of the dune. Yearly elevation measurements of 200 locations along the Dutch coastline were used, taken between 1960 and 2010. From these elevation measurements, beach width and yearly changes in dune volume were derived. Subsequently, measurements were grouped in beach width classes, each containing 100 paired observations of dune volume change and beach width. For these classes, the average and variability of volume changes were calculated. The results show a clear relation between beach width and dune behaviour. Going from narrow to wide beaches, average volume changes increase to a maximum. The beach width at which maximum growth is reached, differs per study area. For extremely wide beaches, average rates are lower. These cases are associated with development of transport inhibiting beach-topography. Inverse to the trend in volume changes, the variability of dune behaviour is highest on narrow beaches and decreases for wider beach classes. The positive relation between dune growth and beach width can be explained by both increased sediment input and reduced dune erosion at wider beaches. Further research is required to separate the effect of beach width on dune accretion from the effect on dune erosion. Keijsers, Joep; Poortinga, Ate; De Groot, Alma; Riksen, Michel 2013-04-01 186 Energy Technology Data Exchange (ETDEWEB) The manner in which isobaric multiplet decay widths are modified by electromagnetic interaction is studied. Arguments based on lowest-order perturbation theory are given that the widths should be quadratic in Tsub(z) if the multiplet is particle unstable in the absence of electromagnetism, but quartic for stable multiplets. The total widths of experimentally known multiplets are analyzed to determine their algebraic Tsub(z) dependence and both quadratic and non-quadratic cases are found. On the basis of a simple model of the Coulomb energy we then determine the masses of these multiplets in the absence of electromagnetism as well as the masses of the lowest T-allowed decay channels. We find the isobaric multiplet width equation to work in some cases while it has been found to be inconclusive in others; because of these uncertainties as to its correctness or range of applicability, we have constructed a soluble model in which tests may be carried out. To avoid difficulties such as the many-body problem, a non-local separable potential model simple enough to solve explicitly was chosen. Although the model is an oversimplification of the real nuclear situation it has been found to work very well. Namely, the quadratic quartic nature of the widths was borne out in the model. Awin, A.M. (Al-Fateh Univ., Tripoli (Libya). Dept. of Mathematics) 1982-09-20 187 DEFF Research Database (Denmark) A combination of wide-band electronic tunability and moderate free-running line width makes the Josephson flux flow oscillator (FFO) a perfect on-chip local oscillator for integrated submillimeter-wave SIS receivers. The possibility of FFO phase locking at all frequencies of interest has to be proven before one initiates real FFO applications. To achieve this goal a comprehensive set of line width measurements of the FFO operating in different regimes has been performed. FFOs with tapered shape have been successfully implemented in order to avoid the superfine resonant structure with voltage spacing of about 20 nV and extremely low differential resistance, recently observed in the IVC of the standard rectangular geometry. The obtained results have been compared with existing theories and FFO models in order to understand and possibly eliminate excess noise in the FFO. The intrinsic line width increases considerably at voltages above the boundary voltage because of the abrupt increase of the internal damping due to Josephson self-coupling. The influence of FFO parameters, in particular the differential resistances associated both with the bias current and with the applied magnetic field on the radiation line width, has been studied. Possible means of decreasing the free-running FFO line width will be discussed. Koshelets, V.P.; Dmitriev, P.N. 2002-01-01 188 CERN Multimedia Promising methods for studying galaxy evolution rely on optical emission line width measurements to compare intermediate-redshift objects to galaxies with equivalent masses at the present epoch. However, emission lines can be misleading. We show empirical examples of galaxies with concentrated central star formation from a survey of galaxies in pairs; HI observations of these galaxies indicate that the optical line emission fails to sample their full gravitational potentials. We use simple models of bulge-forming bursts of star formation to demonstrate that compact optical morphologies and small half-light radii can accompany these anomalously narrow emission lines; thus late-type bulges forming on rapid (0.5-1 Gyr) timescales at intermediate redshift would exhibit properties similar to those of heavily bursting dwarfs. We conclude that some of the luminous compact objects observed at intermediate and high redshift may be starbursts in the centers of massive galaxies and/or bulges in formation. Gillespie, E B; Gillespie, Elizabeth Barton; Zee, Liese van 2002-01-01 189 International Nuclear Information System (INIS) In this work we have proposed an improvement in the shape of the V-shaped microcantilever by varying the width profile. In this paper we have studied the variation of resonant frequency as a function of changes in profile determined by the length of the microcantilever, keeping constant the active area for binding. It is observed that for the optimized nonlinear profile the angle at the tip is 91.410, more than twice the angle at the tip of the linear profile cantilever. The variation of the equivalent spring constant with changes in the profile is also studied. It is proposed that the optimum nonlinear profile cantilever has a spring constant of ?0.39 ?N ?m-1. The resonant frequency is obtained by using the Rayleigh-Ritz method, the deflection model and the SUGAR simulator. The results are compared and an improvement in the performance of the cantilever is observed. 2009-09-21 190 Energy Technology Data Exchange (ETDEWEB) In this work we have proposed an improvement in the shape of the V-shaped microcantilever by varying the width profile. In this paper we have studied the variation of resonant frequency as a function of changes in profile determined by the length of the microcantilever, keeping constant the active area for binding. It is observed that for the optimized nonlinear profile the angle at the tip is 91.41{sup 0}, more than twice the angle at the tip of the linear profile cantilever. The variation of the equivalent spring constant with changes in the profile is also studied. It is proposed that the optimum nonlinear profile cantilever has a spring constant of {approx}0.39 {mu}N {mu}m{sup -1}. The resonant frequency is obtained by using the Rayleigh-Ritz method, the deflection model and the SUGAR simulator. The results are compared and an improvement in the performance of the cantilever is observed. Subramanian, S; Gupta, Navneet, E-mail: [email protected] [Electrical and Electronics Engineering Group, Birla Institute of Technology and Science, Pilani, Rajasthan (India) 2009-09-21 191 Science.gov (United States) In this work we have proposed an improvement in the shape of the V-shaped microcantilever by varying the width profile. In this paper we have studied the variation of resonant frequency as a function of changes in profile determined by the length of the microcantilever, keeping constant the active area for binding. It is observed that for the optimized nonlinear profile the angle at the tip is 91.41°, more than twice the angle at the tip of the linear profile cantilever. The variation of the equivalent spring constant with changes in the profile is also studied. It is proposed that the optimum nonlinear profile cantilever has a spring constant of ~0.39 µN µm-1. The resonant frequency is obtained by using the Rayleigh-Ritz method, the deflection model and the SUGAR simulator. The results are compared and an improvement in the performance of the cantilever is observed. Subramanian, S.; Gupta, Navneet 2009-09-01 192 CERN Document Server Motivated by evidence that the top quark mass lies near the bWZ threshold, we compute the decay rate for t\\rightarrow bWZ in the Standard Model, including the effects of the finite widths of the W and Z bosons. In the limit where the width effects are negligible, our results disagree with previously published calculations. We also examine the decay t\\rightarrow bWH. Although the widths induce a sizable enhancement near threshold for both decays, we find that the rates are still too small to be observed in the present generation of experiments. This means that detection of either mode in one of these experiments would be a signal of new physics. Mahlon, G; Mahlon, Gregory; Parke, Stephen 1994-01-01 193 Energy Technology Data Exchange (ETDEWEB) The advantages of a broader coke oven chamber are primarily the pushing of more coke per oven operation and the possibility of the selecting of an operation of 24 hours by high performance. At the experimental coke oven plant Prosper of the Bergbau-Forschung GmbH, the influence of the chamber width was studied in two ovens with widths of 450 and 600 mm. The correlation of the chamber width with the coking period is described by an exponential function whose exponent changes from 1.35 to 1.20 in the range of the applied heating flue temperatures of 1200 to 1400/sup 0/C. The production loss resulting from the nonlinearity can be compensated by a forced operation and due to the slightly higher bulk density of the coke formed. Rohde, W.; Habermehl, D.; Wuennenberg, W. 1982-09-01 194 CERN Document Server We determine constraints on the partial widths of mixed pentaquark multiplets in the framework of heavy baryon chiral perturbation theory (HB$\\chi$PT). The partial widths satisfy a GMO-type relation at leading order in HB$\\chi$PT, for arbitrary mixing. The widths of N(1440), N(1710), and $\\Theta(1540)$ are not consistent with ideal mixing, $\\theta_{N} = 35.3^{\\circ}$, but are consistent with $\\theta_{N} \\lesssim 25^{\\circ}$. Furthermore, there are parameter values in HB$\\chi$PT that produce such a mixing angle while allowing the identification of the mass spectrum above. As an alternative to non-ideal mixing, we also suggest reasons for giving up on N(1440) as a pure pentaquark state. Mohta, V 2004-01-01 195 CERN Document Server In this article we introduce a technique for finding resonance radii in a disk galaxy. We use a two-dimensional velocity field in H{\\alpha} emission obtained with Fabry-Perot interferometry, derive the classical rotation curve, and subtract it off, leaving a residual velocity map. As the streaming motions should reverse sign at corotation, we detect these reversals, and plot them in a histogram against galactocentric radius, excluding points where the amplitude of the reversal is smaller than the measurement uncertainty. The histograms show well-defined peaks which we assume to occur at resonance radii, identifying corotations as the most prominent peaks corresponding to the relevant morphological features of the galaxy (notably bars and spiral arm systems). We compare our results with published measurements on the same galaxies using other methods and different types of data. Font, Joan; Epinat, Benoît; Fathi, Kambiz; Gutiérrez, Leonel; Hernandez, Olivier 2011-01-01 196 UK PubMed Central (United Kingdom) We propose a strategy based on the combination of experimental NH(N)/C(alpha)H(alpha) dipole/dipole cross-correlated relaxation rates and chemical shift analysis for the determination of Psi torsion angles in proteins. The method allows the determination of a dihedral angle that is not easily accessible by nuclear magnetic resonance (NMR). The measurement of dihedral angle restraints can be used for structure calculation, which is known to improve the quality of NMR structures. The method is of particular interest in the case of large proteins, for which spectral assignment of the nuclear Overhauser effect spectra, and therefore straightforward structural determination, is out of reach. One advantage of the method is that it is reasonably simple to implement, and could be used in association with other methods aiming at obtaining structural information on complex systems, such as residual dipolar coupling measurements. An illustrative example is analyzed in the case of the 30-kDa protein 6-phosphogluconolactonase. Loth K; Abergel D; Pelupessy P; Delarue M; Lopes P; Ouazzani J; Duclert-Savatier N; Nilges M; Bodenhausen G; Stoven V 2006-09-01 197 International Nuclear Information System (INIS) An analysis of pulse width during a rod ejection accident was carried out to help in designing experiments to test fuel behaviour under reactivity initiated accident conditions. The analysis used calculations based on a three-dimensional neutron kinetics code, PARCS, and a model of a pressurized water reactor at both beginning and end of a fuel cycle. Results showed that pulse width varied inversely with the maximum increase in local fuel enthalpy and this is consistent with simple analytical models. The pulse width ranges from 25 to 100 ms for cases where the energy deposition goes from 30 to 10 cal/g. This is the range expected for the most likely REA for which the rod worth is just above prompt critical. It is the most likely REA since the probability of a particular rod worth decreases as one goes to higher rod worths above prompt-critical. The pulse width is 10-15 ms when the maximum increase in fuel enthalpy is in the range of 60-100 cal/g. It is at these enthalpies, or higher, where fuel failure might be expected. Hence, if tests are to be done to test the limits of a fuel pin, the pulse width in the tests should be in the range 10-15 ms. If the tests instead are done with pulse widths that are greater than 25 ms and fuel enthalpies that are in the range where failure is expected, e.g., 100 cal/g, there is an inconsistency 2003-04-30 198 CERN Multimedia We show that the contact process in an ensemble with conserved total particle number, as simulated recently by Tome and de Oliveira [Phys. Rev. Lett. 86 (2001) 5463], is equivalent to the ordinary contact process, in agreement with what the authors assumed and believed. Similar conserved ensembles and equivalence proofs are easily constructed for other models. Hilhorst, H J 2001-01-01 199 CERN Multimedia We introduce the notion of thermal entropy density, and first demonstrated that there exists an equivalence between therm and gravity without depending on the definition of temperature or horizon. This equivalence indicates that gravity possesses thermal features, or, therm possesses effects of gravity. This may shed light on the nature of gravity. Yang, Rong-Jia 2011-01-01 200 Digital Repository Infrastructure Vision for European Research (DRIVER) In view of the well known core equivalence results in atomless economies, coincidence of market game equilibrium allocations with competitive allocations is tantamount to a three way equivalence between market game mechanisms, competitive equilibria and the core. Based on this idea I propose an equi... Koutsougeras, Léonidas 201 CERN Document Server It has been conjectured that the geometric invariant of knots in 3-space called the width is nearly additive. That is, letting w(K) denote the width of a knot K in 3-space, the conjecture is that for all knots K and K', w(K # K') = w(K) + w(K') - 2. We give an example of a knot K so that for K' any 2-bridge knot, it appears that w(K # K') = w(K) contradicting the conjecture. Scharlemann, M; Scharlemann, Martin; Thompson, Abigail 2004-01-01 202 CERN Multimedia The general intractability of the constraint satisfaction problem has motivated the study of restrictions on this problem that permit polynomial-time solvability. One major line of work has focused on structural restrictions, which arise from restricting the interaction among constraint scopes. In this paper, we engage in a mathematical investigation of generalized hypertree width, a structural measure that has up to recently eluded study. We obtain a number of computational results, including a simple proof of the tractability of CSP instances having bounded generalized hypertree width. Chen, H; Chen, Hubie; Dalmau, Victor 2005-01-01 203 International Nuclear Information System (INIS) [en] A method for calculation of the partial-nucleon-escape widths of giant resonances is proposed. The method is exact within the random-phase approximation in the continuum. A phenomenological description of the giant-resonance coupling to many-particle configurations is also given. This approach is applied to evaluation of the partial-nucleon-escape widths of various giant resonances in 208Pb parent nucleus. Our results are compared with the results of other theoretical approaches and with the relevant experimental data. (orig.) 1994-05-23 204 Directory of Open Access Journals (Sweden) Full Text Available This paper describes the design and optimization of gate-all-around (GAA) MOSFETs structures. The optimum value of Fin width and Fin height are investigated for superior subthreshold behavior. Also the performance of Fin shaped GAA with gate oxide HfO2 are simulated and compared with conventional gate oxide SiO2 for the same structure. As a result, it was observed that the GAA with high K dielectric gate oxide has more possibility to optimize the Fin width with improved performance. All the simulations are performed on 3-D TCAD device simulator. S.L.Tripathi; Ramanuj Mishra; R.A.Mishra 2012-01-01 205 CERN Multimedia We compute the difference in decay widths of charged and neutral \\rho(770) vector mesons. The isospin breaking arising from mass differences of neutral and charged \\pi and \\rho mesons, radiative corrections to \\rho -> \\pi\\pi, and the \\rho -> \\pi\\pi\\gamma decays are taken into account. It is found that the width difference \\Delta \\Gamma_rho is very sensitive ot the isospin breaking in the $\\rho$ meson mass \\Delta m_\\rho. This result can be useful to test the correlations observed between the values of these parameters extracted from experimental data. Flores-Baez, F V; Sanchez, G Toledo 2007-01-01 206 UK PubMed Central (United Kingdom) We study the change in the diphoton-invariant-mass distribution for Higgs boson decays to two photons, due to interference between the Higgs resonance in gluon fusion and the continuum background amplitude for gg???. Previously, the apparent Higgs mass was found to shift by around 100 MeV in the standard model in the leading-order approximation, which may potentially be experimentally observable. We compute the next-to-leading-order QCD corrections to the apparent mass shift, which reduce it by about 40%. The apparent mass shift may provide a way to measure, or at least bound, the Higgs boson width at the Large Hadron Collider through "interferometry." We investigate how the shift depends on the Higgs width, in a model that maintains constant Higgs boson signal yields. At Higgs widths above 30 MeV, the mass shift is over 200 MeV and increases with the square root of the width. The apparent mass shift could be measured by comparing with the ZZ^{} channel, where the shift is much smaller. It might be possible to measure the shift more accurately by exploiting its strong dependence on the Higgs transverse momentum. Dixon LJ; Li Y 2013-09-01 207 Energy Technology Data Exchange (ETDEWEB) This paper discusses resonances of narrow width in the context of bound states embedded in the continuum spectrum of nonlocal potentials. Feshbach's theory of nuclear reactions leads directly to resonance theory, and we base our discussion here on the techniques he developed for shifting nuclear many-body aspects into effective single-particle nonlocal potentials. In our formulation, the many-body state of the compound nucleus is represented by a single-particle state. The basis for our discussion is a two channel model of a resonance of zero width, with a continuum bound state originating from the coupling of a bound state to the single-particle scattering state. We give a specific example of a model which leads to an arbitrarily narrow (nonzero width) resonance, and demonstrate that the width of the resonance produced by breaking the continuum bound state is proportional to (..lambda..-1)/sup 2/, where the parameter ..lambda.. is such that ..lambda.. = 1 corresponds to the condition necessary for the existence of a continuum bound state. Bagchi, B.; Mulligan, B.; Seyler, R.G. 1982-07-01 208 Science.gov (United States) We study the change in the diphoton-invariant-mass distribution for Higgs boson decays to two photons, due to interference between the Higgs resonance in gluon fusion and the continuum background amplitude for gg???. Previously, the apparent Higgs mass was found to shift by around 100 MeV in the standard model in the leading-order approximation, which may potentially be experimentally observable. We compute the next-to-leading-order QCD corrections to the apparent mass shift, which reduce it by about 40%. The apparent mass shift may provide a way to measure, or at least bound, the Higgs boson width at the Large Hadron Collider through “interferometry.” We investigate how the shift depends on the Higgs width, in a model that maintains constant Higgs boson signal yields. At Higgs widths above 30 MeV, the mass shift is over 200 MeV and increases with the square root of the width. The apparent mass shift could be measured by comparing with the ZZ* channel, where the shift is much smaller. It might be possible to measure the shift more accurately by exploiting its strong dependence on the Higgs transverse momentum. Dixon, Lance J.; Li, Ye 2013-09-01 209 CERN Multimedia We prove that for any fixed r>=2, the tree-width of graphs not containing K_r as a topological minor (resp. as a subgraph) is bounded by a linear (resp. polynomial) function of their rank-width. We also present refinements of our bounds for other graph classes such as K_r-minor free graphs and graphs of bounded genus. Fomin, Fedor V; Thilikos, Dimitrios M 2009-01-01 210 Directory of Open Access Journals (Sweden) Full Text Available Esthetics is one of the prosthetic treatment goals. Correct selection of anterior teeth, regarding size and appearance, results in a successful treatment. The goal of the present research was to investigate the relationship between interzygomatic width and maxillary anterior teeth width in order to find a better determinant for artificial anterior teeth selection. In this study, the interzygomatic width and maxillary central incisors width and also the width of six maxillary anterior- teeth, in 71 subjects (29females and 42 males) were measured. The results showed a significant difference in maxillary anterior teeth width, comparing men and women, (P<0.05). These measurement in people under study, are less than Europeans. The interzygomatic width was also more in men than women (PO.05), which is, less than of European race. The ratio between interzygomatic and central maxillary incisor width was 15:1 which is less than 16:1 that is used in clinic. Thus, it is recommended to pay more attention to anterior teeth selection, especially in young patients. 2002-01-01 211 Energy Technology Data Exchange (ETDEWEB) Data and systematics on the natural line width, the escape width, and the spreading width of ground state isobaric analog states are presented. The relation between isospin impurity and spreading width, and between escape width and neutron spectroscopic factors is discussed. The neutron decay, possible only through isospin breaking, was measured directly and is found to have a mostly statistical spectral shape. Vanderwerf, S.Y. 1991-01-01 212 CERN Multimedia We construct Quillen equivalences between the model categories of monoids (rings), modules and algebras over two Quillen equivalent model categories under certain conditions. This is a continuation of our earlier work in "Algebras and modules in monoidal model categories" where we established model categories of monoids, modules and algebras. As an application we extend the Dold-Kan equivalence to show that the model categories of simplicial rings, modules and algebras are Quillen equivalent to the associated model categories of connected differential graded rings, modules and algebras. We also show that our classification results in "Stable model categories are categories of modules" translate to any one of the known symmetric monoidal model categories of spectra. Schwede, S; Schwede, Stefan; Shipley, Brooke 2002-01-01 213 Directory of Open Access Journals (Sweden) Full Text Available Human skin not only serves as an important barrier against the penetration of exogenous substances into the body, but also provides a potential avenue for the transport of functional active drugs/reagents/ingredients into the skin (topical delivery) and/or the body (transdermal delivery). In the past three decades, research and development in human skin equivalents have advanced in parallel with those in tissue engineering and regenerative medicine. The human skin equivalents are used commercially as clinical skin substitutes and as models for permeation and toxicity screening. Several academic laboratories have developed their own human skin equivalent models and applied these models for studying skin permeation, corrosivity and irritation, compound toxicity, biochemistry, metabolism and cellular pharmacology. Various aspects of the state of the art of human skin equivalents are reviewed and discussed. Zheng Zhang; Bozena B. Michniak-Kohn 2012-01-01 214 Energy Technology Data Exchange (ETDEWEB) It is shown that the local expression for the electrostatic potential of a point charge suggested from the equivalence principle is different from the one resulting from the global consideration in the Schwarzschild space-time. Leaute, B.; Linet, B. (Paris-6 Univ., 75 (France). Inst. Henri Poincare) 1983-01-01 215 UK PubMed Central (United Kingdom) Dimension schemas are abstract models of the data hierarchiesthat populate OLAP warehouses. Although there is abundant workon schema equivalence in a variety of data models, these works do notcover dimension schemas. In this paper we propose a notion of equivalencethat allows to compare dimension schemas with respect to theirinformation capacity. The proposed notion is intended to capture dimensionschema equivalence in the context of OLAP schema restructuring. 216 Energy Technology Data Exchange (ETDEWEB) An examination is made of the connection between the equivalence principle of general relativity and the non-Euclidean properties of space. The arguments commonly advanced to suggest a necessary connection between these two features of general relativity are reviewed and critically discussed. It is shown that although gravitational time dilation is an immediate consequence of the equivalence principle the corresponding effects on space are not such immediate or logically necessary consequences of this principle. Dugdale, D.E. (Keele Univ. (UK)) 1981-01-01 217 CERN Document Server Let N_1 (resp.N_2) be a nest A (resp. B) be the corresponding nest algebra, A_0 (resp. B_0) be the subalgebra of compact operators. We prove that the nests N_1, N_2 are isomorphic if and only if the algebras A, B are weakly-* Morita equivalent if and only if the algebras A_0, B_0 are strongly Morita equivalent. We characterize the nest isomorphisms which implement stable isomorphism between the corresponding nest algebras. Eleftherakis, G K 2010-01-01 218 International Nuclear Information System (INIS) [en] We calculate decays of a standard model Higgs boson via a virtual massive particle and discuss how this depends on the massive particle total width. If the partial width for a Higgs boson to decay via a virtual massive particle can be measured, this gives a measurement of that massive particle close-quote s width. We discuss how one would go about measuring these partial widths of a Higgs boson experimentally, and how this could lead to a measurement of the W boson and t quark widths. For the latter, extreme dependence on the Higgs boson mass and the small H?tt* branching ratios mean that little can be learned about the t quark width. For the former there is also a larger dependence on the Higgs boson mass; however, this can be removed by taking the ratio of H?WW* decays to H?ZZ* decays. This ratio also has the advantage of being fairly insensitive to physics beyond the standard model. Unfortunately, for Higgs boson masses of interest the H?ZZ* branching ratio is small enough that we require many thousands of tagged Higgs boson decays before an accurate measurement of the W width can be made. This is likely to be hard experimentally. copyright 1996 The American Physical Society 1996-01-01 219 CERN Multimedia We present predictions based on the heavy quark expansion in QCD. We find SU(3) breaking in B mesons suppressed in the framework of the HQE. B_s is expected to have the semileptonic width about 1% lower and Lambda_b about 3% higher when compared to Gamma_{sl}(B_d). The largest partial-rate preasymptotic effect is Pauli interference in the b-->u ell nu channel in Lambda_b, about +10%. We point out that the Omega_b semileptonic width is expected not to exceed that of B_d and may turn out to be the smallest among stable b hadrons despite the large mass. The underlying differences with phase-space models are briefly addressed through the heavy mass expansion. Bigi, I I; Uraltsev, N 2011-01-01 220 CERN Document Server By a closer inspection of the massive Schwinger model within mass perturbation theory we find that, in addition to the $n$-boson bound states, a further type of hybrid bound states has to be included into the model. Further we explicitly compute the decay widths of the three-boson bound state and of the lightest hybrid bound state. By a closer inspection of the massive Schwinger model within mass perturbation theory we find that, in addition to the $n$-boson bound states, a further type of hybrid bound states has to be included into the model. Further we explicitly compute the decay widths of the three-boson bound state and of the lightest hybrid bound state. 1997-01-01 221 Energy Technology Data Exchange (ETDEWEB) The reciprocating Langmuir probe on ASDEX is located in the upper outer divertor and is capable of delivering a maximum of four radial profiles of plasma parameters during a discharge. The power flux profiles allow a direct evaluation of the effective power channel width which apart from offering a direct estimate of target plate power loading, it is also fundamental in understanding SOL transport processes. The evolution of power flux profiles and systematic trends of the corresponding widths for ohmically and NI heated discharges are presented for parametric scans in n{sub e}, I{sub p}, B{sub t} and injected neutral power. Langmuir probe data are compared and correlated with data from the Lithium beam probe which delivers density profiles in the outer midplane and the YAG Thomson scattering system which yields density and temperature near the separatrix at the lower plasma. (author) 6 refs., 4 figs. Kyriakakis, G.; Kakoulidis, E.; Tsois, N. [National Research Centre for the Physical Sciences Democritos, Athens (Greece); McCormick, K.; Neuhauser, J. [Max-Planck-Institut fuer Plasmaphysik, Garching (Germany) 1992-12-31 222 CERN Document Server We prove that, for each nonnegative integer k and each matroid N, if M is a 3-connected matroid containing N as a minor, and the the branch width of M is sufficiently large, then there is a k-element subset X of E(M) such that one of M\\X and M/X is 3-connected and contains N as a minor. Geelen, Jim 2011-01-01 223 Energy Technology Data Exchange (ETDEWEB) Particle-hole partial decay widths are calculated within the continuum RPA exactly, i.e. without any further approximation, in a square well plus Coulomb potential and using a separable residual interaction. The results are compared with the ones obtained by making pole expansions of the single-particle Green functions (Berggren and Mittag-Leffler). It is found that the Berggren and Mittag-Leffler expansions give results in good agreement with the 'exact' ones. (orig.). Vertse, T. (Inst. of Nuclear Research, Hungarian Academy of Sciences, Debrecen (Hungary)); Curutchet, P.; Liotta, R.J. (Manne Siegbahn Inst. of Physics, Stockholm (Sweden)); Bang, J. (Niels Bohr Inst., Copenhagen (Denmark)); Giai, N. van (Inst. de Physique Nucleaire, 91 - Orsay (France)) 1991-07-25 224 International Nuclear Information System (INIS) [en] Particle-hole partial decay widths are calculated within the continuum RPA exactly, i.e. without any further approximation, in a square well plus Coulomb potential and using a separable residual interaction. The results are compared with the ones obtained by making pole expansions of the single-particle Green functions (Berggren and Mittag-Leffler). It is found that the Berggren and Mittag-Leffler expansions give results in good agreement with the 'exact' ones. (orig.) 1991-07-25 225 Directory of Open Access Journals (Sweden) Full Text Available Dentistry of modern era is dominated by restorative procedures which are carried out to meet the demands of not only function but also esthetics. The dentist is having a narrow room of flexibility to wander in order to achieve a good esthetic restoration which is fully functional, the design of preparation and the technique sensitive fabrication form one side of the coin and establishing a harmonious margin for a crown on abutment forms the other side of the coin when trying to insert a fixed prosthetic restoration for replacing missing teeth, the phenomenon of biologic width was less understood till very recently but the growing clinical experience and better diagnostic skills of today has helped us to understand the intricacies of this concept and the need for its maintenance, the violation of which leads to the ultimate failure of the prosthesis. This article attempts to explain the ways of diagnosing biologic width violation, the care needed to exert when preparing a teeth to receive a crown and exactly deciding where to place the margins of the crown to avoid biologic width violation Hari Krishna Reddy S; Chetan Kumar S 2010-01-01 226 CERN Document Server Several different measures for digraph width have appeared in the last few years. However, none of them shares all the "nice" properties of treewidth: First, being \\emph{algorithmically useful} i.e. admitting polynomial-time algorithms for all $\\MS1$-definable problems on digraphs of bounded width. And, second, having nice \\emph{structural properties} i.e. being monotone under taking subdigraphs and some form of arc contractions. As for the former, (undirected) $\\MS1$ seems to be the least common denominator of all reasonably expressive logical languages on digraphs that can speak about the edge/arc relation on the vertex set.The latter property is a necessary condition for a width measure to be characterizable by some version of the cops-and-robber game characterizing the ordinary treewidth. Our main result is that \\emph{any reasonable} algorithmically useful and structurally nice digraph measure cannot be substantially different from the treewidth of the underlying undirected graph. Moreover, we introduce \\... Ganian, Robert; Kneis, Joachim; Meister, Daniel; Obdržálek, Jan; Rossmanith, Peter; Sikdar, Somnath 2010-01-01 227 International Nuclear Information System (INIS) Fundamental properties of unstable particles, including mass, width, and partial widths, are examined on the basis of the Nielsen identities (NI) that describe the gauge dependence of Green functions. In particular, we prove that the pole residues and associated definitions of branching ratios and partial widths are gauge independent to all orders. A simpler, previously discussed definition of branching ratios and partial widths is found to be gauge independent through next-to-next-to-leading order. It is then explained how it may be modified in order to extend the gauge independence to all orders. We also show that the physical scattering amplitude is the most general combination of self-energy, vertex, and box contributions that is gauge independent for arbitrary s, discuss the analytical properties of the NI functions, and exhibit explicitly their one-loop expressions in the Z-? sector of the standard model. 2002-04-15 228 Digital Repository Infrastructure Vision for European Research (DRIVER) 1. The binding of [3H]-alpha beta meATP, [35s]-ATP gamma S and [alpha 33P]-ATP to a human bladder P2X purinoceptor, transiently expressed in CHO-K1 cells using the Semliki Forest Virus (SFV) expression system, was examined. The characteristics of the binding sites were compared with results obtained... Michel, A. D.; Lundström, K.; Buell, G. N.; Surprenant, A.; Valera, S.; Humphrey, P. P. 229 CERN Multimedia We present observations of the nearby barred starburst galaxy, M83 (NGC5236), with the new Fabry-Perot interferometer GHAFAS mounted on the 4.2 meter William Herschel Telescope on La Palma. The unprecedented high resolution observations, of 16 pc/FWHM, of the H-alpha-emitting gas cover the central two kpc of the galaxy. The velocity field displays the dominant disk rotation with signatures of gas inflow from kpc scales down to the nuclear regions. At the inner Inner Lindblad Resonance radius of the main bar and centerd at the dynamical center of the main galaxy disk, a nuclear $5.5 (\\pm 0.9) \\times 10^8 M_\\odot$ rapidly rotating disk with scale length of $60 \\pm 20$ pc has formed. The nuclear starburst is found in the vicinity as well as inside this nuclear disk, and our observations confirm that gas spirals in from the outer parts to feed the nuclear starburst, giving rise to several star formation events at different epochs, within the central 100 pc radius of M83. Fathi, Kambiz; Lundgren, Andreas A; Carignan, Claude; Hernandez, Olivier; Amram, Philippe; Balard, Philippe; Boulesteix, Jacques; Gach, Jean-Luc; Knapen, Johan H; Relaño, Monica 2007-01-01 230 CERN Multimedia We describe a search for H-alpha emission-lined stars in M31, M33, and seven dwarfs in or near the Local Group (IC 10, NGC 6822, WLM, Sextans B, Sextans A, Pegasus and the Phoenix dwarf) using interference filter imaging with the KPNO and CTIO 4-m telescope and Mosaic cameras. The survey is aimed primarily at identifying new Luminous Blue Variables (LBVs) from their spectroscopic similarity to known LBVs, avoiding the bias towards photometric variability, which may require centuries to manifest itself if LBVs go through long quiescent periods. Followup spectroscopy with WIYN confirms that our survey detected a wealth of stars whose spectra are similar to the known LBVs. We "classify" the spectra of known LBVs, and compare these to the spectra of the new LBV candidates. We demonstrate spectacular spectral variability for several of the new LBV candidates, such as AM2, previously classified as a Wolf-Rayet star, which now shows FeI, FeII and Balmer emission lines but neither the NIII 4634,42 nor HeII 4686 emiss... Massey, Philip; Olsen, K A G; Hodge, Paul W; Blaha, Cynthia; Jacoby, George H; Smith, R C; Strong, Shay B 2007-01-01 231 Science.gov (United States) We propose a strategy based on the combination of experimental NH(N)/C(alpha)H(alpha) dipole/dipole cross-correlated relaxation rates and chemical shift analysis for the determination of Psi torsion angles in proteins. The method allows the determination of a dihedral angle that is not easily accessible by nuclear magnetic resonance (NMR). The measurement of dihedral angle restraints can be used for structure calculation, which is known to improve the quality of NMR structures. The method is of particular interest in the case of large proteins, for which spectral assignment of the nuclear Overhauser effect spectra, and therefore straightforward structural determination, is out of reach. One advantage of the method is that it is reasonably simple to implement, and could be used in association with other methods aiming at obtaining structural information on complex systems, such as residual dipolar coupling measurements. An illustrative example is analyzed in the case of the 30-kDa protein 6-phosphogluconolactonase. PMID:16786593 Loth, Karine; Abergel, Daniel; Pelupessy, Philippe; Delarue, Marc; Lopes, Philippe; Ouazzani, Jamal; Duclert-Savatier, Nathalie; Nilges, Michael; Bodenhausen, Geoffrey; Stoven, Véronique 2006-09-01 232 CERN Document Server We use a sample of 90 spectroscopically-confirmed Lyman Break Galaxies with H-alpha and 24 micron observations to constrain the relationship between rest-frame 8 micron luminosity, L(8), and star formation rate (SFR) for L* galaxies at z~2. We find a tight correlation with 0.24 dex scatter between L8 and L(Ha)/SFR for z~2 galaxies with L(IR)~10^10 - 10^12 Lsun. Employing this relationship with a larger sample of 392 galaxies with spectroscopic redshifts, we find that the UV slope can be used to recover the dust attenuation of the vast majority of L* galaxies at z~2 to within 0.4 dex scatter using the local correlation. Separately, young galaxies with ages <100 Myr appear to follow an extinction curve that is steeper than the one found for local starburst galaxies. Therefore, such young galaxies may be significantly less dusty than inferred previously. Our results provide the first direct evidence, independent of the UV slope, for a correlation between UV and bolometric luminosity at high redshift, in the s... Reddy, Naveen A; Pettini, Max; Steidel, Charles C; Shapley, Alice E 2010-01-01 233 Directory of Open Access Journals (Sweden) Full Text Available This paper aims at highlighting the fact that “equivalence” represents a concept worth revisiting and detailing upon when tackling the translation process of economic texts both from English into Romanian and from Romanian into English. Far from being exhaustive, our analysis will focus upon the problems arising from the lack of equivalence at the word level. Consequently, relevant examples from the economic field will be provided to account for the following types of non-equivalence at word level: culturespecific concepts; the source language concept is not lexicalised in the target language; the source language word is semantically complex; differences in physical and interpersonal perspective; differences in expressive meaning; differences in form; differences in frequency and purpose of using specific forms and the use of loan words in the source text. Likewise, we shall illustrate a number of translation strategies necessary to deal with the afore-mentioned cases of non-equivalence: translation by a more general word (superordinate); translation by a more neutral/less expressive word; translation by cultural substitution; translation using a loan word or loan word plus explanation; translation by paraphrase using a related word; translation by paraphrase using unrelated words; translation by omission and translation by illustration. Cristina, Chifane 2012-01-01 234 International Nuclear Information System (INIS) [en] Potentials providing the same complex phase shifts as a given complex potential but with a shallower real part are constructed with supersymmetric transformations. Successive transformations eliminate normalizable solutions corresponding to complex eigenvalues of the Schroedinger equation with the full complex potential. Two numerical techniques, finite differences and Lagrange meshes, are applied to the determination of these normalizable solutions. With respect to real potentials, a new feature is the occurrence of normalizable solutions with complex energies presenting a positive real part. Such solutions can be removed but may lead to complicated equivalent potentials with little physical interest. The derivation of equivalent potentials is tested on complex Poeschl-Teller potentials for which analytical solutions are available. As a physical application, a deep optical potential for the ?+16O scattering is transformed into an l-dependent equivalent shallow optical potential. (orig.) 1996-03-25 235 UK PubMed Central (United Kingdom) One important study objective in drug stability studies is to estimate the shelf-life of a drug. A key statistical problem involved in this is how to assess the practical equivalence of different batches of the same drug so that different batches can be subgrouped to produce a single shelf-life for the drug. In this paper constant-width simultaneous confidence bands are proposed to quantify the magnitude of difference between different batches, with a particular view to establish the practical equivalence of different batches. This approach is suitable for the situation that the intercepts and slopes of the regression lines for the batches cannot be assumed to be equal. It is shown how constant-width simultaneous confidence bands can be easily constructed for the multiple comparison of several general linear regression models. In particular, it is shown that constant-width simultaneous confidence bands have a better chance to establish the equivalence than, and so are preferable to, the hyperbola-shaped simultaneous confidence bands considered. Liu W; Jamshidian M; Zhang Y; Bretz F; Han XL 2007-06-01 236 Science.gov (United States) One important study objective in drug stability studies is to estimate the shelf-life of a drug. A key statistical problem involved in this is how to assess the practical equivalence of different batches of the same drug so that different batches can be subgrouped to produce a single shelf-life for the drug. In this paper constant-width simultaneous confidence bands are proposed to quantify the magnitude of difference between different batches, with a particular view to establish the practical equivalence of different batches. This approach is suitable for the situation that the intercepts and slopes of the regression lines for the batches cannot be assumed to be equal. It is shown how constant-width simultaneous confidence bands can be easily constructed for the multiple comparison of several general linear regression models. In particular, it is shown that constant-width simultaneous confidence bands have a better chance to establish the equivalence than, and so are preferable to, the hyperbola-shaped simultaneous confidence bands considered. PMID:17133619 Liu, W; Jamshidian, M; Zhang, Y; Bretz, F; Han, X L 2007-06-30 237 International Nuclear Information System (INIS) The width of the charge distribution (for a fixed mass split) observed in nuclear fission can be estimated by assuming that it is associated with fluctuations in the collective coordinate corresponding to the flow of neutrons and protons back and forth through the neck connecting the nascent fragments. The possibility that different dynamical trajectories (one-body and viscous damping) can be distinguished is investigated for fission of 236U. It is found that, although the predicted charge dispersion is quite close to the observed value, the curves for the two trajectories are so close that a choice between the trajectories cannot be made. 2 figures 1981-01-01 238 CERN Multimedia In the present paper, we reduce and enhance the scaled Gaussian width(SGW) by 30% from the normal SGW of the systems and see its effect on balance energy. The scaled Gaussian width can be defined as the ratio of Gaussian width used for any nuclei to the Gaussian width used for Au nuclei(i.e. 8.66 $fm^2$). Rajni, 2011-01-01 239 Energy Technology Data Exchange (ETDEWEB) An inverter is connected between a source of DC power and a three-phase AC induction motor, and a microprocessor-based circuit controls the inverter using pulse width modulation techniques. In the disclosed method of pulse width modulation, both edges of each pulse of a carrier pulse train are equally modulated by a time proportional to sin .theta., where .theta. is the angular displacement of the pulse center at the motor stator frequency from a fixed reference point on the carrier waveform. The carrier waveform frequency is a multiple of the motor stator frequency. The modulated pulse train is then applied to each of the motor phase inputs with respective phase shifts of 120.degree. at the stator frequency. Switching control commands for electronic switches in the inverter are stored in a random access memory (RAM) and the locations of the RAM are successively read out in a cyclic manner, each bit of a given RAM location controlling a respective phase input of the motor. The DC power source preferably comprises rechargeable batteries and all but one of the electronic switches in the inverter can be disabled, the remaining electronic switch being part of a "flyback" DC-DC converter circuit for recharging the battery. Slicker, James M. (Union Lake, MI) 1985-01-01 240 CERN Document Server In this paper we go deep into the connection between duality and fields redefinition for general bilinear models involving the 1-form gauge field $A$. A duality operator is fixed based on "gauge embedding" procedure. Dual models are shown to fit in equivalence classes of models with same fields redefinitions. Gomes, M A M 2005-01-01 241 Energy Technology Data Exchange (ETDEWEB) In this paper we go deep into the connection between duality and fields redefinition for general bilinear models involving the 1-form gauge field A. A duality operator is fixed based on a 'gauge embedding' procedure. Dual models are shown to fit in equivalence classes of models with the same fields re-definitions. (authors) Gomes, M.A.M.; Landim, R.R. [Universidade Federal do Ceara, Dept. de Fisica, Ceara (Brazil) 2005-06-01 242 CERN Multimedia In this paper we consider the construction of optimal tests of equivalence hypotheses. Specifically, assume X_1,..., X_n are i.i.d. with distribution P_{\\theta}, with \\theta \\in R^k. Let g(\\theta) be some real-valued parameter of interest. The null hypothesis asserts g(\\theta)\ Romano, J P 2005-01-01 243 CERN Document Server This note elaborates on Th. Voronov's construction [math/0304038,math/0412202] of $L_\\infty$-structures via higher derived brackets with a Maurer-Cartan element. It is shown that gauge equivalent Maurer-Cartan elements induce $L_\\infty$-isomorphic structures. Applications in symplectic, Poisson and Dirac geometry are discussed. Cattaneo, Alberto S 2007-01-01 244 Science.gov (United States) Under fairly general conditions, a nonlinear fractional program, where the function to be maximized has the form f(x)/g(x), is shown to be equivalent to a nonlinear program not involving fractions. The latter program is not generally a convex program, but... B. D. Craven B. Mond 1975-01-01 245 CERN Multimedia We construct pairs of compact K\\"ahler-Einstein manifolds $(M_i,g_i,\\omega_i)$ ($i=1,2)$ of complex dimension $n$ with the following properties: The canonical line bundle $L_i=\\bigwedge^n T^M_i$ has Chern class $[\\omega_i/2\\pi]$, and for each integer $k$ the tensor powers $L_1^{\\otimes k}$ and $L_2^{\\otimes k}$ are isospectral for the bundle Laplacian associated with the canonical connection, while $M_1$ and $M_2$ -- and hence $T^M_1$ and $T^M_2$ -- are not homeomorphic. In the context of geometric quantization, we interpret these examples as magnetic fields which are quantum equivalent but not classically equivalent. Moreover, we construct many examples of line bundles $L$, pairs of potentials $Q_1$, $Q_2$ on the base manifold, and pairs of connections $\ Gordon, Carolyn; Schueth, Dorothee; Webb, David 2010-01-01 246 Science.gov (United States) We present a direct measurement of the width of the W boson using the shape of the transverse mass distribution of W --> enu candidate events. Data from approximately 1 fb(-1) of integrated luminosity recorded at square root of s = 1.96 TeV by the D0 detector at the Fermilab Tevatron pp collider are analyzed. We use the same methods and data sample that were used for our recently published W boson mass measurement, except for the modeling of the recoil, which is done with a new method based on a recoil library. Our result, 2.028 +/- 0.072 GeV, is in agreement with the predictions of the standard model. PMID:20366142 Abazov, V M; Abbott, B; Abolins, M; Acharya, B S; Adams, M; Adams, T; Aguilo, E; Ahsan, M; Alexeev, G D; Alkhazov, G; Alton, A; Alverson, G; Alves, G A; Ancu, L S; Andeen, T; Anzelc, M S; Aoki, M; Arnoud, Y; Arov, M; Arthaud, M; Askew, A; Asman, B; Atramentov, O; Avila, C; BackusMayes, J; Badaud, F; Bagby, L; Baldin, B; Bandurin, D V; Banerjee, S; Barberis, E; Barfuss, A-F; Bargassa, P; Baringer, P; Barreto, J; Bartlett, J F; Bassler, U; Bauer, D; Beale, S; Bean, A; Begalli, M; Begel, M; Belanger-Champagne, C; Bellantoni, L; Benitez, J A; Beri, S B; Bernardi, G; Bernhard, R; Bertram, I; Besançon, M; Beuselinck, R; Bezzubov, V A; Bhat, P C; Bhatnagar, V; Blazey, G; Blessing, S; Bloom, K; Boehnlein, A; Boline, D; Bolton, T A; Boos, E E; Borissov, G; Bose, T; Brandt, A; Brock, R; Brooijmans, G; Bross, A; Brown, D; Bu, X B; Buchholz, D; Buehler, M; Buescher, V; Bunichev, V; Burdin, S; Burnett, T H; Buszello, C P; Calfayan, P; Calpas, B; Calvet, S; Cammin, J; Carrasco-Lizarraga, M A; Carrera, E; Carvalho, W; Casey, B C K; Castilla-Valdez, H; Chakrabarti, S; Chakraborty, D; Chan, K M; Chandra, A; Cheu, E; Cho, D K; Cho, S W; Choi, S; Choudhary, B; Christoudias, T; Cihangir, S; Claes, D; Clutter, J; Cooke, M; Cooper, W E; Corcoran, M; Couderc, F; Cousinou, M-C; Cutts, D; Cwiok, M; Das, A; Davies, G; De, K; de Jong, S J; De La Cruz-Burelo, E; DeVaughan, K; Déliot, F; Demarteau, M; Demina, R; Denisov, D; Denisov, S P; Desai, S; Diehl, H T; Diesburg, M; Dominguez, A; Dorland, T; Dubey, A; Dudko, L V; Duflot, L; Duggan, D; Duperrin, A; Dutt, S; Dyshkant, A; Eads, M; Edmunds, D; Ellison, J; Elvira, V D; Enari, Y; Eno, S; Escalier, M; Evans, H; Evdokimov, A; Evdokimov, V N; Facini, G; Ferapontov, A V; Ferbel, T; Fiedler, F; Filthaut, F; Fisher, W; Fisk, H E; Fortner, M; Fox, H; Fuess, S; Gadfort, T; Galea, C F; Garcia-Bellido, A; Gavrilov, V; Gay, P; Geist, W; Geng, W; Gerber, C E; Gershtein, Y; Gillberg, D; Ginther, G; Golovanov, G; Gómez, B; Goussiou, A; Grannis, P D; Greder, S; Greenlee, H; Greenwood, Z D; Gregores, E M; Grenier, G; Gris, Ph; Grivaz, J-F; Grohsjean, A; Grünendahl, S; Grünewald, M W; Guo, F; Guo, J; Gutierrez, G; Gutierrez, P; Haas, A; Haefner, P; Hagopian, S; Haley, J; Hall, I; Hall, R E; Han, L; Harder, K; Harel, A; Hauptman, J M; Hays, J; Hebbeker, T; Hedin, D; Hegeman, J G; Heinson, A P; Heintz, U; Hensel, C; Heredia-De La Cruz, I; Herner, K; Hesketh, G; Hildreth, M D; Hirosky, R; Hoang, T; Hobbs, J D; Hoeneisen, B; Hohlfeld, M; Hossain, S; Houben, P; Hu, Y; Hubacek, Z; Huske, N; Hynek, V; Iashvili, I; Illingworth, R; Ito, A S; Jabeen, S; Jaffré, M; Jain, S; Jakobs, K; Jamin, D; Jesik, R; Johns, K; Johnson, C; Johnson, M; Johnston, D; Jonckheere, A; Jonsson, P; Juste, A; Kajfasz, E; Karmanov, D; Kasper, P A; Katsanos, I; Kaushik, V; Kehoe, R; Kermiche, S; Khalatyan, N; Khanov, A; Kharchilava, A; Kharzheev, Y N; Khatidze, D; Kirby, M H; Kirsch, M; Klima, B; Kohli, J M; Konrath, J-P; Kozelov, A V; Kraus, J; Kuhl, T; Kumar, A; Kupco, A; Kurca, T; Kuzmin, V A; Kvita, J; Lacroix, F; Lam, D; Lammers, S; Landsberg, G; Lebrun, P; Lee, H S; Lee, W M; Leflat, A; Lellouch, J; Li, L; Li, Q Z; Lietti, S M; Lim, J K; Lincoln, D; Linnemann, J; Lipaev, V V; Lipton, R; Liu, Y; Liu, Z; Lobodenko, A; Lokajicek, M; Love, P; Lubatti, H J; Luna-Garcia, R; Lyon, A L; Maciel, A K A; Mackin, D; Mättig, P; Magaña-Villalba, R; Mal, P K; Malik, S; Malyshev, V L; Maravin, Y; Martin, B; McCarthy, R; McGivern, C L; Meijer, M M; Melnitchouk, A; Mendoza, L; Menezes, D; Mercadante, P G; Merkin, M; Meyer, A; Meyer, J; Mondal, N K; Montgomery, H E; Moore, R W; Moulik, T; Muanza, G S; Mulhearn, M; Mundal, O; Mundim, L; Nagy, E; Naimuddin, M; Narain, M; Neal, H A; Negret, J P; Neustroev, P; Nilsen, H; Nogima, H; Novaes, S F; Nunnemann, T; Obrant, G; Ochando, C; Onoprienko, D; Orduna, J; Oshima, N; Osman, N; Osta, J; Otec, R; Otero y Garzón, G J; Owen, M; Padilla, M; Padley, P; Pangilinan, M; Parashar, N; Park, S-J; Park, S K; Parsons, J; Partridge, R; Parua, N; Patwa, A; Penning, B; Perfilov, M; Peters, K; Peters, Y; Pétroff, P; Piegaia, R; Piper, J; Pleier, M-A; Podesta-Lerma, P L M; Podstavkov, V M; Pogorelov, Y; Pol, M-E; Polozov, P; Popov, A V; Prewitt, M; Protopopescu, S; Qian, J; Quadt, A; Quinn, B; Rakitine, A; Rangel, M S; Ranjan, K; Ratoff, P N; Renkel, P; Rich, P; Rijssenbeek, M; Ripp-Baudot, I; Rizatdinova, F; Robinson, S; Rominsky, M; Royon, C; Rubinov, P; Ruchti, R; Safronov, G; Sajot, G; Sánchez-Hernández, A; Sanders, M P; Sanghi, B; Savage, G; Sawyer, L; Scanlon, T; Schaile, D; Schamberger, R D; Scheglov, Y; Schellman, H; Schliephake, T; Schlobohm, S; Schwanenberger, C; Schwienhorst, R; Sekaric, J; Severini, H; Shabalina, E; Shamim, M; Shary, V; Shchukin, A A; Shivpuri, R K; Siccardi, V; Simak, V; Sirotenko, V; Skubic, P; Slattery, P; Smirnov, D; Snow, G R; Snow, J; Snyder, S; Söldner-Rembold, S 2009-12-04 247 Energy Technology Data Exchange (ETDEWEB) We present a direct measurement of the width of the W boson using the shape of the transverse mass distribution of W {yields} e{nu} candidates selected in 1 fb{sup -1} of data collected with the D0 detector at the Fermilab Tevatron collider in p{bar p} collisions at {radical}s = 1.96 TeV. We use the same methods and data sample that were used for our recently published W boson mass measurement, except for the modeling of the recoil, which is done with a new method based on a recoil library. Our result, 2.028 {+-} 0.072 GeV, is in agreement with the predictions of the standard model and is the most precise direct measurement result from a single experiment to date. Abazov, V.M.; /Dubna, JINR; Abbott, B.; /Oklahoma U.; Abolins, M.; /Michigan State U.; Acharya, B.S.; /Tata Inst.; Adams, M.; /Illinois U., Chicago; Adams, T.; /Florida State U.; Aguilo, E.; /Alberta U. /Simon Fraser U. /McGill U.; Ahsan, M.; /Kansas State U.; Alexeev, G.D.; /Dubna, JINR; Alkhazov, G.; /St. Petersburg, INP; Alton, A.; /Michigan U. /Northeastern U. 2009-09-01 248 CERN Multimedia A phenomenological law, called Benford's law, states that the occurrence of the first digit, i.e.,$1,2,...,9$, of numbers from many real world sources is not uniformly distributed, but instead favors smaller ones according to a logarithmic distribution. We investigate, for the first time, the first digit distribution of the full widths of mesons and baryons in the well defined science domain of particle physics systematically, and find that they agree excellently with the Benford distribution. We also discuss several general properties of Benford's law, i.e., the law is scale-invariant, base-invariant, and power-invariant. This means that the lifetimes of hadrons follow also Benford's law. Shao, Lijing; 10.1142/S0217732309031223 2010-01-01 249 Science.gov (United States) A phenomenological law, called Benford's law, states that the occurrence of the first digit, i.e. 1, 2,…, 9, of numbers from many real world sources is not uniformly distributed, but instead favors smaller ones according to a logarithmic distribution. We investigate, for the first time, the first digit distribution of the full widths of mesons and baryons in the well-defined science domain of particle physics systematically, and find that they agree excellently with the Benford distribution. We also discuss several general properties of Benford's law, i.e. the law is scale-invariant, base-invariant and power-invariant. This means that the lifetimes of hadrons also follow Benford's law. Shao, Lijing; Ma, Bo-Qiang 250 CERN Multimedia This work describes a novel image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wavefronts. The problem of width uniformity is discussed and its importance for the characterization of composite structures normally found in physics and biology highlighted. The methodology involves identifying each cluster (i.e. connected component) of interest, which can correspond to objects or voids, and estimating the respective medial axes by using a recently proposed wavefront propagation approach, which is briefly reviewed. The distance values along such axes are identified and their mean and standard deviation values obtained. As illustrated with respect to synthetic and real objects (in vitro cultures of neuronal cells), the combined use of these two features provide a powerful description of the uniformity of the separation between the objects, presenting potential for several applications in material sciences and biology. Costa, L F; Schubert, D; Costa, Luciano da F.; Mutinari, Giancarlo; Schubert, David 2003-01-01 251 International Nuclear Information System (INIS) An extensive theoretical and experimental work was carried out on the ns-np and np-nd line widths (w) of noble gases after ionization (n=n0+1, were n0 is the principal quantum number of the fundamental configuration). A high current 'pinch' discharge was used as source. Electron density and temperature were estimated to be Ne=2.65x1016 cm-3 and T=1.45x104K respectively. Calculations were based on a semi-empirical approximation and the matrix elements (or transition probabilities) were evaluated in different approximation. Comparing our measurements with those of other authors, a systematic tendency, with a dependence on atomic number Z and ionization energy of the higher level L, was established. Finally, it has been established that for Ne>1017 cm-3, w ? Ne?, where ?=5/6. (Author). 8 refs., 1 fig., 1 tab. 1990-01-01 252 CERN Multimedia We show that if two continuous semi-simple \$$\\ell \$$-adic Galois representations are locally potentially equivalent at a sufficiently large set of places then they are globaly potentially equivalent. We also prove an analogous result for arbitrarily varying powers of character values evaluated at the Frobenius conjugacy classes. In the context of modular forms, we prove: given two non-CM newforms$f$and$g$of weight at least two, such that$a_p(f)^{n_p}=a_p(g)^{n_p}$on a set of primes of positive upper density and for some set of natural numbers$n_p$, then$f$and$g$are twists of each other by a Dirichlet character. Patankar, Vijay M 2010-01-01 253 Energy Technology Data Exchange (ETDEWEB) A direct application of equivalent circuit concepts leads to: (1) confirmation of Perry Wilson's SLED (SLAC Linac Energy Doubler) equation; (2) an equation that applies to a SLED device with input and output waveguides of different characteristic impedances; and (3) an equation that results if we demand that no power be lost by reflection from SLED. If the incident voltage is tailored as prescribed by this equation, the cavity voltage tracks the incident voltage and the reflected voltage is zero. Lippmann, B.A. 1986-05-01 254 CERN Multimedia The traditional thermodynamic Bethe ansatz (TBA) equations for the XXZ model at$\|\\Delta\|\\ge 1$are derived within the quantum transfer matrix (QTM) method. This provides further evidence of the equivalence of both methods. Most importantly, we derive an integral equation for the free energy formulated for just one unknown function. This integral equation is different in physical and mathematical aspects from the established ones. The single integral equation is analytically continued to the regime$\|\\Delta\|<1$. Takahashi, M; Klümper, A; Takahashi, Minoru; Shiroishi, Masahiro; Klumper, Andreas 2001-01-01 255 International Nuclear Information System (INIS) [en] The traditional thermodynamic Bethe ansatz equations for the XXZ model at vertical bar ? vertical bar ? 1 are derived within the quantum transfer matrix method. This provides further evidence of the equivalence of both methods. Most importantly, we derive an integral equation for the free energy formulated for just one unknown function. This integral equation differs in physical and mathematical aspects to the established ones. The single integral equation is analytically continued to the regime vertical bar ? vertical bar 2001-04-06 256 CERN Multimedia We extend the definition of a semidualizing module to associative rings. This enables us to define and study Auslander and Bass classes with respect to a semidualizing bimodule C. We then study the classes of C-flats, C-projectives, and C-injectives, and use them to provide a characterization of the modules in the Auslander and Bass classes. We extend Foxby equivalence to this new setting. This paper contains a few results which are new in the commutative, noetherian setting. Holm, H; Holm, Henrik; White, Diana 2006-01-01 257 International Nuclear Information System (INIS) A direct application of equivalent circuit concepts leads to: (1) confirmation of Perry Wilson's SLED (SLAC Linac Energy Doubler) equation; (2) an equation that applies to a SLED device with input and output waveguides of different characteristic impedances; and (3) an equation that results if we demand that no power be lost by reflection from SLED. If the incident voltage is tailored as prescribed by this equation, the cavity voltage tracks the incident voltage and the reflected voltage is zero. 1986-01-01 258 International Nuclear Information System (INIS) [en] Complex industrial structures are generally divided in several substructures. Even if the global behavior of the structure may by considered as linear, some substructures present local nonlinearities like impacts, sliding, or plasticity. To study the response of the whole structure the usual method consists of replacing the nonlinear substructures by linear models. The effect of the substructure is made equivalent to the nonlinear effect of the real substructure. Such equivalent models are called Linear Equivalent Models (LEM). This paper is mainly focused on the seismic behaviour of structures impacting on supports with gaps (for example pipes, steam generator etc...). Classical approaches to determine LEM consist generally in replacing the nonlinear support by a spring which stiffness is a function of the gap value and the excitation level. The limitations of such method will be identified in the case of a 1 degree of freedom (DOF) nonlinear oscillator. A new principle of LEM will be proposed and applied to this lDOF structure 1991-01-01 259 CERN Multimedia We study conservation laws and potential symmetries of (systems of) differential equations applying equivalence relations generated by point transformations between the equations. A Fokker-Planck equation and the Burgers equation are considered as examples. Using reducibility of them to the one-dimensional linear heat equation, we construct complete hierarchies of local and potential conservation laws for them and describe, in some sense, all their potential symmetries. Known results on the subject are interpreted in the proposed framework. This paper is an extended comment on the paper of J.-q. Mei and H.-q. Zhang [Internat. J. Theoret. Phys., 2006, in press]. Ivanova, N M; Ivanova, Nataliya M.; Popovych, Roman O. 2006-01-01 260 Science.gov (United States) At present, in Moscow metro a track inspection vehicle, defectoscope and portable measurement instruments are used to measure the rail profile and the condition of track. The track inspection vehicle measures 8 parameters, such as rail height, width, lip flow, cant, gauge and rail identification. The main drawback of the existing track control devices is a contact mode of measurement that does not provide required accuracy during the movement of the track inspection vehicle. This drawback can be eliminated using the non-contact photonic system (NPS). NPS consists of four special digital CCD-cameras and four lasers (two cameras and two lasers on each rail), rigidly connected together and mounted underneath the rail inspection vehicle in such a manner that corners of vision and distances from the cameras up to the head of the rail remain fixed during the movement. A special processor is included at the output of each camera. It performs preliminary processing of the stripe image on the appropriate side of a rail and then codes (compresses) and transfers data to central computer. The central computer executes the rail profile restoration and its comparison with the pattern of the rail on the particular section of the track. Ryabichenko, Roman B.; Popov, Sergey V.; Smoleva, Olga S. 1999-10-01 261 International Nuclear Information System (INIS) The reaction 126C(63Li, d)168O at a 6Li bombarding energy of 42 MeV has been used to populate excited states in 16O. The deuteron ejectiles were measured using the high-resolution Munich Q3D spectrograph. A large-acceptance silicon-strip detector array was used to register the recoil and break-up products. This complete kinematic set-up has enabled absolute ?-decay widths to be measured with high-resolution in the 13.9 to 15.9 MeV excitation energy regime in 16O; many for the first time. This energy region spans the 14.4 MeV four-? breakup threshold. Monte-Carlo simulations of the detector geometry and break-up processes yield detection efficiencies for the two dominant decay modes of 40% and 37% for the ?+12C(g.s.) and a+12C(2+1) break-up channels respectively. 2012-09-18 262 CERN Multimedia A method for calculating partial widths of auto-ionizing states is proposed. It combines either a complex absorbing potential or exterior complex scaling with the Lindblad equation. The corresponding classical rate equations are reproduced, and the trace conservation inherent in the Lindblad equation ensures that the partial widths sums up to the total width of the initial auto-ionizing state. Selstø, Sølve 2012-01-01 263 UK PubMed Central (United Kingdom) Step width is a spatiotemporal parameter that may influence lower extremity biomechanics at the hip and knee joint. The purpose of this study was to determine the biomechanical response of the lower extremity joints to step width changes during running. Lower extremity data from 30 healthy runners, half of them male, were collected during running in three step width conditions: preferred, wide, and narrow. Dependent variables and step width were analyzed using a mixed model ANOVA and pairwise t-tests for post hoc comparisons. Step width was successfully altered in the wide and narrow conditions. Generally, frontal plane peak values decreased as step width increased from narrow to preferred to wide. Peak hip adduction and rearfoot eversion angles decreased as step width increased from narrow to wide. Peak knee abduction moment and knee abduction impulse also decreased as step width increased from narrow to wide. Although men and women ran differently, gender only influenced the effect of step width on peak rearfoot inversion moment. In conclusion, step width influences lower extremity biomechanics in healthy runners. When step width increased from narrow to wide, peak values of frontal plane variables decreased. In addition to previously reported changes at the rearfoot, the hip and knee joint biomechanics were also influenced by changes in step width. Brindle RA; Milner CE; Zhang S; Fitzhugh EC 2013-07-01 264 Energy Technology Data Exchange (ETDEWEB) GaO{sub 2}H, {alpha}-Ga{sub 2}O{sub 3} and {beta}-Ga{sub 2}O{sub 3} powders were synthesized from mechanically ground GaN powders with thermal annealing in a nitrogen atmosphere. The structural properties of GaO{sub 2}H, {alpha}-Ga{sub 2}O{sub 3} and {beta}-Ga{sub 2}O{sub 3} powders were investigated by X-ray powder diffraction (XRD), Fourier transform infrared (FT-IR) and scanning electron microscopy (SEM). The studies revealed that the samples obtained by ball-milled GaN for 4 h are orthorhombic crystalline GaO{sub 2}H phase. However, when GaO{sub 2}H were annealed in a nitrogen atmosphere at 550 and 950 deg. C, {alpha}-Ga{sub 2}O{sub 3} and {beta}-Ga{sub 2}O{sub 3} powders were obtained, respectively. SEM images indicated that the morphologies of GaO{sub 2}H, {alpha}-Ga{sub 2}O{sub 3} and {beta}-Ga{sub 2}O{sub 3} are ruleless, and their sizes are in the range of about 300-70, 150-70, and 150-70 nm, respectively. Xiao Hongdi [School of Physics and Microelectronics, Shandong University, Jinan 250100 (China)]. E-mail: [email protected]; Ma Honglei [School of Physics and Microelectronics, Shandong University, Jinan 250100 (China)]. E-mail: [email protected]; Liang Wei [Jinan University, Jinan 250003 (China); Xue Chengshan [Institute of Semiconductor, Shandong Normal University, Jinan 250014 (China); Zhuang Huizhao [Institute of Semiconductor, Shandong Normal University, Jinan 250014 (China); Ma Jin [School of Physics and Microelectronics, Shandong University, Jinan 250100 (China); Hu Wenrong [School of Physics and Microelectronics, Shandong University, Jinan 250100 (China) 2005-12-15 265 CERN Multimedia The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives an approximation algorithm with performance guarantee of pi^2/6 ~ 1.64. The algorithm and its analysis are based on the simple idea of contracting long cycles. (This result is strengthened slightly in On strongly connected digraphs with bounded cycle length'' (1996).) The analysis applies directly to 2-Exchange, a simple local improvement'' algorithm, showing that its performance guarantee is 1.75. Khuller, S; Young, N E; Khuller, Samir; Raghavachari, Balaji; Young, Neal E. 1995-01-01 266 International Nuclear Information System (INIS) A test was performed over an extensive range of irrradiance (approximately five orders of magnitude) to see to what extent organic scintillators responded linearly with x-ray input. At the highest levels of irradiance achievable with the experimental configuration, but only for pulses in the region of 4.0 ns or wider, a degree of nonlinear response was observed for some of the scintillators. The data suggest that at levels below 1 mJ/cm2-ns it is safe to asume that for pulses 6.5 ns and shorter there is no significant level of nonlinearity to x rays with spectrum. For the cases of undoped NE111 and NE111 doped with 10 percent benzophenone, experimental conditions were such that it was possible to accumulate data significantly above the 1 mJ/cm2-ns level of irradiance. It is with these cases that a nonlinear response was observed. It is assumed that the same nonlinearity would have also been noticed had experimental conditions been such that equivalent levels of irradiance could have been achieved at the time the other samples were studied 1978-01-01 267 Energy Technology Data Exchange (ETDEWEB) A circuit generates a global clock signal with a pulse width modification to synchronize processors in a parallel computing system. The circuit may include a hardware module and a clock splitter. The hardware module may generate a clock signal and performs a pulse width modification on the clock signal. The pulse width modification changes a pulse width within a clock period in the clock signal. The clock splitter may distribute the pulse width modified clock signal to a plurality of processors in the parallel computing system. Chen, Dong; Ellavsky, Matthew R.; Franke, Ross L.; Gara, Alan; Gooding, Thomas M.; Haring, Rudolf A.; Jeanson, Mark J.; Kopcsay, Gerard V.; Liebsch, Thomas A.; Littrell, Daniel; Ohmacht, Martin; Reed, Don D.; Schenck, Brandon E.; Swetz, Richard A. 2013-04-02 268 Directory of Open Access Journals (Sweden) Full Text Available The present work shows the results obtained from experimental investigations of the augmentation of turbulent flow heat transfer in a horizontal tube by means of varying width twisted tape inserts with air as the working fluid. In order to reduce excessive pressure drops associated with full width twisted tape inserts, with less corresponding reduction in heat transfer coefficients, reduced width twisted tapes of widths ranging from 10 mm to 22 mm, which are lower than the tube inside diameter of 27.5 mm are used. Experiments were carried out for plain tube with/without twisted tape insert at constant wall heat flux and different mass flow rates. The twisted tapes are of three different twist ratios (3, 4 and 5) each with five different widths (26-full width, 22, 18, 14 and 10 mm) respectively. The Reynolds number varied from 6000 to 13500. Both heat transfer coefficient and pressure drop are calculated and the results are compared with those of plain tube. It was found that the enhancement of heat transfer with twisted tape inserts as compared to plain tube varied from 36 to 48% for full width (26mm) and 33 to 39% for reduced width (22 mm) inserts. Correlations are developed for friction factors and Nusselt numbers for a fully developed turbulent swirl flow, which are applicable to full width as well as reduced width twisted tapes, using a modified twist ratio as pitch to width ratio of the tape. S. Naga Sarada; A.V. Sita Rama Raju; K. Kalyani Radha; L. Shyam Sunder 2010-01-01 269 Energy Technology Data Exchange (ETDEWEB) A simple test problem proposed by Noh, a strong shock reflecting from a rigid wall, demonstrates a generic problem with numerical shock capturing algorithms at boundaries that Noh called excess wall heating. We show that the same type of numerical error occurs in general when shock waves interact. The underlying cause is the non-uniform convergence to the hyperbolic solution of the inviscid limit of the solution to the PDEs with viscosity. The error can be understood from an analysis of the asymptotic solution. For a propagating shock, there is a difference in the total energy of the parabolic wave relative to the hyperbolic shock. Moreover, the relative energy depends on the strength of the shock. The error when shock waves interact is due to the difference in the relative energies between the incoming and outgoing shock waves. It is analogous to a phase shift in a scattering matrix. A conservative differencing scheme correctly describes the Hugoniot jump conditions for a steady propagating shock. Therefore, the error from the asymptotics occurs in the transient when the waves interact. The entropy error that occurs in the interaction region remains localized but does not dissipate. A scaling argument shows that as the viscosity coefficient goes to zero, the error shrinks in spatial extend but is constant in magnitude. Nohs problem of the reflection of a shock from a rigid wall is equivalent to the symmetric impact of two shock waves of the opposite family. The asymptotic argument shows that the same type of numerical error would occur when the shocks are of unequal strength. Thus, Nohs problem is indicative of a numerical error that occurs when shocks interact due to the numerical shock width. Menikoff, R. 1993-03-04 270 Energy Technology Data Exchange (ETDEWEB) A simple test problem proposed by Noh, a strong shock reflecting from a rigid wall, demonstrates a generic problem with numerical shock capturing algorithms at boundaries that Noh called excess wall heating.'' We show that the same type of numerical error occurs in general when shock waves interact. The underlying cause is the non-uniform convergence to the hyperbolic solution of the inviscid limit of the solution to the PDEs with viscosity. The error can be understood from an analysis of the asymptotic solution. For a propagating shock, there is a difference in the total energy of the parabolic wave relative to the hyperbolic shock. Moreover, the relative energy depends on the strength of the shock. The error when shock waves interact is due to the difference in the relative energies between the incoming and outgoing shock waves. It is analogous to a phase shift in a scattering matrix. A conservative differencing scheme correctly describes the Hugoniot jump conditions for a steady propagating shock. Therefore, the error from the asymptotics occurs in the transient when the waves interact. The entropy error that occurs in the interaction region remains localized but does not dissipate. A scaling argument shows that as the viscosity coefficient goes to zero, the error shrinks in spatial extend but is constant in magnitude. Noh's problem of the reflection of a shock from a rigid wall is equivalent to the symmetric impact of two shock waves of the opposite family. The asymptotic argument shows that the same type of numerical error would occur when the shocks are of unequal strength. Thus, Noh's problem is indicative of a numerical error that occurs when shocks interact due to the numerical shock width. Menikoff, R. 1993-03-04 271 UK PubMed Central (United Kingdom) An equivalent-network approach is described for the analysis of surface-acoustic-wave gratings. Circuit parameters can be theoretically determined by applying the finite-element method to an infinite array. In this approach, all of the effects of piezoelectric perturbation, mechanical perturbation, and energy storage are taken into account. To show the validity and usefulness of this approach, examples are computed for groove and metallic gratings. Both short and open circuited metallic gratings are treated. For grooves on isotropic and Y-Z LiNbO(3) substrates, the dependence of reflection characteristics on groove depth is investigated. For aluminum strips on X-112 degrees Y LiTaO(3) 34 degrees Y-X quartz, Y-Z LiNbO(3), and 128 degrees Y -X LiNbO(3) substrates, the dependence on metallization ratio is investigated in detail. Koshiba M; Mitobe S 1988-01-01 272 International Nuclear Information System (INIS) The necessary data to calculate the effective committed dose equivalent and the effective dose-equivalent rate from measured body burdens are presented. Both ingestion and inhalation intakes are considered, for single intake as well as for continuous exposure. 1982-01-01 273 Science.gov (United States) This report describes the development and demonstration of an equivalent mathematical model for the representation of the external system dynamics at the boundary buses of an internal system. These equivalents are needed for different system studies in wh... M. A. H. Ibrahim 1976-01-01 274 Science.gov (United States) This study describes MFC operation with a pulse-width modulated connection of the external resistor (R-PWM mode) at low and high frequencies. Analysis of the output voltage profiles acquired during R-PWM tests showed the presence of slow and fast dynamic components, which can be described by a simple equivalent circuit model suitable for process control applications. At operating frequencies above 100Hz a noticeable improvement in MFC performance was observed with the power output increase of 22-43% as compared to MFC operation with a constant external resistance. PMID:23989037 Coronado, J; Perrier, M; Tartakovsky, B 2013-08-09 275 UK PubMed Central (United Kingdom) This study describes MFC operation with a pulse-width modulated connection of the external resistor (R-PWM mode) at low and high frequencies. Analysis of the output voltage profiles acquired during R-PWM tests showed the presence of slow and fast dynamic components, which can be described by a simple equivalent circuit model suitable for process control applications. At operating frequencies above 100Hz a noticeable improvement in MFC performance was observed with the power output increase of 22-43% as compared to MFC operation with a constant external resistance. Coronado J; Perrier M; Tartakovsky B 2013-11-01 276 Energy Technology Data Exchange (ETDEWEB) We present results from a Almost-Equal-To 100 ks Chandra observation of the 2QZ Cluster 1004+00 structure at z = 2.23 (hereafter 2QZ Clus). 2QZ Clus was originally identified as an overdensity of four optically-selected QSOs at z = 2.23 within a 15 Multiplication-Sign 15 arcmin{sup 2} region. Narrow-band imaging in the near-IR (within the K band) revealed that the structure contains an additional overdensity of 22 z = 2.23 H{alpha}-emitting galaxies (HAEs), resulting in 23 unique z = 2.23 HAEs/QSOs (22 within the Chandra field of view). Our Chandra observations reveal that three HAEs in addition to the four QSOs harbor powerfully accreting supermassive black holes (SMBHs), with 2-10 keV luminosities of Almost-Equal-To (8-60) Multiplication-Sign 10{sup 43} erg s{sup -1} and X-ray spectral slopes consistent with unobscured active galactic nucleus (AGN). Using a large comparison sample of 210 z = 2.23 HAEs in the Chandra-COSMOS field (C-COSMOS), we find suggestive evidence that the AGN fraction increases with local HAE galaxy density. The 2QZ Clus HAEs reside in a moderately overdense environment (a factor of Almost-Equal-To 2 times over the field), and after excluding optically-selected QSOs, we find that the AGN fraction is a factor of Almost-Equal-To 3.5{sup +3.8}{sub -2.2} times higher than C-COSMOS HAEs in similar environments. Using stacking analyses of the Chandra data and Herschel SPIRE observations at 250 {mu}m, we respectively estimate mean SMBH accretion rates ( M-dot{sub BH}) and star formation rates (SFRs) for the 2QZ Clus and C-COSMOS samples. We find that the mean 2QZ Clus HAE stacked X-ray luminosity is QSO-like (L{sub 2-10{sub keV}} Almost-Equal-To [6-10] Multiplication-Sign 10{sup 43} erg s{sup -1}), and the implied M-dot{sub BH}/SFR Almost-Equal-To (1.6-3.2) Multiplication-Sign 10{sup -3} is broadly consistent with the local M{sub BH}/M{sub } relation and z Almost-Equal-To 2 X-ray selected AGN. In contrast, the C-COSMOS HAEs are on average an order of magnitude less X-ray luminous and have M-dot{sub BH}/SFR Almost-Equal-To (0.2-0.4) Multiplication-Sign 10{sup -3}, somewhat lower than the local M{sub BH}/M{sub } relation, but comparable to that found for z Almost-Equal-To 1-2 star-forming galaxies with similar mean X-ray luminosities. We estimate that a periodic QSO phase with duty cycle Almost-Equal-To 2%-8% would be sufficient to bring star-forming galaxies onto the local M{sub BH}/M{sub } relation. This duty cycle is broadly consistent with the observed C-COSMOS HAE AGN fraction ( Almost-Equal-To 0.4%-2.3%) for powerful AGN with L{sub X} {approx}> 10{sup 44} erg s{sup -1}. Future observations of 2QZ Clus will be needed to identify key factors responsible for driving the mutual growth of the SMBHs and galaxies. Lehmer, B. D.; Hornschemeier, A. E. [Department of Physics and Astronomy, Johns Hopkins University, Homewood Campus, Baltimore, MD 21218 (United States); Lucy, A. B. [NASA Goddard Space Flight Centre, Code 662, Greenbelt, MD 20771 (United States); Alexander, D. M.; Harrison, C. M.; Mullaney, J. R.; Swinbank, A. M. [Department of Physics, Durham University, South Road, Durham DH1 3LE (United Kingdom); Best, P. N. [SUPA, Institute for Astronomy, Royal Observatory of Edinburgh, Blackford Hill, Edinburgh EH9 3HJ (United Kingdom); Geach, J. E. [Department of Physics, McGill University, 3600 rue University, Montreal, Quebec H3A 2T8 (Canada); Matsuda, Y. [Chile Observatory, National Astronomical Observatory of Japan, Tokyo 181-8588 (Japan); Smail, Ian [Institute for Computational Cosmology, Durham University, South Road, Durham DH1 3LE (United Kingdom); Sobral, D. [Leiden Observatory, Leiden University, P.O. Box 9513, NL-2300 RA Leiden (Netherlands) 2013-03-10 277 CERN Document Server We prove that for a countable group$\\Gamma$containing a copy of the free group$\\F_n$, for some$2\\leq n\\leq\\infty$, as a normal subgroup, the equivalence relations of conjugacy, orbit equivalence and von Neumann equivalence of the ergodic a.e. free actions of$\\Gamma$are analytic non-Borel equivalence relations in the Polish space of probability measure preserving$\\Gamma$actions. Epstein, Inessa 2011-01-01 278 CERN Multimedia Inverse semigroups are the abstract counterparts of pseudogroups of transformations. The abstract counterparts of atlases in differential geometry are what Wagner termed generalized heaps'. These are sets equipped with a ternary operation satisfying certain axioms. We prove that there is a bijective correspondence between generalized heaps and the equivalence bimodules, defined by Steinberg. Such equivalence bimodules are used to define the Morita equivalence of inverse semigroups. This paper therefore shows that the Morita equivalence of inverse semigroups is determined by Wagner's generalized heaps. Lawson, M V 2011-01-01 279 International Nuclear Information System (INIS) [en] Relations among the decay widths for psi' ? chi/sub J/?, chi/sub J/ ? psi? (where chi/sub J/ is one of the 3P charmonium states) are derived from two Drell-Hearn--type sum rules. The relations, which make no use of the nonrelativistic cc-bar picture of the psi', chi, and psi states, predict ?'2:?'1:?'0 = 1.2:1.3:1.0, ?2:?1:?0 = 0.9:0.8:1.0, where ?'/sub J/ equivalent GAMMA (psi' ? chi/sub J/?)/(2J + 1) k/sub J/'3, ?/sub J/ equivalent GAMMA (chi/sub J/ ? psi?)/k/sub J//sup ts3/ 1977-10-01 280 CERN Document Server In this paper, considering the geometric equivalence for algebras of a variety$_{S}A$of S-acts over a monoid S, we obtain representation theorems describing all types of the equivalence classes of geometrically equivalent S-acts of varieties$_{S}A$over groups S. Katsov, Yefim 2011-01-01 281 CERN Multimedia Spectral equivalences of the quasi-exactly solvable sectors of two classes of Schrodinger operators are established, using Gaudin-type Bethe ansatz equations. In some instances the results can be extended leading to full isospectrality. In this manner we obtain equivalences between PT-symmetric problems and Hermitian problems. We also find equivalences between some classes of Hermitian operators. Dunning, C; Links, J 2008-01-01 282 International Nuclear Information System (INIS) Spectral equivalences of the quasi-exactly solvable sectors of two classes of Schroedinger operators are established, using Gaudin-type Bethe ansatz equations. In some instances the results can be extended leading to full isospectrality. In this manner we obtain equivalences between PT-symmetric problems and Hermitian problems. We also find equivalences between some classes of Hermitian operators. 2008-08-08 283 Energy Technology Data Exchange (ETDEWEB) An investigation of Mounds ability to measure and process bridges was conducted in 1985. Prior to improvements in the measuring system and technique, bridge width was found to have a sigma of 0.00019 in. After improvements were made, a sigma of 0.000047 was realized. Bridge length was found to be more erratic than width, although most of the inaccuracy was caused by measurement uncertainty. Length and width were found to have little or no correlation. Armstrong, K.P. [comp. 1989-05-15 284 Science.gov (United States) We propose a stability-guaranteed width control (SGWC) for the hot strip finishing mill. It is shown that the proposed SGWC guarantees the stability of the width controller by the universal approximation of the neural network. It is shown through the field test in the hot strip mill of POSCO that the stability of the width controller is guaranteed by the proposed control scheme. Park, Cheol Jae; Hwang, I. Cheol 285 CERN Multimedia F. V. Gubarev et al. (On the significance of the vector potential squared'', Phys. Rev. Lett. 86, 2220) have argued that the minimum value of the volume integral of the vector potential squared may have physical meaning, in defiance of the gauge equivalence of potentials. Earlier, R. I. Khrapko proposed a gauge noninvariant electrodynamics spin tensor (Spin density of electromagnetic waves'', [1]). The standard electrodynamics spin tensor is zero. Here we point out that the Biot-Savarat formula uniquely results in a preferred, "true" vector potential field which is generated from a given magnetic field. A similar integral formula uniquely permits to find a "true" scalar potential field generated from a given electric field even in the case of a nonpotential electric field. We say that an exterior derivative of a differential form is the boundary of this form and the integration of a form results in a new form named the generation. Generating from a generation yields zero. A boundary is closed. A generatio... Khrapko, R I 2001-01-01 286 CERN Document Server Momentum widths of the primary fragments and observed final fragments have been investigated within the framework of an Antisymmetrized Molecular Dynamics transport model code (AMD-V) with a sequential decay afterburner (GEMINI). It is found that the secondary evaporation effects cause the values of a reduced momentum width,$\\sigma_0$, derived from momentum widths of the final fragments to be significantly less than those appropriate to the primary fragment but close to those observed in many experiments. Therefore, a new interpretation for experiemental momentum widths of projectile-like fragments is presented. Ma, Y G; Hagel, K; Murray, M; Ono, A; Wang, J S; Qin, L J; Makeev, A G; Smith, P; Natowitz, J B 2002-01-01 287 International Nuclear Information System (INIS) The new integral formalism for the calculation of the width of the quasistationary states without using smallness of the barrier penetration factor is proposed. Asymptotic formula for the width of the short-living quasistationary states on the base of saddle-point approximation is derived. On the base of our approach the widths of ?-decay of the Pb isotopes, baryon resonances and dibaryon resonances were calculated. A good agreement of the theory and experiment was demonstrated. The natural explanation of the small widths of low lying dibaryon resonances was argued. (author). 23 refs., 1 fig., 4 tabs 1995-01-01 288 UK PubMed Central (United Kingdom) We analyze the statistics of resonance widths in a many-body Fermi system with open decay channels. Depending on the strength of continuum coupling, such a system reveals growing deviations from the standard chi-square (Porter-Thomas) width distribution. The deviations emerge from the process of increasing interaction of intrinsic states through common decay channels; in the limit of perfect coupling this process leads to the superradiance phase transition. The width distribution depends also on the intrinsic dynamics (chaotic versus regular). The results presented here are important for understanding the recent experimental data concerning the width distribution for neutron resonances in nuclei. Celardo GL; Auerbach N; Izrailev FM; Zelevinsky VG 2011-01-01 289 Directory of Open Access Journals (Sweden) Full Text Available The paper concentrates on the equivalent simplification method for the micro-grid system connection into distributed network. The equivalent simplification method proposed for interaction study between micro-grid and distributed network. Micro-grid network, composite load, gas turbine synchronous generation, wind generation are equivalent simplification and parallel connect into the point of common coupling. A micro-grid system is built and three phase and single phase grounded faults are performed for the test of the equivalent model of micro-grid. The simulation results show that the equivalent model of micro-grid is effective, and the dynamic of equivalent model is similar with the detailed model of micro-grid. The equivalent simplification method for the micro-grid network and distributed components is suitable for the study of micro-grid. Cai Changchun; Cao Xiangqin 2013-01-01 290 CERN Multimedia Given a permutation pattern p and an equivalence relation on permutations, we study the corresponding equivalence classes all of whose members avoid p. Four relations are studied: Conjugacy, order isomorphism, Knuth-equivalence and toric equivalence. Each of these produces a known class of permutations or a known counting sequence. For example, involutions correspond to conjugacy, and permutations whose insertion tableau is hook-shaped with 2 in the first row correspond to Knuth-equivalence. These permutations are equinumerous with certain congruence classes of graph endomorphisms. In the case of toric equivalence we find a class of permutations that are counted by the Euler totient function, with a subclass counted by the number-of-divisors function. We also provide a new symmetry for bivincular patterns that produces some new non-trivial Wilf-equivalences Ulfarsson, Henning 2010-01-01 291 CERN Multimedia In Paper I of this series (astro-ph/9911117) we described observations of 15 extragalactic targets taken with the Hubble Space Telescope GHRS/G160M grating for studies of the low-z Lya forest. We reported the detection of 110 Lya absorbers at significance level >3 sigma in the redshift range z=0.002-0.069, over a total pathlength of 116,000 km/s. In this second paper, we evaluate the physical properties of these Lya absorbers and compare them to their high-z counterparts. The distribution of Doppler parameters is similar to that at high redshift, with mean b = 35.0 +- 16.6 km/s. The true Doppler parameter may be somewhat lower, owing to component blends and non-thermal velocities. The distribution of equivalent widths exhibits a significant break at W~133mA, with an increasing number of weak absorbers (10mA-100mA). Adopting a curve of growth with b = 25 +- 5km/s and applying a sensitivity correction as a function of equivalent width and wavelength, we derive the distribution in column density, Nh^{-1.80+-0.05... Penton, S V; Stocke, J T; Penton, Steven V.; Stocke, John T. 1999-01-01 292 Science.gov (United States) The width of the decay Z-->???? in the presence of a possible nonstandard four-fermion ?-? interaction is calculated. From the invisible width of the Z-boson measured at LEP the upper bound on the strength F of such an effective interaction has been obtained: Fl?l?? is also presented. Bilenky, M.; Bilenky, S. M.; Santamaria, A. 1993-03-01 293 International Nuclear Information System (INIS) [en] The method for calculation of giant resonance (GR) partial escape widths has been applied to the calculation of the partial proton escape widths of the Gamow-Teller (GTR) in 9091Zr, 208Pb nuclei. The method has been generalized to the case of nuclei in which the strong neutron pairing takes place. 16 refs 1994-01-01 294 Digital Repository Infrastructure Vision for European Research (DRIVER) Mandibular arch widths and ratios are computed for unilateral cleft patients. The mandibular dental arch dimensions in unilateral cleft are different from that of the normals. Studies were made on the arch widths of normals of our population, but the arch dimensions of the cleft patients are not tha... SUJA ANI G 295 Science.gov (United States) We present a procedure for measuring slit width and separation in single- and double-slit diffraction experiments. Intensity spectra of diffracted laser light are measured with an optical sensor (PIN diode). Slit widths and separations are extracted by fitting to the measured spectra. We present a simple fitting procedure to account for the… Gan, K. K.; Law, A. T. 2009-01-01 296 CERN Document Server We investigate logics and equivalence relations that capture the qualitative behavior of Markov Decision Processes (MDPs). We present Qualitative Randomized CTL (QRCTL): formulas of this logic can express the fact that certain temporal properties hold over all paths, or with probability 0 or 1, but they do not distinguish among intermediate probability values. We present a symbolic, polynomial time model-checking algorithm for QRCTL on MDPs. The logic QRCTL induces an equivalence relation over states of an MDP that we call qualitative equivalence: informally, two states are qualitatively equivalent if the sets of formulas that hold with probability 0 or 1 at the two states are the same. We show that for finite alternating MDPs, where nondeterministic and probabilistic choices occur in different states, qualitative equivalence coincides with alternating bisimulation, and can thus be computed via efficient partition-refinement algorithms. On the other hand, in non-alternating MDPs the equivalence relations cann... Chatterjee, Krishnendu; Faella, Marco; Legay, Axel 2009-01-01 297 Energy Technology Data Exchange (ETDEWEB) The equivalent linearization of an intershaft squeeze film damper in a two shaft engine system is investigated. The two shaft centers at the damper position are assumed to move in different elliptical offset orbits and at synchronous frequency with the unbalanced rotor (e.g., the high pressure rotor). The nonlinear damper force is resolved into two orthogonal components along the absolute coordinate directions and, in turn, each of these force components is supposed to be equivalent to the sum of an average force, a linear spring force, and a linear damping force in the corresponding direction. By using the method of equivalent linearization by harmonic balance, the six parameters of the equivalent forces, including two average forces, two equivalent spring coefficients, and two equivalent damping coefficients, are expressed analytically by the squeeze film forces and the assumed orbital motion of the two shaft centers at the damper position. 10 references. Chen, S.; Liu, S. 1986-10-01 298 Directory of Open Access Journals (Sweden) Full Text Available The paper deals with the methodology of replacing complicated parts of an airplane skin by simple homogeneous equivalents, which can exhibit similar shielding efficiency. On one hand, the airplane built from the virtual homogeneous equivalents can be analyzed with significantly reduced CPU-time demands and memory requirements. On the other hand, the equivalent model can estimate the internal fields satisfactory enough to evaluate the electromagnetic immunity of the airplane. T. Zvolensky; Z. Raida; P. Tobola 2009-01-01 299 CERN Document Server Let R be an equivalence relation on graphs. By the strengthening of R we mean the relation R' such that graphs G and H are in the relation R' if for every graph F, the union of the graphs G and F is in the relation R with the union of the graphs H and F. We study strengthenings of equivalence relations on graphs. The most important case that we consider concerns equivalence relations defined by graph properties. We obtain results on the strengthening of equivalence relations determined by the properties such as being a k-connected graph, k-colorable, hamiltonian and planar. Lonc, Zbigniew 2010-01-01 300 CERN Document Server We introduce Brauer complex of symmetric SB-algebra, and reformulate in terms of Brauer complex the so far known invariants of stable and derived equivalence of symmetric SB-algebras. In particular, the genus of Brauer complex turns out to be invariant under derived equivalence. We study transformations of Brauer complexes which preserve class of derived equivalence. Additionally, we establish a new invariant of derived equivalence of symmetric SB-algebras. As a consequence, symmetric SB-algebras with Brauer complex of genus 0 are classified. Keywords: Brauer tree algebras, special biserial algebras, tilting complex. Antipov, M 2007-01-01 301 Directory of Open Access Journals (Sweden) Full Text Available Some equivalent stress methods, applicable for life prediction in case of multiaxial loading, are presented in this paper, such as empirical equivalent stresses, frequency and “signed von Mises” stress. To apply the latter method, a calculation program that allows the transformation of a fluctuating load cycle into a fully reversed cycle is developed. The authors extend the equivalent stress concept towards critical plane models. This is illustrated by a calculated equivalent shear stress based on the Yokobori criterion. Both the „signed von Mises” and Yokobori approaches have the advantage of allowing multiaxial fatigue calculations for limited durability, as opposed to classical methods which are applicable only for unlimited durability. DUMITRU Ion; KUN Lorand; DREUCEAN Mircea; MENYHARDT Karoly 2011-01-01 302 CERN Multimedia We use a sample of rest-frame UV selected and spectroscopically observed galaxies at redshifts 1.9H-alpha and Spitzer MIPS 24 micron data, to derive the most robust measurements of the rest-frame UV, H-alpha, and infrared (IR) luminosity functions (LFs) at these redshifts. Our sample is by far the largest of its kind, with over 2000 spectroscopic redshifts in the range 1.9 Reddy, Naveen A; Pettini, Max; Adelberger, Kurt L; Shapley, Alice E; Erb, Dawn K; Dickinson, Mark 2007-01-01 303 International Nuclear Information System (INIS) Effects of the width of electrical steel sheets on dynamic magnetic properties are investigated by solving diffusion equation on the cross-section of the sheet. Linear and non-linear cases are studied, and are compared with measurement on Epstein frame. For the first one an analytical solution is found, while for the second, a 2D finite element simulation is achieved. The influence of width is highlighted for a width thickness ratio lower than 10. It is shown that the behaviour modification in such cases is conditioned by the excitation signal waveform, amplitude and also frequency 2000-06-02 304 Energy Technology Data Exchange (ETDEWEB) The width of the giant dipole resonance (GDR) built on excited states was determined from a measurement of {gamma}-decays in coincidence with {sup 17}O particles scattered inelastically from {sup 120}Sn. The bombarding energy was 80 MeV/u. A width of 4{+-}1 MeV, consistent with the width of the GDR built on the ground state, was found at a temperature T=1 MeV. This result is in disagreement with adiabatic thermal shape fluctuation calculations, indicating an overestimation of the influence of thermal shape fluctuations at low temperature. Heckman, P.; Bazin, D.; Beene, J.R.; Blumenfeld, Y.; Chromik, M.J.; Halbert, M.L.; Liang, J.F.; Mohrmann, E.; Nakamura, T.; Navin, A.; Sherrill, B.M.; Snover, K.A.; Thoennessen, M.; Tryggestad, E.; Varner, R.L 2003-02-27 305 CERN Multimedia Effects of the width of electrical steel sheets on dynamic magnetic properties are investigated by solving diffusion equation on the cross-section of the sheet. Linear and non-linear cases are studied, and are compared with measurement on Epstein frame. For the first one an analytical solution is found, while for the second, a 2D finite element simulation is achieved. The influence of width is highlighted for a width thickness ratio lower than 10. It is shown that the behaviour modification in such cases is conditioned by the excitation signal waveform, amplitude and also frequency. Chevalier, T; Cornut, B 2000-01-01 306 Digital Repository Infrastructure Vision for European Research (DRIVER) The paper deals with the methodology of replacing complicated parts of an airplane skin by simple homogeneous equivalents, which can exhibit similar shielding efficiency. On one hand, the airplane built from the virtual homogeneous equivalents can be analyzed with significantly reduced CPU-time dema... T. Zvolensky; Z. Raida; P. Tobola 307 CERN Document Server We investigate bisimulation equivalence on Petri nets under durational semantics. Our motivation was to verify the conjecture that in durational setting, the bisimulation equivalence checking problem becomes more tractable (which is the case, e.g., over communication-free nets). We disprove this conjecture in three of four proposed variants of durational semantics. The fourth case remains an interesting open problem. Lasota, Slawomir 2009-01-01 308 Digital Repository Infrastructure Vision for European Research (DRIVER) When the patent of a small molecule drug expires generics may be introduced. They are considered therapeutically equivalent once pharmaceutical equivalence (i.e. identical active substances) and bioequivalence (i.e. comparable pharmacokinetics) have been established in a cross-over volunteer study. ... Schellekens, H.; Klinger, E.; Mühlebach, S.; Brin, J-F.; Storm, G.; Crommelin, D.J.A. 309 UK PubMed Central (United Kingdom) Two cases of a Galeazzi-equivalent lesion in adolescence are described. Accurate diagnosis of the epiphyseal injury of the distal ulna, rigid fixation of the distal radius, and stabilization of the distal radioulnar joint are keys in obtaining a good result in the treatment of Galeazzi-equivalent lesion in adolescence. Kamano M; Honda Y 2002-07-01 310 CERN Multimedia We generalize Brenner and Butler's Theorem as well as Happel's Theorem on the equivalences induced by a finitely generated tilting module over artin algebras, to the case of an infinitely generated tilting module over an arbitrary associative ring establishing the equivalences induced between subcategories of module categories and also at the level of derived categories. Bazzoni, Silvana 2009-01-01 311 Energy Technology Data Exchange (ETDEWEB) To clarify the cause of incurvated nail, the relation between the nail plate and the distal phalanx of the patient of incurvated/ingrown nail and normal subjects was compared, by measuring CT scan images. The investigation was made on 12 incurvated nails, 8 ingrown nails and 8 normal nails of the first toes which were clinically diagnosed as such. Each toe was scanned at 1 mm intervals with the same CT scanner under the same conditions. The pictures taken on the film were scanned and input into a computer. The transverse width of the distal phalanx and the width of the nail plate were measured on each slice. The minimum transverse width of the distal phalanx in both stages of slightly and intensively incurvated nail was smaller as compared to that in the stages of normal nail and ingrown nail. The ratios of the width of the nail plate to the minimum transverse width of the distal phalanx in the stages of normal nail, ingrown nail and intensively incurvated nail were nearly equal, while the ratio in the stage of slightly incurvated nail was outstandingly large. Based on the results of this investigation, it can be considered that the transverse width of the distal phalanx is reduced first, and consequently, the incurvation of the nail plate occurs, then the width of the nail plate is reduced as the incurvation becomes more intense. (author). Yamaguchi, Akinobu [Showa Univ., Tokyo (Japan). School of Medicine 1995-06-01 312 International Nuclear Information System (INIS) To clarify the cause of incurvated nail, the relation between the nail plate and the distal phalanx of the patient of incurvated/ingrown nail and normal subjects was compared, by measuring CT scan images. The investigation was made on 12 incurvated nails, 8 ingrown nails and 8 normal nails of the first toes which were clinically diagnosed as such. Each toe was scanned at 1 mm intervals with the same CT scanner under the same conditions. The pictures taken on the film were scanned and input into a computer. The transverse width of the distal phalanx and the width of the nail plate were measured on each slice. The minimum transverse width of the distal phalanx in both stages of slightly and intensively incurvated nail was smaller as compared to that in the stages of normal nail and ingrown nail. The ratios of the width of the nail plate to the minimum transverse width of the distal phalanx in the stages of normal nail, ingrown nail and intensively incurvated nail were nearly equal, while the ratio in the stage of slightly incurvated nail was outstandingly large. Based on the results of this investigation, it can be considered that the transverse width of the distal phalanx is reduced first, and consequently, the incurvation of the nail plate occurs, then the width of the nail plate is reduced as the incurvation becomes more intense. (author) 1995-01-01 313 CERN Multimedia We introduce an analog of the theory of Borel equivalence relations in which we study equivalence relations that are decidable by an infinite time Turing machine. The Borel reductions are replaced by the more general class of infinite time computable functions. Many basic aspects of the classical theory remain intact, with the added bonus that it becomes sensible to study some special equivalence relations whose complexity is beyond Borel or even analytic. We also introduce an infinite time generalization of the countable Borel equivalence relations, a key subclass of the Borel equivalence relations, and again show that several key properties carry over to the larger class. Lastly, we collect together several results from the literature regarding Borel reducibility which apply also to absolutely Delta_1^2 reductions, and hence to the infinite time computable reductions. Coskey, Samuel 2009-01-01 314 Energy Technology Data Exchange (ETDEWEB) We ventilate buildings to provide acceptable indoor air quality (IAQ). Ventilation standards (such as American Society of Heating, Refrigerating, and Air-Conditioning Enginners [ASHRAE] Standard 62) specify minimum ventilation rates without taking into account the impact of those rates on IAQ. Innovative ventilation management is often a desirable element of reducing energy consumption or improving IAQ or comfort. Variable ventilation is one innovative strategy. To use variable ventilation in a way that meets standards, it is necessary to have a method for determining equivalence in terms of either ventilation or indoor air quality. This study develops methods to calculate either equivalent ventilation or equivalent IAQ. We demonstrate that equivalent ventilation can be used as the basis for dynamic ventilation control, reducing peak load and infiltration of outdoor contaminants. We also show that equivalent IAQ could allow some contaminants to exceed current standards if other contaminants are more stringently controlled. Sherman, Max; Walker, Iain; Logue, Jennifer 2011-08-01 315 International Nuclear Information System (INIS) [en] Damping of collective excitations of fast-rotating nuclei has been investigated within the framework of a Fermi liquid drop model with provision for dissipation. Spread widths of collective excitation have been calculated 1986-04-15 316 Energy Technology Data Exchange (ETDEWEB) We consider classes of uniformly bounded convex functions defined on convex compact bodies in R{sup d} and satisfying a Lipschitz condition and establish the exact orders of their Kolmogorov, entropy, and pseudo-dimension widths in the L{sub 1}-metric. We also introduce the notions of pseudo-dimension and pseudo-dimension widths for classes of sets and determine the exact orders of the entropy and pseudo-dimension widths of some classes of convex bodies in R{sup d}relative to the pseudo-metric defined as the d-dimensional Lebesgue volume of the symmetric difference of two sets. We also find the exact orders of the entropy and pseudo-dimension widths of the corresponding classes of characteristic functions in L{sub p}-spaces, 1{<=}p{<=}{infinity}. Konovalov, V N [Institute of Mathematics of Ukrainian National Academy of Sciences, Kiev (Ukraine); Maiorov, Vitalii E [Technion - Israel Institute of Technology, Haifa (Israel) 2010-02-28 317 CERN Document Server We analyze the effect of frequency on the width of a single finger displacing a viscoelastic fluid. We derive a generalized Darcy's law in the frequency domain for a linear viscoelastic fluid flowing in a Hele Shaw cell. This leads to an analytic expression for the dynamic permeability that has maxima which are several orders of magnitude larger than the static permeability. We then follow an argument of de Gennes to obtain the smallest possible finger width when viscoelasticity is important. Using this, and a conservation law, we obtain a lowest bound for the width of a single finger displacing a viscoelastic fluid. Our results indicate that when a small amplitude signal of the frequency that maximizes the permeability is overimposed to a constant pressure drop, gigantic variations are obtained for the finger width. Poire, E C; Poire, Eugenia Corvera 2002-01-01 318 UK PubMed Central (United Kingdom) A systematic analysis of the observed reduced widths obtained in relativistic heavy ion fragmentation reactions is used to develop a phenomenological parametrization of these data. The parametrization is simple, accurate, and completely general in applicability. Tripathi RK; Townsend LW 1994-04-01 319 International Nuclear Information System (INIS) [en] Estimates for the Kolmogorov widths in the Lq,v-metric of weighted Sobolev classes as well as for the approximation numbers of the corresponding embedding operators are found. Bibliography: 33 titles. 2010-09-02 320 DEFF Research Database (Denmark) Methods for estimating the spectral width of a narrowband optical signal are investigated. Spectral analysis and Fourier spectroscopy are compared. Optimum and close-to-optimum estimators are developed under the constraint of having only one photodetector. Lading, Lars; Skov Jensen, A. 1980-01-01 321 International Nuclear Information System (INIS) A method is proposed to evaluate the effect of the change of the Fermi sea on the width of the giant dipole resonance at finite temperature. In a schematic model it is found that, indeed, in 208Pb the width increases very sharply up to about T=4 MeV but shows a much weaker variation for higher temperature. (author) 26 refs., 7 figs., 2 tabs. 1992-01-01 322 DEFF Research Database (Denmark) We obtain a characterization of ACC 0 in terms of a natural class of constant width circuits, namely in terms of constant width polynomial size planar circuits. This is shown via a characterization of the class of acyclic digraphs which can be embedded on a cylinder surface in such a way that all arcs flow along the same direction of the axis of the cylinder. Hansen, K.A. 2004-01-01 323 Energy Technology Data Exchange (ETDEWEB) A discussion of the techniques used for estimating the subpulse widths of pulsars concludes that Gaussian fitting has advantages over autocorrelation techniques for single pulse data recorded with millisecond resolution at radio frequencies around 400 MHz. Measurements are presented for 53 pulsars, made from radio observations obtained at Jodrell Bank. A relation is found between the subpulse widths and the polarization properties of the pulsars, which we interpret in terms of current polar-cap models of the radio emission. Ashworth, M. 1988-01-01 324 Directory of Open Access Journals (Sweden) Full Text Available Dual x-ray absorptiometry (DXA) is the most widely used measurement for the assessment of bone mass in osteoporosis. In clinical measurement, bone width can affect bone mineral parameters. The purpose of this study was to examine the dependence of bone mineral pa-rameters on bone width. In this study, DXA measurements were conducted on rabbit bone in vivo using clinical instruments. We have selected rabbit’s bones that have low BMD and more collagen tissue to predict structure not only measures BMD, but is also sensitive to the structure of the bone. To investigate the effect of bone width on the measured parameters, three regions of femur and tibia bones (N=132) were processed: upper (1/3 of length), middle (1/2 of length) and lower (2/3 of length) for BMC, areal BMD and volumetric BMD. The ANOVA analysis of bone mineral extracted by DXA showed significant differences (P<0.05) between BMC, BMDa and BMDv of six groups of upper, middle and lower parts of the femur and the tibia. It shows that BMC and BMD correlate well with the bone width, but BMDv inversely correlates with bone width. Linear and nonlinear regression analyses were used to examine the relationship between DXA characteristics with bone width and the regression function for each parameter is given. We concluded that BMC, areal BMD, and volumetric BMD in rabbit's bone with collagen fibers more than bone mineral are dependent on bone width. This result may be at least in part due to large precision error measurement of the bone width, in vivo. M. Mokhtari-Dizaji; M.R. Dadras; B. Larijani 2006-01-01 325 International Nuclear Information System (INIS) The decay widths of the Higgs boson into ??,Z?,ZZ and W+W- are calculated on the one-loop level of the electroweak theory. Exact analytic formulae in terms of complex-valued dilogarithms are obtained. The dependence of the decay widths on the Higgs boson mass and on the top-quark mass are investigated. 12 refs.; 10 figs.; 1 tab 1991-01-01 326 CERN Multimedia Based on 85 pb$^{-1}$data of \\ppbar collisions at$\\sqrt{s}=1.8$\\tev\\ collected using the D{\\O}detector at Fermilab during the 1994-1995 run of the Tevatron, we present a direct measurement of the total decay width of the \\wb\\ boson,$\\Gamma_W$. The width is determined from the transverse mass spectrum in the$W \\to e+\ 2002-01-01 327 International Nuclear Information System (INIS) [en] Measurement of the relative sign of inelastic proton-channel amplitudes permits the determination of amplitude correlations. Data were obtained for 45 5/2+ resonances in 49V. Although the reduced widths in each channel followed a Porter-Thomas distribution, large amplitude correlations were observed. The results are compared with the reduced-width--amplitude distribution of Krieger and Porter. This is the first direct test of the Krieger-Porter distribution 1980-10-13 328 Energy Technology Data Exchange (ETDEWEB) Measurement of the relative sign of inelastic proton-channel amplitudes permits the determination of amplitude correlations. Data were obtained for 45 5/2/sup +/ resonances in /sup 49/V. Although the reduced widths in each channel followed a Porter-Thomas distribution, large amplitude correlations were observed. The results are compared with the reduced-width--amplitude distribution of Krieger and Porter. This is the first direct test of the Krieger-Porter distribution. Chou, B.H.; Mitchell, G.E.; Bilpuch, E.G.; Westerfeldt, C.R. 1980-10-13 329 UK PubMed Central (United Kingdom) BACKGROUND:: The aim of this cadaver study was to evaluate the amount of ridge expansion with screw spreaders. METHODS:: Eleven edentulous maxillae providing 20 eligible sites were used. Ridges with initial width of 3 to 6 mm were expanded using a set of 6 screw spreaders, and implants (ø3.7 × 10 mm) were subsequently placed. Ridge width at 2 mm apical to the crest was measured at the baseline, after expansion, and implant placement. Buccal plate thickness and incidence of buccal dehiscence after implant placement were measured. RESULTS:: The mean initial ridge width was 3.97 ± 0.82 mm. After the expansion, the mean ridge width increased to 4.76 ± 0.77 mm ([INCREMENT] = 0.79 mm). Majority of sites (7/9 sites) with an initial ridge width of <4 mm had a buccal dehiscence after implant placement. A buccal plate thickness of ?1 mm was consistently present in cases with an initial ridge width of ?4.5 mm after implant placement. CONCLUSIONS:: The screw spreaders had a modest effect on ridge expansion. Their use might be limited because additional bone augmentation might be required to prevent or correct the bony dehiscence encountered in ridges <4.5 mm wide. Therefore, using this particular instrument kit for horizontal ridge augmentation is only indicated in specific cases. Chan HL; Fu JH; Koticha T; Benavides E; Wang HL 2013-09-01 330 International Nuclear Information System (INIS) [en] A recently developed method for calculating the widths of atomic and molecular resonances is reviewed. The method is based on the golden-rule definition of the resonance width, GAMMA(E). The method uses only square-integrable, L2, basis functions to describe both the resonant and the non-resonant parts of the scattering wave function. It employs Stieltjes-moment-theory techniques to extract a continuous approximation for the width discrete representation of the background continuum. Its implementation requires only existing atomic and molecular structure codes. Many-electron effects, such as correlation and polarization, are easily incorporated into the calculation of the width via configuration interaction techniques. Once the width, GAMMA(E), has been determined, the energy shift can be computed by a straightforward evaluation of the required principal-value integral. The main disadvantage of the method is that it provides only the total width of a resonance which decays into more than one channel in a multichannel problem. A review of the various aspects of the theory is given first, and then representative results that have been obtained with this method for several atomic and molecular resonances are discussed. 28 references, 3 figures, 4 tables 1978-01-01 331 CERN Document Server We present a preliminary measurement of the resonance parameters of the Upsilon(10580) resonance with the BABAR detector at the SLAC PEP-II asymmetric B factory. We measure the total decay width to be (20.7 +- 1.6 +- 2.5) MeV, the partial electronic width to be (0.321 +- 0.017 +- 0.029) kev and the mass to be (10.5793 +- 0.0004 +- 0.0012) GeV. Aubert, Bernard; Abe, T; Abrams, G S; Adye, T; Ahmed, S; Alam, M S; Albert, J; Aleksan, Roy; Allison, J; Altenburg, D; Andreotti, M; Angelini, C; Anulli, F; Aston, D; Azzolini, V; Baak, M A; Back, J J; Bailey, S; Baldini-Ferroli, R; Band, H R; Banerjee, Sw; Barate, R; Barlow, N R; Barlow, R J; Bartoldus, R; Batignani, G; Bauer, J M; Beck, T W; Behera, P K; Bellini, F; Benayoun, M; Berger, N; Beringer, J; Bernard, D; Berryhill, J W; Best, D; Bettarini, S; Bettoni, D; Bevan, A J; Bhimji, W; Bianchi, F; Biasini, M; Blanc, F; Blaylock, G; Blinov, V E; Bloom, P; Bondioli, M; Bonneaud, G R; Borean, C; Borgland, A W; Bosisio, L; Boutigny, D; Bowerman, D A; Boyarski, A M; Boyd, J T; Bozzi, C; Brandt, T; Brau, B; Brau, J E; Breon, A B; Briand, H; Brigljevic, V; Brochard, F; Brose, J; Brown, C L; Brown, C M; Brown, D; Brown, D N; Bruinsma, M; Brunet, S; Bucci, F; Buchanan, C; Buchmüller, O L; Bugg, W; Bukin, A D; Burchat, Patricia R; Button-Shafer, J; Buzzo, A; Bóna, M; Cahn, R N; Calabrese, R; Calcaterra, A; Calderini, G; Campagnari, C; Capra, R; Carpinelli, M; Cartaro, C; Cavallo, N; Cavoto, G; Chao, M; Charles, E; Chauveau, J; Chen, E; Chen, J C; Chen, S; Cheng, C H; Chevalier, N; Christ, S; Cibinetto, G; Clark, P J; Cochran, J; Cohen-Tanugi, J; Colberg, T; Colecchia, F; Coleman, J P; Contri, R; Convery, M R; Cote-Ahern, D; Cottingham, W N; Coupal, D P; Cowan, G; Cowan, R; Crawley, H B; Cremaldi, L M; Crosetti, G; Dahmes, B; Dallapiccola, C; Danielson, N; Dasu, S; Datta, M; Dauncey, P D; David, P; Davier, M; Davis, C L; Day, C T; De Groot, N; De Nardo, Gallieno; De Sangro, R; Del Buono, L; Del Gamba, V; Del Re, D; Della Ricca, G; Di Lodovico, F; Dickopp, M; Dittongo, S; Donald, M; Dong, D; Dorfan, J; Dorigo, A; Dubitzky, R S; Dubois-Felsmann, G P; Dujmic, D; Dunwoodie, W M; Dvoretskii, A; Eckmann, R; Edwards, A J; Egede, U; Eichenbaum, A M; Eigen, G; Eisner, A M; Elmer, P; Emery, S; Ernst, J A; Eschenburg, V; Eschrich, I; Fabozzi, F; Faccini, R; Falciai, D; Farbin, A; Ferrarotto, F; Ferroni, F; Field, R C; Finocchiaro, G; Fisher, A; Flack, R L; Flächer, H U; Flood, K T; Ford, K; Ford, W T; Forti, A C; Forti, F; Fortin, D; Franek, B J; Frey, R; Fry, J R; Gabathuler, Erwin; Gabriel, T A; Gaidot, A; Gaillard, J M; Gaillard, J R; Galeazzi, F; Gallo, F; Gamba, D; Gamet, R; Gan, K K; Ganzhur, S F; Gaspero, M; Gatto, C; Geddes, N I; George, S; Gill, M S; Giorgi, M A; Giraud, P F; Gladney, L; Glanzman, T; Godang, R; Goetzen, K; Golubev, V B; Gopal, G P; Gowdy, S J; Grancagnolo, S; Graugès-Pous, E; Green, M G; Grenier, G J; Grenier, P; Gritsan, A V; Grosdidier, G; Groysman, Y; Guo, Q H; Hadavand, H K; Hadig, T; Haire, M; Halyo, V; Hamel de Monchenault, G; Hamon, O; Harrison, P F; Harrison, T J; Hart, P A; Hartfiel, B L; Harton, J L; Hast, C; Hauke, A; Hawkes, C M; Hearty, C; Held, T; Hertzbach, S S; Heusch, C A; Hicheur, A; Hill, E J; Hitlin, D G; Hodgkinson, M C; Honscheid, K; Hrynóva, T; Hu, T; Hufnagel, D; Höcker, A; Innes, W R; Ivanchenko, V N; Izen, J M; Jackson, F; Jackson, P D; Jacobsen, R G; Jawahery, A; Jayatilleke, S M; Jessop, C P; John, M J J; Johnson, J R; Judd, D; Kadel, R W; Kadyk, J; Kagan, H; Karyotakis, Yu; Kass, R; Kay, M; Kelly, M P; Kelsey, M H; Kerth, L T; Khan, A; Kim, H; Kim, P; Kirkby, D; Kitayama, I; Knowles, D J; Koch, H; Kocian, M L; Kofler, R; Kolomensky, Yu G; Koptchev, V B; Kovalskyi, D; Kowalewski, R V; Kozanecki, Witold; Kral, J F; Kravchenko, E A; Krishnamurthy, M; Kroeger, R; Kukartsev, G; Kurup, A; Kutter, P E; Kuznetsova, N; Kyberd, P; La Vaissière, C de; Lacker, H M; Lae, C K; Lafferty, G D; Lamsa, J; Lanceri, L; Lange, D J; Langenegger, U; Langer, M; Lankford, A J; Laplace, S; Latham, T E; Lavin, D; Lazzaro, A; Le Clerc, C; Le Diberder, F R; Lee, S J; Lees, J P; Legendre, M; Leith, D W G S; Lepeltier, V; Leruste, P; Levesque, J A; Levi, M E; Levy, S L; Lewandowski, B; Li, H; Lillard, V; Lista, L; Liu, R; Lo Vetere, M; LoSecco, J M; Lockman, W S; London, G W; Long, O; Lou, X C; Lu, A; Luitz, S; Luppi, E; Lusiani, A; Lutz, A M; Lynch, G; Lynch, H L; Lyon, A J; Lü, C; Lüth, V; MacFarlane, D B; MacKay, C; Macri, M; Mallik, U; Maly, E; Mancinelli, G; Mandelkern, M A; Manfredi, P F; Mangeol, D J J; Marchiori, G; Margoni, M; Marker, C E; Marsiske, H; Martínez-Vidal, F; Mattison, T S; Mayer, B; Mazur, M A; Mazzoni, M A; McKemey, A K; McKenna, J A; McMahon, T R; Meadows, B T; Messner, R; Meyer, T I; Meyer, W T; Miftakov, V; Mihályi, A; Mir, L M; Mohapatra, A K; Mommsen, R K; Monge, M R; Moore, T B; Morandin, M; Morgan, S E; Morganti, M; Morganti, S; Morii, M; Morton, G W; Muheim, F; Müller, D R; Müller-Pfefferkorn, R; Narsky, I; Nash, J A; Nauenberg, U; Neal, H; Negrini, M; Neri, N; Nicholson, H; Nogowski, R; O'Grady, C P; Ocariz, J; Oddone, P J; Ofte, I; Olaiya, E O; Olivas, A; Olsen, J; Onuchin, A P; Orimoto, T J; Otto, S; Ozcan, V E; Paar, H P 2003-01-01 332 International Nuclear Information System (INIS) [en] A definition of low dimension equivalence in reactor physics calculations is given. Introducing a leakage buckling BL2, the axial equivalence equation for one dimension, as an example, is developed by the conservation of neutron and the weighted residual method in physics and mathematics respectively. YPARAM code has been developed to calculate the one dimension equivalence parameters. The eqivalent 1-D results are compared with the 3-D results for a 3-D test problem. The calculation errors of Keff and power distribution are within the accuracy limits of engineering design 1988-01-01 333 CERN Multimedia General Relativity formulated with Noncommutative geometry allows one to obtain, via the fluctuation of Dirac operator, an exact equivalence principle: generation of curvature and torsion from flat space. The fluctuation method presented in this report is applied on two examples. Marciante, Mathieu 2012-01-01 334 Directory of Open Access Journals (Sweden) Full Text Available We discuss here possible tests for Palatini f(R)-theories together with their implications for different formulations of the Equivalence Principle. We shall show that Palatini f(R)-theories obey the Weak Equivalence Principle and violate the Strong Equivalence Principle. The violations of the Strong Equivalence Principle vanish in vacuum (and purely electromagnetic) solutions as well as on short time scales with respect to the age of the universe. However, we suggest that a framework based on Palatini f(R)-theories is more general than standard General Relativity (GR) and it sheds light on the interpretation of data and results in a way which is more model independent than standard GR itself. Lorenzo Fatibene; Mauro Francaviglia 2013-01-01 335 CERN Multimedia In this paper, we consider $n$-perforated Yoneda algebras for $n$-angulated categories, and show that, under some conditions, $n$-angles induce derived equivalences between the quotient algebras of $n$-perforated Yoneda algebras. This result generalizes some results of Hu, K\\"{o}nig and Xi. And it also establishes a connection between higher cluster theory and derived equivalences. Namely, in a cluster tilting subcategory of a triangulated category, any Auslander-Reiten $n$-angle implies a derived equivalence between two quotient algebras. This result can be compared with the fact that an Auslander-Reiten sequence suggests a derived equivalence between two algebras which was proved by Hu and Xi. Chen, Yiping 2011-01-01 336 CERN Document Server We prove that a certain homological epimorphism between two algebras induces a triangle equivalence between their singularity categories. Applying the result to a construction of matrix algebras, we describe the singularity categories of some non-Gorenstein algebras. Chen, Xiao-Wu 2011-01-01 337 CERN Multimedia The paper proposes and motivates a conjecture on the invariance of cohomological support loci under derived equivalence. It contains a proof in the case of surfaces, and explains further developments and consequences. Popa, Mihnea 2012-01-01 338 CERN Multimedia Linear logic Concurrent Constraint programming (LCC) is an extension of concurrent constraint programming (CC) where the constraint system is based on Girard's linear logic instead of the classical logic. In this paper we address the problem of program equivalence for this programming framework. For this purpose, we present a structural operational semantics for LCC based on a label transition system and investigate different notions of observational equivalences inspired by the state of art of process algebras. Then, we demonstrate that the asynchronous \\pi-calculus can be viewed as simple syntactical restrictions of LCC. Finally we show LCC observational equivalences can be transposed straightforwardly to classical Concurrent Constraint languages and Constraint Handling Rules, and investigate the resulting equivalences. Haemmerlé, Rémy 2011-01-01 339 UK PubMed Central (United Kingdom) In 2006, the American College of Clinical Pharmacy (ACCP) charged the Task Force on Residency Equivalency to define the professional experience expected of a clinically mature practitioner that would meet or exceed the knowledge and skills of an accredited postgraduate year one residency-trained pharmacist. In this commentary, the Task Force discusses both the qualitative and quantitative components of documentation by means of a residency equivalency portfolio. The potential roles of academia, pharmacy professional organizations, and employers and the possible barriers to an equivalency process are addressed. This commentary lays the foundation for establishing a residency equivalency process that could promote the growth and development of existing and future residency programs and allow qualified practitioners to demonstrate their capabilities. The ACCP implores invested stakeholders to take an active part in this collaborative effort as the profession transitions toward residency training as a prerequisite for all pharmacists providing direct patient care by 2020. Jordan CJ; Wall GC; Lobo B; Wilkinson J; Creekmore FM; Sorrells K; Hartis C; Miller S; Uchal L 2009-12-01 340 CERN Multimedia We consider the role of the internal kinetic energy of bound systems of matter in tests of the Einstein equivalence principle. Using the gravitational sector of the standard model extension, we show that stringent limits on equivalence principle violations in antimatter can be indirectly obtained from tests using bound systems of normal matter. We estimate the bound kinetic energy of nucleons in a range of light atomic species using Green's function Monte Carlo calculations, and for heavier species using a Woods-Saxon model. We survey the sensitivities of existing and planned experimental tests of the equivalence principle, and report new constraints at the level of between a few parts in $10^{6}$ and parts in $10^{8}$ on violations of the equivalence principle for matter and antimatter. Hohensee, Michael A; Wiringa, R B 2013-01-01 341 Energy Technology Data Exchange (ETDEWEB) Measurements of Mg II k, Ca II K, and H..cap alpha.. line widths in late-type stars are compiled together with stellar basic parameters and the net radiative losses of their chromospheres estimated from the Mg II emission line intensities. We found that in giants and supergiants the Mg II k1 width corrected for activity and abundance difference (W1) shows a different power dependence on the stellar surface gravity from that in dwarfs. The widths of Mg II k and Ca II K lines are linearly correlated even in these giants and supergiants and suggests that the density-dependent effects of the partial frequency redistribution are not the cause of the change in the power index in W1(k). These facts indicate that the extended chromosphere is a universal phenomenon in the low-gravity late-type stars. The width of H..cap alpha.. shows a nearly constant velocity field in the chromosphere irrespective of gravity, providing that in hybrid stars a small portion of the systematic outflow velocity is superposed on the intrinsic width. Watanabe, Tetsuya 1988-01-01 342 Energy Technology Data Exchange (ETDEWEB) A switching power supply includes an FET full bridge, a controller to drive the FETs, a programmable controller to dynamically control final output current by adjusting pulse width, and a variety of protective systems, including an overcurrent latch for current control. Power MOSFETS are switched at a variable frequency from 20-50 kHz to charge a capacitor load from 0 to 6 kV. A ferrite transformer steps up the DC input. The transformer primary is a full bridge configuration with the FET switches and the secondary is fed into a high voltage full wave rectifier whose output is connected directly to the energy storage capacitor. The peak current is held constant by varying the pulse width using predetermined timing resistors and counting pulses. The pulse width is increased as the capacitor charges to maintain peak current. A digital ripple counter counts pulses, and after the desired number is reached, an up-counter is clocked. The up-counter output is decoded to choose among different resistors used to discharge a timing capacitor, thereby determining the pulse width. A current latch shuts down the supply on overcurrent due to either excessive pulse width causing transformer saturation or a major bridge fault, i.e., FET or transformer failure, or failure of the drive circuitry. Mihalka, Alex M. (Livermore, CA) 1986-01-01 343 International Nuclear Information System (INIS) The problem of s-equivalent lagrangians is considered in the realm of generalized mechanics. Some results corresponding to the ordinary (non-generalized) mechanics are extended to the generalized case. A theorem for the reduction of the higher order lagrangian description to the usual order is found to be useful for the analysis of generalized mechanical systems and leads to a new class of equivalence between lagrangian functions. Some new perspectives are pointed out. (Author) 1985-01-01 344 UK PubMed Central (United Kingdom) Rotator cuff repair techniques continue to evolve in an effort to improve repair biomechanics, maximize the biologic environment for tendon healing, and ultimately improve patient outcomes. The arthroscopic transosseous-equivalent technique was developed to replicate the favorable tendon-bone contact area for healing seen in open transosseous tunnel repair. In this technical note and accompanying video, we present our all-arthroscopic transosseous-equivalent rotator cuff repair technique with a focus on technical pearls. Lavery KP; Rasmussen JF; Dhawan A 2013-05-01 345 CERN Multimedia In this work we present an explicit operad morphism that is also a homotopy equivalence between the operad given by the real Fulton MacPherson compactification of configuration spaces and the little $n$-disks operad. In particular, the construction gives an operadic homotopy equivalence between the associahedra and the little intervals explicitly. It can also be extended to the case of Kontsevich compactification and Voronov swiss-cheese operad. Hoefel, Eduardo 2011-01-01 346 International Nuclear Information System (INIS) A new approach to the equivalence problem (in phase space) is presented. Given a Hamiltonian describing a system of particles with two degrees of freedom (and the corresponding Hamilton-Jacobi equation), it is shown how to find the most general family of Hamiltonian functions that generates new Hamilton-Jacobi equation with the following (and essential) characteristic, here defined as equivalence: every new solution is also a solution of the original Hamilton-Jacobi equation and vice-versa. (Author). 1985-01-01 347 CERN Document Server In this paper we introduce filtration pairs for isolated invariant sets of continuous maps. We prove the existence of filtration pairs and show that, up to shift equivalence, the induced map on the corresponding pointed space is an invariant of the isolated invariant set. Moreover, the maps defining the shift equivalence can be chosen canonically. Lastly, we define partially ordered Morse decompositions and prove the existence of Morse set filtrations for such decompositions. Franks, J; Franks, John; Richeson, David 1999-01-01 348 CERN Multimedia We give a brief overview of a few criteria equivalent to the Riemann Hypothesis. Next we concentrate on the Riesz and B{\\'a}ez-Duarte criteria. We proof that they are equivalent and we provide some computer data to support them. It is not compressed to six pages version of the talk delivered by M.W. during the XXVII Workshop on Geometrical Methods in Physics, 28 June -- 6 July, 2008, Bia{\\l}owie{\\.z}a, Poland. Cislo, J 2008-01-01 349 Energy Technology Data Exchange (ETDEWEB) Motivated by the study of ultraviolet properties of different versions of supergravities duality transformations at the quantum level are discussed. Using the background field method it is proven on shell quantum equivalence for several pairs of dual field theories known to be classically equivalent. The examples considered include duality in chiral model, duality of scalars and second rank antisymmetric gauge tensors, vector duality and duality of the Einstein theory with cosmological term and the Eddington-Schroedinger theory. 1985-06-01 350 International Nuclear Information System (INIS) An explicit formulation is presented to determine widths of magnetic island separatrices generated by magnetic field perturbations in a general toroidal stellarator geometry. The method, which is based on a representation of three-dimensional flux surfaces by double Fourier series, allows rapid and accurate calculation of the island widths in real vacuum field configurations, without the need to follow field lines through numerical integration of the field line equations. The procedure does not involve any simplifying approximations and can be used for fields with multiple small perturbations. Numerical results of the island width obtained in the flux co-ordinate representation for the Advanced Toroidal Facility agree closely with those determined from Poincare puncture points obtained by following field lines. The effects of resonance coupling are analysed. (author). Letter-to-the-editor. 19 refs, 1 fig., 3 tabs. 1990-01-01 351 International Nuclear Information System (INIS) [en] We use scalar gluonia dominance of the anomalous trace of the energy-momentum tensor and some results from QCD low-energy theorems and spectral sum rules in order to analyze the hadronic and ?? widths of a light Higgs boson of the standard model with a mass below the charm threshold. Large enhancements of the ?? and ??' modes occur respectively on the top of the ?(0.9) and G(1.6) poles, while the ?? width can be important around the G mass. Consequently, the Higgs into ?+?- branching ratio, which is about 10-2 on these gluonia poles, is much smaller than naively expected. Values of these various widths versus the Higgs boson mass are given. A search for the Higgs boson from the study of the ?? and ?'? invariant masses could be feasible. (orig.) 1989-09-28 352 Directory of Open Access Journals (Sweden) Full Text Available For many robotics and smart car applications it is vitally important to calculate the width. The present paper proposes a new approach for finding the width of a corridor within a constructed image frame that would keep a robot on a safe track away from walls. The main advantage of this approach is less computation time and hence faster response for path recognition. In this new approach, the Hugh Transform technique is also used as the basis of the provided algorithm. Within the determination of corridor width, in order to avoid the accident in the future researches, some approaches such as identify open space, modeling and reconstruction of three-dimensional space, can also be used. 2012-01-01 353 Energy Technology Data Exchange (ETDEWEB) Stark widths of many prominent 6s-6p and 5d-6p transitions have been measured and compared with theoretical results. A high current pinched discharge was used as a spectroscopic source. Electron density and temperature were estimated in 2.65x10{sup 22} m{sup -3} and 1.45x10{sup 4} K respectively. Experimental Stark widths agree well with previous theoretical results. Our data are compared with those of other authors concerning to the homologous ions Ne II, Ar II, Kr II and Xe II. (orig.). Bertuccelli, D.; Bertuccelli, G.; Rocco, H.O. di (Inst. de Fisica Arroyo Seco, Dept. de Fisica, Univ. Nacional del Centro de la Provincia de Buenos Aires, Tandil (Argentina)) 1991-05-01 354 Energy Technology Data Exchange (ETDEWEB) Both escape and spreading widths are evaluated microscopically in a consistent framework for the isobaric analog of the /sup 206/Pb ground state. A TDA Green function is obtained within the space of discretized J=0/sup +/ proton-particle neutron-hole configurations using the Skyrme interaction. Couplings of these configurations with continuum and more complicated configurations are included into TDA matrix elements with a form of energy dependent terms. The energy and the widths of the isobaric analog resonance are obtained as a result of the matrix diagonalization. Comparison is made of the results with the former theoretical calculations as well as experimental data. 1987-01-19 355 International Nuclear Information System (INIS) Based on a quantum statistical many-particle theory, the shift and the width of some He II lines have been evaluated. Ion dynamics have been treated within the model microfield method. Furthermore, fine structure splitting has been taken into account in order to check whether this effect is the cause for the existing large discrepancies between theoretical and experimental line widths. Besides the electronic contributions to the line shift, the shift due to the inhomogeneities of the ionic microfield as well as that due to the quadratic Stark effect has been included. (Copyright (c) 1998 Elsevier Science B.V., Amsterdam. All rights reserved.) 1998-10-01 356 Energy Technology Data Exchange (ETDEWEB) The hypothesis is advanced that, provided Young's modulus and Poisson's ratio of the rock are known, the length/width ratios of tension fractures can be used to estimate the tensile stress (assumed constant along the length of each fracture) at the time of fracture formation. The hypothesis is tested on a fissure swarm in 10,000-yr- old basaltic lava in Iceland. The length/width ratios of the fissure give the average tensile stress as of the order of a few MPa. 12 references. Gudmundsson, A. 1983-01-01 357 CERN Multimedia The energy spectrum of the high energy gamma-rays in coincidence with the prompt gamma rays has been measured for the spontaneous fission of 252Cf. The nucleus-nucleus coherent bremsstrahlung of the accelerating fission fragments is observed and the result has been substantiated with a theoretical calculation based on the coulomb acceleration model. The width of the giant dipole resonance (GDR) decay from the excited fission fragments has been extracted for the first time and compared with the thermal shape fluctuation model (TSFM) in the liquid drop formalism. The extracted GDR width is significantly smaller than the predictions of TSFM. Pandit, Deepak; Bhattacharya, Srijit; Pal, Surajit; De, A; Banerjee, S R 2009-01-01 358 International Nuclear Information System (INIS) [en] The energy spectrum of the high energy ?-rays in coincidence with the prompt ?-rays has been measured for the spontaneous fission of 252Cf. The nucleus-nucleus coherent bremsstrahlung of the accelerating fission fragments is observed and the result has been substantiated with a theoretical calculation based on the Coulomb acceleration model. The width of the giant dipole resonance (GDR) decay from the excited fission fragments has been extracted for the first time and compared with the thermal shape fluctuation model (TSFM) in the liquid drop formalism. The extracted GDR width is significantly smaller than the predictions of TSFM. 2010-07-05 359 Energy Technology Data Exchange (ETDEWEB) We present a procedure for measuring slit width and separation in single- and double-slit diffraction experiments. Intensity spectra of diffracted laser light are measured with an optical sensor (PIN diode). Slit widths and separations are extracted by fitting to the measured spectra. We present a simple fitting procedure to account for the integration (averaging) of light across the finite sensor aperture. This experiment provides students with a quantitative, in-depth verification of diffraction theory, as well as hands-on experience in sophisticated fitting methods. Gan, K K; Law, A T [Department of Physics, Ohio State University, Columbus, OH 43210 (United States)], E-mail: [email protected] 2009-11-15 360 International Nuclear Information System (INIS) [en] We present cross sections for e+e-? hadrons, e+e-, and ?+?- near 3095 MeV. The psi (3095) resonance is established as having an assignment J/supP//supC/=1--. The mass is 3095 plus-or-minus4 MeV. The partial width to electrons is GAMMA/sube/=4.8plus-or-minus0.6 keV and the total width GAMMA=69plus-or-minus15 keV. Total rates and interference measurements for the lepton channels are in accord with ?-e universality 1975-05-26 361 International Nuclear Information System (INIS) [en] The fluctuations of the s-wave neutron reduced widths for many nuclei have been analyzed with emphasis on recent measurements by a statistical procedure which is based on the method of maximum likelihood. It is shown that the s-wave neutron reduced widths of nuclei follow single channel Porter Thomas distribution (x2-distribution with degree of freedom ? = 1) for most of the cases. However there are apparent deviations from ? = 1 and possible explanation and significance of this deviation is given. These considerations are likely to modify the evaluation of neutron cross section. (author) 1992-01-01 362 International Nuclear Information System (INIS) [en] The fluctuations of the p-wave neutron reduced widths for fifty one nuclei have been analyzed with emphasis on recent measurements by a statistical procedure which is based on the method of maximum likelihood. It is shown that the p-wave neutron reduced widths of even-even nuclei fallow single channel Porter Thomas distribution (?2-distribution with degree of freedom ?=1) for most of the cases where there are no intermediate structure. It is emphasized that the distribution in nuclei other than even-even may differ from a ?2-distribution with one degree of freedom. Possible explanation and significance of this deviation from ?=1 is given. (author) 2000-01-01 363 CERN Document Server This article is dedicated to solve the equivalence problem for two third order differential operators on the line under general fiber--preserving transformation using the Cartan method of equivalence. We will do three versions of the equivalence problems: first via the direct equivalence problem, second equivalence problem is to determine conditions on two differential operators such that there exists a fiber-preserving transformations mapping one to the other according to gauge equivalence and last via fully projective equivalence method. 2011-01-01 364 CERN Multimedia Motivated by deformation quantization, we introduced in an earlier work the notion of formal Morita equivalence in the category of $^$-algebras over a ring $\\ring C$ which is the quadratic extension by $\\im$ of an ordered ring $\\ring R$. The goal of the present paper is twofold. First, we clarify the relationship between formal Morita equivalence, Ara's notion of Morita $^$-equivalence of rings with involution, and strong Morita equivalence of $C^$-algebras. Second, in the general setting of $^$-algebras over $\\ring C$, we define closed' $^$-ideals as the ones occuring as kernels of $^$-representations of these algebras on pre-Hilbert spaces. These ideals form a lattice which we show is invariant under formal Morita equivalence. This result, when applied to Pedersen ideals of $C^$-algebras, recovers the so-called Rieffel correspondence theorem. The triviality of the minimal element in the lattice of closed ideals, called the minimal ideal', is also a formal Morita invariant and this fact can be used ... Bursztyn, H; Bursztyn, Henrique; Waldmann, Stefan 2000-01-01 365 International Nuclear Information System (INIS) A directional dose equivalent monitor is introduced which consists of a 30 cm diameter spherical phantom hosting a superheated drop detector embedded at a depth of 10 mm. The device relies on the similarity between the fluence response of neutron superheated drop detectors based on halocarbon-12 and the quality-factor-weighted kerma factor. This implies that these detectors can be used for in-phantom dosimetry and provide a direct reading of dose equivalent at depth. The directional dose equivalent monitor was characterised experimentally with fast neutron calibrations and numerically with Monte Carlo simulations. The fluence response was determined at angles of 0, 45, 90, 135 and 180 degrees for thermal to 20 MeV neutrons. The response of the device is closely proportional to the fluence-to-directional dose equivalent conversion coefficient, H'F(10;a,E). Therefore, our monitor is suitable for a direct measurement of neutron directional dose equivalent, H'(10), regardless of angle and energy distribution of the neutron fluence. (author) 2001-01-01 366 CERN Multimedia In this paper we show the equivalence of various (non-threshold) bound state solutions of branes, or equivalently branes in background potentials, in ten- and eleven-dimensional supergravity. We compare solutions obtained in two very different ways. One method uses a zero mode analysis to make an Ansatz which makes it possible to solve the full non-linear supergravity equations. The other method utilises T-duality techniques to turn on the fields on the brane. To be specific, in eleven dimensions we show the equivalence for the (M2,M5) bound state, or equivalently an M5-brane in a C_3 field, where we also consider the (MW,M2,M2',M5) solution, which can be obtained from the (M2,M5) bound state by a boost. In ten dimensions we show the equivalence for the ((F,D1),D3) bound state as well as the bound states of (p,q) 5-branes with lower dimensional branes in type IIB, corresponding to D3-branes in B_2 and C_2 fields and (p,q) 5-branes in B_2, C_2 and C_4 fields. We also comment on the recently proposed V-duality ... Gran, U G; Gran, Ulf; Nielsen, Mikkel 2001-01-01 367 Energy Technology Data Exchange (ETDEWEB) An approach describing the width of the giant dipole resonance in hot nuclei is proposed. The numerical calculations in the schematic model with equally degenerate equidistant shells for a hot nucleus of mass A=110 carrying no angular momentum are performed which provide a good agreement with the behavior of the recent experimental data. (authors). 30 refs., 5 figs. Dinh Dang, N. [Viet Nam National Atomic Energy Commission, Hanoi (Viet Nam); Baldo, M. [Istituto Nazionale di Fisica Nucleare, Catania (Italy) 1995-12-31 368 UK PubMed Central (United Kingdom) The effect of shortening the pulse width of the electrical stimulus when administering electroconvulsive therapy (ECT) has recently been systematically studied with promising results. This review examines reported outcomes from three randomized controlled trials which compared ultrabrief (?0.3 ms) with brief (0.5-1.5 ms) pulse width ECT, and other recent clinical trials of ultrabrief pulse width ECT. The emerging evidence for ultrabrief pulse right unilateral (RUL) ECT suggests clinically meaningful efficacy and substantially reduced neuropsychological side effects compared with standard (brief) pulse ECT; this may represent a generational advance in the ECT technique. However, it is unclear if patients receiving ultrabrief pulse RUL ECT may have a slower speed of response and require additional treatments compared with brief pulse ECT. Therefore, until further data are available, clinicians may be well advised to use brief pulse ECT in situations requiring an urgent clinical response. The evidence base for ultrabrief bilateral ECT is limited, with findings that efficacy may be reduced compared with brief pulse width ECT. Thus ultrabrief bilateral ECT should not be used outside the research setting. Loo CK; Katalinic N; Martin D; Schweitzer I 2012-03-01 369 CERN Document Server We suggest using the half-width rule to make an estimate of the 1/Nc errors in hadronic models containing resonances. We show simple consequences ranging from the analysis of meson Regge trajectories, the hadron resonance gas at finite temperature and generalized hadronic form factors. Arriola, Enrique Ruiz; Masjuan, Pere 2012-01-01 370 CERN Document Server Atomic level widths obtained from experimental measurements are collected in Table I, along with the corresponding theoretical widths derived from the Evaluated Atomic Data Library (EADL) of Lawrence Livermore National Laboratory; these EADL values are based upon the Dirac-Hartree-Slater version of the independent-particle model. In a minority of cases, many-body theory predictions are also provided. A brief discussion of the manner in which the experimental widths were deduced from spectroscopic data is included. The bulk of the data are for elements in the solid state, but a few data for gases and simple compounds are included. For the K, L2, L3, and M5 levels, where Coster-Kronig contributions do not contribute or contribute only to a small extent to the overall widths, the EADL predictions appear satisfactory for elements in the solid state. For other levels, where Coster-Kronig and super-Coster-Kronig transitions have large probabilities within the independent-particle model, this model is not satisfacto... Campbell, J L 2001-01-01 371 UK PubMed Central (United Kingdom) A flexible lumen (10, 10', 10'', 110, 210) made from a solid, relatively rigid tubing (12, 12', 12'', 112, 212) that is made flexible by cutting a series of grooves (14, 14', 14'', 114, 214) of varying width and depth through the side of the tubing (12, 12', 12'', 112, 212). INJEV Valentine P. 372 CERN Document Server This is an investigation on the dynamical screening of an atom confined within a fullerene of finite width. The two surfaces of the fullerene lead to the presence of two surface plasmon eigenmodes. It is shown that, in the vicinity of these two eigenfrequencies, there is a large enhancement of the confined atom's photoabsorption rate. Lo, S; Solovyov, A V 2007-01-01 373 Digital Repository Infrastructure Vision for European Research (DRIVER) The effect of shortening the pulse width of the electrical stimulus when administering electroconvulsive therapy (ECT) has recently been systematically studied with promising results. This review examines reported outcomes from three randomized controlled trials which compared ultrabrief (?0.3 ms) w... Loo, Colleen K.; Katalinic, Natalie; Martin, Donel; Schweitzer, Isaac 374 CERN Multimedia In the framework of effective field theory we show that, at two-loop order, the mass and width of the \\Delta resonance defined via the (relativistic) Breit-Wigner parametrization both depend on the choice of field variables. In contrast, the complex-valued position of the pole of the propagator is independent of this choice. Djukanovic, D; Scherer, S 2007-01-01 375 CERN Document Server We analyze a contribution of the finite-width (mass-smearing) effects to the mixing of neutral mesons. It was shown, that this contribution is dominant in the D-meson system and large in the K-meson one. An account of the mass-smearing effects allows to explain some discrepancy between standard predictions and experimental data in these cases. Kuksa, V I 2009-01-01 376 International Nuclear Information System (INIS) It is shown that reflexes with form factor equal to zero are not absent, but have very small Darwin table width, which is determined by shift of the Bragg point and by form factors of another type. It is pointed out that this effect cannot be obtained within Ewald theory of dynamical diffraction on single crystals. 9 refs 1996-01-01 377 Digital Repository Infrastructure Vision for European Research (DRIVER) We present a measurement of the top-quark width in the lepton+jets decay channel of tt events produced in p p collisions at Fermilab's Tevatron collider and collected by the CDF II detector. From a data sample corresponding to 4.3 fb(-1) of integrated luminosity, we identify 756 candidate events. Th... Aaltonen, T; Álvarez González, B; Amerio, S; Amidei, D; Anastassov, A 378 Energy Technology Data Exchange (ETDEWEB) We present an improved determination of the total width of the top quark, {Gamma}{sub t}, using 5.4 fb{sup -1} of integrated luminosity collected by the D0 Collaboration at the Tevatron p{bar p} Collider. The total width {Gamma}{sub t} is extracted from the partial decay width {Gamma}(t {yields} Wb) and the branching fraction {Beta}(t {yields} Wb). {Gamma}(t {yields} Wb) is obtained from the t-channel single top-quark production cross section and {Beta}(t {yields} Wb) is measured in t{bar t} events. For a top mass of 172.5 GeV, the resulting width is {Gamma}{sub t} = 2.00{sub -0.43}{sup +0.47} GeV. This translates to a top-quark lifetime of {tau}{sub t} = (3.29{sub -0.63}{sup +0.90}) x 10{sup -25} s. We also extract an improved direct limit on the Cabibbo-Kobayashi-Maskawa quark-mixing matrix element 0.81 < \|V{sub tb}\| {le} 1 at 95% C.L. and a limit of \|V{sub tb}\| < 0.59 for a high-mass fourth-generation bottom quark assuming unitarity of the fourth-generation quark-mixing matrix. Abazov V. M.; Abbott B.; Acharya B. S.; Adams M.; Adams T.; Alexeev G. D.; Alkhazov G.; Alton A.; Alverson G.; Aoki M.; Askew A.; Asman B.; Atkins S.; Atramentov O.; Augsten K.; Avila C.; BackusMayes J.; Badaud F.; Bagby L.; Baldin B.; Bandurin D. V.; Banerjee S.; Barberis E.; Baringer P.; Barreto J.; Bartlett J. F.; Bassler U.; Bazterra V.; Bean A.; Begalli M.; Belanger-Champagne C.; Bellantoni L.; Beri S. B.; Bernardi G.; Bernhard R.; Bertram I.; Besancon M.; Beuselinck R.; Bezzubov V. A.; Bhat P. C.; Bhatia S.; Bhatnagar V.; Blazey G.; Blessing S.; Bloom K.; Boehnlein A.; Boline D.; Boos E. E.; Borissov G.; Bose T.; Brandt A.; Brandt O.; Brock R.; Brooijmans G.; Bross A.; Brown D.; Brown J.; Bu X. B.; Buehler M.; Buescher V.; Bunichev V.; Burdin S.; Burnett T. H.; Buszello C. P.; Calpas B.; Camacho-Perez E.; Carrasco-Lizarraga M. A.; Casey C. K.; Castilla-Valdez H.; Chakrabarti S.; Chakraborty D.; Chan M.; Chandra A.; Chapon E.; Chen G.; Chevalier-Thery S.; Cho D. K.; Cho S. W.; Choi S.; Choudhary B.; Cihangir S.; Claes D.; Clutter J.; Cooke M.; Cooper W. E.; Corcoran M.; Couderc F.; Cousinou M. -C.; Croc A.; Cutts D.; Das A.; Davies G.; de Jong S. J.; De La Cruz-Burelo E.; Deliot F.; Demina R.; Denisov D.; Denisov S. P.; Desai S.; Deterre C.; DeVaughan K.; Diehl H. T.; Diesburg M.; Ding P. F.; Dominguez A.; Dorland T.; Dubey A.; Dudko L. V.; Duggan D.; Duperrin A.; Dutt S.; Dyshkant A.; Eads M.; Edmunds D.; Ellison J.; Elvira V. D.; Enari Y.; Evans H.; Evdokimov A.; Evdokimov V. N.; Facini G.; Ferbel T.; Fiedler F.; Filthaut F.; Fisher W.; Fisk H. E.; Fortner M.; Fox H.; Fuess S.; Garcia-Bellido A.; Garcia-Guerra G. A.; Gavrilov V.; Gay P.; Geng W.; Gerbaudo D.; Gerber C. E.; Gershtein Y.; Ginther G.; Golovanov G.; Goussiou A.; Graf C. P.; Grannis P. D.; Greder S.; Greenlee H.; Greenwood Z. D.; Gregores E. M.; Grenier G.; Gris Ph.; Grivaz J. -F.; Grohsjean A.; Gruenendahl S.; Gruenewald M. W.; Guillemin T.; Gutierrez G.; Gutierrez P.; Haas A.; Hagopian S.; Haley J.; Han L.; Harder K.; Harel A.; Hauptman J. M.; Hays J.; Head T.; Hebbeker T.; Hedin D.; Hegab H.; Heinson A. P.; Heintz U.; Hensel C.; La Cruz I. Heredia-De; Herner K.; Hesketh G.; Hildreth M. D.; Hirosky R.; Hoang T.; Hobbs J. D.; Hoeneisen B.; Hohlfeld M.; Hubacek Z.; Hynek V.; Iashvili I.; Ilchenko Y.; Illingworth R.; Ito A. S.; Jabeen S.; Jaffre M.; Jamin D.; Jayasinghe A.; Jesik R.; Johns K.; Johnson M.; Jonckheere A.; Jonsson P.; Joshi J.; Jung A. W.; Juste A.; Kaadze K.; Kajfasz E.; Karmanov D.; Kasper P. A.; Katsanos I.; Kehoe R.; Kermiche S.; Khalatyan N.; Khanov A.; Kharchilava A.; Kharzheev Y. N.; Kohli J. M.; Kozelov A. V.; Kraus J.; Kulikov S.; Kumar A.; Kupco A.; Kurca T.; Kuzmin V. A.; Lammers S.; Landsberg G.; Lebrun P.; Lee H. S.; Lee S. W.; Lee W. M.; Lellouch J.; Li H.; Li L.; Li Q. Z.; Lietti S. M.; Lim J. K.; Lincoln D.; Linnemann J.; Lipaev V. V.; Lipton R.; Liu Y.; Lobodenko A.; Lokajicek M.; de Sa R. Lopes; Lubatti H. J.; Luna-Garcia R.; Lyon A. L.; Maciel A. K. A.; Mackin D.; Madar R.; Magana-Villalba R.; Malik S.; Malyshev V. L.; Maravin Y.; Martinez-Ortega J.; McCarthy R.; McGivern C. L.; Meijer M. M.; Melnitchouk A.; Menezes D.; Mercadante P. G.; Merkin M.; et al. 2012-05-04 379 International Nuclear Information System (INIS) The model-potential method (MPM), previously developed for describing single-electron excitations, is generalized to the case of two-electron transitions in atoms. A method is proposed for computing autoionization state widths with the help of the MPM, and the autoionization probabilities of He and Li atoms are calculated 1982-01-01 380 Digital Repository Infrastructure Vision for European Research (DRIVER) Porous alumina films had been fabricated by anodizing from aluminum films after an electropolishing procedure. Alumina stripes without pores can be distinguished on the surface of the porous alumina films. The width of the alumina stripes increases proportionally with the anodizing voltage. And the ... Huang, Kai; Huang, Shi-Ming; Pu, Lin; Shi, Yi; Wu, Zhi-Ming; Ji, Li; Kang, Jun-Yong 381 Directory of Open Access Journals (Sweden) Full Text Available Inverters inherently have the property of controlling output frequency but the output voltage can’t be varied. Usually to vary output voltage we have to vary supply voltage which is not always possible for this reason PWM techniques gained momentum. Basic aim of PWM technique is to control output voltage and harmonic reduction. Pulse-width modulation (PWM), or pulseduration modulation (PDM), is a commonly used technique for controlling power to inertial electrical devices, made practical by modern electronic power switches. Here we apply PWM techniques like Sinusoidal pulse width modulation (SPWM) and Space Vector Pulse width Modulation (SVPWM) to inverter and study its performance. In Sinusoidal Pulse width modulation (SPWM) we generate the gating signals by comparing a sinusoidal reference signal with a triangular carrier wave. In Space vector Modulation (SVPWM) we consider a rotating phased which is obtained by adding all the three voltages. Modulation is accomplished by switching state of an inverter. Thus by comparing these two techniques we study the performance of our inverter. K. Mounika#1 , B. Kiran Babu 2013-01-01 382 International Nuclear Information System (INIS) [en] A general method is developed for calculating the width, due to magnetic perturbations, of the scrape-off layer of a tokamak with a divertor. The general method is applied to a simple analytic model of a divertor to indicate the magnitude of the effects that would be expected 1977-01-01 383 UK PubMed Central (United Kingdom) The Phenylalanine Content of Foods, an equivalency system used in the dietary treatment of phenylketonuria, was prepared in 1975. Recently this system was revised to include a total of 372 food items in various raw and processed states. Food lists are available in a simple version for parents listing the serving size per phenylalanine equivalent, and in a more comprehensive version for dietitians providing weights for the serving sizes as well as values for phenylalanine, protein, and energy per equivalent. Subsequently, the system was modified to form a low protein equivalency system for use in designing low protein diets for a number of other inherited metabolic disorders. Chan L; Bell L; Hanley WB 1982-10-01 384 CERN Multimedia A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set B of Boolean functions. We consider the problem of determining whether two given constraint satisfaction instances are equivalent and prove a Dichotomy Theorem by showing that for all sets C of allowed constraints, this problem is either polynomial-time solvable or coNP-complete, and we give a simple criterion to determine which case holds. A more general problem addressed in this paper is the isomorphism problem, the problem of determining whether there exists a renaming of the variables that makes two given constraint satisfaction instances equivalent in the above sense. We prove that this problem is coNP-hard if the corresponding equivalence problem is coNP-hard, and polynomial-time many-one reducible to the graph isomorphism problem in all other cases. Böhler, E; Reith, S; Vollmer, H; Reith, Steffen; Vollmer, Heribert 2002-01-01 385 CERN Multimedia Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Our main result is that a quadratic function is CCZ-equivalent to an APN Gold function if and only if it is EA-equivalent to that Gold function. As an application of this result, we prove that a trinomial family of APN functions that exist on finite fields of order 2^n where n = 2 mod 4 are CCZ inequivalent to the Gold functions. The proof relies on some knowledge of the automorphism group of a code associated with such a function. Byrne, Eimear; McGuire, Gary; Nebe, Gabriele 2011-01-01 386 International Nuclear Information System (INIS) We show in this paper that the autonomous nonlinear dynamical system ?(A,B,F): x' = Ax+Bu+F(x) is topologically equivalent to the linear dynamical system ?(A,B,O): x' = Ax+Bu if the projection of A on the complement in Rn of the controllable vectorial subspace is hyperbolic and if lipschitz constant of F is sufficiently small () and F(x) = 0 when parallel x parallel is sufficiently large (). In particular, if ?(A,B,O) is controllable, it is topologically equivalent to ?(A,B,F) when it is only that F satisfy (). (author). 18 refs. 1995-01-01 387 CERN Document Server Here, we develop a theory of radiative heat transfer based on an equivalent electrical network representation for the hot material slabs in an arbitrary multilayered environment with arbitrary distribution of temperatures and electromagnetic properties among the layers. Our approach is fully equivalent to the known theories operating with the fluctuating current density, while being significantly simpler in analysis and applications. A practical example of the near-infrared heat transfer through the micron gap filled with an indefinite metmaterial is considered using the suggested method. The giant enhancement of the transferred heat compared to the case of the empty gap is shown. Maslovski, Stanislav I; Tretyakov, Sergei A 2012-01-01 388 Energy Technology Data Exchange (ETDEWEB) Purpose: Neutron exposure is of concern in proton therapy, and varies with beam delivery technique, nozzle design, and treatment conditions. Uniform scanning is an emerging treatment technique in proton therapy, but neutron exposure for this technique has not been fully studied. The purpose of this study is to investigate the neutron dose equivalent per therapeutic dose, H/D, under various treatment conditions for uniform scanning beams employed at our proton therapy center. Methods: Using a wide energy neutron dose equivalent detector (SWENDI-II, ThermoScientific, MA), the authors measured H/D at 50 cm lateral to the isocenter as a function of proton range, modulation width, beam scanning area, collimated field size, and snout position. They also studied the influence of other factors on neutron dose equivalent, such as aperture material, the presence of a compensator, and measurement locations. They measured H/D for various treatment sites using patient-specific treatment parameters. Finally, they compared H/D values for various beam delivery techniques at various facilities under similar conditions. Results: H/D increased rapidly with proton range and modulation width, varying from about 0.2 mSv/Gy for a 5 cm range and 2 cm modulation width beam to 2.7 mSv/Gy for a 30 cm range and 30 cm modulation width beam when 18 Multiplication-Sign 18 cm{sup 2} uniform scanning beams were used. H/D increased linearly with the beam scanning area, and decreased slowly with aperture size and snout retraction. The presence of a compensator reduced the H/D slightly compared with that without a compensator present. Aperture material and compensator material also have an influence on neutron dose equivalent, but the influence is relatively small. H/D varied from about 0.5 mSv/Gy for a brain tumor treatment to about 3.5 mSv/Gy for a pelvic case. Conclusions: This study presents H/D as a function of various treatment parameters for uniform scanning proton beams. For similar treatment conditions, the H/D value per uncollimated beam size for uniform scanning beams was slightly lower than that from a passive scattering beam and higher than that from a pencil beam scanning beam, within a factor of 2. Minimizing beam scanning area could effectively reduce neutron dose equivalent for uniform scanning beams, down to the level close to pencil beam scanning. Zheng Yuanshui; Liu Yaxi; Zeidan, Omar; Schreuder, Andries Niek; Keole, Sameer [ProCure Proton Therapy Center, 5901 West Memorial Road, Oklahoma City, Oklahoma 73142 (United States); INTEGRIS Cancer Insititute, 5911 West Memorial Road, Oklahoma City, Oklahoma 73142 (United States); ProCure Proton Therapy Center, 5901 West Memorial Road, Oklahoma City, Oklahoma 73142 (United States); ProCure Treatment Centers, 420 North Walnut Street, Bloomington, Indiana 47404 (United States); ProCure Proton Therapy Center, 5901 West Memorial Road, Oklahoma City, Oklahoma 73142 (United States) 2012-06-15 389 Energy Technology Data Exchange (ETDEWEB) A procedure for the determination of equivalent weight of amines is described. This procedure is based on an acid-base reaction performed in glacial acetic acid. The sum of primary, secondary, and tertiary amines are determined by titration with standard perchloric acid in glacial acetic acid. 1 ref. Selig, W.S. 1987-01-08 390 Science.gov (United States) \|A retarded boy, unable to read orally or with comprehension, was taught to match spoken to printed words and was then capable of reading comprehension (matching printed words to picture) and oral reading (naming printed words aloud), demonstrating that certain learned auditory-visual equivalences are sufficient prerequisites for reading… Sidman, Murray 1971-01-01 391 CERN Multimedia The model of Cremmer-Scherck and Proca are considered in dimensions greater than 3+1. It is obtained that the Proca model correspond to a gauged fixed version of the Cremmer-Scherck one, and we show their canonical equivalence. Arias, P J; Arias, Pio J.; Perez-Mosquera, Jean C. 2004-01-01 392 CERN Document Server In this paper we investigate operators unitarily equivalent to truncated Toeplitz operators. We show that this class contains certain sums of tensor products of truncated Toeplitz operators. In particular, it contains arbitrary inflations of truncated Toeplitz operators; this answers a question posed by Cima, Garcia, Ross, and Wogen. Strouse, Elizabeth; Zarrabi, Mohamed 2010-01-01 393 Science.gov (United States) Several studies have recently been conducted on cultured skin equivalent (SE), prepared using human keratinocytes seeded on various types of dermal equivalents (DE). We previously showed the advantages of our anchorage method in preventing the severe surface reduction of DE due to fibroblast contractile properties in vitro. A new anchored human SE was established in our laboratory in order to obtain a bioengineered tissue that would possess the appropriate histological and biological properties. In order to compare the effects of different collagen origins on the evolution of SE in vitro, human keratinocytes were seeded on three types of anchored DE. A comparative study was carried out between bovine SE (bSE), human SE (hSE), and human skin equivalent containing additional dermal matrix components (hSE+). Immunohistological analysis showed that hSE and hSE+ presented good structural organization, including the deposition of several basement membrane constituents. Higher amounts of transglutaminase, ceramides, and keratin 1 were detected in the epidermal layers of all SE when cultured at the air-liquid interface. However, a 92 kDa gelatinase activity was higher in bovine skin equivalent (bSE) compared to hSE cultures. The use of human collagens comparatively to bovine collagen as SE matricial component delayed the degradation of the dermal layer in culture. PMID:8589886 Auger, F A; López Valle, C A; Guignard, R; Tremblay, N; Noël, B; Goulet, F; Germain, L 1995-06-01 394 UK PubMed Central (United Kingdom) Several studies have recently been conducted on cultured skin equivalent (SE), prepared using human keratinocytes seeded on various types of dermal equivalents (DE). We previously showed the advantages of our anchorage method in preventing the severe surface reduction of DE due to fibroblast contractile properties in vitro. A new anchored human SE was established in our laboratory in order to obtain a bioengineered tissue that would possess the appropriate histological and biological properties. In order to compare the effects of different collagen origins on the evolution of SE in vitro, human keratinocytes were seeded on three types of anchored DE. A comparative study was carried out between bovine SE (bSE), human SE (hSE), and human skin equivalent containing additional dermal matrix components (hSE+). Immunohistological analysis showed that hSE and hSE+ presented good structural organization, including the deposition of several basement membrane constituents. Higher amounts of transglutaminase, ceramides, and keratin 1 were detected in the epidermal layers of all SE when cultured at the air-liquid interface. However, a 92 kDa gelatinase activity was higher in bovine skin equivalent (bSE) compared to hSE cultures. The use of human collagens comparatively to bovine collagen as SE matricial component delayed the degradation of the dermal layer in culture. Auger FA; López Valle CA; Guignard R; Tremblay N; Noël B; Goulet F; Germain L 1995-06-01 395 Directory of Open Access Journals (Sweden) Full Text Available In this paper we compute equivalent martingale measures when the asset price returns are modelled by a Lévy process. We follow the approach introduced by Gerber and Shiu (1994).Neste trabalho calculamos as medidas martingalas equivalentes quando os retornos dos preços dos ativos são modelados por um Processo de Lévy. Seguimos a formulação introduzida por Gerber and Shiu (1994). José Santiago Fajardo 2006-01-01 396 Digital Repository Infrastructure Vision for European Research (DRIVER) A basic problem in electromagnetics involves solving the Maxwell equations in a non-empty space, i.e. in a space with interfaces or boundaries. In this dissertation the wanted electromagnetic fields are searched via equivalence methods: a full electromagnetic problem is transformed to a simpler solv... Hänninen, Jari J. 397 Digital Repository Infrastructure Vision for European Research (DRIVER) This thesis studies behavioural equivalences on labelled infinite transition graphs and the role that they can play in the context of modal logics and notions from language theory. A natural class of such infinite graphs is that corresponding to the SnS-definable tree languages first studied by Rabi... Hüttel, Hans 398 Science.gov (United States) We performed a literature review and found that many equivalent circuit models of hysteresis motors in use today are incorrect. The model by Miyairi and Kataoka (1965) is the correct one. We extended the model by transforming it to quadrature coordinates,... B. A. Kirkendall E. T. Scharlemann J. J. Nitao 2009-01-01 399 CERN Multimedia In this paper we show the equivalence of the conjectures of Giuga and Agoh in a direct way which leads to a combined conjecture. This conjecture is described by a sum of fractions from which all conditions can be derived easily. Kellner, B C 2004-01-01 400 UK PubMed Central (United Kingdom) We extract the total width of the top quark, ?(t), from the partial decay width ?(t ? Wb) measured using the t-channel cross section for single top-quark production and from the branching fraction B(t ? Wb) measured in tt events using up to 2.3??fb(-1) of integrated luminosity collected by the D0 Collaboration at the Tevatron pp Collider. The result is ?(t) = 1.99(-0.55)(+0.69)??GeV, which translates to a top-quark lifetime of ?(t) = (3.3(-0.9)(+1.3)) × 10(-25) ??s. Assuming a high mass fourth generation b' quark and unitarity of the four-generation quark-mixing matrix, we set the first upper limit on \|V(tb')\| < 0.63 at 95% C.L. 2011-01-01 401 International Nuclear Information System (INIS) We extract the total width of the top quark, ?t, from the partial decay width ?(t?Wb) measured using the t-channel cross section for single top-quark production and from the branching fraction B(t?Wb) measured in tt events using up to 2.3 fb-1 of integrated luminosity collected by the D0 Collaboration at the Tevatron pp Collider. The result is ?t=1.99-0.55+0.69 GeV, which translates to a top-quark lifetime of ?t=(3.3-0.9+1.3)x10-25 s. Assuming a high mass fourth generation b' quark and unitarity of the four-generation quark-mixing matrix, we set the first upper limit on \|Vtb'\| 2011-01-14 402 Science.gov (United States) We extract the total width of the top quark, ?(t), from the partial decay width ?(t ? Wb) measured using the t-channel cross section for single top-quark production and from the branching fraction B(t ? Wb) measured in tt events using up to 2.3??fb(-1) of integrated luminosity collected by the D0 Collaboration at the Tevatron pp Collider. The result is ?(t) = 1.99(-0.55)(+0.69)??GeV, which translates to a top-quark lifetime of ?(t) = (3.3(-0.9)(+1.3)) × 10(-25) ??s. Assuming a high mass fourth generation b' quark and unitarity of the four-generation quark-mixing matrix, we set the first upper limit on \|V(tb')\| < 0.63 at 95% C.L. PMID:21405220 2011-01-11 403 Directory of Open Access Journals (Sweden) Full Text Available ????????????? ?????? ????????????????? ?????????? ?????????? ?????? ????????? ?????? ?? ?????? ??????? ???????? ?? ??? ??????????? ?????????, ?????????? ???????? ? ?????? ? ??????????? ?????????????? ?????? ? ????? ?????????????? ????????. ????? ???????? ??? ????????? ?? ???????? ?????? ? ??????????? ????????????, ????????? ??????????????? ??????? ????? ??????. ?????????? ???????? ????????????????? ?????????? ?????? ????????? ?????? ?????????????? ???????????. The tasks of experimental researches have been formulated, basic of which are: definition of width disclosing cracks at a level of the working fixture and in several levels above the stretched fixture; changes of distance between cracks and length of cracks in process of increase of loading with check of multilevel process of formation cracks; definition of deformations of the fixture and concrete with deformation account of effect in a vicinity of a two-console element. The technique of experimental researches of width of disclosing cracks of ferro-concrete designs from a position of the mechanics destruction is developed which has allowed to decide the put tasks. C????????????? ?????? ????????????????? ????????????, ??????????? ?????? ????????? ?????? ?? ??????? ??????? ???????? ? ??? ?????????? ?????????, ?????????? ???????? ? ?????? ? ?????? ??????????????? ??????? ? ??????????? ??????????????? ????????, ????????? ?????????? ????? ????????? ? ????? ?????? ? ??????????? ????????, ???????? ??????????????? ???????? ??????????? ??????. ??????????? ???????? ????????????????? ???????????? ?????? ????????? ?????? ?????????????? ???????????. ?.?. ????????; ????? ??? ????? 2006-01-01 404 International Nuclear Information System (INIS) In this paper, the authors study the effects of a possible new heavy neutral vector boson ZH on the partial and total widths of the ZL which are being studied at LEP. The analysis is formulated in as general terms as possible, without commitment to a particular model. The constraints on mzH from CDF and the new data on mw/mZL and mzL are taken into account. As expected, the induced deviations are at the level of a few percent. The allowed range decreases with increasing mL. The lepton widths and the peak cross-sections are particularly sensitive. A fourth light neutrino is excluded also in extended gauge models. 1990-01-01 405 CERN Multimedia In the context of statistical physics, Chandrasekharan and Wiese recently introduced the \\emph{fermionant} $\\Ferm_k$, a determinant-like quantity where each permutation $\\pi$ is weighted by $-k$ raised to the number of cycles in $\\pi$. We show that computing $\\Ferm_k$ is #P-hard under Turing reductions for any constant $k > 2$, and is $\\oplusP$-hard for $k=2$, even for the adjacency matrices of planar graphs. As a consequence, unless the polynomial hierarchy collapses, it is impossible to compute the immanant $\\Imm_\\lambda \\,A$ as a function of the Young diagram $\\lambda$ in polynomial time, even if the width of $\\lambda$ is restricted to be at most 2. In particular, if $\\Ferm_2$ is in P, or if $\\Imm_\\lambda$ is in P for all $\\lambda$ of width 2, then $\\NP \\subseteq \\RP$ and there are randomized polynomial-time algorithms for NP-complete problems. Mertens, Stephan 2011-01-01 406 CERN Document Server Based on the extended Greenwich-NOAA/USAF catalogue of sunspot groups it is demonstrated that the parameters describing the latitudinal width of the sunspot generating zone (SGZ) are closely related to the current level of solar activity, and the growth of the activity leads to the expansion of SGZ. The ratio of the sunspot number to the width of SGZ shows saturation at a certain level of the sunspot number, and above this level the increase of the activity takes place mostly due to the expansion of SGZ. It is shown that the mean latitudes of sunspots can be reconstructed from the amplitudes of solar activity. Using the obtained relations and the group sunspot numbers by Hoyt and Schatten (1998), the latitude distribution of sunspot groups ("the Maunder butterfly diagram") for the 18th and the first half of the 19th centuries is reconstructed and compared with historical sunspot observations. Ivanov, V G; 10.1007/s11207-010-9665-6 2010-01-01 407 CERN Multimedia We extract the total width of the top quark, Gamma_t, from the partial decay width Gamma(t -> W b) measured using the t-channel cross section for single top quark production and from the branching fraction B(t -> W b) measured in ttbar events using up to 2.3 fb^-1 of integrated luminosity collected by the D0 Collaboration at the Tevatron ppbar Collider. The result is Gamma_t = 1.99 +0.69 -0.55 GeV, which translates to a top-quark lifetime of tau_t = (3.3 +1.3 -0.9) x 10^-25 s. Assuming a high mass fourth generation b' quark and unitarity of the four-generation quark-mixing matrix, we set the first upper limit on \|Vtb'\| < 0.63 at 95% C.L. 2010-01-01 408 Energy Technology Data Exchange (ETDEWEB) Instabilities in the SOL plasma can strongly influence the SOL plasma behaviour and in particular the SOL width. The SOL stability analysis shows that there exists a critical ratio of the thermal energy and the magnetic energy. If the SOL beta is greater than this critical value, the magnetic field cannot prevent the plasma displacement and a strong MHD instability in the SOL occurs. In the opposite case only slower resistive instabilities can develop. A theoretical investigation of the SOL plasma stability is presented for JET single-null and double-null divertor configurations. The dependence of the stability threshold on the SOL beta and on the sheath resistance is established. Applying a simple mixing length argument gives the scaling of the SOL width. 5 refs., 2 figs. Kerner, W. [Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking; Pogutse, O. [Kurchatov institute, Moscow (Russian Federation) 1994-07-01 409 CERN Document Server 2-D diffraction patterns arising in the far-field region were investigated theoretically for the case, when the plane wave with non collinear group and phase velocities is incident on the wide slit in opaque screen with arbitrary orientation. This investigation was carried out by consideration as an example of magnetostatic surface wave diffraction in tangentially magnetized ferrite slab. It was deduced the universal analytical formula, which one can use to calculate the angular width of diffractive beam in any 2-D anisotropic geometries for the waves of various nature. It was shown, that in 2-D anisotropic geometries this width may be not only more or less then the value L/D (L - wavelength of incident wave, D - length of slit), but it also may be equal to zero in certain conditions. Lock, Edwin H 2011-01-01 410 Energy Technology Data Exchange (ETDEWEB) The concepts of pole mass and width are extended to unstable fermions in the general framework of parity-nonconserving gauge theories, such as the Standard Model. In contrast with the conventional on-shell definitions, these concepts are gauge independent and avoid severe unphysical singularities, properties of great importance since most fundamental fermions in nature are unstable particles. General expressions for the unrenormalized and renormalized dressed propagators of unstable fermions and their field-renormalization constants are presented. (orig.) Kniehl, B.A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Sirlin, A. [New York Univ., NY (United States). Dept. of Physics 2008-01-15 411 CERN Multimedia The acquisition stage in GNSS receivers determines Doppler shifts and code phases of visible satellites. Acquisition is thus a search in two continuous dimensions, where the digital algorithms require a partitioning of the search space into cells. We present analytic expressions for the acquisition performance depending on the partitioning of the Doppler frequency domain. In particular, the impact of the number and width of Doppler bins is analyzed. The presented results are verified by simulations. Geiger, Bernhard C 2011-01-01 412 UK PubMed Central (United Kingdom) By using the LHC and Tevatron measurements of the cross sections to various decay channels relative to the standard model Higgs boson, the total width of the putative 125 GeV Higgs boson is determined as 6.1(-2.9)(+7.7) MeV. We describe a way to estimate the branching fraction for the Higgs-boson decay to dark matter. We also discuss a no-go theorem for the ?? signal of the Higgs boson at the LHC. Barger V; Ishida M; Keung WY 2012-06-01 413 International Nuclear Information System (INIS) The two-body pionic weak-decay of ??5H is investigated to see the feasibility of the double-? nuclear identification by using monoenergetic decay pions. The obtained width is 0.459 ??, and the branching ratio of the two-body decay to the total decay is estimated to be about 25%. Differences between two-body decays of ?4H and of ??5H are also discussed. (author) 1996-01-01 414 CERN Document Server Let $G$ be a non-elementary hyperbolic group. Let $w$ be a group word such that the set $w[G]$ of all its values in $G$ does not coincide with $G$ or 1. We show that the width of verbal subgroup $w(G)=$ is infinite. That is, there is no such $l\\in\\mathbb Z$ that any $g\\in w(G)$ can be represented as a product of $\\le l$ values of $w$ and their inverses. Myasnikov, Alexei 2011-01-01 415 Science.gov (United States) We present a one-step synthesis process for ultrathin non-crystalline MnO2 nanosheets. Their thickness is about 2 nm and the width varies from 5 to 20 nm. They induce a higher capacitance than zero-dimensional spheres or one-dimensional rods. When heat treated at elevated temperature MnO2 nanosheets partly grow into crystalline Mn2O3 rods. PMID:23851984 Xu, Chengjun; Shi, Shan; Sun, Yige; Chen, Yanyi; Kang, Feiyu 2013-07-23 416 International Nuclear Information System (INIS) Thermally induced fuel fragmentation and relocation has been demonstrated to influence the thermal behavior of a fuel rod in two ways. The effective fuel pellet conductivity is decreased and pellet-to-cladding heat transfer is improved. This paper presents a correlation between as-built and relocated gap width which, used with the Ross and Stoute Gap Conductance Correlation and an appropriate fuel thermal expansion model, closely predicts the measured gap conductances 1978-11-17 417 CERN Multimedia Energy shifts and line widths of X-ray transitions in kaonic atoms have been measured with an accuracy of about 10%. These data have been interpreted in terms of an optical potential. Whereas earlier approaches based on the free K-N scattering lengths fail to reproduce the data, a set of effective parameters consistent with all now available experiments could be derived. (20 refs). Backenstoss, Gerhard; Bergström, I; Bounin, P; Bunaciu, T; Egger, J; Hultberg, S; Koch, H; Krell, M; Lynen, U; Ritter, H G; Schwitter, A; Stearns, R 1972-01-01 418 International Nuclear Information System (INIS) A new expression for the branching ratio for the decay via the E1 process in the normal-deformed band of superdeformed nuclei is given within a simple two-level model. Using this expression, the spreading or tunneling width ?? for superdeformed decay can be expressed entirely in terms of experimentally known quantities. We show how to determine the tunneling matrix element V from the measured value of ?? and a statistical model of the energy levels. 2004-09-13 419 International Nuclear Information System (INIS) I present a measurement of the W boson mass (MW) and width (?W) using 200 and 350 pb-1 of CDF Run II data respectively. The measurements, performed in both the electron and muon decay channels, rely on a fit to the W transverse mass distribution. We measure MW = 80413 ± 48 MeV and ?W = 2032 ± 71 MeV which represent the world's single most precise measurements to date. 2007-01-01 420 UK PubMed Central (United Kingdom) Electrolytic acid or alkaline water having a NMR half line width using 17O of from about 45 to less than 51 Hz, and an oxide reduction potential of from -1000 to +200 mV, or from +600 to +1300 mV, topical compositions that contain such water, uses for such water to hydrate skin, deliver drugs and treat various skin and mucosal conditions, and methods and apparatus for manufacturing the water. CHEN YONGGE; DE NONI ROBERTO 421 UK PubMed Central (United Kingdom) Electrolytic acid or alkaline water having a NMR half line width using 17O of from about 45 to less than 51 Hz, and an oxide reduction potential of from -1000 to +200 mV, or from +600 to +1300 mV, topical compositions that contain such water, uses for such water to hydrate skin, deliver drugs and treat various skin and mucosal conditions, and methods and apparatus for manufacturing the water. CHEN YONGGE; NONI ROBERTO DE 422 Science.gov (United States) Porous alumina films had been fabricated by anodizing from aluminum films after an electropolishing procedure. Alumina stripes without pores can be distinguished on the surface of the porous alumina films. The width of the alumina stripes increases proportionally with the anodizing voltage. And the pores tend to be initiated close to the alumina stripes. These phenomena can be ascribed to the electric field distribution in the alumina barrier layer caused by the geometric structure of the aluminum surface. PMID:21170406 Huang, Kai; Huang, Shi-Ming; Pu, Lin; Shi, Yi; Wu, Zhi-Ming; Ji, Li; Kang, Jun-Yong 2010-08-21 423 Directory of Open Access Journals (Sweden) Full Text Available It is proved that the moments of the width of Galton-Watson trees of size n and with offspring variance ? 2 are asymptotically given by (?? n) p m p where m p are the moments of the maximum of the local time of a standard scaled Brownian excursion. This is done by combining a weak limit theorem and a tightness estimate. The method is quite general and we state some further applications. Michael Drmota; Bernhard Gittenberger 2004-01-01 424 UK PubMed Central (United Kingdom) We present a one-step synthesis process for ultrathin non-crystalline MnO2 nanosheets. Their thickness is about 2 nm and the width varies from 5 to 20 nm. They induce a higher capacitance than zero-dimensional spheres or one-dimensional rods. When heat treated at elevated temperature MnO2 nanosheets partly grow into crystalline Mn2O3 rods. Xu C; Shi S; Sun Y; Chen Y; Kang F 2013-07-01 425 Science.gov (United States) Porous alumina films had been fabricated by anodizing from aluminum films after an electropolishing procedure. Alumina stripes without pores can be distinguished on the surface of the porous alumina films. The width of the alumina stripes increases proportionally with the anodizing voltage. And the pores tend to be initiated close to the alumina stripes. These phenomena can be ascribed to the electric field distribution in the alumina barrier layer caused by the geometric structure of the aluminum surface. Huang, Kai; Huang, Shi-Ming; Pu, Lin; Shi, Yi; Wu, Zhi-Ming; Ji, Li; Kang, Jun-Yong 2010-12-01 426 Directory of Open Access Journals (Sweden) Full Text Available Abstract Porous alumina films had been fabricated by anodizing from aluminum films after an electropolishing procedure. Alumina stripes without pores can be distinguished on the surface of the porous alumina films. The width of the alumina stripes increases proportionally with the anodizing voltage. And the pores tend to be initiated close to the alumina stripes. These phenomena can be ascribed to the electric field distribution in the alumina barrier layer caused by the geometric structure of the aluminum surface. Huang Kai; Huang Shi-Ming; Pu Lin; Shi Yi; Wu Zhi-Ming; Ji Li; Kang Jun-Yong 2010-01-01 427 UK PubMed Central (United Kingdom) Porous alumina films had been fabricated by anodizing from aluminum films after an electropolishing procedure. Alumina stripes without pores can be distinguished on the surface of the porous alumina films. The width of the alumina stripes increases proportionally with the anodizing voltage. And the pores tend to be initiated close to the alumina stripes. These phenomena can be ascribed to the electric field distribution in the alumina barrier layer caused by the geometric structure of the aluminum surface. Huang K; Huang SM; Pu L; Shi Y; Wu ZM; Ji L; Kang JY 2010-01-01 428 International Nuclear Information System (INIS) Sonographic evaluation of the width of spinal canal information received, concerning accuracy and especially quantity of CT or myelography is inferior compared to. The advantage of sonography is the lacking of X-ray exposure, the non-invasive procedure and the low cost of us apparat and operational time. For these reasons sonography is favoured as a screening method in detecting spinal canal stenosis in a group whose handicap was largely occupational or Sport-related. (orig.). 1985-01-01 429 Energy Technology Data Exchange (ETDEWEB) Sonographic evaluation of the width of spinal canal information received, concerning accuracy and especially quantity of CT or myelography is inferior compared to. The advantage of sonography is the lacking of X-ray exposure, the non-invasive procedure and the low cost of us apparat and operational time. For these reasons sonography is favoured as a screening method in detecting spinal canal stenosis in a group whose handicap was largely occupational or Sport-related. Helzel, M.V.; Betz, H.; Gladziwa, U.; Frey, M. 1985-06-01 430 UK PubMed Central (United Kingdom) We calculate the axial couplings of mesons and baryons containing a heavy quark in the static limit using lattice QCD. These couplings determine the leading interactions in heavy hadron chiral perturbation theory and are central quantities in heavy quark physics, as they control strong decay widths and the light quark mass dependence of heavy hadron observables. Our analysis makes use of lattice data at six different pion masses, 227 MeVwidths with experimental data for ?(c)() decays, we obtain ?[?(b)()??(b)?(±)]=4.2(1.0), 4.8(1.1), 7.3(1.6), 7.8(1.8) MeV for the ?(b)(+), ?(b)(-), ?(b)(+), ?(b)(-) initial states, respectively. We also derive upper bounds on the widths of the ?(b)(I()) baryons. Detmold W; Lin CJ; Meinel S 2012-04-01 431 Directory of Open Access Journals (Sweden) Full Text Available The clock distribution and generation circuitry forms a critical component of current synchronous digital systems. A digital system’s clocks must have not only low jitter, low skew, but also well-controlled duty cycle in order to facilitate versatile clocking techniques. In high-speed CMOS clock buffer design, the duty cycle of a clock is liable to be changed when the clock passes through a multistage buffer because the circuit is not pure digital [8]. In this paper, we propose a pulse width control loop referred as MPWCL (modified pulse width control loop) that adopts the same architecture as the conventional PWCL, but with a new pulse generator and new charge pump circuit as a constituent of the duty cycle detector. Thanks to using new building blocks the proposed pulse width control loop can control the duty cycle in a wide range, and what is more important it becomes operative in saturation region too, what provides conditional for fast locking time. For 1.2 µm double-metal double-poly CMOS process with Vdd = 5 V and operating frequency of 133 MHz, results of SPICE simulation show that the duty cycle can be well controlled in the range from 20 % up to 80 % if the loop parameters are properly chosen. Jovanovi? Goran; Stoj?ev Mile K. 2004-01-01 432 UK PubMed Central (United Kingdom) We present an approach to predicting extrinsic electron resonance widths within quantum corral nanostructures based on analogies with acoustics. Established quantum mechanical methods for calculating resonance widths, such as multiple scattering theory, build up the scattering atom by atom, ignoring the structure formed by the atoms, such as walls or enclosures. Conversely, particle-in-a-box models, assuming continuous walls, have long been successful in predicting quantum corral energy levels, but not resonance widths. In acoustics, partial reflection from walls and various enclosures has long been incorporated for determining reverberation times. Pursuing an exact analogy between the local density of states of a quantum corral and the acoustic impedance of a concert hall, we show electron lifetimes in nanoscopic structures of arbitrary convex shape are well accounted for by the Sabine formula for acoustic reverberation times. This provides a particularly compact and intuitive prescription for extrinsic finite lifetimes in a particle-in-a-box with leaky walls, including quantum corral atomic walls, given single particle scattering properties. Barr MC; Zaletel MP; Heller EJ 2010-09-01 433 Science.gov (United States) We present an approach to predicting extrinsic electron resonance widths within quantum corral nanostructures based on analogies with acoustics. Established quantum mechanical methods for calculating resonance widths, such as multiple scattering theory, build up the scattering atom by atom, ignoring the structure formed by the atoms, such as walls or enclosures. Conversely, particle-in-a-box models, assuming continuous walls, have long been successful in predicting quantum corral energy levels, but not resonance widths. In acoustics, partial reflection from walls and various enclosures has long been incorporated for determining reverberation times. Pursuing an exact analogy between the local density of states of a quantum corral and the acoustic impedance of a concert hall, we show electron lifetimes in nanoscopic structures of arbitrary convex shape are well accounted for by the Sabine formula for acoustic reverberation times. This provides a particularly compact and intuitive prescription for extrinsic finite lifetimes in a particle-in-a-box with leaky walls, including quantum corral atomic walls, given single particle scattering properties. PMID:20684508 Barr, Matthew C; Zaletel, Michael P; Heller, Eric J 2010-09-01 434 CERN Document Server We refute the conjecture that all negative translations are intuitionistically equivalent by giving two counterexamples. Then we characterise the negative translations intuitionistically equivalent to the usual ones. Gaspar, Jaime 2010-01-01 435 UK PubMed Central (United Kingdom) The composition of the female breast is an elusive variable in screen-film mammography that has a vital role in determining both the radiographic image quality and breast radiation dose. Despite the large volume of research in mammography only two studies known to the author define the chemical composition of the two major breast constituents, fibrous glandular tissue and adipose tissue. Unfortunately there is not complete agreement between these two studies. Upon this basis, a variety of breast phantom materials have been suggested and developed. This paper examines the radiographic equivalence of some of these materials dealing notably with formulations given by Hammerstein et al and ICRU Report 44, as well as BR12, water, and lucite. Radiographic equivalence was calculated using a computer simulation of mammographic spectra (after the example of Birch and Marshall and Tucker et al, and fitted to available FDA data) applied to attenuation data of phantom materials, in turn based on elemental linear attenuation coefficient data. A software algorithm was written that iteratively calculates the thickness of a nominated material required to match the attenuation of another material of particular thickness. The equivalence of 2-8 cm of lucite to various phantom materials was calculated for molybdenum target, molybdenum filter (Mo/Mo) x-ray beams from 25 to 35 kVp and for Mo/Rh and Rh/Rh beams from 27 to 35 kVp. It was found that for Mo/Mo beams the equivalent thickness of breast phantom material for certain thicknesses of lucite was largely independent of x-ray beam energy with the range of thickness equivalences being less than 3% at 8 cm of lucite and less than 0.5% at 2 cm of lucite. The RMI 156 breast phantom was found to be equivalent to 42 mm of Hammerstein et al. 50% glandular/50% adipose phantom material for Mo/Mo beams at 27 kVp, increasing to 43 mm for the range of Rh/Rh beams. While some questions remain on the accuracy of the present composition of breast constituents, it is clear that various breast compositions can be successfully simulated by using an appropriate thickness of lucite material. The use of lucite breast phantoms is then seen as an effective and reliable way of evaluating mammographic image quality and for calculating breast dose for varying required breast compositions. McLean D 1997-03-01 436 International Nuclear Information System (INIS) [en] Full text: The composition of the female breast is an allusive variable in screen-film mammography that has a vital role in determining both the radiographic image quality and breast radiation dose. Despite the large volume of research in mammography only two studies known to the author define the chemical composition of the two major breast constituents, fibrous glandular tissue and adipose tissue. Unfortunately there is not complete agreement between these two studies. Upon this basis a variety of breast phantom materials have been suggested and developed. This paper examines the radiographic equivalence of some of these material dealing notably with the formulations given by Hammerstein GR et al (Radiol, 130:485-491, 1979) and ICRU (Report 44, 1989) as well as BR12 (White DR, et al, Brit. J. Radiol. 50:814821, 1977), water and lucite. Radiographic equivalence was calculated using a computer simulation of mammographic spectra (after the example of Birch and Marshall (Phys Med Biol 24(3):505-517, 1979) and Tucker et al (Med. Phys. 18(3):402-407, 1991) and fitted to available FDA data) applied to attenuation data of phantom materials in turn based on elemental linear attenuation coefficient data. A software algorithm was written that iteratively calculates the thickness of a nominated material required to match the attenuation of another material of particular thickness. The equivalence of 2 - 8 cm of lucite to various phantom materials was calculated for molybdenum target, molybdenum filter (Mo/Mo) x-ray beams from 25 to 35 kVp and for Mo/Rh and Rh/Rh beams from 27 to 35 kVp. It was found that for Mo/Mo beams the equivalent thickness of breast phantom material for certain thicknesses of lucite was largely independent of x-ray beam energy with the range of thickness equivalences being less than 3% at 8 cm of lucite and less than 0.5% at 2 cm of lucite. The RMI 156 breast phantom was found to be equivalent to 42 cm of Hammerstein 50% glandular/ 50% adipose phantom material for Mo/Mo beams at 27 kVp, increasing to 43 cm for the range of Rh/Rh beams. While some question does remain on the accuracy of the present composition of breast constituents it is clear that various breast compositions can be successfully simulated by using an appropriate thickness of lucite material. The use of lucite breast phantoms is then seen as an effective and reliable way of evaluating mammographic image quality and for calculating breast dose for varying required breast compositions 1996-01-01 437 CERN Multimedia Using 13.4 $fb^{-1}$ of data collected with the CLEO detector at the Cornell Electron Storage Ring, we have observed 300 events for the two-photon production of ground-state pseudo-scalar charmonium in the decay $\\eta_c$ -> $K_S K^{\\mp} \\pi^{\\pm}$. We have measured the $\\eta_c$ mass to be (2980.4 +- 2.3 (stat) +- 0.6 (sys)) MeV and its full width as (27.0 +- 5.8 (stat) +- 1.4 (sys)) MeV. We have determined the two-photon partial width of the $\\eta_c$ meson to be (7.6 +- 0.8 (stat) +- 0.4 (sys) +- 2.3 (br)) keV, with the last uncertainty associated with the decay branching fraction. Brandenburg, G; Gao, Y S; Kim, D Y J; Wilson, R; Browder, T E; Li, Y; Rodríguez, J L; Yamamoto, H; Bergfeld, T; Eisenstein, B I; Ernst, J; Gladding, G E; Gollin, G D; Hans, R M; Johnson, E; Karliner, I; Marsh, M A; Palmer, M; Plager, C; Sedlack, C; Selen, M; Thaler, J J; Williams, J; Edwards, K W; Janicek, R; Patel, P M; Sadoff, A J; Ammar, R; Bean, A; Besson, D; Davis, R; Kwak, N; Zhao, X; Anderson, S; Frolov, V V; Kubota, Y; Lee, S J; Mahapatra, R; O'Neill, J J; Poling, R A; Riehle, T; Smith, A; Stepaniak, C J; Urheim, J; Ahmed, S; Alam, M S; Athar, S B; Jian, L; Ling, L; Saleem, M; Timm, S; Wappler, F; Anastassov, A; Duboscq, J E; Eckhart, E; Gan, K K; Gwon, C; Hart, T; Honscheid, K; Hufnagel, D; Kagan, H; Kass, R; Pedlar, T K; Schwarthoff, H; Thayer, J B; Von Törne, E; Zoeller, M M; Richichi, S J; Severini, H; Skubic, P L; Undrus, A; Chen, S; Fast, J; Hinson, J W; Lee, J; Miller, D H; Shibata, E I; Shipsey, I P J; Pavlunin, V; Cronin-Hennessy, D; Lyon, A L; Thorndike, E H; Jessop, C P; Marsiske, H; Perl, Martin Lewis; Savinov, V; Ugolini, D W; Zhou, X; Coan, T E; Fadeev, V; Maravin, Y; Narsky, I; Stroynowski, R; Ye, J; Wlodek, T; Artuso, M; Ayad, R; Boulahouache, C; Bukin, K; Dambasuren, E; Karamov, S; Majumder, G; Moneti, G C; Mountain, R; Schuh, S; Skwarnicki, T; Stone, S; Viehhauser, G; Wang, J C; Wolf, A; Wu, J; Kopp, S E; Mahmood, A H; Csorna, S E; Danko, I; McLean, K W; Marka, S; Xu, Z; Godang, R; Kinoshita, K; Lai, I C; Schrenk, S; Bonvicini, G; Cinabro, D; McGee, S; Perera, L P; Zhou, G J; Lipeles, E; Pappas, S P; Schmidtler, M; Shapiro, A; Sun, W M; Weinstein, A J; Würthwein, F; Jaffe, D E; Masek, G E; Paar, H P; Potter, E M; Prell, S; Sharma, V; Asner, D M; Eppich, A; Hill, T S; Morrison, R J; Briere, R A; Ferguson, T; Vogel, H; Behrens, B H; Ford, W T; Gritsan, A; Roy, J D; Smith, J G; Alexander, J P; Baker, R; Bebek, C; Berger, B E; Berkelman, K; Blanc, F; Boisvert, V; Cassel, David G; Dickson, M; Drell, P S; Ecklund, K M; Ehrlich, R; Foland, A D; Gaidarev, P B; Galik, R S; Gibbons, L K; Gittelman, B; Gray, S W; Hartill, D L; Heltsley, B K; Hopman, P I; Jones, C D; Kreinick, D L; Lohner, M; Magerkurth, A; Meyer, T O; Mistry, N B; Nordberg, E; Patterson, J R; Peterson, D; Riley, D; Thayer, J G; Thies, P G; Urner, D; Valant-Spaight, B L; Warburton, A; Avery, P; Prescott, C; Rubiera, A I; Yelton, J; Zheng, J 2000-01-01 438 UK PubMed Central (United Kingdom) Using 13.4 fb(-1) of data collected with the CLEO detector at the Cornell Electron Storage Ring, we have observed 300 events for the two-photon production of ground-state pseudoscalar charmonium in the decay eta(c)-->K(0)(S)K-/+pi(+/-). We have measured the eta(c) mass to be [2980.4+/-2.3 (stat)+/-0.6 (syst)] MeV and its full width as [27.0+/-5.8 (stat)+/-1.4 (syst)] MeV. We have determined the two-photon partial width of the eta(c) meson to be [7.6+/-0.8 (stat)+/-0.4 (syst)+/-2.3 (br)] keV, with the last uncertainty associated with the decay branching fraction. Brandenburg G; Ershov A; Gao YS; Kim DY; Wilson R; Browder TE; Li Y; Rodriguez JL; Yamamoto H; Bergfeld T; Eisenstein BI; Ernst J; Gladding GE; Gollin GD; Hans RM; Johnson E; Karliner I; Marsh MA; Palmer M; Plager C; Sedlack C; Selen M; Thaler JJ; Williams J; Edwards KW; Janicek R; Patel PM; Sadoff AJ; Ammar R; Bean A; Besson D; Davis R; Kwak N; Zhao X; Anderson S; Frolov VV; Kubota Y; Lee SJ; Mahapatra R; O'Neill JJ; Poling R; Riehle T; Smith A; Stepaniak CJ; Urheim J; Ahmed S; Alam MS; Athar SB; Jian L; Ling L; Saleem M; Timm S; Wappler F; Anastassov A; Duboscq JE; Eckhart E; Gan KK; Gwon C; Hart T; Honscheid K; Hufnagel D; Kagan H; Kass R; Pedlar TK; Schwarthoff H; Thayer JB; von Toerne E; Zoeller MM; Richichi SJ; Severini H; Skubic P; Undrus A; Chen S; Fast J; Hinson JW; Lee J; Miller DH; Shibata EI; Shipsey IP; Pavlunin V; Cronin-Hennessy D; Lyon AL; Thorndike EH; Jessop CP; Marsiske H; Perl ML; Savinov V; Ugolini D; Zhou X; Coan TE; Fadeyev V; Maravin Y; Narsky I; Stroynowski R; Ye J; Wlodek T; Artuso M; Ayad R; Boulahouache C; Bukin K; Dambasuren E; Karamov S; Majumder G; Moneti GC; Mountain R; Schuh S; Skwarnicki T; Stone S; Viehhauser G; Wang JC; Wolf A; Wu J; Kopp S; Mahmood AH; Csorna SE; Danko I; McLean KW; Márka S; Xu Z; Godang R; Kinoshita K; Lai IC; Schrenk S; Bonvicini G; Cinabro D; McGee S; Perera LP; Zhou GJ; Lipeles E; Pappas SP; Schmidtler M; Shapiro A; Sun WM; Weinstein AJ; Würthwein F; Jaffe DE; Masek G; Paar HP; Potter EM; Prell S; Sharma V; Asner DM; Eppich A; Hill TS; Morrison RJ; Briere RA; Ferguson T; Vogel H; Behrens BH; Ford WT; Gritsan A; Roy J; Smith JG; Alexander JP; Baker R; Bebek C; Berger BE; Berkelman K; Blanc F; Boisvert V; Cassel DG; Dickson M; Drell PS; Ecklund KM; Ehrlich R; Foland AD; Gaidarev P; Galik RS; Gibbons L; Gittelman B; Gray SW; Hartill DL; Heltsley BK; Hopman PI; Jones CD; Kreinick DL; Lohner M; Magerkurth A; Meyer TO; Mistry NB; Nordberg E; Patterson JR; Peterson D; Riley D; Thayer JG; Thies PG; Urner D; Valant-Spaight B; Warburton A; Avery P; Prescott C; Rubiera AI; Yelton J; Zheng J 2000-10-01 439 Directory of Open Access Journals (Sweden) Full Text Available We extend the Equivalence Theory (ET) formulated by Absi [1] for the statics of isotropic materials to the statics and dynamics of orthotropic materials. That theory relies on the assumption that any real body mod- eling may be substituted by another one that, even though it may possibly have material constitutive laws and geometric properties with no physical sense (like negative cross sections or Young modulus), is intended to be more advantageous for calculus. In our approach, the equivalence is expressed by equating both the effective strain energies of the two models and the material structural weights in dynamics [2]. We provide a numerical analysis of the convergence properties of ET approach while comparing its numerical results with those predicted by the analytical theory and the Finite Elements Method for thin plates.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8934765458106995, "perplexity": 4805.3642499879015}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997904391.23/warc/CC-MAIN-20140722025824-00022-ip-10-33-131-23.ec2.internal.warc.gz"}
https://socratic.org/questions/how-do-you-simplify-abs-18	Algebra Topics # How do you simplify abs(-18)? The answer is $18$. Absolute value is the distance of a number from zero. On a number line, $- 18$ is $18$ units left of zero.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.965080201625824, "perplexity": 667.3266248312486}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141186761.30/warc/CC-MAIN-20201126055652-20201126085652-00678.warc.gz"}
https://math.stackexchange.com/questions/1268431/evaluate-the-limit-lim-x-to-2-frac-sinx2-4x2-x-2	# Evaluate the limit $\lim_{x\to 2} \frac {\sin(x^2 -4)}{x^2 - x -2}$ $$\lim_{x\to 2} \frac {\sin(x^2 -4)}{x^2 - x -2}$$ Attempt at solution: So I know I can rewrite denominator: $$\frac {\sin(x^2 -4)}{(x-1)(x+2)}$$ So what's next? I feel like I'm supposed to multiply by conjugate of either num or denom.... but by what value...? Don't tell me I'm simply supposed to plug in $x = 2$ I need to simplify fractions somehow first, how? • Can you use the L'Hôpital's rule? – user226387 May 5 '15 at 16:17 • Your factorisation is incorrect: it should be $(x+1)(x-2)$ (which makes the problem non-trivial, of course). – Chappers May 5 '15 at 16:17 • The factorization of the bottom is wrong. Find the right factorization and multiply top and bottom by $x+2$. – André Nicolas May 5 '15 at 16:18 $$\frac {\sin(x^2 -4)}{(x-2)(x+1)}\cdot\frac{x+2}{x+2} = \frac{(x+2)\sin(x^2 - 4)}{(x+1)(x^2 - 4)} = \dfrac{x+2}{x+1}\cdot \dfrac{\sin(x^2 - 4)}{x^2 - 4}$$ $$\frac{\sin(x^2-4)}{(x+1)(x-2)}=\frac{\sin(x^2-4)}{x^2-4}\,\frac{x^2-4}{(x+1)(x-2)}$$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.873773455619812, "perplexity": 559.6506810220552}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986672431.45/warc/CC-MAIN-20191016235542-20191017023042-00502.warc.gz"}
http://etna.mcs.kent.edu/volumes/2011-2020/vol40/abstract.php?vol=40&pages=311-320	Chebyshev acceleration of the GeneRank algorithm Michele Benzi and Verena Kuhlemann Abstract The ranking of genes plays an important role in biomedical research. The GeneRank method of Morrison et al. [BMC Bioinformatics, 6:233 (2005)] ranks genes based on the results of microarray experiments combined with gene expression information, for example from gene annotations. The algorithm is a variant of the well known PageRank iteration, and can be formulated as the solution of a large, sparse linear system. Here we show that classical Chebyshev semi-iteration can considerably speed up the convergence of GeneRank, outperforming other acceleration schemes such as conjugate gradients. Full Text (PDF) [246 KB] Key words GeneRank, computational genomics, Chebyshev semi-iteration, polynomials of best uniform approximation, conjugate gradients AMS subject classifications 65F10, 65F50; 9208, 92D20	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.903800368309021, "perplexity": 4484.3555181157135}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583509170.2/warc/CC-MAIN-20181015100606-20181015122106-00428.warc.gz"}
https://www.physicsforums.com/threads/path-integral-question.289669/	# Path integral question 1. Feb 3, 2009 ### weejee Hi, I'm going through the details of the path integral, and have a question about its derivation. When we discretize the time interval and evaluate <p_n\|exp(-iH(t_n-t_n-1)\|q_n-1>, a Hamiltonian of the form H(p,q)=T(p)+V(q) becomes a number T(p_n)+V(q_n-1). However, when the Hamiltonian contains a term like 1/2[pf(q)+f(q)p], it becomes f(q_n')*p_n with q_n'=(q_n+q_n-1)/2. I understand the mathematics behind it but it seems to me that it doesn't really matter whether we use q_n-1 or q_n' as the time interval goes to positive infinitesimal. Can anyone explain to me why this actually matters? Thanks in advance. Share this great discussion with others via Reddit, Google+, Twitter, or Facebook Can you offer guidance or do you also need help? Draft saved Draft deleted	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9607393145561218, "perplexity": 1404.0822075638291}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590069.15/warc/CC-MAIN-20180718060927-20180718080927-00170.warc.gz"}
http://www.math.uah.edu/stat/apps/SpecialSimulation.html	Special Distribution Simulator Distribution graph Description This app simulates values from a random variable with a specified special distribution. the following distributions can be chosen with the selection box: In each case, the parameters can be set with the input controls.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8194231986999512, "perplexity": 1484.0121065085634}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320582.2/warc/CC-MAIN-20170625203122-20170625223122-00388.warc.gz"}
http://eprint.iacr.org/2007/365	## Cryptology ePrint Archive: Report 2007/365 Pairings on Jacobians of Hyperelliptic Curves Christian Robenhagen Ravnshoj Abstract: Consider the jacobian of a hyperelliptic genus two curve defined over a finite field. Under certain restrictions on the endomorphism ring of the jacobian we give an explicit description all non-degenerate, bilinear, anti-symmetric and Galois-invariant pairings on the jacobian. From this description it follows that no such pairing can be computed more efficiently than the Weil pairing. To establish this result, we need an explicit description of the representation of the Frobenius endomorphism on the l-torsion subgroup of the jacobian. This description is given. In particular, we show that if the characteristic polynomial of the Frobenius endomorphism splits into linear factors modulo l, then the Frobenius is diagonalizable. Finally, under the restriction that the Frobenius element is an element of a certain subring of the endomorphism ring, we prove that if the characteristic polynomial of the Frobenius endomorphism splits into linear factors modulo l, then the embedding degree and the total embedding degree of the jacobian with respect to l are the same number. Category / Keywords: public-key cryptography / Hyperelliptic curve cryptography	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9830993413925171, "perplexity": 241.95161628718435}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542520.47/warc/CC-MAIN-20161202170902-00165-ip-10-31-129-80.ec2.internal.warc.gz"}
https://unapologetic.wordpress.com/2009/10/02/examples-and-notation/?like=1&source=post_flair&_wpnonce=c1ce40f6e1	# The Unapologetic Mathematician ## Examples and Notation Okay, let’s do some simple examples of differentials, which will lead to some notational “syntactic sugar”. First of all, if we pick an orthonormal basis $\left\{e_i\right\}_{i=1}^n$ we can write any point as $x=x^ie_i$. This gives us $n$ nice functions to consider: $x^i:\mathbb{R}^n\rightarrow\mathbb{R}$ is the function that takes a point and returns its $i$th coordinate. This is actually a sort of subtle point that’s important to consider deeply. We’re used to thinking of $x^i$ as a variable, which stands in for some real number. I’m saying that we want to consider it as a function in its own right. In a way, this is just extending what we did when we considered polynomials as functions and we can do everything algebraically with abstract “variables” as we can with specific “functions” as our $x^i$. Analytically, though, we can ask how the function $x^i$ behaves as we move our input point around. It’s easy to find the partial derivatives. If $k\neq i$ then $\displaystyle\left[D_kx^i\right](x)=\lim\limits_{t\to0}\frac{x^i(x+te_k)-x^i(x)}{t}=\lim\limits_{t\to0}\frac{0}{t}=0$ since moving in the $e_k$ direction doesn’t change the $i$th component. On the other hand, if $k=i$ then $\displaystyle\left[D_kx^i\right](x)=\lim\limits_{t\to0}\frac{x^i(x+te_k)-x^i(x)}{t}=\lim\limits_{t\to0}\frac{t}{t}=1$ since moving a distance $t$ in the $e_k$ direction adds exactly $t$ to the $i$th component. That is, we can write $D_kx^i=\delta_k^i$ — the Kronecker delta. Of course, since ${0}$ and ${1}$ are both constant, they’re clearly continuous everywhere. Thus by the condition we worked out yesterday the differential of $x^i$ exists, and we find $\displaystyle dx^i(x;t)=\delta_k^it^k=t^i$ We can also write the differential as a linear functional $dx^i(x)$. Since this takes a vector $t$ and returns its $i$th component, it is exactly the dual basis element $\eta^i$. That is, once we pick an orthonormal basis for our vector space of displacements, we can actually write the dual basis of linear functionals as the differentials $dx^i$. And from now on that’s exactly what we’ll do. So, for example, let’s say we’ve got a differentiable function $f:\mathbb{R}^n\rightarrow\mathbb{R}$. Then we can write its differential as a linear functional $df(x)=\left[D_1f\right](x)dx^1+\dots+\left[D_nf\right](x)dx^n=\left[D_if\right](x)dx^i$ In the one-dimensional case, we write $df(x)=f'(x)dx$, leading us to the standard Leibniz notation $\displaystyle\frac{df}{dx}=f'$ If we have to evaluate this function, we use an “evaluation bar” $\frac{df}{dx}\bigr\vert_{x}=f'(x)$, or $\frac{df}{dx}\bigr\vert_{x=a}=f'(a)$ telling us to substitute $a$ for $x$ in the formula for $\frac{df}{dx}$. We also can write the operator that takes in a function and returns its derivative by simply removing the function from this Leibniz notation: $\frac{d}{dx}$. Now when it comes to more than one variable, we can’t just “divide” by one of the differentials $dx^i$, but we’re going to use something like this notation to read off the coefficient anyway. In order to remind us that we’re not really dividing and that there are other variables floating around, we replace the $d$ with a curly version: $\partial$. Then we can write the partial derivative $\displaystyle\frac{\partial f}{\partial x^i}=D_if$ and the whole differential as $\displaystyle df=\frac{\partial f}{\partial x^1}dx^1+\dots+\frac{\partial f}{\partial x^n}dx^n=\frac{\partial f}{\partial x^i}dx^i$ Notice here that when we see an upper index in the denominator of this notation, we consider it to be a lower index. Similarly, if we find a lower index in the denominator, we’ll consider it to be like an upper index for the purposes of the summation convention. We can even incorporate evaluation bars $\displaystyle df(a)=\frac{\partial f}{\partial x^1}\biggr\vert_{x=a}dx^1+\dots+\frac{\partial f}{\partial x^n}\biggr\vert_{x=a}dx^n=\frac{\partial f}{\partial x^i}\biggr\vert_{x=a}dx^i$ or strip out the function altogether to write the “differential operator” $\displaystyle d=\frac{\partial}{\partial x^1}dx^1+\dots+\frac{\partial}{\partial x^n}dx^n=\frac{\partial}{\partial x^i}dx^i$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 45, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9474261403083801, "perplexity": 153.8176948557887}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608120.92/warc/CC-MAIN-20170525180025-20170525200025-00262.warc.gz"}
http://www.lecture-notes.co.uk/susskind/quantum-entanglements/lecture-4/spin-in-arbitrary-directions/	Spin in arbitrary directions Definition We can now define general spin operators (for a single electron) mathematically but, in fact, they have had to be confirmed experimentally. Suppose we define a direction in normal space to be the unit vector, $$\hat{n} = \begin{bmatrix}n_x\\n_y\\n_z\end{bmatrix} \in \mathbb{R}^3$$ Then the spin operator that measures the spin of an electron in the $\hat{n}$ direction is given by $$\sigma_n = \sigma_x n_x + \sigma_y n_y + \sigma_z n_z$$ We can define a triple, $$\vec{\sigma} = (\sigma_x, \sigma_y, \sigma_z)$$ so that we can write $$\vec{\sigma} \cdot \hat{n} = \sigma_n$$ which is analogous to the definition of the spin vector in classical mechanics. Nb. Professor Susskind uses slightly different notation, and usually uses numeric subscripts, $\sigma_1, \sigma_2, \sigma_3$, rather than latin $\sigma_x, \sigma_y, \sigma_z$. We can write the operator as a matrix \begin{align}\sigma_n &= \sigma_x n_x + \sigma_y n_y + \sigma_z n_z\\&= \begin{bmatrix}0 & 1\\1 & 0\end{bmatrix} n_x + \begin{bmatrix}0 & -\mathrm{i}\\\mathrm{i} & 0\end{bmatrix} n_y + \begin{bmatrix}1 & 0\\0 & -1\end{bmatrix} n_z\\&= \begin{bmatrix}n_z & n_x - \mathrm{i} n_y \\ n_x + \mathrm{i} n_y & -n_z\end{bmatrix}\\&= \begin{bmatrix}n_z & n_- \\ n_+ & -n_z\end{bmatrix}\end{align} where $n_{\pm} = n_x \pm \mathrm{i}n_y$ are complex conjugates. So, by definition, $\sigma_n$ is a Hermitian matrix (diagonal values are real, cross-diagonal are complex conjugates). Also, because $\hat{n}$ is a unit vector, we have the following identities: \begin{align}n_x^2 + n_y^2 + n_z^2 &= 1\\n_+ n_- &= (n_x + \mathrm{i}n_y)(n_x - \mathrm{i} n_y)\\&= n_x^2 + n_y^2\\&= 1 - n_z^2\end{align} Eigenvalues We have already seen in an earlier lecture that matrices of the form $$M = \begin{bmatrix}a & b^* \\ b & -a\end{bmatrix}$$ where $a \in \mathbb{R}$ and $b \in \mathbb{C}$, are Hermitian matrices with the property that if $$M^2 = \mathbf{I}$$ then its eigenvalues satisfy $$\lambda_{\pm} = \pm 1$$ The spin operator, $$\sigma_n = \begin{bmatrix}n_z & n_- \\ n_+ & -n_z\end{bmatrix}$$ satisfies this condition, so we want to find eigenstates, $\ket{\pm n}$, that satisfy \begin{align}\sigma_n \ket{+n} &= \ket{+n}\\\sigma_n \ket{-n} &= -\ket{-n}\end{align} Nb. Professor Susskind uses the more explicit notation $\ket{\vec{\sigma} \cdot \hat{n} = \pm 1}$ instead of $\ket{\pm n}$. Eigenstates The eigenstates of the spin operator are given by $$\ket{\pm n} = \ket{\pm z} \text{ if } n_z = 1$$ $$\ket{\pm n} = \sqrt{\frac{1 \pm n_z}{2}} \: \begin{bmatrix}1 \\ \frac{\pm 1 - n_z}{n_-} \end{bmatrix} \text{ if } n_z \neq 1$$ Trivially, if $n_z = 1$ then we must have that $$n_+ = n_- = 0$$ which implies that $$\sigma_n = \begin{bmatrix}1 & 0 \\ 0 & -1 \end{bmatrix} = \sigma_z$$ and so the eigenstates are simply $$\ket{\pm n} = \ket{\pm z}$$ Now suppose that $n_z \neq 1$ and write $$\ket{+n} = \begin{bmatrix}\alpha \\ \beta\end{bmatrix}$$ where $\alpha, \beta \in \mathbb{C}$ and $\alpha^\alpha + \beta^\beta = 1$. Case 1: $\lambda = +1$ We want to find $\ket{+n}$ such that $$\sigma_n \ket{+n} = \ket{+n}$$ which leads to the following equation $$n_z \alpha + n_- \beta = \alpha$$ (there are actually two equations, but both lead to the same conclusion). Now, $$n_z \neq 1 \Rightarrow n_+ \neq 0 \Rightarrow n_- \neq 0$$ so we can write $$\beta = \alpha \frac{1 - n_z}{n_-}$$ We now use the fact that states are unit vectors hence we want that \begin{align}1 &= \braket{+n}{+n}\\&= \alpha^ \alpha + \beta^* \beta\\&= \alpha^* \alpha + \left( \alpha\frac{1 - n_z}{n_-} \right)^* \left( \alpha \frac{1 - n_z}{n_-} \right)\\&= \alpha^* \alpha \left( 1 + \left( \frac{\left( 1 - n_z \right)^2}{n_+ n_-} \right) \right)\\&= \alpha^* \alpha \left( \frac{n_+ n_- + \left( 1 - n_z \right)^2}{n_+ n_-} \right)\\&= \alpha^* \alpha \left( \frac{1 - n_z^2 + \left( 1 - n_z \right)^2}{1 - n_z^2} \right)\\&= \alpha^* \alpha \left( \frac{2 \left(1 - n_z\right)}{1 - n_z^2} \right)\\&= \alpha^* \alpha \left( \frac{2}{1 + n_z} \right)\end{align} which leads to $$\alpha^ \alpha = \frac{1 + n_z}{2}$$ The general solution is $$\alpha = \sqrt{\frac{1 + n_z}{2}}e^{i\theta}$$ of which the simplest - and the one derived by experiment - is $$\alpha = \sqrt{\frac{1 + n_z}{2}}$$ Thus, the eigenstate corresponding to the $\lambda_+ = +1$ eigenvalue is $$\ket{+n} = \sqrt{\frac{1 + n_z}{2}} \: \begin{bmatrix}1 \\ \frac{1 - n_z}{n_-} \end{bmatrix}$$ Case 2: $\lambda = -1$ A similar calculation for the other eigenvalue leads to $$\ket{-n} = \sqrt{\frac{1 - n_z}{2}} \: \begin{bmatrix}1 \\ \frac{-1 - n_z}{n_-} \end{bmatrix}$$ Given this more general definition of the spin operator and its eigenstates, we can recover the special cases of the three coordinate directions. For example, $$\hat{n} = \hat{x} = \begin{bmatrix}1 \\ 0 \\ 0 \end{bmatrix} \quad \Rightarrow \quad \left\{\begin{matrix}\sigma_n = \sigma_x = \begin{bmatrix}0 & 1\\1 & 0 \end{bmatrix}\\\ket{\pm n} = \ket{\pm x} = \tfrac{1}{\sqrt{2}} \begin{bmatrix}1\\\pm 1\end{bmatrix}\end{matrix}\right.$$ Average value Given an arbitrary spin state and a direction in normal space, $$\ket{a} = \begin{bmatrix}\alpha \\ \beta \end{bmatrix} \:,\quad \hat{n} = \begin{bmatrix}n_x\\n_y\\n_z\end{bmatrix}$$ it is useful to calculate the average value of the general spin operator in that state, \begin{align}\bra{a} \sigma_n \ket{a} &= \begin{bmatrix} \alpha^ & \beta^* \end{bmatrix} \begin{bmatrix} n_z & n_- \\ n_+ & -n_z \end{bmatrix} \begin{bmatrix} \alpha \\ \beta \end{bmatrix}\\&= \begin{bmatrix} \alpha^* & \beta^* \end{bmatrix} \begin{bmatrix} n_z \alpha + n_- \beta \\ n_+ \alpha - n_z \beta \end{bmatrix}\\&= \alpha^* \left( n_z \alpha + n_- \beta \right) + \beta^* \left( n_+ \alpha - n_z \beta \right)\\&= \alpha^* \left( n_z \alpha + n_x \beta -\mathrm{i} n_y \beta \right) + \beta^* \left( n_x \alpha + \mathrm{i} n_y \alpha - n_z \beta \right)\\&= \left( \beta^\alpha + \alpha^ \beta \right)n_x + \mathrm{i}\left( \beta^\alpha - \alpha^ \beta \right)n_y + \left( \alpha^\alpha - \beta^ \beta \right)n_z\end{align} We can also express the average in terms of the coordinate spin operators, \begin{align}\bra{a} \sigma_n \ket{a} &= \bra{a} \left( \sigma_x n_x + \sigma_y n_y + \sigma_z n_z \right) \ket{a}\\&= \bra{a} \sigma_x \ket{a} n_x + \bra{a} \sigma_y \ket{a} n_y + \bra{a} \sigma_z \ket{a} n_z\end{align} Thus, we can write \begin{align}\bra{a} \sigma_x \ket{a} &= \beta^\alpha + \alpha^ \beta\\\bra{a} \sigma_y \ket{a} &= \mathrm{i} \left( \beta^\alpha - \alpha^ \beta \right)\\\bra{a} \sigma_z \ket{a} &= \alpha^\alpha - \beta^ \beta\end{align} The last of these averages is clearly real, and it is simple to show that the first two are real as well, hence the average is real in general. To see why the first two are real, note that for any $z = a + \mathrm{i}b \in \mathbb{C}$, we have $$\begin{matrix}z + z^ &=& a + \mathrm{i}b + a -\mathrm{i} b &=& 2a &\in \mathbb{R}\\i\left(z - z^\right) &=& i\left(a + \mathrm{i}b - a + \mathrm{i}b\right) &=& -2b &\in \mathbb{R}\end{matrix}$$ Then set $$z = \beta^\alpha$$ so that $$z^* = \alpha^*\beta$$ and the result follows.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.000002384185791, "perplexity": 1397.0470515500688}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934803906.12/warc/CC-MAIN-20171117185611-20171117205611-00231.warc.gz"}
http://mathhelpforum.com/geometry/200909-challenging-find-hashed-area-question.html	Math Help - Challenging "Find the Hashed Area" Question 1. Challenging "Find the Hashed Area" Question See attached question. It asks: "A circle is inside a square, which is also found inside another square with with 6 meter sides. Find the hashed area". Is the correct answer: 9pi/2 meters^2 or 9pi meters^2? Can you please systematically outline the steps that you took to arrive at the answer? Thank you for your help and explanation. Attached Thumbnails 2. Re: Challenging "Find the Hashed Area" Question The side length of the smaller square is $3 \sqrt{2}$ (do you see why?). Therefore the diameter of the circle is $3 \sqrt{2}$, so the radius is $\frac{3 \sqrt{2}}{2}$. The area of the circle is $(\frac{3 \sqrt{2}}{2})^2 \pi = \frac{9 \pi}{2}$. 3. Re: Challenging "Find the Hashed Area" Question Hi Richard, Thanks for the quick response. I do not see how you got the side length of the smaller square to be $3 \sqrt{2}$. Can you please explain how you got to that step? Thanks a million! 4. Re: Challenging "Find the Hashed Area" Question Hint: The side length of the larger square is the diagonal of the smaller square. 5. Re: Challenging "Find the Hashed Area" Question I understand the rest of it but just can't the length of the inner square. I'm sorry my brain isn't working today. I know it has something to do with the Phytagoreans Theorem. Can you please tell me how you got the side length of the inner square. 6. Re: Challenging "Find the Hashed Area" Question A square is composed of two 45-45-90 triangles. The side length of the large square is the diagonal of the small square, so the diagonal of the small square is 6. The diagonal is like the "hypotenuse" of the 45-45-90 triangles, you should be able to find the side length now. 7. Re: Challenging "Find the Hashed Area" Question Thank you Richard for the step-wise explanation. I now understand. Since the diagonal of the small square is 6; it would be b^2 + b^2 = 6^2; so solving for b, you would take square root of 36 so 6, then another square root of 6 so "b" (the side of the square) would be 3 sqrt 2. From here, we know that the diameter of the circle is 3 sqrt 2 and we can find radius and then area as you had outlined. Thanks for your help! 8. Re: Challenging "Find the Hashed Area" Question Hello, danielmc! A circle is inside a square, which is also found inside another square with with 6 m sides. Code: E o 3 * * 3 * * * * A * * B o-------* * -------o \| ::::::::::: \| * 3 * \| ::::::::::::::: \| * 3 * \|:::::::::::::::::\| * * \|:::::::::::::::::::\| * * ::::::::::::::::::: * H o :::::::::o::::::::: o F * ::::::::::::::::::: * * \|:::::::::::::::::::\| * 3 * \|:::::::::::::::::\| * 3 * \| ::::::::::::::: \| * * \| ::::::::::: \| * o-------* * -------o D * C * * 3 * * 3 * * o G Is the correct answer: $\tfrac{9\pi}{2}\:m^2\,\text{ or }\,9\pi\:m^2\,?$ I'd like to know how you got those two answers . . . The circle is inscribed in square $ABCD$ . . which is inscribed in square $EFGH$ as shown. The top triangle $ABE$ is an isosceles right triangle with legs of length 3. . . Hence: $AB = 3\sqrt{2}$ But $AB$ is the diameter of the circle. . . Hence, the radius is: . $r \:=\:\frac{3\sqrt{2}}{2}$ Now you can find the area of the circle . . . right?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.960818886756897, "perplexity": 949.6454424177946}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257824037.46/warc/CC-MAIN-20160723071024-00308-ip-10-185-27-174.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/268017/evaluating-the-sum-of-omegan-in-an-arithmetic-progression	# Evaluating the sum of $\omega(n)$ in an arithmetic progression [closed] Let $\omega(k)$ count how many distinct prime factors k has, Then I can prove that for any coprime integers $a,b$ $$\lim_{n\to\infty}\frac{\sum_{k=2}^n\omega(ak+b)}{\sum_{k=2}^n\omega(k)}=1$$ Does anyone think this is a deep result? Its essentially saying on average all linear polynomials with co prime coefficients Have around the same number of prime factors - ## closed as not a real question by Jasper Loy, Asaf Karagila, Austin Mohr, Fabian, Alexander Gruber♦Dec 31 '12 at 8:46 It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question. On MSE, try to avoid wording questions in the form "I can prove this, is it known?" It is generally preferred when people ask either for a reference request, or how to solve the problem. – Eric Naslund Dec 31 '12 at 6:46 There's no need to restrict to coprime $a,b$, since $\omega(n) \le \omega(nd) \le \omega(n)+\omega(d)$. A common factor of $d$ thus affects each term by at most a constant (depending on $d$), and that's negligible compared to the average value $\log \log n$ in the denominator. – Erick Wong Dec 31 '12 at 6:53 Yes there is a need to restrict co prime a,b your reasoning is wrong – Ethan Dec 31 '12 at 7:01 @Ethan Care to elaborate? Where does $(a,b)\not= 1$ fail? – Alexander Gruber Dec 31 '12 at 8:46 look at my lower sum, what you are trying to argue is incorrect – Ethan Dec 31 '12 at 9:13 This type of result, and the tools needed to prove it, would usually be discussed in a graduate level Analytic Number Theory text. My personal preference is Montgomery and Vaughn's "Multiplicative Number Theory I. Classical Theory." Here is another way to see why this result is true. Lets examine the sum $$\sum_{\begin{array}{c} n\leq x\\ n\equiv a\ (q) \end{array}}\omega(n).$$ Since $\omega(n)=\sum_{p\|n}1,$ the above becomes $$\sum_{\begin{array}{c} n\leq x\\ n\equiv a\ (q) \end{array}}\sum_{p\|n}1=\sum_{p\leq x}\sum_{\begin{array}{c} n\leq x,\ p\|n\\ n\equiv a\ (q) \end{array}}1.$$ This equals $$\sum_{\begin{array}{c} p\leq x\\ p\nmid q \end{array}}\sum_{\begin{array}{c} n\leq\frac{x}{p}\\ n\equiv p^{-1}a\ (q) \end{array}}1=\sum_{\begin{array}{c} p\leq x\\ p\nmid q \end{array}}\left(\frac{x}{pq}+O(1)\right)$$ $$=\frac{x}{q}\log\log x+\frac{B_{1}x}{q}+O\left(\frac{x}{\log x}\right),$$ where $B_1$ is Mertens constant. From here, we can recover your asymptotic since $\log \log \left(\frac{x}{q}\right)\sim \log \log x$, and so $$\sum_{n\leq x }\omega(nq+a)\sim\sum_{n\leq x }\omega(n)\sim x \log \log x.$$ - Did you use dirichlets theorem here? – Ethan Dec 31 '12 at 7:03 @Ethan: I did not, I used only Merten's estimate, that $$\sum_{p\leq x}\frac{1}{p}=\log \log x+B_1+O\left(\frac{x}{\log x}\right).$$ Note that if you wanted to prove something similar and evaluate the average of $\omega_{q,a}(n)$ which I define to be the number of distinct prime factors $p$ dividing $n$ with $p\equiv a \pmod{q}$, then you would need some kind of result regarding primes in arithmetic progressions, such as a form of Mertens estimate for arithmetic progressions. – Eric Naslund Dec 31 '12 at 7:09 Eric could you derive this result? – Ethan Dec 31 '12 at 7:10 For Merten's Theorem in arithmetic progressions, there is a paper by Languasco and Zaccagnini. To derive what I said about $\omega_{q,a}(n)$, it suffices show that $$\sum_{n\leq x}\omega_{q,a}(n)=\sum_{\begin{array}{c} p\leq x\\ p\equiv a\ (q) \end{array}}\left[\frac{x}{p}\right].$$ From here, we find that $$\sum_{n\leq x}\omega_{q,a}(n)=\frac{x}{\phi(q)}\log\log x+C(q,a)x+O\left(\frac{x}{\log x}\right)$$ uniformely for $q\leq\left(\log x\right)^{A}.$ – Eric Naslund Dec 31 '12 at 7:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8909056186676025, "perplexity": 473.11362016730413}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701163512.72/warc/CC-MAIN-20160205193923-00030-ip-10-236-182-209.ec2.internal.warc.gz"}

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