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http://openstudy.com/updates/55c50f90e4b0c7f4a97911a4
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## anonymous one year ago Can someone help me find an equation for the inverse of the function. g(x)=x-3/2 Delete Cancel Submit
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1. campbell_st
• one year ago
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is the equation $g(x) = \frac{x -3}{2}$
2. anonymous
• one year ago
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To find the inverse of an equation, flip the x and y values first. Your equation will turn from $g(x)=\frac{ x-3 }{ 2 }$ to $x =\frac{ y -3 }{ 2 }$ After you've done that, solve for y.
3. anonymous
• one year ago
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Yes @campbell_st
4. anonymous
• one year ago
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Is y 1/2?
5. anonymous
• one year ago
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To get the inverse, solve for y. By solving for y, you need to isolate it. $x =\frac{ y -3 }{ 2 }$ Multiply both sides of the equation by 2 to get rid of the division sign.
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https://itprospt.com/num/21304067/a-sofl-drink-distributor-is-studying-the-effectiveness-of
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1
# A sofl drink distributor is studying the effectiveness of 'delivery methods. Three diflerent types ofhand trucks have been developed, and an experiment is perf...
## Question
###### A sofl drink distributor is studying the effectiveness of 'delivery methods. Three diflerent types ofhand trucks have been developed, and an experiment is performed in the company methods engineering laboratory: The variable of interest is the delivery time in minutes (y); however; delivery tine is also strongly related t0 the case volume delivered (x)_ Each hand truck used four times and the data that follow are obtained_ Analyze these data and draw appropriate conclusions Use &=0.05_
A sofl drink distributor is studying the effectiveness of 'delivery methods. Three diflerent types ofhand trucks have been developed, and an experiment is performed in the company methods engineering laboratory: The variable of interest is the delivery time in minutes (y); however; delivery tine is also strongly related t0 the case volume delivered (x)_ Each hand truck used four times and the data that follow are obtained_ Analyze these data and draw appropriate conclusions Use &=0.05_ Hand Truck Type 27 4 41 25 35 46 26 26 32 42 15 40 22 53 18 38 26 50 20 4 35 40
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https://export.arxiv.org/abs/2010.07920
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cs.DC
(what is this?)
# Title: Scheduling Opportunistic Links in Two-Tiered Reconfigurable Datacenters
Abstract: Reconfigurable optical topologies are emerging as a promising technology to improve the efficiency of datacenter networks. This paper considers the problem of scheduling opportunistic links in such reconfigurable datacenters. We study the online setting and aim to minimize flow completion times. The problem is a two-tier generalization of classic switch scheduling problems. We present a stable-matching algorithm which is $2\cdot (2/\varepsilon+1)$-competitive against an optimal offline algorithm, in a resource augmentation model: the online algorithm runs $2+\varepsilon$ times faster. Our algorithm and result are fairly general and allow for different link delays and also apply to hybrid topologies which combine fixed and reconfigurable links. Our analysis is based on LP relaxation and dual fitting.
Subjects: Distributed, Parallel, and Cluster Computing (cs.DC); Data Structures and Algorithms (cs.DS); Networking and Internet Architecture (cs.NI) Cite as: arXiv:2010.07920 [cs.DC] (or arXiv:2010.07920v1 [cs.DC] for this version)
## Submission history
From: Stefan Schmid [view email]
[v1] Thu, 15 Oct 2020 17:52:10 GMT (172kb)
Link back to: arXiv, form interface, contact.
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|
http://tex.stackexchange.com/questions/64942/can-we-use-a-single-frame-to-create-the-following-effect/64944
|
Can we use a single frame to create the following effect?
I want to create a slide to show how the clipping works as shown in the following animation.
I used two frames, the last frame is needed because I want to hide the unwanted (trimmed) parts of cropped areas of the previous slides. I want to avoid using two frames and repeating the codes.
Can we force beamer to delay the clipping code and hiding the previous painting? I am new to beamer, only knows \pause. :-)
\documentclass{beamer}
\usepackage[active,tightpage]{preview}
\PreviewBorder=0pt
\PreviewEnvironment{pspicture}
\begin{document}
\begin{frame}
\begin{pspicture}(6,6)
\pnode(0,0){A}
\pnode(6,0){B}
\pnode(6,6){C}
\pnode(0,6){D}
\pnode(1,1){P}
\pnode(5,1){Q}
\pnode(3,5){R}
\pspolygon*[linecolor=red](A)(B)(Q)(P)\pause
\pspolygon*[linecolor=green](B)(C)(R)(Q)\pause
\pspolygon*[linecolor=blue](C)(D)(R)\pause
\pspolygon*[linecolor=yellow](D)(A)(P)(R)
\end{pspicture}
\end{frame}
\begin{frame}
\begin{pspicture}(6,6)
\pnode(0,0){A}
\pnode(6,0){B}
\pnode(6,6){C}
\pnode(0,6){D}
\pnode(1,1){P}
\pnode(5,1){Q}
\pnode(3,5){R}
\psclip{\pscircle[linestyle=none,dimen=middle](3,3){3}}
\pspolygon*[linecolor=red](A)(B)(Q)(P)
\pspolygon*[linecolor=green](B)(C)(R)(Q)
\pspolygon*[linecolor=blue](C)(D)(R)
\pspolygon*[linecolor=yellow](D)(A)(P)(R)
\endpsclip
\end{pspicture}
\end{frame}
\end{document}
-
You can use \only or \onslide; an example with \only:
\documentclass{beamer}
\usepackage[active,tightpage]{preview}
\PreviewBorder=0pt
\PreviewEnvironment{pspicture}
\begin{document}
\begin{frame}
\begin{pspicture}(6,6)
\pnode(0,0){A}
\pnode(6,0){B}
\pnode(6,6){C}
\pnode(0,6){D}
\pnode(1,1){P}
\pnode(5,1){Q}
\pnode(3,5){R}
\only<5>{\psclip{\pscircle[linestyle=none,dimen=middle](3,3){3}}}
\only<1->{\pspolygon*[linecolor=red](A)(B)(Q)(P)}
\only<2->{\pspolygon*[linecolor=green](B)(C)(R)(Q)}
\only<3->{\pspolygon*[linecolor=blue](C)(D)(R)}
\only<4->{\pspolygon*[linecolor=yellow](D)(A)(P)(R)}
\only<5>{\endpsclip}
\end{pspicture}
\end{frame}
\end{document}
Edit: After getting a multipe-page PDF, we can also make use of it to create a PDF animation, a GIF animation and PNG images. TeX the following with pdflatex --shell-escape. ImageMagick must be installed in your computer.
\documentclass[preview,border=0pt]{standalone}
\usepackage{filecontents}
\begin{filecontents*}{dummy.tex}
\documentclass[serif]{beamer}
\usepackage[active,tightpage]{preview}
\PreviewBorder=0pt
\PreviewEnvironment{pspicture}
\begin{document}
\begin{frame}
\begin{pspicture}(6,6)
\pnode(0,0){A}
\pnode(6,0){B}
\pnode(6,6){C}
\pnode(0,6){D}
\pnode(1,1){P}
\pnode(5,1){Q}
\pnode(3,5){R}
\only<5>{\psclip{\pscircle[linestyle=none,dimen=middle](3,3){3}}}
\only<1->{\pspolygon*[linecolor=red](A)(B)(Q)(P)}
\only<2->{\pspolygon*[linecolor=green](B)(C)(R)(Q)}
\only<3->{\pspolygon*[linecolor=blue](C)(D)(R)}
\only<4->{\pspolygon*[linecolor=yellow](D)(A)(P)(R)}
\only<5>{\endpsclip}
\end{pspicture}
\end{frame}
\end{document}
\end{filecontents*}
\usepackage{animate}
\begin{document}
% create PDF
\immediate\write18{latex dummy}
\immediate\write18{dvips dummy}
\immediate\write18{ps2pdf dummy.ps}
% convert to GIF animation
\immediate\write18{convert -delay 100 -loop 0 -density 200 -alpha remove dummy.pdf \jobname.gif}
% convert to PNG
\makeatletter
\immediate\write18{convert -density 200 -alpha remove dummy.pdf \jobname-\@percentchar02d.png}
\makeatother
% create PDF animation
\begin{preview}
\animategraphics[controls]{2}{dummy}{}{}
\end{preview}
\end{document}
-
@HiggsBoson thank you very much! Animation added! – Gonzalo Medina Jul 27 '12 at 19:13
For those who want to make use of the produced multiple-page PDF to create a PDF animation, a GIF animation and PNG images, please see the last edit. – kiss my armpit Jul 29 '12 at 11:14
Which is the most appropriate among \uncover, \only, \onslide, etc for my problem above? – kiss my armpit Oct 18 '12 at 9:48
Why cannot your first code be compiled now while it worked several times ago? – kiss my armpit Jul 22 '14 at 8:19
You could use TikZ, which is reasonably well integrated with Beamer already, and do something like:
\begin{frame}
\begin{tikzpicture}
\clip<5> (3,3) circle (3);
\node [coordinate] (A) at (0,0) {};
\node [coordinate] (B) at (6,0) {};
\node [coordinate] (C) at (6,6) {};
\node [coordinate] (D) at (0,6) {};
\node [coordinate] (P) at (1,1) {};
\node [coordinate] (Q) at (5,1) {};
\node [coordinate] (R) at (3,5) {};
\fill<1-> [red] (A) -- (B) -- (Q) -- (P) -- cycle;
\fill<2-> [green] (B) -- (C) -- (R) -- (Q) -- cycle;
\fill<3-> [blue] (C) -- (D) -- (R) -- cycle;
\fill<4-> [yellow] (D) -- (A) -- (P) -- (R) -- cycle;
\end{tikzpicture}
\end{frame}
Result:
-
The first slide is wrong; the red trapezoid "jumps". – Gonzalo Medina Jul 27 '12 at 22:37
@GonzaloMedina: The first canvas might have different dimension as TikZ provides the smallest but enough canvas automatically. Specifying the canvas dimension in advance will solve this issue. – kiss my armpit Jul 28 '12 at 5:46
|
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|
http://mathhelpforum.com/differential-geometry/120258-poincare-find-distance-between-points.html
|
# Math Help - poincare: find the distance between the points
1. ## poincare: find the distance between the points
I need some help finding the Poincare distance
I have tried to do this problem, but I know my answer is wrong!
Let Gamma be the interior of the unit disk centered at the origin in the xy-plane, (x^2+y^2 <1). Find the poincare distance between the following pairs of points.
(0,0) and (1/2,0).
2. Originally Posted by mandy123
I need some help finding the Poincare distance
I have tried to do this problem, but I know my answer is wrong!
Let Gamma be the interior of the unit disk centered at the origin in the xy-plane, (x^2+y^2 <1). Find the poincare distance between the following pairs of points.
(0,0) and (1/2,0).
Okay, what have you done to get your "wrong" answer? In particular, what formulas are you using?
I assume you are talking about the Poincare disk model for hyperbolic geometry.
3. Find A’
· TU is the line x= ½
· T= (½ , (√3)/2)
· U=(½ , - (√3)/2)
· Find the equation of the line tangent to gamma at T (Perpendicular to radius of T)
o The slope of point T is √3
o Slope of the perpendicular to the radius is -1/√3
o Equation of the line: y = -1/√3 x + 2/√3
· A’
o 0= -1/√3 x + 2/√3
o X=2
o A’ =(2,0)
Find midpoint of AA’
· ( 5/4 , 0)
Equation of the perpendicular bisector
· X= 5/4
Midpoint of BA
· (¼ , 0)
Intersection of midpoint and perpendicular bisector
· (5/4, 0)
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https://pub.uni-bielefeld.de/publication/2736461
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# Triple Higgs coupling as a probe of the twin-peak scenario
Ahriche A, Arhrib A, Nasri S (2015)
Physics Letters B 743: 279-283.
862.75 KB
Journal Article | Original Article | Published | English
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Abstract
In this letter, we investigate the case of a twin peak around the observed 125 GeV scalar resonance, using di-Higgs production processes at both LHC and e(+)e(-) Linear Colliders. We have shown that both at LHC and Linear Collider the triple Higgs couplings play an important role to identify this scenario; and also that this scenario can be distinguishable from any Standard Model extension by extra massive particles which might modify the triple Higgs coupling. We also introduce a criterion that can be used to rule out the twin peak scenario. (C) 2015 The Authors. Published by Elsevier B.V.
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Open Access publishing charge funded by SCOAP$^3$ – Sponsoring Consortium for Open Access Publishing in Particle Physics and Bielefeld University.
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### Cite this
Ahriche A, Arhrib A, Nasri S. Triple Higgs coupling as a probe of the twin-peak scenario. Physics Letters B. 2015;743:279-283.
Ahriche, A., Arhrib, A., & Nasri, S. (2015). Triple Higgs coupling as a probe of the twin-peak scenario. Physics Letters B, 743, 279-283. doi:10.1016/j.physletb.2015.02.062
Ahriche, A., Arhrib, A., and Nasri, S. (2015). Triple Higgs coupling as a probe of the twin-peak scenario. Physics Letters B 743, 279-283.
Ahriche, A., Arhrib, A., & Nasri, S., 2015. Triple Higgs coupling as a probe of the twin-peak scenario. Physics Letters B, 743, p 279-283.
A. Ahriche, A. Arhrib, and S. Nasri, “Triple Higgs coupling as a probe of the twin-peak scenario”, Physics Letters B, vol. 743, 2015, pp. 279-283.
Ahriche, A., Arhrib, A., Nasri, S.: Triple Higgs coupling as a probe of the twin-peak scenario. Physics Letters B. 743, 279-283 (2015).
Ahriche, Amine, Arhrib, Abdesslam, and Nasri, Salah. “Triple Higgs coupling as a probe of the twin-peak scenario”. Physics Letters B 743 (2015): 279-283.
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https://math.stackexchange.com/questions/3152653/calculate-weighted-mean-based-on-simple-mean
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# Calculate weighted mean based on simple mean
I need to calculate the mobile weighted mean of a quantity, $$a_i$$, based on $$b_i$$.
I have a tool that allows me to calculate the mobile mean of a given series, so we can say I have a function:
$$F(a_i) = \frac{1}{N}\Sigma_i a_i$$
Is it right to say that $$\frac{\Sigma_i a_i*b_i}{\Sigma_i b_i} = \frac{F(a_i*b_i)}{F(b_i)} (1)$$ ?
Is there any condition on which this equality holds that I'm assuming implicitly? I can only think of $$N \ne 0$$, is there anything else I'm missing?
EDIT:
To clarify the situation, I have a source of dynamic data from which I get $$a_i$$ and $$b_i$$ and I have a module which I can give these data to and that will calculate the mobile mean, taking care of excluding older samples. The function $$F(a_i)$$ is meant to represent the module.
Since I only get the simple mean from the module, and not the sum, my idea was to calculate the simple mean of $$a_i*b_i$$ and of $$b_i$$ and divide the two means to obtain the weighted mean, but before doing that I wanted to be sure about the conditions at which equation (1) holds.
• I don't really follow what you mean by the equation that you wrote. If $F$ is an average operator, the number of entries just divides out and your equation is true. But what is this $b_i$? Are those the weights? If you have the average of $a_i$'s and you want to to calculate the weighted average (average of $a_i \times b_i$), I don't think there's a way to do it if you don't have all the values of $a_i$'s ... – Matti P. Mar 18 at 11:23
• Edited the question to better specify the situation, thanks for the comment @MattiP. – bracco23 Mar 18 at 11:32
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https://www.physicsforums.com/threads/bicycles-question-about-energy-conservation.976425/
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# B Bicycles: Question about Energy Conservation
• Start date
#### Djf321
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I just have a basic physics question about bicycles that has been confusing me. Consider three situations. In the first situation a person, of mass m, is running down a street at constant velocity v1. In this case the person is converting energy stored in their body into translational kinetic energy of their moving body ½mv12. In the second situation the same person is riding a standard simple single-gear bicycle down the same street going at constant velocity v2, where of course v2>v1. So again the person is converting energy stored in their body into translational kinetic energy of their moving body ½mv22. Finally, the third situation involves the same person now riding the Aerovelo, a super-fast recumbent bicycle that can go 89 mph, down the same street at constant velocity v3 (v3>v2>v1). Now the energy stored in this same person's body, in the form of biochemical energy, is being converted into a much greater value of translational kinetic energy of their body ½mv32.
There are two parts that I am confused about. For one, how can it be that bicycles allow for so much more biochemical energy stored in the body to be transferred to translational kinetic energy in comparison to running? I would have naively imagined that the amount of biochemical energy released would be entirely dependent on the speed with which you moved your limbs, and yet you don't necessarily move your limbs more when biking. And second, why is it that when riding a standard bicycle, where you are going much faster than running, the bicycle riding makes you less tired than running even though you can be going faster? And in the extreme case compare the Aerovelo to running. I would have thought that how quickly you became tired would be dependent on how quickly and how much biochemical energy gets converted into translational kinetic energy of your body. And yet you clearly become tired more quickly running than biking even though less translational kinetic energy is being produced when running.
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#### PeroK
Homework Helper
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I just have a basic physics question about bicycles that has been confusing me. Consider three situations. In the first situation a person, of mass m, is running down a street at constant velocity v1. In this case the person is converting energy stored in their body into translational kinetic energy of their moving body ½mv12. In the second situation the same person is riding a standard simple single-gear bicycle down the same street going at constant velocity v2, where of course v2>v1. So again the person is converting energy stored in their body into translational kinetic energy of their moving body ½mv22. Finally, the third situation involves the same person now riding the Aerovelo, a super-fast recumbent bicycle that can go 89 mph, down the same street at constant velocity v3 (v3>v2>v1). Now the energy stored in this same person's body, in the form of biochemical energy, is being converted into a much greater value of translational kinetic energy of their body ½mv32.
There are two parts that I am confused about. For one, how can it be that bicycles allow for so much more biochemical energy stored in the body to be transferred to translational kinetic energy in comparison to running? I would have naively imagined that the amount of biochemical energy released would be entirely dependent on the speed with which you moved your limbs, and yet you don't necessarily move your limbs more when biking. And second, why is it that when riding a standard bicycle, where you are going much faster than running, the bicycle riding makes you less tired than running even though you can be going faster? And in the extreme case compare the Aerovelo to running. I would have thought that how quickly you became tired would be dependent on how quickly and how much biochemical energy gets converted into translational kinetic energy of your body. And yet you clearly become tired more quickly running than biking even though less translational kinetic energy is being produced when running.
It takes no energy to move at constant velocity. All the energy in the cases you mention is used to overcome resistance to motion of one form or another.
You need energy initially, of course, to reach your cruising speed.
Running is very inefficient biomechanically. Bicycles and any wheeled vehicles are much more efficient.
#### anorlunda
Mentor
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It seems that your question is not about physics but bio-mechanical efficiency. Consider this.
I can lift a weight with my arm, but my finger is too weak to lift it at all. Attempting to lift it with my finger results in zero bio-mechanical efficiency. Chemical work expended, but zero useful work done. It even takes nonzero chemical energy to think about moving the weight. The point is that you really can't apply ordinary physical mechanics to bio processes.
#### jrmichler
842
746
Some things to include in your thoughts:
1) Air resistance is proportional to speed squared times frontal area times coefficient of drag. The Aerovelo has low frontal area and very low coefficient of drag.
2) The runner lifts him/herself up every step. That takes work.
3) The runner's legs move back and forth every step. That takes work.
5) Bicycles have rolling resistance.
The $\frac 1 2 mv^2$ translational kinetic energy does not include any of the above. But all of the above need to be included to understand why bicycles are faster than running.
I tried to run directly into a 45 MPH headwind once. The key word here is "tried".
#### Delta2
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I think the main reason that bicycles are more efficient in converting body energy to speed (kinetic energy) is that they have wheels!. Our legs just cant function as wheels when we are running, a lot of energy is lost in bending our knees e.t.c when we are running with legs, and this energy is not converted into kinetic energy of our body. On the contrary when we are using bicycles most of the energy that comes out from our bodies goes into kinetic energy of the wheels and the bicycle.
#### A.T.
9,609
1,477
Running is very inefficient biomechanically. Bicycles and any wheeled vehicles are much more efficient.
This very much depends on the terrain. There is a reason why bicycles, a relatively simple machine, became really popular relatively late, when enough smooth hard surface was available to ride on.
#### PeroK
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This very much depends on the terrain. There is a reason why bicycles, a relatively simple machine, became really popular relatively late, when enough smooth hard surface was available to ride on.
That begs the question why the Romans, Greeks or any ancient civilisation never invented the humble bicycle, despite the engineering marvels they did achieve.
#### A.T.
9,609
1,477
That begs the question why the Romans, Greeks or any ancient civilisation never invented the humble bicycle, despite the engineering marvels they did achieve.
Riding a simple bicycle on cobblestone, sand or mud is no fun. Especially in hilly areas. I think the improvement of roads was one factor that made bicycles popular. But other advancement in technology were also needed to make it light, durable and efficient enough.
#### PeroK
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Riding a simple bicycle on cobblestone, sand or mud is no fun. Especially in hilly areas. I think the improvement of roads was one factor that made bicycles popular. But other advancement in technology were also needed to make it light, durable and efficient enough.
The bicycle became popular before proper paved roads. Its effect was transformational in rural areas in Britain in the early 20th century. Even on country roads a journey to a nearby village could be made much faster than on foot.
Ironically, of course, one significant development in recent years has been the mountain bike, where riders seek out rugged terrain.
#### Torbert
38
26
Roll and unshod wooden wheel and a rubber tired wheel down an unpaved incline.
How much faster and further does the rubber tired wheel go compared to the solid wheel?
This efficiency difference may have delayed bicycles until the technology reached rubber tires on the wheels.
The visuals were so compelling measurements were not taken, my youthful self was easily convinced.
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https://terrytao.wordpress.com/tag/sigma-algebras/
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You are currently browsing the tag archive for the ‘sigma algebras’ tag.
Asgar Jamneshan and I have just uploaded to the arXiv our paper “An uncountable Moore-Schmidt theorem“. This paper revisits a classical theorem of Moore and Schmidt in measurable cohomology of measure-preserving systems. To state the theorem, let ${X = (X,{\mathcal X},\mu)}$ be a probability space, and ${\mathrm{Aut}(X, {\mathcal X}, \mu)}$ be the group of measure-preserving automorphisms of this space, that is to say the invertible bimeasurable maps ${T: X \rightarrow X}$ that preserve the measure ${\mu}$: ${T_* \mu = \mu}$. To avoid some ambiguity later in this post when we introduce abstract analogues of measure theory, we will refer to measurable maps as concrete measurable maps, and measurable spaces as concrete measurable spaces. (One could also call ${X = (X,{\mathcal X}, \mu)}$ a concrete probability space, but we will not need to do so here as we will not be working explicitly with abstract probability spaces.)
Let ${\Gamma = (\Gamma,\cdot)}$ be a discrete group. A (concrete) measure-preserving action of ${\Gamma}$ on ${X}$ is a group homomorphism ${\gamma \mapsto T^\gamma}$ from ${\Gamma}$ to ${\mathrm{Aut}(X, {\mathcal X}, \mu)}$, thus ${T^1}$ is the identity map and ${T^{\gamma_1} \circ T^{\gamma_2} = T^{\gamma_1 \gamma_2}}$ for all ${\gamma_1,\gamma_2 \in \Gamma}$. A large portion of ergodic theory is concerned with the study of such measure-preserving actions, especially in the classical case when ${\Gamma}$ is the integers (with the additive group law).
Let ${K = (K,+)}$ be a compact Hausdorff abelian group, which we can endow with the Borel ${\sigma}$-algebra ${{\mathcal B}(K)}$. A (concrete measurable) ${K}$cocycle is a collection ${\rho = (\rho_\gamma)_{\gamma \in \Gamma}}$ of concrete measurable maps ${\rho_\gamma: X \rightarrow K}$ obeying the cocycle equation
$\displaystyle \rho_{\gamma_1 \gamma_2}(x) = \rho_{\gamma_1} \circ T^{\gamma_2}(x) + \rho_{\gamma_2}(x) \ \ \ \ \ (1)$
for ${\mu}$-almost every ${x \in X}$. (Here we are glossing over a measure-theoretic subtlety that we will return to later in this post – see if you can spot it before then!) Cocycles arise naturally in the theory of group extensions of dynamical systems; in particular (and ignoring the aforementioned subtlety), each cocycle induces a measure-preserving action ${\gamma \mapsto S^\gamma}$ on ${X \times K}$ (which we endow with the product of ${\mu}$ with Haar probability measure on ${K}$), defined by
$\displaystyle S^\gamma( x, k ) := (T^\gamma x, k + \rho_\gamma(x) ).$
This connection with group extensions was the original motivation for our study of measurable cohomology, but is not the focus of the current paper.
A special case of a ${K}$-valued cocycle is a (concrete measurable) ${K}$-valued coboundary, in which ${\rho_\gamma}$ for each ${\gamma \in \Gamma}$ takes the special form
$\displaystyle \rho_\gamma(x) = F \circ T^\gamma(x) - F(x)$
for ${\mu}$-almost every ${x \in X}$, where ${F: X \rightarrow K}$ is some measurable function; note that (ignoring the aforementioned subtlety), every function of this form is automatically a concrete measurable ${K}$-valued cocycle. One of the first basic questions in measurable cohomology is to try to characterize which ${K}$-valued cocycles are in fact ${K}$-valued coboundaries. This is a difficult question in general. However, there is a general result of Moore and Schmidt that at least allows one to reduce to the model case when ${K}$ is the unit circle ${\mathbf{T} = {\bf R}/{\bf Z}}$, by taking advantage of the Pontryagin dual group ${\hat K}$ of characters ${\hat k: K \rightarrow \mathbf{T}}$, that is to say the collection of continuous homomorphisms ${\hat k: k \mapsto \langle \hat k, k \rangle}$ to the unit circle. More precisely, we have
Theorem 1 (Countable Moore-Schmidt theorem) Let ${\Gamma}$ be a discrete group acting in a concrete measure-preserving fashion on a probability space ${X}$. Let ${K}$ be a compact Hausdorff abelian group. Assume the following additional hypotheses:
• (i) ${\Gamma}$ is at most countable.
• (ii) ${X}$ is a standard Borel space.
• (iii) ${K}$ is metrisable.
Then a ${K}$-valued concrete measurable cocycle ${\rho = (\rho_\gamma)_{\gamma \in \Gamma}}$ is a concrete coboundary if and only if for each character ${\hat k \in \hat K}$, the ${\mathbf{T}}$-valued cocycles ${\langle \hat k, \rho \rangle = ( \langle \hat k, \rho_\gamma \rangle )_{\gamma \in \Gamma}}$ are concrete coboundaries.
The hypotheses (i), (ii), (iii) are saying in some sense that the data ${\Gamma, X, K}$ are not too “large”; in all three cases they are saying in some sense that the data are only “countably complicated”. For instance, (iii) is equivalent to ${K}$ being second countable, and (ii) is equivalent to ${X}$ being modeled by a complete separable metric space. It is because of this restriction that we refer to this result as a “countable” Moore-Schmidt theorem. This theorem is a useful tool in several other applications, such as the Host-Kra structure theorem for ergodic systems; I hope to return to these subsequent applications in a future post.
Let us very briefly sketch the main ideas of the proof of Theorem 1. Ignore for now issues of measurability, and pretend that something that holds almost everywhere in fact holds everywhere. The hard direction is to show that if each ${\langle \hat k, \rho \rangle}$ is a coboundary, then so is ${\rho}$. By hypothesis, we then have an equation of the form
$\displaystyle \langle \hat k, \rho_\gamma(x) \rangle = \alpha_{\hat k} \circ T^\gamma(x) - \alpha_{\hat k}(x) \ \ \ \ \ (2)$
for all ${\hat k, \gamma, x}$ and some functions ${\alpha_{\hat k}: X \rightarrow {\mathbf T}}$, and our task is then to produce a function ${F: X \rightarrow K}$ for which
$\displaystyle \rho_\gamma(x) = F \circ T^\gamma(x) - F(x)$
for all ${\gamma,x}$.
Comparing the two equations, the task would be easy if we could find an ${F: X \rightarrow K}$ for which
$\displaystyle \langle \hat k, F(x) \rangle = \alpha_{\hat k}(x) \ \ \ \ \ (3)$
for all ${\hat k, x}$. However there is an obstruction to this: the left-hand side of (3) is additive in ${\hat k}$, so the right-hand side would have to be also in order to obtain such a representation. In other words, for this strategy to work, one would have to first establish the identity
$\displaystyle \alpha_{\hat k_1 + \hat k_2}(x) - \alpha_{\hat k_1}(x) - \alpha_{\hat k_2}(x) = 0 \ \ \ \ \ (4)$
for all ${\hat k_1, \hat k_2, x}$. On the other hand, the good news is that if we somehow manage to obtain the equation, then we can obtain a function ${F}$ obeying (3), thanks to Pontryagin duality, which gives a one-to-one correspondence between ${K}$ and the homomorphisms of the (discrete) group ${\hat K}$ to ${\mathbf{T}}$.
Now, it turns out that one cannot derive the equation (4) directly from the given information (2). However, the left-hand side of (2) is additive in ${\hat k}$, so the right-hand side must be also. Manipulating this fact, we eventually arrive at
$\displaystyle (\alpha_{\hat k_1 + \hat k_2} - \alpha_{\hat k_1} - \alpha_{\hat k_2}) \circ T^\gamma(x) = (\alpha_{\hat k_1 + \hat k_2} - \alpha_{\hat k_1} - \alpha_{\hat k_2})(x).$
In other words, we don’t get to show that the left-hand side of (4) vanishes, but we do at least get to show that it is ${\Gamma}$-invariant. Now let us assume for sake of argument that the action of ${\Gamma}$ is ergodic, which (ignoring issues about sets of measure zero) basically asserts that the only ${\Gamma}$-invariant functions are constant. So now we get a weaker version of (4), namely
$\displaystyle \alpha_{\hat k_1 + \hat k_2}(x) - \alpha_{\hat k_1}(x) - \alpha_{\hat k_2}(x) = c_{\hat k_1, \hat k_2} \ \ \ \ \ (5)$
for some constants ${c_{\hat k_1, \hat k_2} \in \mathbf{T}}$.
Now we need to eliminate the constants. This can be done by the following group-theoretic projection. Let ${L^0({\bf X} \rightarrow {\bf T})}$ denote the space of concrete measurable maps ${\alpha}$ from ${{\bf X}}$ to ${{\bf T}}$, up to almost everywhere equivalence; this is an abelian group where the various terms in (5) naturally live. Inside this group we have the subgroup ${{\bf T}}$ of constant functions (up to almost everywhere equivalence); this is where the right-hand side of (5) lives. Because ${{\bf T}}$ is a divisible group, there is an application of Zorn’s lemma (a good exercise for those who are not acquainted with these things) to show that there exists a retraction ${w: L^0({\bf X} \rightarrow {\bf T}) \rightarrow {\bf T}}$, that is to say a group homomorphism that is the identity on the subgroup ${{\bf T}}$. We can use this retraction, or more precisely the complement ${\alpha \mapsto \alpha - w(\alpha)}$, to eliminate the constant in (5). Indeed, if we set
$\displaystyle \tilde \alpha_{\hat k}(x) := \alpha_{\hat k}(x) - w(\alpha_{\hat k})$
then from (5) we see that
$\displaystyle \tilde \alpha_{\hat k_1 + \hat k_2}(x) - \tilde \alpha_{\hat k_1}(x) - \tilde \alpha_{\hat k_2}(x) = 0$
while from (2) one has
$\displaystyle \langle \hat k, \rho_\gamma(x) \rangle = \tilde \alpha_{\hat k} \circ T^\gamma(x) - \tilde \alpha_{\hat k}(x)$
and now the previous strategy works with ${\alpha_{\hat k}}$ replaced by ${\tilde \alpha_{\hat k}}$. This concludes the sketch of proof of Theorem 1.
In making the above argument rigorous, the hypotheses (i)-(iii) are used in several places. For instance, to reduce to the ergodic case one relies on the ergodic decomposition, which requires the hypothesis (ii). Also, most of the above equations only hold outside of a set of measure zero, and the hypothesis (i) and the hypothesis (iii) (which is equivalent to ${\hat K}$ being at most countable) to avoid the problem that an uncountable union of sets of measure zero could have positive measure (or fail to be measurable at all).
My co-author Asgar Jamneshan and I are working on a long-term project to extend many results in ergodic theory (such as the aforementioned Host-Kra structure theorem) to “uncountable” settings in which hypotheses analogous to (i)-(iii) are omitted; thus we wish to consider actions on uncountable groups, on spaces that are not standard Borel, and cocycles taking values in groups that are not metrisable. Such uncountable contexts naturally arise when trying to apply ergodic theory techniques to combinatorial problems (such as the inverse conjecture for the Gowers norms), as one often relies on the ultraproduct construction (or something similar) to generate an ergodic theory translation of these problems, and these constructions usually give “uncountable” objects rather than “countable” ones. (For instance, the ultraproduct of finite groups is a hyperfinite group, which is usually uncountable.). This paper marks the first step in this project by extending the Moore-Schmidt theorem to the uncountable setting.
If one simply drops the hypotheses (i)-(iii) and tries to prove the Moore-Schmidt theorem, several serious difficulties arise. We have already mentioned the loss of the ergodic decomposition and the possibility that one has to control an uncountable union of null sets. But there is in fact a more basic problem when one deletes (iii): the addition operation ${+: K \times K \rightarrow K}$, while still continuous, can fail to be measurable as a map from ${(K \times K, {\mathcal B}(K) \otimes {\mathcal B}(K))}$ to ${(K, {\mathcal B}(K))}$! Thus for instance the sum of two measurable functions ${F: X \rightarrow K}$ need not remain measurable, which makes even the very definition of a measurable cocycle or measurable coboundary problematic (or at least unnatural). This phenomenon is known as the Nedoma pathology. A standard example arises when ${K}$ is the uncountable torus ${{\mathbf T}^{{\bf R}}}$, endowed with the product topology. Crucially, the Borel ${\sigma}$-algebra ${{\mathcal B}(K)}$ generated by this uncountable product is not the product ${{\mathcal B}(\mathbf{T})^{\otimes {\bf R}}}$ of the factor Borel ${\sigma}$-algebras (the discrepancy ultimately arises from the fact that topologies permit uncountable unions, but ${\sigma}$-algebras do not); relating to this, the product ${\sigma}$-algebra ${{\mathcal B}(K) \otimes {\mathcal B}(K)}$ is not the same as the Borel ${\sigma}$-algebra ${{\mathcal B}(K \times K)}$, but is instead a strict sub-algebra. If the group operations on ${K}$ were measurable, then the diagonal set
$\displaystyle K^\Delta := \{ (k,k') \in K \times K: k = k' \} = \{ (k,k') \in K \times K: k - k' = 0 \}$
would be measurable in ${{\mathcal B}(K) \otimes {\mathcal B}(K)}$. But it is an easy exercise in manipulation of ${\sigma}$-algebras to show that if ${(X, {\mathcal X}), (Y, {\mathcal Y})}$ are any two measurable spaces and ${E \subset X \times Y}$ is measurable in ${{\mathcal X} \otimes {\mathcal Y}}$, then the fibres ${E_x := \{ y \in Y: (x,y) \in E \}}$ of ${E}$ are contained in some countably generated subalgebra of ${{\mathcal Y}}$. Thus if ${K^\Delta}$ were ${{\mathcal B}(K) \otimes {\mathcal B}(K)}$-measurable, then all the points of ${K}$ would lie in a single countably generated ${\sigma}$-algebra. But the cardinality of such an algebra is at most ${2^{\alpha_0}}$ while the cardinality of ${K}$ is ${2^{2^{\alpha_0}}}$, and Cantor’s theorem then gives a contradiction.
To resolve this problem, we give ${K}$ a coarser ${\sigma}$-algebra than the Borel ${\sigma}$-algebra, which we call the reduced ${\sigma}$-algebra ${{\mathcal B}^\otimes(K)}$, thus coarsening the measurable space structure on ${K = (K,{\mathcal B}(K))}$ to a new measurable space ${K_\otimes := (K, {\mathcal B}^\otimes(K))}$. In the case of compact Hausdorff abelian groups, ${{\mathcal B}^{\otimes}(K)}$ can be defined as the ${\sigma}$-algebra generated by the characters ${\hat k: K \rightarrow {\mathbf T}}$; for more general compact abelian groups, one can define ${{\mathcal B}^{\otimes}(K)}$ as the ${\sigma}$-algebra generated by all continuous maps into metric spaces. This ${\sigma}$-algebra is equal to ${{\mathcal B}(K)}$ when ${K}$ is metrisable but can be smaller for other ${K}$. With this measurable structure, ${K_\otimes}$ becomes a measurable group; it seems that once one leaves the metrisable world that ${K_\otimes}$ is a superior (or at least equally good) space to work with than ${K}$ for analysis, as it avoids the Nedoma pathology. (For instance, from Plancherel’s theorem, we see that if ${m_K}$ is the Haar probability measure on ${K}$, then ${L^2(K,m_K) = L^2(K_\otimes,m_K)}$ (thus, every ${K}$-measurable set is equivalent modulo ${m_K}$-null sets to a ${K_\otimes}$-measurable set), so there is no damage to Plancherel caused by passing to the reduced ${\sigma}$-algebra.
Passing to the reduced ${\sigma}$-algebra ${K_\otimes}$ fixes the most severe problems with an uncountable Moore-Schmidt theorem, but one is still faced with an issue of having to potentially take an uncountable union of null sets. To avoid this sort of problem, we pass to the framework of abstract measure theory, in which we remove explicit mention of “points” and can easily delete all null sets at a very early stage of the formalism. In this setup, the category of concrete measurable spaces is replaced with the larger category of abstract measurable spaces, which we formally define as the opposite category of the category of ${\sigma}$-algebras (with Boolean algebra homomorphisms). Thus, we define an abstract measurable space to be an object of the form ${{\mathcal X}^{\mathrm{op}}}$, where ${{\mathcal X}}$ is an (abstract) ${\sigma}$-algebra and ${\mathrm{op}}$ is a formal placeholder symbol that signifies use of the opposite category, and an abstract measurable map ${T: {\mathcal X}^{\mathrm{op}} \rightarrow {\mathcal Y}^{\mathrm{op}}}$ is an object of the form ${(T^*)^{\mathrm{op}}}$, where ${T^*: {\mathcal Y} \rightarrow {\mathcal X}}$ is a Boolean algebra homomorphism and ${\mathrm{op}}$ is again used as a formal placeholder; we call ${T^*}$ the pullback map associated to ${T}$. [UPDATE: It turns out that this definition of a measurable map led to technical issues. In a forthcoming revision of the paper we also impose the requirement that the abstract measurable map be $\sigma$-complete (i.e., it respects countable joins).] The composition ${S \circ T: {\mathcal X}^{\mathrm{op}} \rightarrow {\mathcal Z}^{\mathrm{op}}}$ of two abstract measurable maps ${T: {\mathcal X}^{\mathrm{op}} \rightarrow {\mathcal Y}^{\mathrm{op}}}$, ${S: {\mathcal Y}^{\mathrm{op}} \rightarrow {\mathcal Z}^{\mathrm{op}}}$ is defined by the formula ${S \circ T := (T^* \circ S^*)^{\mathrm{op}}}$, or equivalently ${(S \circ T)^* = T^* \circ S^*}$.
Every concrete measurable space ${X = (X,{\mathcal X})}$ can be identified with an abstract counterpart ${{\mathcal X}^{op}}$, and similarly every concrete measurable map ${T: X \rightarrow Y}$ can be identified with an abstract counterpart ${(T^*)^{op}}$, where ${T^*: {\mathcal Y} \rightarrow {\mathcal X}}$ is the pullback map ${T^* E := T^{-1}(E)}$. Thus the category of concrete measurable spaces can be viewed as a subcategory of the category of abstract measurable spaces. The advantage of working in the abstract setting is that it gives us access to more spaces that could not be directly defined in the concrete setting. Most importantly for us, we have a new abstract space, the opposite measure algebra ${X_\mu}$ of ${X}$, defined as ${({\bf X}/{\bf N})^*}$ where ${{\bf N}}$ is the ideal of null sets in ${{\bf X}}$. Informally, ${X_\mu}$ is the space ${X}$ with all the null sets removed; there is a canonical abstract embedding map ${\iota: X_\mu \rightarrow X}$, which allows one to convert any concrete measurable map ${f: X \rightarrow Y}$ into an abstract one ${[f]: X_\mu \rightarrow Y}$. One can then define the notion of an abstract action, abstract cocycle, and abstract coboundary by replacing every occurrence of the category of concrete measurable spaces with their abstract counterparts, and replacing ${X}$ with the opposite measure algebra ${X_\mu}$; see the paper for details. Our main theorem is then
Theorem 2 (Uncountable Moore-Schmidt theorem) Let ${\Gamma}$ be a discrete group acting abstractly on a ${\sigma}$-finite measure space ${X}$. Let ${K}$ be a compact Hausdorff abelian group. Then a ${K_\otimes}$-valued abstract measurable cocycle ${\rho = (\rho_\gamma)_{\gamma \in \Gamma}}$ is an abstract coboundary if and only if for each character ${\hat k \in \hat K}$, the ${\mathbf{T}}$-valued cocycles ${\langle \hat k, \rho \rangle = ( \langle \hat k, \rho_\gamma \rangle )_{\gamma \in \Gamma}}$ are abstract coboundaries.
With the abstract formalism, the proof of the uncountable Moore-Schmidt theorem is almost identical to the countable one (in fact we were able to make some simplifications, such as avoiding the use of the ergodic decomposition). A key tool is what we call a “conditional Pontryagin duality” theorem, which asserts that if one has an abstract measurable map ${\alpha_{\hat k}: X_\mu \rightarrow {\bf T}}$ for each ${\hat k \in K}$ obeying the identity ${ \alpha_{\hat k_1 + \hat k_2} - \alpha_{\hat k_1} - \alpha_{\hat k_2} = 0}$ for all ${\hat k_1,\hat k_2 \in \hat K}$, then there is an abstract measurable map ${F: X_\mu \rightarrow K_\otimes}$ such that ${\alpha_{\hat k} = \langle \hat k, F \rangle}$ for all ${\hat k \in \hat K}$. This is derived from the usual Pontryagin duality and some other tools, most notably the completeness of the ${\sigma}$-algebra of ${X_\mu}$, and the Sikorski extension theorem.
We feel that it is natural to stay within the abstract measure theory formalism whenever dealing with uncountable situations. However, it is still an interesting question as to when one can guarantee that the abstract objects constructed in this formalism are representable by concrete analogues. The basic questions in this regard are:
• (i) Suppose one has an abstract measurable map ${f: X_\mu \rightarrow Y}$ into a concrete measurable space. Does there exist a representation of ${f}$ by a concrete measurable map ${\tilde f: X \rightarrow Y}$? Is it unique up to almost everywhere equivalence?
• (ii) Suppose one has a concrete cocycle that is an abstract coboundary. When can it be represented by a concrete coboundary?
For (i) the answer is somewhat interesting (as I learned after posing this MathOverflow question):
• If ${Y}$ does not separate points, or is not compact metrisable or Polish, there can be counterexamples to uniqueness. If ${Y}$ is not compact or Polish, there can be counterexamples to existence.
• If ${Y}$ is a compact metric space or a Polish space, then one always has existence and uniqueness.
• If ${Y}$ is a compact Hausdorff abelian group, one always has existence.
• If ${X}$ is a complete measure space, then one always has existence (from a theorem of Maharam).
• If ${X}$ is the unit interval with the Borel ${\sigma}$-algebra and Lebesgue measure, then one has existence for all compact Hausdorff ${Y}$ assuming the continuum hypothesis (from a theorem of von Neumann) but existence can fail under other extensions of ZFC (from a theorem of Shelah, using the method of forcing).
• For more general ${X}$, existence for all compact Hausdorff ${Y}$ is equivalent to the existence of a lifting from the ${\sigma}$-algebra ${\mathcal{X}/\mathcal{N}}$ to ${\mathcal{X}}$ (or, in the language of abstract measurable spaces, the existence of an abstract retraction from ${X}$ to ${X_\mu}$).
• It is a long-standing open question (posed for instance by Fremlin) whether it is relatively consistent with ZFC that existence holds whenever ${Y}$ is compact Hausdorff.
Our understanding of (ii) is much less complete:
• If ${K}$ is metrisable, the answer is “always” (which among other things establishes the countable Moore-Schmidt theorem as a corollary of the uncountable one).
• If ${\Gamma}$ is at most countable and ${X}$ is a complete measure space, then the answer is again “always”.
In view of the answers to (i), I would not be surprised if the full answer to (ii) was also sensitive to axioms of set theory. However, such set theoretic issues seem to be almost completely avoided if one sticks with the abstract formalism throughout; they only arise when trying to pass back and forth between the abstract and concrete categories.
In these notes we quickly review the basics of abstract measure theory and integration theory, which was covered in the previous course but will of course be relied upon in the current course. This is only a brief summary of the material; of course, one should consult a real analysis text for the full details of the theory.
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https://quantumcomputing.stackexchange.com/questions/8941/exponentiating-hermitian-matrix-for-use-in-qpe-hhl
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# Exponentiating Hermitian Matrix for use in QPE/HHL
I am currently trying to understand HHL by implementing a very inefficient Qiskit simulation script that performs HHL on an arbitrary hermitian matrix $$A$$ and a vector $$b$$.
Because I am currently only attempting to understand the higher-level workings of the HHL algorithm itself, I am cheating and just using Qiskit simulator features to implement the operators $$e^{iAt/T}$$ and to 'prepare' $$|b>$$
So far, I am trying to get it to work on two examples: the HHL example here and the problem done in this paper. It works as expected on the former, but not on the latter. This makes me wonder if i am correctly implementing the operators $$e^{iAt/T}$$ used in the QPE section of HHL.
So my question is whether I am implementing $$e^{iAt/T}$$ correctly or not. I have written a function that takes a hermitian matrix, exponentiates it using the scipy function expm, adds a control to this matrix, and then turns it into an operator using the Qiskit Operator function.
Does this function return the intended unitary operator, $$e^{iAt/T}$$? If it is ill-conceived, why?
from qiskit.quantum_info.operators import Operator
from scipy.linalg import expm
def hermitian_to_controlled_U(hermitian_matrix,T):
U_matrix = expm(2j*pi*hermitian_matrix/T)
M0 = np.asarray([[1,0],\
[0,0]])
M1 = np.asarray([[0,0],\
[0,1]])
I = np.eye(np.shape(hermop)[0])
controlled_U_matrix = np.kron(M0,I)+np.kron(M1,U_matrix)
controlled_U_gate = Operator(controlled_U_matrix)
return controlled_U_gate
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https://www.tuitionwithjason.sg/blog/
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# Math Blog
Home/Math Blog/
## Additional Math – Differentiation – Quotient Rule (Challenging)
By |2022-03-07T11:11:15+08:00March 7th, 2022|A-Math - Differentiation|
Differentiate $latex \displaystyle\ y=\frac{{{{x}^{2}}\sqrt{{x+1}}}}{{x-1}}$ with respect to x. Simplify the Numerator (otherwise you need to use both quotient rule for [...]
## Additional Math – Binomial theorem – Using Normal Expansion vs Binomial Theorem
By |2022-01-07T14:47:45+08:00January 6th, 2022|A-Math - Binomial|
The above video shows two method of expanding the expression; using the algebraic expansion (rainbow method) versus the binomial theorem. [...]
## Additional Math – Trigonometry – Solve cotangent half angle – 2cosine half angle = 2
By |2021-04-05T22:51:56+08:00April 5th, 2021|A-Math - Trigonometry|
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https://www.hackmath.net/en/math-problem/6960
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Square metal sheet
Four squares of 300 mm side were cut out from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet.
Correct result:
f = 0.265
p = 26.5 %
Solution:
$a=0.7 \ \text{m} \ \\ b=300 \ mm \rightarrow m=300 / 1000 \ m=0.3 \ m \ \\ \ \\ S_{1}=a^2=0.7^2=\dfrac{ 49 }{ 100 }=0.49 \ \text{m}^2 \ \\ S_{2}=4 \cdot \ b^2=4 \cdot \ 0.3^2=\dfrac{ 9 }{ 25 }=0.36 \ \\ \ \\ o=S_{1}-S_{2}=0.49-0.36=\dfrac{ 13 }{ 100 }=0.13 \ \text{m}^2 \ \\ f=\dfrac{ o }{ S_{1} }=\dfrac{ 0.13 }{ 0.49 }=\dfrac{ 13 }{ 49 }=0.265$
$p=100 \cdot \ f=100 \cdot \ 0.2653=\dfrac{ 53 }{ 2 }=26.5 \%$
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http://windowsontheory.org/2014/02/17/discrepancy-bounds-from-convex-geometry/
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In the last post we discussed some questions about discrepancy and the ‘Six Standard Deviations Suffice’ theorem stated below (without the ${6}$, which is not too important, but makes for a great title):
Theorem 1 For vectors ${a^1,\ldots,a^n \in \{1,-1\}^n}$, there exists ${\epsilon \in \{1,-1\}^n}$ such that for every ${j \in [n]}$, ${|\langle a^j,\epsilon\rangle| = O(\sqrt{n})}$.
In this post (second and the most technical of the three post series) we will see a proof of the above result. The theorem was proved by Spencer in 1985 using Beck’s partial coloring approach. Independently of Spencer, the result was proved by Gluskin in 1988 in a convex geometric context. Here we will review Gluskin’s proof which is quite beautiful.
Gluskin’s proof will also give us an excuse to look at some elegant (and simple to describe) results in convex geometry which may be of use elsewhere. Finally, the geometric view here will actually be useful in the next post when we discuss an algorithmic proof. Gluskin’s paper is truly remarkable and seems to reinvent several key ideas from scratch such as Sidak’s lemma, a version of Kanter’s lemma for Gaussians in convex geometry and even has the partial coloring approach implicit in it. I recommend taking a look at the paper even if it is a bit of a tough read. Much of the content in the post is based on discussions with Shachar Lovett and Oded Regev, but all mistakes are mine.
Gluskin’s proof follows the partial coloring approach with the crucial lemma proved using a volume argument. The partial coloring method was introduced by Beck in 1981 and all proofs of Theorem 1 and many other important discrepancy results in fact use this method. Here, instead of looking for a ${\epsilon \sim \{1,-1\}^n}$ solution as in the theorem, one looks for a ${\{1,0,-1\}^n}$ solution first. This is meaningless to begin with as we can just output the all zeros vector. The main idea is to instead look for a ${\{1,0,-1\}^n}$ solution which has ${\Omega(n)}$ support. We then recurse on the set of coordinates which are set to ${0}$. If everything goes according to plan, as we are geometrically decreasing the ambient dimension, we similarly get geometrically decreasing discrepancy bounds which we can tolerate. I won’t go into the details here, but let’s accept that it suffices to show the following:
Lemma 2 For vectors ${a^1,\ldots,a^n \in \{1,-1\}^n}$, there exists ${\epsilon \in \{1,0,-1\}^n}$ such that for every ${j \in [n]}$, ${\langle a^j,\epsilon\rangle = O(\sqrt{n})}$ and ${|Support(\epsilon)| = \Omega(n)}$.
To prove the above partial-coloring-lemma, let us first rephrase the problem in a geometric language. Let ${\mathcal{K} \subseteq R^n}$ be the symmetric convex set (symmetric meaning ${x \in \mathcal{K}}$ implies ${-x \in \mathcal{K}}$) defined as follows for ${\Delta = O(\sqrt{n})}$ to be chosen later:
$\displaystyle \mathcal{K} = \{x: |\langle a^j,x\rangle| \leq \Delta, \forall j \in [n]\}.$
We want to show that ${\mathcal{K}}$ contains a ${\{1,0,-1\}^n}$ lattice point of large support. We show this indirectly by proving that ${\mathcal{K}}$ instead contains a lot of points from ${\{1,0,-1\}^n}$. Gluskin does this by a clever volume argument: first show that the volume of ${\mathcal{K} \cap [-1,1]^n}$ is large and then apply Minkowski’s theorem to show that there are many lattice points. To lower bound the first volume, Gluskin actually works in the Gaussian space.
I don’t have a clear intuitive reason for why the Gaussian distribution is better than the Lebesgue measure in this context. But if one looks at the analysis, a clear advantage is that projections behave better (when considering volumes) in the Gaussian space. For example, if we take a set like ${S = \{x \in R^n\,:\,|x_1| \leq 1\}}$, then the Lebsgue volume of ${S}$ is infinite, but if we project along the first coordinate it becomes finite. In the Gaussian case, both volumes are the same.
We next go over all the main pieces in Gluskin’s proof.
Sidak’s Lemma Suppose we have a standard Gaussian vector ${g \sim \mathcal{N}(0,1)^n}$. Then, for any unit vector ${v \in R^n}$, ${\langle v,g\rangle}$ has the standard normal distribution. Now, suppose we have several unit vectors ${v_1,\ldots,v_m \in R^n}$. Then, the random variables ${X_i = \langle v_i,g\rangle}$ are individually standard normals, but are correlated with one another. Sidak’s lemma (1967) says that no matter what the correlations of ${X_i}$‘s are, to bound the probability that none of the ${X_i}$‘s is too large, the “worst-behaviour” one could expect is for them to be independent. Concretely:
Lemma 3 (Sidak’s Lemma) Let ${v_1,\ldots,v_m \in R^n}$ and let ${g \sim \mathcal{N}(0,1)^n}$ be a standard Gaussian vector. Then, for all ${t_1,\ldots,t_m \in R_+}$,
$\displaystyle Pr\left[|\langle v_1,g\rangle| \leq t_1 \;\wedge\; |\langle v_2,g\rangle| \leq t_2\;\wedge\; \cdots \;\wedge\; |\langle v_m,g\rangle| \leq t_m\right] \geq$
$\displaystyle \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; Pr\left[|\langle v_1,g\rangle |\leq t_1\right] \cdot Pr\left[|\langle v_2,g\rangle|\leq t_2\right] \cdots Pr\left[|\langle v_m,g\rangle|\leq t_m\right].$
The proof of the lemma is actually not too hard and an excellent exposition can be found in this paper.
The lemma is actually a very special case of a longstanding open problem called the Correlation Conjecture. Let me digress a little bit to state this beautiful question. In the above setup, let slab ${C_i = \{x \in R^n: |\langle v_i,x\rangle| \leq t_i\}}$. Then, Sidak’s lemma says that for ${g \sim \mathcal{N}(0,1)^n}$,
$\displaystyle Pr[g \in C_1 \wedge C_2 \wedge \cdots \wedge C_m] \geq Pr[g \in C_1] \cdot Pr[g \in C_2] \cdots Pr[g \in C_m].$
The correlation conjecture asserts that this inequality is in fact true for all symmetric convex sets (in fact, we only need to look at ${m=2}$). Sidak’s lemma says the conjecture is true for slabs. It is also known to be true for ellipsoids. The statement for ellipsoids also has a discrepancy implication leading to a vector generalization of Spencer’s theorem (pointed to me by Krzysztof Oleszkiewicz). But that’s for another day.
Kanter’s Lemma The second inequality we need is a comparison inequality due to Kanter. The lemma essentially lets us lift certain relations between two distributions ${p,q}$ to their product distributions ${p^n, q^n}$ and I think should be useful in other contexts. For instance, I recently used it in this paper in a completely different context. To state the lemma, we need the notion of peakedness of distributions.
Let ${p,q}$ be two symmetric distributions on ${R^m}$ for some ${m}$. We say ${p}$ is less peaked than ${q}$ (written ${p \preceq q}$) if for all symmetric convex sets ${\mathcal{K}}$, ${p(\mathcal{K}) \leq q(\mathcal{K})}$. Intuitively, this means that ${p}$ is putting less of its mass near the origin than ${q}$ (hence the term less peaked). For example, ${\mathcal{N}(0,2) \preceq \mathcal{N}(0,1)}$.
Kanter’s lemma says that the peakedness relation tensorises provided we have unimodality. A univariate distribution is unimodal if the corresponding probability density function has a single maximum and no other local maxima. I won’t define what it means for a multivariate distribution to be unimodal here, but we only need the lemma for univariate distributions. See this survey for the formal definition.
Lemma 4 (Kanter’s lemma) Let ${p,q}$ be two symmetric distributions on ${R^n}$ such that ${p \preceq q}$ and let ${\mu}$ be a unimodal distribution on ${R^m}$. Then, the product distributions ${p \times \mu}$, ${q \times \mu}$ on ${R^{n \times m}}$, satisfy ${p \times \mu \preceq q \times \mu}$.
The proof of the lemma is not too hard, but is non-trivial in that it uses the Brunn-Minkowski’s inequality. Combining the above lemma with the not-too-hard fact that the standard Gaussian distribution is less peaked than the uniform distribution on ${[-1,1]}$, we get:
Corollary 5 Let ${\mu}$ be the uniform distribution on ${[-1,1]}$. Then, ${\mathcal{N}(0,1)^n \preceq \mu^n}$.
Minkowski’s Theorem The final piece we need is the classical Minkowski’s theorem form lattice geometry:
Theorem 6 (Minkowski’s Theorem) Let ${C \subseteq R^n}$ be a symmetric convex set of Lebesgue volume more than ${2^n \cdot \ell}$ for an integer ${\ell \geq 1}$. Then, ${C}$ contains at least ${\ell}$ points from the integer lattice ${\mathbb{Z}^n}$.
Putting Things Together We will prove the partial coloring lemma Lemma 2. The proof will be a sequence of simple implications using the above lemmas. Recall the definition of ${\mathcal{K}}$:
$\displaystyle \mathcal{K} = \{x: |\langle a^j,x\rangle| \leq \Delta, \forall j \in [n]\}.$
Our goal (Lemma 2) is equivalent to showing that ${\mathcal{K}}$ contains a ${\{1,0,-1\}}$ point of large support.
Note that ${\mathcal{K}}$ is the intersection of ${n}$ slabs. Therefore, by Sidak’s lemma, for ${g \sim \mathcal{N}(0,1)^n}$,
$\displaystyle Pr[g \in \mathcal{K}] \geq \prod_{j=1}^n Pr[|\langle a^j,g\rangle| \leq \Delta] \geq \prod_{j=1}^n\left(1-2\exp(-\Delta^2/2n)\right),$
where the last inequality follows from the fact that ${\langle a^j,g\rangle}$ has the Gaussian distribution with standard deviation ${\sqrt{n}}$. Therefore, if we pick ${\Delta = O(\sqrt{n})}$, sufficiently big then
$\displaystyle Pr[g \in \mathcal{K}] \geq (3/4)^n.$
Now, let ${\mu}$ be the uniform distribution on ${[-1,1]}$. Then, by Corollary 5, and the definition of peakedness, ${\mu^n(\mathcal{K}) \geq (3/4)^n}$. Hence, the Lebesgue volume of ${\mathcal{K}' = \mathcal{K} \cap [-1,1]^n}$ is at least ${2^n (3/4)^n = (3/2)^n}$. Therefore, for sufficiently small ${\delta > 0}$, Lebesgue volume of ${(2-\delta)\mathcal{K}' \geq (2-\delta)^n \cdot (3/2)^n = 2^n \cdot 2^{\Omega(n)}}$. Thus, by applying Minkowski’s theorem to the symmetric convex set ${(2-\delta) \mathcal{K}'}$ we get that ${(2-\delta)\mathcal{K}'}$ has at least ${2^{\Omega(n)}}$ lattice points.
Now, note that the only lattice points in ${(2-\delta)\mathcal{K}'}$ are elements of ${\{1,0,-1\}^n}$ inside ${\mathcal{K}}$. Therefore ${\mathcal{K}}$ has at least ${2^{\Omega(n)}}$ points from ${\{1,0,-1\}^n}$. By a simple counting argument at least one of these lattice points, ${\epsilon}$, must ${\Omega(n)}$ non-zero coordinates – which is exactly what we need to prove Lemma 2!
Discussion The above argument can actually be simplified by replacing the use of Kanter’s lemma with an appropriate version of Miknowski’s theorem for Gaussian volume as done here. But I like any excuse to discuss Kanter’s lemma.
More importantly, the proof seems to be more amenable to generalization. The core of the proof really is to use Sidak’s lemma to lower bound the Gaussian volume of the convex set ${\mathcal{K}}$. Whenever you have such a statement you should even get a corresponding discrepancy statement. In particular, the matrix discrepancy conjecture from last post, essentially reduces to the following probability question:
Question Is it true that for a universal constant ${C}$, for all symmetric matrices ${A_1,\ldots,A_n \in R^{n \times n}}$ with ${\|A_i\| \leq 1}$,
$\displaystyle Pr_{g \sim \mathcal{N}^n}\left[\|g_1 A_1 + g_2 A_2 + \cdots + g_n A_n \| \leq C \sqrt{n}\right] \geq (3/4)^n\,?$
Acknowledgments Thanks to Shachar Lovett, Oded Regev and Nikhil Srivastava for helpful suggestions, comments, and corrections during the preparation of this post.
1. February 20, 2014 2:07 am
Very nice post!
I may be missing something, but I think Giannopoulos’s proof also gives the implication from Gaussian volume lower bounds to a partial coloring.
Let $K$ be the set of “small discrepancy fractional colorings” (the same set you define), and assume $\Pr_g[g \in K] > 2^{-c_1n}$. Then let $f_K(g)$ be the number of sign sequences $\varepsilon \in \{-1, 1\}^n$ such that $g \in 0.01\varepsilon + K$. From looking at the pdf of the standard gaussian, $\Pr[g \in 0.01\varepsilon + K] >= 2^{-c_2n}$ for some $c_2 = 2^{(1 - c_2)n}$. So there must exist a point $\latex x$ which is in at least $N = 2^{(1-c_2)n}$ sets $\varepsilon^{1} + 100K, \ldots, \varepsilon^{N} + 100K$. For any two $i, j$, $\varepsilon^i - \varepsilon^j \in 200K$, and since $N$ is so large, there must exist two $i, j$ such that $\frac{\varepsilon^i - \varepsilon^j}{2} \in 100K$ and $\frac{\varepsilon^i - \varepsilon^j}{2}$ has large support. I chose 0.01 very conservatively, much better constants should do the job.
But Kanter’s lemma is cool in any case!
• February 20, 2014 6:00 am
Indeed, Giannopoulos’s proof is simpler – one can view the argument you described (a typo: c_2 should be a constant) as a kind of Gaussian version of Minkowski’s theorem which by itself is a nice thing to know.
• February 20, 2014 8:14 pm
Sorry for the typo. I wish there was a way to preview comments by the way.
I could’ve been more explicit: $\Pr[g \in x + K] \geq e^{0.5\|x\|_2^2}$ for any centrally symmetric $K$ and any $x$, so $c_2 = c_1 + 0.005\log_2 e \leq c_1 + 0.008$. I guess I was really conservative with constants.
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http://mathhelpforum.com/calculus/98643-flux-integrals-verifying-stokes-theorem.html
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# Math Help - Flux integrals - verifying Stokes Theorem
1. ## Flux integrals - verifying Stokes Theorem
Ok, I've been stuck on this problem for hours now and its really irritating, so I need help!
Here is the question:
-------------------------------------------------------------
Verify Stokes Theorem for the vector field
F = yi + 2zj + xzk
and the surface S defined by
x^2 + y^2 + z^2 = 25 & Z>=4
--------------------------------------------------------------
Right, I'm quite new to these so please explain clearly if possible, cheers!
So far I've computed the line integral and got a result of -Pi
Now I'm stuck on the flux integral. I've worked out that Curl F = -2i -zj -k but I'm not sure what the normal vector is or the limits.
Any help much appreciated!
2. The surface is the portion of the hemi -sphere x^2 +y^2 +z^2 =25
above z= 4
z= sqrt(25-x^2 -y^2)
N = -dz/dx i -dz/dy j + K
N = x/sqrt(25-x^2) i + y /sqrt(25-y^2) j + k
The region of integration is the circle x^2 + y^2 = 9
(using z=4)
See the attachment for the calculation of the line integral using both Stokes Theorem and the definition of line integral
Attached Files
3. Gah so my line integral result is incorrect?
4. you're computing the line integral around the circle of radius 3 , 4units
above the x-y plane.
How'd you compute the line integral ?
What was your parameterization and F*dr/dt ?
5. I had circle radius 1, 4 units
My parameterization was r(t) = cos(t)i +sin(t)j +4k for 0<t<2Pi
F.dr = -sin^2(t) + 8cos(t)
6. x^2 + y^2 +z^2 = 25
if z = 4 x^2 + y^2 = 9
Which gives x=3cos(t) y = 3sin(t) z = 4
r ' = -3sin(t) i +3cos(t) j
F = 3sin(t) i - 4 j + 12cos(t) k
As in the attachment. you then end up with -9pi which is the - 28.274 in the attachment
7. How did you go about doing the first integral, ie "we obtain using the parameterization". In the word document i meant
8. The first integral is the integral curl F*N
Then using the pararmaterization for the bounding curve we obtain the second integral of F*dr/dt
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http://www.r-bloggers.com/the-shape-of-floating-point-random-numbers/
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# The Shape of Floating Point Random Numbers
October 15, 2012
By
(This article was first published on John Myles White » Statistics, and kindly contributed to R-bloggers)
[Updated 10/18/2012: Fixed a typo in which mantissa was replaced with exponent.]
Over the weekend, Viral Shah updated Julia’s implementation of randn() to give a 20% speed boost. Because we all wanted to test that this speed-up had not come at the expense of the validity of Julia’s RNG system, I spent some time this weekend trying to get tests up and running. I didn’t get far, but thankfully others chimed in and got things done.
Testing an RNG is serious business. In total, we’ve considered using four different test suites:
All of these suites can be easily used to test uniform random numbers over unsigned integers. Some are also appropriate for testing uniform random numbers over floatint-point values.
But we wanted to test a Gaussian RNG. To do that, we followed Thomas et al.’s lead and mapped the Gaussian RNG’s output through a high-precision quantile function to produce uniform random floating point values. As our high-precision quantile function we ended up using the one described in Marsaglia’s 2004 JSS paper.
With that in place, I started to try modifying my previous RNG testing code. When we previously tried to test Julia’s rand() function, I got STS working on my machine and deciphered its manual well enough to run a suite of tests on a bit stream from Julia.
Unfortunately I made a fairly serious error in how I attempted to test Julia’s RNG. Because STS expects a stream of random 0′s and 1′s, I converted random numbers into 0′s and 1′s by testing whether the floating point numbers being generated were greater than 0.5 or less than 0.5. While this test is not completely wrong, it is very, very weak. Its substantive value comes from two points:
1. It confirms that the median of the RNG is correctly positioned at 0.5.
2. It confirms that the placement of successive entries relative to 0.5 is effectively random. In short, there is not trivial correlation between successive values.
Unfortunately that’s about all you learn from this method. We needed something more. So I started exploring how to convert a floating point into bits. Others had the good sense to avoid this and pushed us forward by using the TestU01 suite.
I instead got lost exploring the surprising complexity of trying to work with the individual bits of random floating point numbers. The topic is so subtle because the distribution of bits in a randomly generated floating point number is extremely far from a random source of individual bits.
For example, a uniform variable’s representation in floating point has all the following non-random properties:
1. The sign bit is never random because uniform variables are never negative.
2. The exponent is not random either because uniform variables are strictly contained in the interval [0, 1].
3. Even the mantissa isn’t random. Because floating point numbers aren’t evenly spaced in the reals, the mantissa has to have complex patterns in it to simulate the equal-spacing of uniform numbers.
Inspired by all of this, I decided to get a sense for the bit pattern signature of different RNG’s. Below I’ve plotted the patterns for uniform, normal, gamma and Cauchy variables using lines that describe the mean value of the i-th bit in the bit string. At a minimum, a completely random bit stream would have a flat horizontal line through 0.5, which many of the lines touch for a moment, but never perfectly match.
Some patterns:
1. The first bit (shown on the far left) is the sign bit: you can clearly see which distributions are symmetric by looking for a mean value of 0.5 versus those that are strictly positive and have a mean value of 0.0.
2. The next eleven bits are the exponent and you can clearly see which distributions are largely concentrated in the interval [-1, 1] and which have substantial density outside of that region. This bit would clue you into the variance of the distribution.
3. You can see that there is a lot of non-randomness in the last few bits of the mantissa for uniform variables. There’s also non-randomness in the first few bits for all variables. I don’t yet have any real intuition for those patterns.
You can go beyond looking at the signatures of mean bit patterns by looking at covariance matrices as well. Below I show these covariances matrices in a white-blue coloring scheme in which white indicates negative values, light blue indicates zero and dark blue indicates positive values. Note that matrices, generated using R’s image() function are reflections of the more intuitive matrix ordering in which the [1,1] entry of the matrix occurs in the top-left instead of the bottom-left.
#### Cauchy Variables
I find these pictures really helpful for reminding me how strangely floating point numbers behave. The complexity of these images is so far removed from the simplicity of the bit non-patterns in randomly generated unsigned integers, which can be generated using IID random bits and concatenating them together.
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http://www.mathworks.com/help/optim/examples/analyzing-the-effect-of-uncertainty-using-semi-infinite-programming.html?prodcode=OP&language=en&requestedDomain=www.mathworks.com&nocookie=true
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Accelerating the pace of engineering and science
# Optimization Toolbox
## Analyzing the Effect of Uncertainty Using Semi-Infinite Programming
This example shows how to use semi-infinite programming to investigate the effect of uncertainty in the model parameters of an optimization problem. We will formulate and solve an optimization problem using the function fseminf, a semi-infinite programming solver in Optimization Toolbox™.
The problem illustrated in this example involves the control of air pollution. Specifically, a set of chimney stacks are to be built in a given geographic area. As the height of each chimney stack increases, the ground level concentration of pollutants from the stack decreases. However, the construction cost of each chimney stack increases with height. We will solve a problem to minimize the cumulative height of the chimney stacks, hence construction cost, subject to ground level pollution concentration not exceeding a legislated limit. This problem is outlined in the following reference:
Air pollution control with semi-infinite programming, A.I.F. Vaz and E.C. Ferreira, XXVIII Congreso Nacional de Estadistica e Investigacion Operativa, October 2004
In this example we will first solve the problem published in the above article as the Minimal Stack Height problem. The models in this problem are dependent on several parameters, two of which are wind speed and direction. All model parameters are assumed to be known exactly in the first solution of the problem.
We then extend the original problem by allowing the wind speed and direction parameters to vary within given ranges. This will allow us to analyze the effects of uncertainty in these parameters on the optimal solution to this problem.
### Minimal Stack Height Problem
Consider a 20km-by-20km region, R, in which ten chimney stacks are to be placed. These chimney stacks release several pollutants into the atmosphere, one of which is sulfur dioxide. The x, y locations of the stacks are fixed, but the height of the stacks can vary.
Constructors of the stacks would like to minimize the total height of the stacks, thus minimizing construction costs. However, this is balanced by the conflicting requirement that the concentration of sulfur dioxide at any point on the ground in the region R must not exceed the legislated maximum.
First, let's plot the chimney stacks at their initial height. Note that we have zoomed in on a 4km-by-4km subregion of R which contains the chimney stacks.
h0 = [210;210;180;180;150;150;120;120;90;90]; plotChimneyStacks(h0, 'Chimney Stack Initial Height');
There are two environment related parameters in this problem, the wind speed and direction. Later in this example we will allow these parameters to vary, but for the first problem we will set these parameters to typical values.
% Wind direction in radians theta0 = 3.996; % Wind speed in m/s U0 = 5.64;
Now let's plot the ground level concentration of sulfur dioxide (SO2) over the entire region R (remember that the plot of chimney stacks was over a smaller region). The SO2 concentration has been calculated with the chimney stacks set to their initial heights.
We can see that the concentration of SO2 varies over the region of interest. There are two features of the Sulfur Dioxide graph of note:
• SO2 concentration rises in the top left hand corner of the (x,y) plane
• SO2 concentration is approximately zero throughout most of the region
In very simple terms, the first feature is due to the prevailing wind, which is blowing SO2 toward the top left hand corner of the (x,y) plane in this example. The second factor is due to SO2 being transported to the ground via diffusion. This is a slower process compared to the prevailing wind and thus SO2 only reaches ground level in the top left hand corner of the region of interest.
For a more detailed discussion of atmospheric dispersion from chimney stacks, consult the reference cited in the introduction.
The pink plane indicates a SO2 concentration of . This is the legislated maximum for which the Sulfur Dioxide concentration must not exceed in the region R. It can be clearly seen from the graph that the SO2 concentration exceeds the maximum for the initial chimney stack height.
Examine the MATLAB file concSulfurDioxide to see how the sulfur dioxide concentration is calculated.
plotSulfurDioxide(h0, theta0, U0, ... 'Sulfur Dioxide Concentration at Initial Stack Height');
### How fseminf Works
Before we solve the minimal stack height problem, we will outline how fseminf solves a semi-infinite problem. A general semi-infinite programming problem can be stated as:
such that
(Linear inequality constraints)
(Linear equality constraints)
(Nonlinear Inequality Constraints)
(Nonlinear Equality Constraints)
(Bounds)
and
, where for (Nonlinear semi-infinite constraints)
This algorithm allows you to specify constraints for a nonlinear optimization problem that must be satisfied over intervals of an auxiliary variable, . Note that for fseminf, this variable is restricted to be either 1 or 2 dimensional for each semi-infinite constraint.
The function fseminf solves the general semi-infinite problem by starting from an initial value, , and using an iterative procedure to obtain an optimum solution, .
The key component of the algorithm is the handling of the "semi-infinite" constraints, . At it is required that the must be feasible at every value of in the interval . This constraint can be simplified by considering all the local maxima of with respect to in the interval . The original constraint is equivalent to requiring that the value of at each of the above local maxima is feasible.
fseminf calculates an approximation to all the local maximum values of each semi-infinite constraint, . To do this, fseminf first calculates each semi-infinite constraint over a mesh of values. A simple differencing scheme is then used to calculate all the local maximum values of from the evaluated semi-infinite constraint.
As we will see later, you create this mesh in your constraint function. The spacing you should use for each coordinate of the mesh is supplied to your constraint function by fseminf.
At each iteration of the algorithm, the following steps are performed:
1. Evaluate over a mesh of -values using the current mesh spacing for each -coordinate.
2. Calculate an approximation to all the local maximum values of using the evaluation of from step 1.
3. Replace each in the general semi-infinite problem with the set of local maximum values found in steps 1-2. The problem now has a finite number of nonlinear constraints. fseminf uses the SQP algorithm used by fmincon to take one iteration step of the modified problem.
4. Check if any of the SQP algorithm's stopping criteria are met at the new point . If any criteria are met the algorithm terminates; if not, fseminf continues to step 5. For example, if the first order optimality value for the problem defined in step 3 is less than the specified tolerance then fseminf will terminate.
5. Update the mesh spacing used in the evaluation of the semi-infinite constraints in step 1.
### Writing the Nonlinear Constraint Function
Before we can call fseminf to solve the problem, we need to write a function to evaluate the nonlinear constraints in this problem. The constraint to be implemented is that the ground level Sulfur Dioxide concentration must not exceed at every point in region R.
This is a semi-infinite constraint, and the implementation of the constraint function is explained in this section. For the minimal stack height problem we have implemented the constraint in the MATLAB file airPollutionCon.
type airPollutionCon.m
function [c, ceq, K, s] = airPollutionCon(h, s, theta, U) %AIRPOLLUTIONCON Constraint function for air pollution demo % % [C, CEQ, K, S] = AIRPOLLUTIONCON(H, S, THETA, U) calculates the % constraints for the air pollution Optimization Toolbox (TM) demo. This % function first creates a grid of (X, Y) points using the supplied grid % spacing, S. The following constraint is then calculated over each point % of the grid: % % Sulfur Dioxide concentration at the specified wind direction, THETA and % wind speed U <= 1.25e-4 g/m^3 % % See also AIRPOLLUTION % Copyright 2008 The MathWorks, Inc. % Initial sampling interval if nargin < 2 || isnan(s(1,1)) s = [1000 4000]; end % Define the grid that the "infinite" constraints will be evaluated over w1x = -20000:s(1,1):20000; w1y = -20000:s(1,2):20000; [t1,t2] = meshgrid(w1x,w1y); % Maximum allowed sulphur dioxide maxsul = 1.25e-4; % Calculate the constraint over the grid K = concSulfurDioxide(t1, t2, h, theta, U) - maxsul; % Rescale constraint to make it 0(1) K = 1e4*K; % No finite constraints c = []; ceq = [];
This function illustrates the general structure of a constraint function for a semi-infinite programming problem. In particular, a constraint function for fseminf can be broken up into three parts:
1. Define the initial mesh size for the constraint evaluation
Recall that fseminf evaluates the "semi-infinite" constraints over a mesh as part of the overall calculation of these constraints. When your constraint function is called by fseminf, the mesh spacing you should use is supplied to your function. Fseminf will initially call your constraint function with the mesh spacing, s, set to NaN. This allows you to initialize the mesh size for the constraint evaluation. Here, we have one "infinite" constraint in two "infinite" variables. This means we need to initialize the mesh size to a 1-by-2 matrix, in this case, s = [1000 4000].
2. Define the mesh that will be used for the constraint evaluation
A mesh that will be used for the constraint evaluation needs to be created. The three lines of code following the comment "Define the grid that the "infinite" constraints will be evaluated over" in airPollutionCon can be modified for most 2-d semi-infinite programming problems.
3. Calculate the constraints over the mesh
Once the mesh has been defined, the constraints can be calculated over it. These constraints are then returned to fseminf from the above constraint function.
Note that in this problem, we have also rescaled the constraints so that they vary on a scale which is closer to that of the objective function. This helps fseminf to avoid scaling issues associated with objectives and constraints which vary on disparate scales.
### Solve the Optimization Problem
We can now call fseminf to solve the problem. The chimney stacks must all be at least 10m tall and we use the initial stack height specified earlier. Note that the third input argument to fseminf below (1) indicates that there is only one semi-infinite constraint.
lb = 10*ones(size(h0)); [hsopt, sumh, exitflag] = fseminf(@(h)sum(h), h0, 1, ... @(h,s) airPollutionCon(h,s,theta0,U0), [], [], [], [], lb); fprintf('\nMinimum computed cumulative height of chimney stacks : %7.2f m\n', sumh);
Local minimum possible. Constraints satisfied. fseminf stopped because the predicted change in the objective function is less than the default value of the function tolerance and constraints are satisfied to within the default value of the constraint tolerance. Minimum computed cumulative height of chimney stacks : 3667.19 m
The minimum cumulative height computed by fseminf is considerably higher than the initial total height of the chimney stacks. We will see how the minimum cumulative height changes when parameter uncertainty is added to the problem later in the example. For now, let's plot the chimney stacks at their optimal height.
Examine the MATLAB file plotChimneyStacks to see how the plot was generated.
plotChimneyStacks(hsopt, 'Chimney Stack Optimal Height');
### Check the Optimization Results
Recall that fseminf determines that the semi-infinite constraint is satisfied everywhere by ensuring that discretized maxima of the constraint are below the specified bound. We can verify that the semi-infinite constraint is satisfied everywhere by plotting the ground level sulfur dioxide concentration for the optimal stack height.
Note that the sulfur dioxide concentration takes its maximum possible value in the upper left corner of the (x, y) plane, i.e. at x = -20000m, y = 20000m. This point is marked by the blue dot in the figure below and verified by calculating the sulfur dioxide concentration at this point.
Examine the MATLAB file plotSulfurDioxide to see how the plots was generated.
titleStr = 'Optimal Sulfur Dioxide Concentration and its maximum (blue)'; xMaxSD = [-20000 20000]; plotSulfurDioxide(hsopt, theta0, U0, titleStr, xMaxSD); SO2Max = concSulfurDioxide(-20000, 20000, hsopt, theta0, U0); fprintf('Sulfur Dioxide Concentration at x = -20000m, y = 20000m : %e g/m^3\n', SO2Max);
Sulfur Dioxide Concentration at x = -20000m, y = 20000m : 1.250000e-04 g/m^3
### Considering Uncertainty in the Environmental Factors
The sulfur dioxide concentration depends on several environmental factors which were held at fixed values in the above problem. Two of the environmental factors are wind speed and wind direction. See the reference cited in the introduction for a more detailed discussion of all the problem parameters.
We can investigate the change in behavior for the system with respect to the wind speed and direction. In this section of the example, we want to make sure that the sulfur dioxide limits are satisfied even if the wind direction changes from 3.82 rad to 4.18 rad and mean wind speed varies between 5 and 6.2 m/s.
We need to implement a semi-infinite constraint to ensure that the sulfur dioxide concentration does not exceed the limit in region R. This constraint is required to be feasible for all pairs of wind speed and direction.
Such a constraint will have four "infinite" variables (wind speed and direction and the x-y coordinates of the ground). However, any semi-infinite constraint supplied to fseminf can have no more than two "infinite" variables.
To implement this constraint in a suitable form for fseminf, we recall the SO2 concentration at the optimum stack height in the previous problem. In particular, the SO2 concentration takes its maximum possible value at x = -20000m, y = 20000m. To reduce the number of "infinite" variables, we will assume that the SO2 concentration will also take its maximum value at this point when uncertainty is present. We then require that SO2 concentration at this point is below for all pairs of wind speed and direction.
This means that the "infinite" variables for this problem are wind speed and direction. To see how this constraint has been implemented, inspect the MATLAB file uncertainAirPollutionCon.
type uncertainAirPollutionCon.m
function [c, ceq, K, s] = uncertainAirPollutionCon(h, s) %UNCERTAINAIRPOLLUTIONCON Constraint function for air pollution demo % % [C, CEQ, K, S] = UNCERTAINAIRPOLLUTIONCON(H, S) calculates the % constraints for the fseminf Optimization Toolbox (TM) demo. This % function first creates a grid of wind speed/direction points using the % supplied grid spacing, S. The following constraint is then calculated % over each point of the grid: % % Sulfur Dioxide concentration at x = -20000m, y = 20000m <= 1.25e-4 % g/m^3 % % See also AIRPOLLUTIONCON, AIRPOLLUTION % Copyright 2008 The MathWorks, Inc. % Maximum allowed sulphur dioxide maxsul = 1.25e-4; % Initial sampling interval if nargin < 2 || isnan(s(1,1)) s = [0.02 0.04]; end % Define the grid that the "infinite" constraints will be evaluated over w1x = 3.82:s(1,1):4.18; % Wind direction w1y = 5.0:s(1,2):6.2; % Wind speed [t1,t2] = meshgrid(w1x,w1y); % We assume the maximum SO2 concentration is at [x, y] = [-20000, 20000] % for all wind speed/direction pairs. We evaluate the SO2 constraint over % the [theta, U] grid at this point. K = concSulfurDioxide(-20000, 20000, h, t1, t2) - maxsul; % Rescale constraint to make it 0(1) K = 1e4*K; % No finite constraints c = []; ceq = [];
This constraint function can be divided into same three sections as before:
1. Define the initial mesh size for the constraint evaluation
The code following the comment "Initial sampling interval" initializes the mesh size.
2. Define the mesh that will be used for the constraint evaluation
The next section of code creates a mesh (now in wind speed and direction) using a similar construction to that used in the initial problem.
3. Calculate the constraints over the mesh
The remainder of the code calculates the SO2 concentration at each point of the wind speed/direction mesh. These constraints are then returned to fseminf from the above constraint function.
We can now call fseminf to solve the stack height problem considering uncertainty in the environmental factors.
[hsopt2, sumh2, exitflag2] = fseminf(@(h)sum(h), h0, 1, ... @uncertainAirPollutionCon, [], [], [], [], lb); fprintf('\nMinimal computed cumulative height of chimney stacks with uncertainty: %7.2f m\n', sumh2);
Local minimum possible. Constraints satisfied. fseminf stopped because the predicted change in the objective function is less than the default value of the function tolerance and constraints are satisfied to within the default value of the constraint tolerance. Minimal computed cumulative height of chimney stacks with uncertainty: 3812.15 m
We can now look at the difference between the minimum computed cumulative stack height for the problem with and without parameter uncertainty. You should be able to see that the minimum cumulative height increases when uncertainty is added to the problem. This expected increase in height allows the SO2 concentration to remain below the legislated maximum for all wind speed/direction pairs in the specified range.
We can check that the sulfur dioxide concentration does not exceed the limit over the region of interest via inspection of a sulfur dioxide plot. For a given (x, y) point, we plot the maximum SO2 concentration for the wind speed and direction in the stated ranges. Note that we have zoomed in on the upper left corner of the X-Y plane.
titleStr = 'Optimal Sulfur Dioxide Concentration under Uncertainty'; thetaRange = 3.82:0.02:4.18; URange = 5:0.2:6.2; XRange = [-20000,-15000]; YRange = [15000,20000]; plotSulfurDioxideUncertain(hsopt2, thetaRange, URange, XRange, YRange, titleStr);
We finally plot the chimney stacks at their optimal height when there is uncertainty in the problem definition.
plotChimneyStacks(hsopt2, 'Chimney Stack Optimal Height under Uncertainty');
There are many options available for the semi-infinite programming algorithm, fseminf. Consult the Optimization Toolbox™ User's Guide for details, in the Using Optimization Toolbox Solvers chapter, under Constrained Nonlinear Optimization: fseminf Problem Formulation and Algorithm.
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https://socratic.org/questions/how-do-you-graph-y-x-5-1
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Algebra
Topics
# How do you graph y= x+ 5 ?
Jul 6, 2018
As below.
#### Explanation:
$y = x + 5$
We can form a set of ordered pairs.
$x \textcolor{w h i t e}{\circ} 2 \textcolor{w h i t e}{\circ} 1 \textcolor{w h i t e}{\circ} 0 \textcolor{w h i t e}{\circ} - 1 \textcolor{w h i t e}{\circ} - 2$
$y \textcolor{w h i t e}{\circ} 7 \textcolor{w h i t e}{\circ} 6 \textcolor{w h i t e}{\circ} 5 \textcolor{w h i t e}{\circ \circ} 4 \textcolor{w h i t e}{\circ \circ \circ} 3$
Now we plot for (x,y) in a graph sheet to form the line.
graph{x + 5 [-10, 10, -5, 5]}
##### Impact of this question
910 views around the world
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http://math.stackexchange.com/questions/167498/is-this-function-decreasing-on-0-1
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# Is this function decreasing on $(0,1)$?
While doing some research I got stuck trying to prove that the following function is decreasing
$$f(k):= k K(k) \sinh \left(\frac{\pi}{2} \frac{K(\sqrt{1-k^2})}{K(k)}\right)$$ for $k \in (0,1)$.
Here $K$ is the Complete elliptic integral of the first kind, defined by $$K(k):= \int_{0}^{1} \frac{dt}{\sqrt{1-t^2} \sqrt{1-k^2t^2}}.$$
This seems to be true, as the graph below suggests :
I really don't know much about elliptic integrals, so perhaps someone here can give some insight. Any relevant reference on elliptic integrals of the first kind is welcome.
Thank you, Malik
EDIT (2012-07-09) :
Using J.M.'s suggestion to rewrite the function $f(k)$ as $$f(k) = kK(k) \frac{1-q(k)}{2 \sqrt{q(k)}}$$ and using the derivative formulas $$K'(k) = \frac{E(k)}{k(1-k^2)} - \frac{K(k)}{k},$$ $$q'(k)=\frac{\pi^2}{2} \frac{q(k)} { K(k)^2 (1-k^2)k}$$ where $E(k)$ is the Complete elliptic integral of the second kind, I was able to calculate $f'(k)$ and reduce the problem to showing that the following function is negative for $k \in (0,1)$ :
$$g(k):= 4(1-q(k))K(k)E(k) - \pi^2 (1+q(k)).$$
Below is the graph of $g$ obtained with Maple :
EDIT (19-07-2012)
I asked the question on MathOverflow!
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At least $$f(k) = \pi - \frac{\pi}{16} k^{2} - \frac{3 \pi}{128} k^{4} - \frac{27 \pi}{2048} k^{6} - \frac{575 \pi}{65536} k^{8} + \operatorname{O} \bigl(k^{10}\bigr),$$ as $k \to 0+$, so it is decreasing near $k=0$. – GEdgar Jul 6 '12 at 15:31
Note that your function can also be expressed in terms of the elliptic nome: $$k\,K(k)\,\frac{1-q(k)}{2\sqrt{q(k)}}$$ – J. M. Jul 8 '12 at 14:04
The following comment was posted by Henry Cohn on meta.MO: It's definitely possible to prove that your function is decreasing by an ugly and unilluminating calculation that shows that the derivative is nonpositive everywhere. Specifically, near $k=0$ you can compute the Taylor series expansion and bound the error. For larger $k$, you can check the values of the derivative at a bunch of points and verify that there are no sign changes in between by bounding the second derivative. So if you just need this result to get a rigorous proof of some theorem, then it will be doable... – Dan Petersen Jul 12 '12 at 6:15
On the other hand, much more seems to be true. Specifically, all the derivatives seem to be negative, not just the first derivative. You can see this in the Taylor series expansion, which has all negative coefficients beyond the constant term (well, it's an even function, so the odd terms vanish, but the even terms all have negative coefficients). And the terms are pretty nice: the coefficient of $k^{2i}$ seems to be pi times a rational number with denominator dividing $16^i$. – Dan Petersen Jul 12 '12 at 6:16
I don't know how to prove any of this, but it's more remarkable than just being a decreasing function, and all this suggests that there should be a nice way of understanding this function. Plenty of functions are decreasing for no especially good reason, but this sort of absolute monotonicity is much less common. – Dan Petersen Jul 12 '12 at 6:16
## 2 Answers
A few more terms for those investigating. From Maple. These coefficients are not listed in the On-line Encyclopedia of Integer Sequences.
$$\frac{4}{\pi} \sqrt{m} \;K(4 \sqrt{m}) \sinh \biggl(\frac{\pi\; K(\sqrt{1 - 16 m})}{2\;K(4 \sqrt{m})}\biggr) \\ = 1 - m - 6 m^{2} - 54 m^{3} - 575 m^{4} - 6715 m^{5} - 83134 m^{6} - 1071482 m^{7} - \\ \quad{}\quad{} 14221974 m^{8} - 193050435 m^{9} - 2667157340 m^{10} - 37378279402 m^{11} - \\ \quad{}\quad{} 530024062361 m^{12} - 7590192561912 m^{13} - \\ \quad{}\quad{}109610113457650 m^{14} - 1594344146568120 m^{15} - \\ \quad{}\quad{}23336667998911128 m^{16} - 343468859344118109 m^{17} - \\ \quad{}\quad{}5079858166426507168 m^{18} - 75457168334744888190 m^{19} - \\ \quad{}\quad{}1125223725054635766392 m^{20} + \operatorname{O} \bigl(m^{21}\bigr)$$
added
Who knows if this is relevant? See A002849 $$\frac{2}{\pi}K(4\sqrt{m}) = 1+4m+36m^2+400m^3+4900m^4+\dots =\sum_{n=0}^\infty \binom{2n}{n}^2m^n$$
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Thank you. I have absolutely no idea why once you divide $f$ by $\pi$ and make the change of variable $m=(k/4)^2$, all the coefficients seem to be negative integers... That's very interesting! – Kalim Jul 13 '12 at 14:42
Note that the last formula can also be found in the wikipedia link for elliptic integrals given in the question. – Kalim Jul 19 '12 at 19:13
See the developments here. It seems all that is left is (reasonable) numerical work.
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thanks for the info! – Kalim Jul 23 '12 at 20:40
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http://www.r-bloggers.com/tag/model/
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# Posts Tagged ‘ model ’
## Text Mining
October 15, 2012
By
When it comes down to it R does a really good job handling structured data like matrices and data frames. However, its ability to work with unstructured data is still a work in progress. It can and it does handle text mining but the documentation is incomplete and the capabilities still don’t compare to other
## lme4 stands 4 Linear mixed-effects…
February 19, 2010
By
There is a certain hype about mixed (and random) effects among statistician and analysts. You can show some love to Douglas Bates and Martin Maechler for maintaing the lme4 package for our cupid, R I copy the entity of the information of the projects page. Doxygen documentation of the underlying C functions is here. The
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https://www.geosci-instrum-method-data-syst.net/8/77/2019/
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Journal topic
Geosci. Instrum. Method. Data Syst., 8, 77–96, 2019
https://doi.org/10.5194/gi-8-77-2019
Geosci. Instrum. Method. Data Syst., 8, 77–96, 2019
https://doi.org/10.5194/gi-8-77-2019
Research article 13 Feb 2019
Research article | 13 Feb 2019
# Description of the Baseline Surface Radiation Network (BSRN) station at the Izaña Observatory (2009–2017): measurements and quality control/assurance procedures
Description of the Baseline Surface Radiation Network (BSRN) station at the Izaña Observatory (2009–2017): measurements and quality control/assurance procedures
Rosa Delia García1,2,3, Emilio Cuevas2, Ramón Ramos2, Victoria Eugenia Cachorro3, Alberto Redondas2, and José A. Moreno-Ruiz4 Rosa Delia García et al.
• 1Air Liquide España, Delegación Canarias, Candelaria, Spain
• 2Izaña Atmospheric Research Center (IARC), State Meteorological Agency (AEMET), Santa Cruz de Tenerife, Spain
• 4Department of Computer Science, Almería University, Almería, Spain
Correspondence: Emilio Cuevas ([email protected])
Abstract
1 Introduction
The World Meteorological Organization (WMO) through its Global Change Observing System (GCOS) defined several essential climate variables (ECVs) as physical, chemical or biological variables or a group of linked variables that critically contributes to the characterization of Earth's climate. The ECVs have been selected with the aim to obtain enough evidence that effectively led us to predict the climate evolution and its possible associated risks.
Figure 1(a) Location of the Izaña station (IZA) on a global map of all BSRN stations (http://bsrn.awi.de, last access: 7 February 2019). (b) Izaña Atmospheric Observatory. Views of Izaña radiation station: (c) northern and eastern views (azimuth 360, inclination 0; azimuth 90, inclination 0, respectively); (d) southern and western views (azimuth 180, inclination 0; azimuth 270, inclination 0, respectively).
Table 1Basic-BSRN radiation instruments installed between 2009 and 2017 at IZA BSRN (SWD, DIR, DIF and LWD). The instruments currently in operation are marked in bold. WRMC is the World Radiation Monitoring Center.
Among others, the surface radiation budget and more specifically the surface Earth radiation budget (ERB) longwave and surface ERB shortwave have been identified as ECVs, due to their key role in the general circulation of the atmosphere and ocean, and the thermal structure of the atmosphere, as well as being a main factor in the Earth's climate system . The surface ERB comprises the fluxes absorbed by the Earth's surface and the upward and downward thermal radiative fluxes emitted by the surface and atmosphere, respectively .
The first surface solar radiation measurements started in the 1920s in some sites in Europe. The study of these historic datasets reveals an increase in the surface solar radiation until the 1950s, known as “early brightening” (Ohmura2009; Wild2009), but only observed in Europe due to the scarcity of available data. The study of surface solar radiation long-term records shows decadal changes with a decline of surface solar radiation from the first available records, around 1950, until the middle of the 1980s , a period known as “global dimming”, and an increment in the surface solar radiation since the middle of 1980s, a period known as “global brightening” .
All these studies remark on the variable quality of the data due to the technical advances in the instruments since the 1970s; thus, the confidence of the long-term trends observed should be taken into account when analyzing the results. With the aim to obtain data with the best possible quality, in the 1990s, efforts were made to establish measurement networks around the Earth with high-quality requirements to avoid introducing undesirable uncertainties in the long-term series. In this context, the Baseline Surface Radiation Network (BSRN) was proposed in 1980 by the WMO and created in 1992 to provide accurate irradiances at selected sites around the Earth, with a high temporal resolution. The BSRN is a project of the World Climate Research Programme (WCRP). In 2004, it was designated as the baseline network for GCOS. The available data cover a period from 1992 to the present thanks to the contribution of 59 stations covering various climate zones (http://bsrn.awi.de/nc/stations/maps/, last access: 7 February 2019). The BSRN data have been widely used, due to their quality and reliability in the validation of satellite observations, as input to climate models and to monitor the solar radiation reaching the Earth's surface (Ohmura2009).
The BSRN imposes very strict measurement requirements in order to assure the required quality of data . A BSRN site must be representative of the surrounding area and avoid pollution sources, unnatural reflectance, microclimate conditions and human activities that can affect its representativity of the surroundings (McArthur2005). Consequently, BSRN sites cannot be located near major roadways, airports, vehicle parking areas and buildings.
In 2009, the Izaña Atmospheric Observatory (IZA, BSRN station no. 61) started its process to become a BSRN station through a specific agreement between the State Meteorological Agency of Spain (AEMET) and the University of Valladolid. IZA was proposed and accepted to be part of the BSRN at the 11th BSRN Workshop and Scientific Review meeting was held in Queenstown, New Zealand, in August 2012 (WRCP2012), and has since remained a member of the network without interruption.
Between 2013 and 2014, the UV-A and UV-B radiation measurements performed at IZA were used for satellite-based data validation. The validation resulted in a good agreement with satellite-based data, and it is the starting point for further developments of Flyby's elaboration processes (WRCP2014).
The main goal of this work is to present the status of the Izaña BSRN (IZA) between 2009 and 2017. Section 2 describes the IZA site. The main characteristics of the instruments and measurements that are part of IZA BSRN as well as instrument calibrations are presented in Sect. 3. Section 4 illustrates data processing and quality control procedures applied to the measurements, and the shipment station-to-BSRN archive. Finally, a summary and conclusions are given in Sect. 6.
2 Site description
IZA station (http://izana.aemet.es, last access: 7 February 2019) is managed by the Izaña Atmospheric Research Center (IARC) and is part of AEMET. It is located on the island of Tenerife (Canary Islands, Spain, at 28.3 N, 16.5 W; 2373 m a.s.l.) (Fig. 1).
Figure 2Basic-BSRN radiation instruments currently in operation at IZA BSRN. (a) SWD: EKO MS-802F pyranometer installed on a table (horizontal); (b) DIF: EKO MS-802F pyranometer; (c) LWD: Kipp & Zonen CGR4 pyrgeometer; (d) DIR: EKO MS-56 pyrheliometer; and (e) Sun tracker: Owel INTRA 3.
Table 2Extended-BSRN radiation instruments installed between 2009 and 2017 at IZA BSRN (UV-B, UV-A, SWD and LWU). Same as Table 1.
Figure 3Extended-BSRN radiation instruments currently in operation at IZA BSRN. (a) UV-B: Yankee YES pyranometer; (b) UV-A: Kipp & Zonen UV-A-S-T pyranometer; and (c) SWU and LWU: EKO M-60 net radiation sensor.
IZA is a high-mountain station above a quasi-permanent strong temperature inversion layer that prevents the arrival of local pollution from lower levels of the island. This meteorological feature favors measurements under free troposphere conditions . As a result, the climate in the area of the station is extremely dry for the majority of the year; this, together with clean air from middle/upper troposphere, gives the area a high scientific interest. Pristine conditions are alternated with periodical intrusions of the dust-laden Saharan air layer , mainly in summertime. IZA registers the highest average annual insolation duration of Spain with about 3473 h of sunshine per year and an average of 179.5 days per year of clear days in the climate period (1981–2010) (for more information, see http://www.aemet.es, last access: 7 February 2019).
IZA enrolled in the WMO Global Atmosphere Watch (GAW) programme in 1989. In addition, IZA has contributed to several international networks such as NDACC (Network for the Detection of Atmospheric Composite Change; http://www.ndsc.ncep.noaa.gov, last access: 7 February 2019) since 1999, and GAW-PFR (Precision Filter Radiometer Network; http://www.pmodwrc.ch/worcc, last access: 7 February 2019) since 2001. In 2003, the WMO/GAW Regional Brewer Calibration Centre for Europe (RBCC-E; http://www.rbcc-e.org, last access: 7 February 2019) was established at IZA. IZA has been part of the Aerosol Robotic Network (AERONET; http://aeronet.gsfc.nasa.gov, last access: 7 February 2019) since 2004, as one of the two absolute AERONET calibration sites. IZA has also been a BSRN station since 2009 . Moreover, in 2014, IZA was appointed by WMO as a CIMO (Commission for Instruments and Methods of Observation) test bed for aerosols and water vapor remote sensing instruments (WMO2014). A detailed description of the IZA site and its observation programs can be found in .
3 Measurements and instruments
## 3.1 Basic-BSRN measurements
The basic-BSRN measurements of the BSRN program at IZA are global shortwave radiation (SWD), direct radiation (DIR), diffuse radiation (DIF) and longwave downward radiation (LWD) (Table 1).
Figure 4Other instruments currently providing data to IZA BSRN: (a) radiosonde profiles, (b) the Brewer spectrophotometer and (c) SONA camera (automatic cloud observation system) installed at IZA and examples of images taken by the SONA camera.
Figure 5Daily control test of the Owel INTRA solar tracker at IZA. (a) Front view of the quadrants of the Sun detector. The numbers indicated are pins of the sensor/connector, respectively; (b) Sun-sensor signals in the four quadrants and the total signal from the quadrants; (c) board temperature (C); and (d) current from base shunt of motor0 driver (azimuth axis, mA) (red color) and current from base shunt of motor1 driver (elevation axis, mA) (black color) (INTRA2010).
At present, SWD and DIF are measured with unshaded and shaded EKO MS-802F pyranometers (Fig. 2a and b) (ISO-9060 classification: secondary standard), respectively. This pyranometer is a high-precision instrument with a spectral range from 285 to 3000 nm with a response time less than 5 s (95 %, confidence level) and an expected uncertainty $<±\mathrm{1}$ % for daily totals. The BSRN accuracy target for DIF and SWD is 2 % (5 W m−2) and 2 % (3 W m−2), respectively (McArthur2005).
DIR is measured with an EKO MS-56 pyrheliometer (Fig. 2d) (ISO-9060 classification: first class). This instrument has a full operating view angle of 5 and slope angle of 1. The spectral range covers from 200 to 4000 nm (50 % points) with a response time >1 s (95 %). The expected uncertainty is $<±\mathrm{1}$ % for daily totals. The BSRN accuracy target for DIR is 0.5 % (1.5 W m−2) (McArthur2005). LWD is measured with a shaded Kipp & Zonen CGR4 pyranometer (Fig. 2c) (ISO-9060 classification: secondary standard). The spectral range is 4.5–42 µm (50 % points) with a response time less than 6 s (63 % response). The expected uncertainty is <3 % for daily totals (95 %). The BSRN accuracy target for LWD is 2 % (3 W m−2) (McArthur2005).
Figure 6Absolute cavity radiometer (PMO6) mounted on the IZA BSRN Sun tracker during a calibration campaign.
Table 3Summary of calibrations of the different radiation instruments performed at IZA between 2009 and 2017. PMOD is the Physikalisch-Meteorologisches Observatorium Davos, and WRC is the World Radiation Center.
* (W m−2) V−1.
These instruments are installed on a Sun tracker, with the exception of the EKO MS-802F pyranometers for SWD and DIF measurements, which are installed on a horizontal table (Fig. 2a). The Sun tracker is an Owel INTRA 3 (Fig. 2e). This is an intelligent tracker which combines the advantages of automatic-tracking operation (automatic alignment with the system of astronomical coordinates) and actively controlled tracking (a four-quadrant Sun sensor). It is constructed for use under extreme weather conditions; its operational temperature range is between −20 and 50 C. It can sustain about 50 kg of carefully balanced load. The tracker motors have a special grease for use in low temperatures. It moves back to the start (morning) position at the corresponding midnight. The drive unit has a zenith rotation >90. The unit has an angular resolution ≤0.1, an angular repeatability of $\le \sim \mathrm{0.05}$ and an angular velocity ≥1.5 s−1 on the outgoing shafts. The maximum speed is 2.42 s−1 .
Figure 7Flowchart of data from measurements to the BSRN database.
Table 4The lower and upper limits for the physically possible limits (PPLs) and extremely rare limits (ERLs) used in flagging the radiation measurements. µo is the cosine of the solar zenith angle and Sa is the solar constant adjusted for the Earth–Sun distance.
In addition, the measurements of pressure (P), relative humidity (RH) and temperature (T) are included in this measurement group. The pressure is measured a with Setra 470 pressure transducer, and RH and T are measured with Campbell Scientific CS215-L sensors.
## 3.2 Extended-BSRN measurements
The extended-BSRN measurements included in the IZA BSRN program are shortwave upward radiation (SWU), ultraviolet measurements (UV-A and UV-B) and longwave upward radiation (LWU) (Table 2).
Figure 8Example of data-removing process. The rejected data were caused by shadows during cleaning operations. The dashed line represents the pyrheliometer cleaning time (a) before removing rejected data and (b) after removing rejected data.
A Yankee YES pyranometer (Fig. 3a) measures global radiation in the UV-B spectral range from 280 to 315 nm with a response time around 100 ms. The UV-A (315–400 nm) is measured with a Kipp & Zonen UV-A-S-T pyranometer (Fig. 3b) with a response time less than 1.5 s (95 %). The expected uncertainty is <5 % for daily totals (95 %). SWU and LWU are measured with a MS-60 EKO radiometer (Fig. 3c) (ISO-9060 classification: secondary standard). This system is formed by two pyranometers and two pyrgeometers. The spectral range of the pyranometers is 280–3000 nm with a response time ∼17 s, while the spectral range of the pyrgeometers is 3–50 µm.
The radiation measurements are acquired with a Campbell CR5000. This data logger is a rugged, high-performance data-acquisition system with a built-in keyboard, graphics display and PCMCIA card slot. It combines a 16-bit resolution with a maximum of 5000 measurements per second. In particular, the measurements are taken with a time step of 5 s. The minimum, average, maximum and standard deviation are stored every minute.
Table 5Same as Table 4 except for the “comparison” intervals used for flagging the radiation quantities. σ is the Stefan–Boltzmann constant ($\mathrm{5.67}×{\mathrm{10}}^{-\mathrm{8}}$ W m−2 K4), SZA is solar zenith angle, T is air temperature (K), and SumSWD is DIR × cos(SZA) + DIF.
## 3.3 Ancillary measurements
Ancillary measurements, such as radiosonde data (Fig. 4a) and total ozone column (TOC), are performed at IZA BSRN station.
Vertical profiles of pressure, temperature, relative humidity and wind direction and speed are measured using Vaisala RS92 radiosondes that are launched twice a day, at 00:00 and 12:00 UTC at the Güimar station (WMO GRUAN station no. 60018; 105 m a.s.l.), managed by the Meteorological Centre of Santa Cruz de Tenerife (AEMET). This station is located near the coastline at a distance in a straight line from IZA of ∼15 km. The TOC measurements are performed with the Brewer spectrophotometer (Fig. 4b) (precision better than 1 %) . An automatic cloud observation system (SONA camera) (Fig. 4c) developed by Sieltec Canarias S.L. takes all-sky images every 5 min, day and night. This camera consists of a resolution of 640×480 pixels and an 8-bit color response CCD sensor with a Bayer filter, with a spectral range from 400 to 700 nm. A rotating shadow band is used for protecting the sensor from direct sunlight.
## 3.4 Instrument checks and maintenance
All the instruments of the BSRN are checked on a daily basis by meteorological observers of the Izaña observatory. Routine checks consist of cleaning the domes, cable connections inspection and instrument leveling, as well as checking the proper functioning of the solar tracker and shading system of the instruments for DIF and LWD measurements. Recently, a tool to test the Owel INTRA solar tracker real-time check-up has been implemented. This test consists in controlling the four quadrants of the solar tracker (see Sect. 3.1), checking its leveling, the board temperature and the intensity of the base shunt of motor in azimuth and elevation axis (Fig. 5).
Figure 9Percentage of rejected data (red color) and accepted data (blue color) according to the PPLs and ERLs, and comparison of various irradiance components (SWD, SumSWD, DIF, LWD and air temperature) at IZA between 2009 and 2017.
## 3.5 Instrument calibrations
All the radiation instruments (Tables 1 and 2) have been periodically calibrated following the recommendations of the BSRN (Table 3) and are regularly compared with reference instruments with recent calibration from the World Radiation Center (WRC) at Davos.
An absolute cavity pyrheliometer PMO6 designed at PMOD (Physikalisch-Meteorologisches Observatorium Davos) (Fig. 6) that is regularly calibrated at the WRC is used as a reference instrument and is directly traceable to the World Radiometric Reference. Periodical calibrations with PMO6 allow us to assure the reliability of the measurements and correct time degradation on the calibration constants. A large calibration campaign of BSRN pyranometers and pyrheliometers was performed during 2014 using the aforementioned PMO6. The ISO 9059:1990(E) and ISO 9846:1993(E) recommendations were met. The calibration of a field pyranometer/pyrheliometer by means of a reference pyrheliometer is accomplished by exposing the two instruments to the same solar radiation and comparing their corresponding measurements. This allows us to compare target instruments to high-accuracy radiation sensors. A second calibration campaign was held in July–August 2018.
4 BSRN IZA management
During 2009, a BSRN database was developed in order to manage the large volume of BSRN data. This tool not only allows the management of a large volume of information that is automatically generated, but it is also used for checking of real-time measurements and becoming a comprehensive quality control system with corresponding alarms.
The BSRN data management flowchart is shown in Fig. 7. It includes daily and monthly semi-automatic processes to collect and check the measurements, and generate the station-to-archive file sent every month to the BSRN database. This daily process can be executed automatically, or on demand, producing several warning alerts if human checking is needed.
Data are stored in a CR5000 data logger (see Sect. 3.2). This data logger generates a raw data file that is stored in a database for further analysis, if necessary, which is also available on an internal web for real-time access. The raw data file is checked in order to assess the format integrity and detect gaps.
Table 6The input parameters of the LibRadtran model, their sources and corresponding references.
Figure 10Scatterplots and histograms of the instantaneous (W m−2) and daily (MJ m−2) radiation measurements and simulations for the period 2009–2017: (a, d, g, j) SWD, (b, e, h, k) DIR and (c, f, i, l) DIF. The fitting parameters are shown in the legend.
Several corrections are applied to raw data to obtain the final radiation data. These corrections are as follows:
• Zero offset: This is defined as the signal caused by changes in the instrument temperature. The zero offset is measured for each instrument as part of the observation sequence when possible. For instruments that are not capable of obtaining a zero offset with each observation, it is measured at night and subtracted from daytime values (McArthur2005). The average values of zero offset compared to the radiation values performed during the day are rather small, representing 0.3 % and 0.02 % of the SWD and DIR signals for 1000 W m−2, respectively .
• Cleaning operations: As remarked in Sect. 3.4, daily cleaning of domes is performed. Some artificial shadows are caused when the observers perform these operations. Data corresponding to cleaning activities are identified and removed from the database (Fig. 8).
• Exceptional situations: Shadows or gaps in raw data are also observed due to exceptional situations, such as severe weather, repairing of instruments and maintenance operations, etc. Data stored during these non-operational periods are also removed from the database.
## 4.2 Quality control (QC)
Once the corrections are made, a Dep data file is obtained, which will be used to perform the quality control (QC) tests. The IZA QC procedure has two main parts: the recommended BSRN controls and the comparison with simulations with radiative transfer models (RTMs).
The first part of the QC consists of applying the QC methods that the WRMC recommends to the BSRN data . These quality control procedures are based on checking whether the measurements are within certain limits: physically possible limits (PPLs), extremely rare limits (ERLs) and the comparison of various irradiance components.
The PPL procedure is introduced for detecting extremely large errors in radiation data, while the ERL procedure is used to identify measurements exceeding the extremely rare limit. Radiation data exceeding these limits normally occur under very rare conditions and over very short time periods. These tests are based on empirical relations of different quantities (Table 4).
The final BSRN QC procedure is the comparison of various radiation components, i.e., the ratio between the DIR, directly measured with a pyrheliometer, and the derived value from the difference between the SWD and DIF (SumSWD), and the ratio between DIF and SWD. These tests capture smaller errors that have not been detected by the PPL and ERL procedures (Table 5).
Table 7Statistics for the bias between instantaneous and daily SWD, DIR and DIF simulations and measurements at IZA BSRN for the period 2009–2017. MB is mean bias; SD is standard deviation; RMSE is root mean square error.
At IZA, the measurements' quality assessment is performed taking into account the tests described above, by using the BSRN Toolbox software developed for the BSRN community and WRMC. This software also includes a data format check for the station to archive files and for PANGAEA download files (see below). Data quality checks as outlined in the BSRN global network recommended QC tests V2.0 can also be performed with this software. We have found that <1 % of all radiation measurements at IZA are outside the PPL and ERL limits (see Fig. 9a and b) between 2009 and 2017 for solar zenith angles (SZAs) <90.
The ratio between the different components also confirms the high quality of the SWD, DIR and DIF measurements. For SWD/SumSWD and SZA <75, >98 % (Fig. 9c) of the data are between 0.92 and 1.08, while for 75< SZA <93, 96 % of the measurements range from 0.85 to 1.15 (Fig. 9d). For DIF/SWD, the results present a high quality with 99 % within the established limits, for both SZA <75 and 75< SZA < 93 (Fig. 9e and f). The IZA radiation measurements largely meet the BSRN quality controls.
Figure 11BSRN Izaña station home page (http://www.bsrn.aemet.es, last access: 7 February 2019).
Figure 12BSRN Izaña: BSRN data description, QC test (BSRN global network recommended QC for SWD, DIR and DIF) and BSRN–model comparison for SWD, DIR, DIF and UV-B radiation at IZA using the LibRadtran RTM (http://www.bsrn.aemet.es, last access: 7 February 2019).
The second part of the QC is the comparison of instantaneous and daily radiation measurements with simulations performed with RTMs during clear periods. An adaption of Long and Ackerman's method for IZA, performed by , is used for detecting instantaneous clear-sky periods. This method is based on 1 min SWD and DIF measurements to which four individual tests are applied to normalized SWD, maximum DIF, change in SWD with time and normalized DIF ratio variability.
Following the BSRN recommendations, the instantaneous clear-sky periods detected are simulated and compared with instantaneous and daily radiation measurements. The RTM model used is LibRadtran (http://www.libradtran.org, last access: 7 February 2019; ), which has been extensively tested at IZA . The measured input parameters used in the LibRadtran model simulations are shown in Table 6. The model input parameters – precipitable water vapor (PWV), aerosol optical depth (AOD), total ozone column and surface albedo – are measured at IZA . The straightforward comparison between the instantaneous and daily SWD, DIR and DIF simulations and measurements shows an excellent agreement (Fig. 10). The variance of daily (instantaneous) measurements overall agrees within 99 % (98 %) of the variance of daily (instantaneous) simulations.
The simulations slightly underestimate the instantaneous/daily measurements of SWD (−1.68 %$/-\mathrm{1.24}$ %) and DIR (−1.57 %$/-\mathrm{1.82}$ %), while the DIF simulations overestimate the instantaneous/daily measurements (0.08 %∕0.84 %). The RMSE is <2.5 % for SWD and DIR for both instantaneous and daily comparisons, while for DIF it increases to 9.89 % and 9.11 % for instantaneous and daily comparisons, respectively (Table 7). These results are in agreement with those obtained by .
## 4.3 Web tool
With the aim to have, at a glance, an overview of the state of the BSRN station, a web site has been developed for the IZA BSRN station (Fig. 11; http://www.bsrn.aemet.es, last access: 7 February 2019). Plots for several variables such as SWD, DIR, DIF, UV-B and UVI index are automatically available at the home web page, as well as corresponding simulations performed with actual input data at the IZA station. These plots are provided in near-real time (every 10 min).
Figure 13IZA time series of daily SWD, DIR, DIF, UV-A and UV-B measurements, and instantaneous LWD data series (11:00 UTC) for the period 2009–2017.
On the web page, there are links to the comparison between measurements and simulations, QC control results, long-term series and derived products, among other additional information. Additional information on the installed instrumentation and the BSRN-related publications is also available (Fig. 12). In the following paragraphs, we present a short description of the BSRN Izaña, long-term series and derived products.
• BSRN Izaña: In this menu, it is possible to select any date and plot the results of applying the QC recommended by the BSRN (see Sect. 4.2) for SWD, DIR and DIF. It is also possible to plot the comparison of measured and simulated SWD, DIR, DIF and UV-B radiation at IZA using LibRadtran RTM and input parameters measured at IZA. This section of the web is automatically updated every night, once the measured input parameters for the model are available, and the QC tests are applied, according to the flowchart shown in Fig. 7.
• Long-term series: Daily values of SWD, DIR, DIF, UV-A and UV-B measurements and instantaneous (11:00 UTC) values of LWD are correspondingly updated on the web (Fig. 13). SWD measurements started in 1977 with a bimetallic pyranometer (PYR) being replaced in 1992 by different instruments (Kipp & Zonen: CM-5, CM-11 and CM-21) .
• Derived products: From DIR measurements and following the methodology developed by , the apparent transmission is automatically calculated for the purposes of monitoring clear-sky solar transmission (Fig. 14). This apparent transmission is defined as the ratio of the output from a normal-incidence pyrheliometer for a specific pair of SZA corresponding to integer air masses on the morning of a given day:
$\begin{array}{}\text{(1)}& \mathit{\tau }=\left({I}_{\mathrm{dir}}/{I}_{\mathrm{TOA}}×\mathrm{sin}h{\right)}^{\mathrm{1}/{m}_{\mathrm{a}}},\end{array}$
where Idir is DIR, ITOA is the top of the atmosphere (TOA) irradiance, ma is absolute air mass and h is solar elevation angle.
Figure 14Data time series of direct solar radiation atmospheric transmission determined at IZA for the period 2009–2017.
## 4.4 Station-to-BSRN archive file
The last step in the IZA data management is to create the station-to-archive file, which is submitted to the BSRN database on a monthly basis. This procedure is performed using the radiation measurements (Sect. 3.1 and 3.2), radiosonde profiles and total ozone data (Sect. 3.3).
Figure 15Example of (a) visualization of daily data of SWD, DIR, DIF and LWD radiation at IZA on August 2017 (software: PanPlot; ) and (b) intercomparison between SWD on the x axis and SumSWD (defined as the sum of DIF and DIR on a horizontal plane) on the y axis calculated using the BSRN Toolbox .
As shown in Fig. 7, the process includes the application of QC tests again to the radiation data using the specific software tools developed by the BSRN. A visual inspection of the monthly data series is made to avoid outliers or detect erroneous data of the different variables before submitting the file to the BSRN database (Fig. 15). Finally, if the checks are correct, the station-to-archive file is sent by ftp (http://ftp.bsrn.awi.de, last access: 7 February 2019).
5 Scientific exploitation of IZA BSRN data
A detailed description of the BSRN database has recently been published by . In this paper, some end-user applications of the IZA BSRN data are described.
The IZA BSRN data have been used in diverse research works encompassing several research fields. The most recent publications that have used the IZA BSRN data as part of their work are listed in Table 8, grouped by the research field. Here, we only remark on the peer-reviewed works but it should be noted that there are many contributions and proceedings that are related also to a greater or lesser extent to the IZA BSRN data.
Table 8Publications that used the IZA BSRN data in the last 5 years.
In future research, the IZA BSRN data will be essential to accurately analyze the attenuation of different types of clouds in UV, visible and infrared radiation, and to study the optical and radiative properties of mineral dust, as well as for solar energy applications, such as solar radiation nowcasting.
6 Conclusions
The Izaña station has been part of the BSRN since 2009. IZA BSRN contributes with basic-BSRN radiation measurements: global shortwave radiation (SWD), direct radiation (DIR), diffuse radiation (DIF) and longwave downward radiation (LWD); extended-BSRN measurements: ultraviolet radiation (UV-A and UV-B), shortwave upward radiation (SWU) and longwave upward radiation (LWU); and other measurements: vertical profiles of temperature, humidity and wind obtained from radiosonde profiles (WMO station no. 60018) and total ozone column thickness from the Brewer spectrophotometer.
Following the recommendations of the BSRN, the quality control tests have been routinely applied. The analysis of the QC results shows very good data quality that meets the BSRN requirements. The percentage of measurements that are outside the PPLs and ERLs is <1 % for SZA <90 in the period 2009–2017. The ratios between components also provide good results, with >98 % of measurements within the limits for SZA <75. The poorest result is the SWD/SumSWD for 75< SZA <93 with >96 % of measurements within the defined limits.
In addition, we have compared the instantaneous and daily SWD, DIR and DIF measurements with simulations obtained with the LibRadtran RTM. The observed agreement between measurements and simulations is very good: the variance of daily and instantaneous measurements overall agrees within 99 % and 98 %, respectively. The simulations underestimate the instantaneous/daily measurements of SWD (−1.68 %$/-\mathrm{1.24}$ %) and DIR (−1.57 %$/-\mathrm{1.82}$ %), while DIF simulations overestimate the instantaneous/daily measurements (0.08 %∕0.84 %). The RMSE is lower than 2.5 % for SWD and DIF for both instantaneous and daily comparisons. These results demonstrated a high consistency between the measurements and simulations reinforcing the reported data quality. The results show also the usefulness of the RTM as a tool for quality control radiation measurements over time.
Data availability
Data availability.
The BSRN Izaña radiation measurements are available at https://doi.org/10.1594/PANGAEA.882526 (Cuevas-Agulló, 2017).
• Global shortwave radiation (SWD) is the radiation received from a solid angle of 2π sr on a horizontal surface in a spectral range between 285 and 3000 nm. The SWD on a horizontal surface is equal to the direct normal radiation multiplied by the cosine of the solar zenith angle plus the diffuse irradiance (WMO2014).
• Direct radiation (DIR) is the radiation measured at the surface of the Earth at a given location with a surface element perpendicular to the Sun in a spectral range between 200 and 4000 nm (WMO2014).
• Diffuse radiation (DIF) is the radiation measured on a horizontal surface with radiation coming from all points in the sky excluding circumsolar radiation in a spectral range between 285 and 3000 nm (WMO2014).
• Longwave downward radiation (LWD) is thermal irradiance emitted in all directions by the atmosphere: gases, aerosols and clouds as received by an horizontal upward facing surface in a spectral range between 4500 and 42 000 nm (WMO2014).
• Ultraviolet radiation (UV-B) is the radiation received from a solid angle of 2π sr on a horizontal surface spectral range between 280 and 315 nm (WMO2014).
• Ultraviolet radiation (UV-A) is the radiation received from a solid angle of 2π sr on a horizontal surface spectral range between 315 and 400 nm (WMO2014).
Author contributions
Author contributions.
The paper was prepared by RDG and EC with contributions from all co-authors. RDG was responsible for the data QA–QC and data calibration; RR was in charge of the installation and instrumentation maintenance at IZA. EC and RR were responsible for Izaña BSRN. VEC, AR and JMR contributed to the revision of the paper.
Competing interests
Competing interests.
The authors declare that they have no conflict of interest.
Acknowledgements
Acknowledgements.
This work is part of the activities of the World Meteorological Organization (WMO) Commission for Instruments and Methods of Observations (CIMO) Izaña test bed for aerosols and water vapor remote sensing instruments. The authors thank the BSRN for providing quality control tools and maintaining a centralized quality-assured database. Authors are grateful to Robert P. Stone (NOAA, National Oceanic and Atmospheric Administration) for his audit visit to the Izaña Observatory and corresponding proposal to enroll in the BSRN, and to Ells Dutton (who passed away in 2012) for presenting the candidacy of the Izaña station at the 11th Biennial Baseline Surface Radiation Network (BSRN) Scientific Review and Workshop (New Zealand). The careful daily maintenance work made by IZA observers and SIELTEC Canarias technicians is very much appreciated. Antonio Cruz, the Izaña Atmospheric Research Center computer technician, helped in the development of BSRN. Most of the instrument pictures in this work were provided by Conchy Bayo. The authors appreciate the PMOD/WRC calibration facilities and collaboration. The IZA BSRN program has benefited from results obtained within POLARMOON project funded by the Ministerio de Economía y Competividad from Spain, CTM2015-66742-R. We also acknowledge our colleague Dr. Celia Milford for improving the English language of the manuscript.
Edited by: Luis Vazquez
Reviewed by: four anonymous referees
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https://mathhelpboards.com/threads/what-is-the-origin-of-your-username.2920/
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### Welcome to our community
• #1
#### MarkFL
Staff member
Feb 24, 2012
13,775
I thought it might be fun to find out how we all decided on our usernames.
I used to participate heavily on performance car forums, and since I began with a Camaro SS, I used the name gauSSian, to both indicate my affinity for mathematics and to use the letters SS in the center.
However, when I joined my first math help forum, I thought it would take a lot of nerve to use the derivative of the name of such a brilliant mathematician as my username, so I decided on MarkFL, as my name is Mark, I am from Florida (abbreviated here in the U.S. as FL) and my middle and last initials are F and L respectively.
#### Chris L T521
##### Well-known member
Staff member
Jan 26, 2012
995
I thought it might be fun to find out how we all decided on our usernames.
I used to participate heavily on performance car forums, and since I began with a Camaro SS, I used the name gauSSian, to both indicate my affinity for mathematics and to use the letters SS in the center.
However, when I joined my first math help forum, I thought it would take a lot of nerve to use the derivative of the name of such a brilliant mathematician as my username, so I decided on MarkFL, as my name is Mark, I am from Florida (abbreviated here in the U.S. as FL) and my middle and last initials are F and L respectively.
Mine was an old screen name that I used when AIM (AOL Instant Messenger) was pretty popular. It's derived from my name (Christopher L. Toni [I'm okay with people knowing my name, since, after all, you can find that info in one [or more] of the links in my signature]) and my birthday (May 21st - 5/21). Hence, I'm Chris L T521.
#### Jameson
Staff member
Jan 26, 2012
4,043
My first name, obviously.
However when not using my first name I like using mathematicians' names or Russian names. On some other sites I've gone by Euler, Riemann and Putin, usually with some numbers after them since those names are often taken.
Last edited:
#### topsquark
##### Well-known member
MHB Math Helper
Aug 30, 2012
1,123
Care to read a few Physics texts?
I was at Purdue U. and needed a new username. Being on a particle physics track I went into quark names. I originally wanted "upquark" but that, and the other five quark names were already in use. So I had the mad idea of using a supersymmetric partner to the quark: an s-quark. (Look up the supersymmetry thing yourself or I can post my own thread on it if you like. It'll take a while.)
Anyway, the first one I tried, top s-quark, wasn't in use. So there we are. It would seem that no one else has had this idea. I've been able to get the topsquark tag on any site I've signed up for.
-Dan
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#### dwsmith
##### Well-known member
Feb 1, 2012
1,673
Mine is rather simple. First initial, middle initial, and one of the most common last name (my last name).
#### Deveno
##### Well-known member
MHB Math Scholar
Feb 15, 2012
1,967
mine is a contraction of Deva (the sanskrit word for "heavenly being") + Eno (for Brian Eno), being both a sly reference to the ubiquitous "Eno is God" graffitti of the mid-1980's in New York City, and a play on my given first name, David.
#### soroban
##### Well-known member
Feb 2, 2012
409
My parents came from Japan; I was born in the USA.
The Japanese word for abacus is soroban.
I thought it was funny to call myself a 'Japanese calculator'.
Am I the only one laughing?
#### ModusPonens
##### Well-known member
Jun 26, 2012
45
Mine is the name of a logical deduction rule, namely {P,P=>Q}|- Q
#### Sudharaka
##### Well-known member
MHB Math Helper
Feb 5, 2012
1,621
Mine is simply my first name. I like it because it's very uncommon even in my country.
#### CaptainBlack
##### Well-known member
Jan 26, 2012
890
Mine is based on an old school joke, my first name and the Gerry Anderson TV show Captain Scarlet. Mr Ron $$\to$$ Mysteron $$\to$$ Captain Black the reanimated agent of the Mysterons.
CB
#### Opalg
##### MHB Oldtimer
Staff member
Feb 7, 2012
2,705
Mine just tells you that my research field (back in the days when I was actually doing research) was OPerator ALGebras.
#### earboth
##### Active member
Jan 30, 2012
74
When I was looking for a username I took my first and my family-name, distorted them severely - and what was left is now my username.
#### Attachments
• 58 KB Views: 32
#### Bacterius
##### Well-known member
MHB Math Helper
Jan 26, 2012
644
I've had this username for years and use it everywhere I want to be known. You can probably find me on a lot of different forums via this username. I don't know where it came from, I just thought it up and thought it sounded cool
#### chisigma
##### Well-known member
Feb 13, 2012
1,704
The greak letter $\chi$ is the initial of my first name [Carlo] and the greak letter $\sigma$ is the initial of my last name [Sabatini]...
Kind regards
$\chi$ $\sigma$
#### SuperSonic4
##### Well-known member
MHB Math Helper
Mar 1, 2012
249
Mine isn't difficult to figure, it's Super Sonic from Sonic the Hedgehog 2 onwards plus my favourite number which is 4.
edit: a user named MI6 was reading this thread before I posted, thought they'd be invisible on Her Majesty's duty
#### anemone
##### MHB POTW Director
Staff member
Feb 14, 2012
3,683
Many people will think of the sea anemone when they see my username here, but as a matter of fact, I wasn't referring to it, but a type of flowering plant.
The main reason it had become the perfect choice for my username was because it could last about nine days after being cut to make bouquets, and in Chinese tradition, we tend to believe that number 9 is an auspicious number and it is a homophone for longevity, which symbolizes that love will never fade in our romantic relationships.
Yes, I'm a female of Chinese descent from Asia.
#### MI6
##### New member
Dec 29, 2012
1
edit: a user named MI6 was reading this thread before I posted, thought they'd be invisible on Her Majesty's duty
Cover blown!
#### kanderson
##### Member
Jul 7, 2012
13
First letter of my name, K, then my last name Anderson
#### Plato
##### Well-known member
MHB Math Helper
Jan 27, 2012
196
About usernames. Many of you know that at heart I am basically interested in philosophy. I do have advanced degrees in both mathematics and religious studies. But I hold odd views in both. I truly think that mathematics is the product of the brain. That is a total non-Platonic view. There is a well known article on why Mathematics is so Successful?. Well the point that I have argued with the author is that the answer is simple: it is successful because it's our reality we are measuring. So what more ironic name to use than Plato?
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#### Deveno
##### Well-known member
MHB Math Scholar
Feb 15, 2012
1,967
About usernames. Many of you know that at heart I am basically interested in philosophy. I do have advanced degrees in both mathematics and religious studies. But I hold odd views in both. I truly think that mathematics is the product of the brain. That is a total non-Platonic view. There is a well known article on why Mathematics is so Successful?. Well the point that I have argued with the author is that the answer is simple: it is successful because it's our reality we are measuring. So what more ironic name to use than Plato?
i have no idea what you mean by "our reality", but if by this you mean our brain's interpretation of reality, that makes perfect sense (to my brain, that is). i cannot argue with your conclusion that mathematics is ultimately a by-product of how our brains function (the natural numbers, for example, seem to be "hard-coded" into our neurological function, in that we have electro-physical sensory systems that function as "difference filters". once you have 1 and 0, it's pretty much downhill from there. i conjecture that some animals with similar nervous systems ought to be able to count, with perhaps a lower limit on the size of memory space allotted for "number storage"). in a sense, this seems to me to "beg the question", in that our brains are surely the by-product of some external forces (do these obey mathematical laws, or do we only imagine them to?).
i would be interested in hearing your "odd" views of religion. one often hears views that rational thought (and thus mathematical/logical reasoning in particular) is diametrically opposed to spiritual views, a sort of "either/or" choice of a soulless or "soulful" universe. and yet, one also often hears an "opposite" argument, that the inherent beauty and intricate and delicate interplay of mathematics is surely reason to suspect there is PURPOSE to things. my own religious views are "unorthodox" to say the least, and i often find myself at odds with rational humanists and fundamentalists alike.
#### Fernando Revilla
##### Well-known member
MHB Math Helper
Jan 29, 2012
661
I thought it might be fun to find out how we all decided on our usernames.
My first name is Fernando, and my last name, Revilla (just as a cousin of mine). So, I decided as username the first name and the last name of my cousin.
MHB Math Helper
Jan 29, 2012
661
#### alane1994
##### Active member
Oct 16, 2012
126
alane1994
First Name: Austin
Last Name: Lane
Birth Year: 1994
Pretty simple... no?
#### jakncoke
##### Active member
Jan 11, 2013
68
I came up with the name when i was under the influence of ... guess.
Feb 13, 2012
1,704
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https://indico.nucleares.unam.mx/event/1488/contributions
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# 10th International Workshop on Charm Physics (CHARM 2020)
from 31 May 2021 to 4 June 2021
Mexico/General timezone
Thanks for your contribution to the success of this workshop!!
Home > Contribution List
## Contribution List
Displaying 203 contributions out of 203
Session: In media
Presented by Mr. Kaifeng SHEN on 3 Jun 2021 at 11:40
Heavy quarkonia are ideal probes of the Quark-Gluon Plasma (QGP). $J/\psi$ is the most abundantly produced quarkonium state accessible experimentally and its suppression due to the color screening effect in hot and dense medium has been suggested as a signature of the formation of the QGP. Besides the screening effect, there are other mechanisms, such as the cold nuclear effects and charm quark re ... More
Presented by Mr. Kaifeng SHEN
Understanding the nature of the hidden charm pentaquark(like) signals in the LHCb data for $\Lambda_b^0\to J/\psi p K^-$ is a central problem of hadron spectroscopy. We propose a scenario completely different from previous ones such as hadron molecules and compact pentaquarks. We identify relevant double triangle mechanisms with leading or lower-order singularities. The associated anomalous thre ... More
Presented by Dr. Satoshi NAKAMURA
Presented by Dr. Satoshi NAKAMURA on 3 Jun 2021 at 11:40
Presented by Mr. William PARROTT on 4 Jun 2021 at 13:10
Semileptonic $D \to{}K \ell \nu$ decays provide one angle of attack to get at the CKM matrix element $V_{cs}$, complementary to the study of leptonic $D_s$ decays. Here we present the results of an improved determination of $V_{cs}$, recently released on the arXiv (2104.09883). With a new, precise determination of $D\to K$ scalar and vector form factors from lattice QCD, combined with experime ... More
Presented by Mr. William PARROTT
We present in full analytic form the partial widths for the lepton flavour violating decays $L^\pm \to \ell^\pm \ell'^{+} \ell'^{-}$, with $L = \tau, \mu$ and $\ell(') = \mu, e$, mediated by neutrino oscillations in the one-loop diagrams. Compared to the first result by Petcov:1976ff, which was obtained in the nonphysical zero momentum limit $\mathcal{P} \ll m_{\nu} \ll M_W$, we retain full d ... More
Presented by Patrick BLACKSTONE
Session: Taus
Presented by Patrick BLACKSTONE on 3 Jun 2021 at 12:00
We report on a precision measurement of the ratio $R_{\tau\mu} = BF(\Upsilon(3S)\to\tau^+\tau^-)/BF(\Upsilon(3S)\to\mu^+\mu^-)$ using data collected with the BABAR detector at the SLAC PEP-II $e^+e^-$ collider. The measurement is based on a 28 ${\mathrm{fb^-1}}$ data sample collected at a center-of-mass energy of 10.355 ${\mathrm{GeV}}/c^2$ which corresponds to a sample 122 million $\Upsilon(3S)$ ... More
Presented by Prof. Swagato BANERJEE
Session: Taus
Presented by Dr. Swagato BANERJEE on 3 Jun 2021 at 11:40
Session: Exotics
Presented by Prof. Tomasz SKWARNICKI on 31 May 2021 at 09:20
The suppressed helicity flip amplitude in baryon-antibaryon decays of $J/\psi$ is calculated within the effective field theory framework. It is shown that at the leading-order approximation this contribution is factorisable and the overlap with the hadronic final state can be described by collinear matrix elements. The obtained contribution depends on the nucleon light-cone distribution amplitu ... More
Presented by Nikolay KIVEL
Presented by Dr. Nikolay KIVEL on 4 Jun 2021 at 12:30
Session: Production
We perform a combined study of $D^+ \to K^-\pi^+\pi^+$ and $D_s \to \pi^- K^+ K^+$ decays using the naive factorization approach. The formalism allows for a description of such decays in terms of the well-known vector- and scalar- $K\pi$ form factors as well as those appearing in semileptonic $D^+ \to K^-\pi^+ \ell^+\nu$ decays. We propose a useful—yet simple—parametrization to describe the l ... More
Presented by Dr. Pablo SANCHEZ-PUERTAS
Presented by Dr. Pablo SANCHEZ-PUERTAS on 1 Jun 2021 at 12:05
Presented by Oleg MESHKOV on 3 Jun 2021 at 12:40
The ATLAS experiment has performed accurate measurements of mixing and CP violation in the neutral B mesons,and also of rare neutral B-meson decays proceeding via electroweak FCNC-suppressed processes. This talk will focus on the latest results from ATLAS, such as rate measurements of B^0_s → mu mu and B^0 → mu mu decays; and CP violation in B_s^0 —> J/psi phi decays. In the latter, the Sta ... More
Presented by Yuji ENARI
Session: Production
Presented by Zijun XU on 3 Jun 2021 at 12:40
Recent results from the ATLAS experiment on the charmonium production, B_c production and exotic heavy hadrons will be presented. The measurement of J/psi and psi(2S) differential cross sections at large transverse momentum values in proton-proton collisions at 13 TeV will be reported. The measurement of the ratios of the B_c+ and B+ production cross sections in proton-proton collisions at 8 TeV ... More
Presented by Yuji ENARI
Session: Exotics
Presented by Dr. Alessandro PILLONI on 31 May 2021 at 10:20
Session: Taus
Presented by Mr. Alejandro DE YTA HERNÁNDEZ on 3 Jun 2021 at 13:20
Presented by Prof. Bruno EL-BENNICH on 1 Jun 2021 at 12:30
I will discuss theoretical continuum approaches to bound-state calculations, strong and weak decays and effective couplings related to D mesons. The associated wave functions, light-front distribution amplitudes and hadronic matrix elements are expressions of nonperturbative QCD. After motivating their origin in QCD factorization and heavy quark effective theory, we retrace their evolution from ea ... More
Presented by Prof. Bruno EL-BENNICH
Presented by Dr. Ayan PAUL on 4 Jun 2021 at 08:30
Presented by Angelo CARBONE on 4 Jun 2021 at 07:00
Presented by Carlos RAMIREZ on 3 Jun 2021 at 13:20
The physics of CPV and oscillations in the charn sector is reviewed. Topics like the recent discover of direct CPV, the latest measurements, the respective SM predictions and the present absence of new physics in this sector.
Presented by Carlos RAMIREZ
Presented by Dr. Tatiana KHARLAMOVA on 1 Jun 2021 at 08:30
Presented by Dr. Stefan SCHACHT on 4 Jun 2021 at 09:00
Presented by Prof. Xiaoyan SHEN on 1 Jun 2021 at 07:30
Presented by Prof. Roy BRIERE on 31 May 2021 at 11:40
Presented by Jhovanny MEJIA on 31 May 2021 at 13:10
The production cross sections of open heavy-flavour hadrons can be obtained by the factorisation approach described as the convolution of the initial parton distribution functions of the incoming partons, the perturbative QCD partonic cross section, and the fragmentation functions for the hadronisation parametrised from measurements in $\mathrm{e^+e^-}$ collisions. Recent measurements of charm-ba ... More
Presented by Ms. Jinjoo SEO
Presented by Ms. Jinjoo SEO on 1 Jun 2021 at 12:20
In this contribution, we discuss the internal structure of heavy baryons and the different interpretations of the internal structure of hidden-charm pentaquarks. We present the hidden-charm pentaquarks as superpositions of meson-baryon channels coupled to a $uudc\bar{c}$ compact core by employing an interaction satisfying the heavy quark and chiral symmetries. Our model can reproduce the masses a ... More
Presented by Dr. Hugo GARCIA TECOCOATZI
Presented by Dr. Hugo GARCIA TECOCOATZI
The LHCb experiment collected the world's largest sample of charmed hadrons during LHC Run 1 and Run 2. With this data set, LHCb is currently providing the world's most precise measurements of properties and production of known charmed baryons, as well as discovering many previously unobserved states. The latest results from the LHCb Collaboration on charmed baryons are presented
Presented by Dr. Dana BOBULSKA
Presented by Dr. Dana BOBULSKA on 3 Jun 2021 at 12:20
Presented by Dr. Mikhasenko MIKHAIL on 1 Jun 2021 at 10:50
Presented by Prof. Pol GOSSIAUX on 3 Jun 2021 at 09:20
Session: Production
Presented by Mr. Antonio PALASCIANO on 3 Jun 2021 at 13:20
Experimental measurements of the charm quark showering processes are an important test for the current understanding of QCD. At the same time, in heavy-ion collisions, charm quarks represent ideal probes for studying the Quark-Gluon Plasma (QGP), being them produced in the very early stages of the collision from a hard-parton scattering. In particular, angular correlation measurements are sensib ... More
Presented by Mr. Antonio PALASCIANO
Presented by Dr. Christopher THOMAS on 2 Jun 2021 at 10:20
The measurement of charm production in hadronic collisions provides a powerful tool to understand QCD due to its creation in initial parton-parton interactions, with the heavy quark mass providing the hard scale for the process. At the LHC the measurement of the correlation of the produced $\rm c\bar{c}$ quark pairs shows sensitivity to the production mechanisms at hand. The large branching rati ... More
Presented by Mr. Horst Sebastian SCHEID
Session: Production
Presented by Mr. Horst Sebastian SCHEID on 3 Jun 2021 at 12:00
Charm quarks, created during an early stage of the heavy-ion collision via hard scattering, have a large thermalization time within quark-gluon plasma (QGP) due to their large mass. They witness the entire evolution of QGP and hence can be used as an effective probe to study the strongly interacting matter. We studied the effect of collision and gluon radiation by charm quark on its transport coef ... More
Session: In media
Presented by Ms. Adiba SHAIKH on 3 Jun 2021 at 12:00
Presented by Dr. Melissa Maria CRUZ TORRES on 2 Jun 2021 at 07:30
Session: NP in charm
Presented by Mr. Jitendra KUMAR on 4 Jun 2021 at 12:10
The Belle II experiment at the asymmetric $e^+e^-$ collider, SuperKEKB, aims to record 50 ab$^{-1}$ of data over the next decade, a factor of 50 more than Belle. During the first 1.5 years of operations, around 90 fb$^{-1}$ of data were collected. This dataset is used to measure the lifetimes of a few charm hadrons, confirming the expected performance of the Belle II detector, in particular the v ... More
Presented by Dr. Jitendra KUMAR
Presented by Frank NERLING on 31 May 2021 at 12:10
Presented by Prof. Xiao-Rui LIU on 3 Jun 2021 at 07:00
Presented by Dr. Marco Antonio BEDOLLA on 3 Jun 2021 at 13:00
Presented by Dr. Roberto MUSSA on 2 Jun 2021 at 09:50
Presented by Prof. Enrico SCOMPARIN on 3 Jun 2021 at 10:20
Results for the $\eta_c$- and $J/\Psi$-nucleus bound state energies for various nuclei are presented. These results are obtained using effective Lagrangians at the hadronic level. Essential input for the calculation, namely the medium-modified $D$ and $D^{*}$ meson masses, as well as the density distributions in nuclei, are calculated within the quark-meson coupling model. The attractive potent ... More
Presented by Dr. Javier COBOS-MARTINEZ
Session: In media
Presented by Dr. Javier COBOS-MARTINEZ on 3 Jun 2021 at 13:40
Session: Production
Charmonium production studies in hadronic collisions are a powerful tool for improving our understanding of QCD, the theory of the strong interaction. The production of the charm-quark pair can be described within perturbative QCD, whereas the evolution of this pair into a colorless bound state involves soft scale processes. In addition, multiplicity dependent studies of charmonia in both proton- ... More
Presented by Mr. Jon-Are SÆTRE
Session: Production
Presented by Mr. Jon-are SÆTRE on 1 Jun 2021 at 12:20
Presented by Dr. Geoffrey BODWIN on 2 Jun 2021 at 11:40
I will present results from the first lattice QCD+QED computations of the properties of ground-state charmonium mesons. These calculations include the effect of up, down, strange and charm quarks in the sea and cover a wide range of values of the lattice spacing enabling very accurate results in the continuum limit (with physical quark masses). We tune the charm quark's mass so that the mass of th ... More
Presented by Prof. Christine DAVIES
Presented by Prof. Christine DAVIES on 3 Jun 2021 at 12:00
A nonperturbative charm production contribution, known as intrinsic charm, has long been speculated but has never been satisfactorily proven. The SeaQuest experiment at FNAL is in an ideal kinematic region to provide evidence of $J/\psi$ production by intrinsic charm. Here, $J/\psi$ production in the SeaQuest kinematics is calculated with a combination of perturbative QCD and intrinsic charm ... More
Presented by Ramona VOGT
Session: In media
Presented by Ramona Vogt VOGT on 3 Jun 2021 at 12:40
Presented by Dr. Clara MURGUI on 3 Jun 2021 at 08:30
Presented by Dr. Patricia MAGALHAES on 1 Jun 2021 at 10:20
Presented by Prof. Alex KAGAN on 4 Jun 2021 at 07:30
LHCb has collected the world's largest sample of charmed hadrons. This sample is used to measure direct $CP$ violation in $D$ mesons and charmed baryons. New measurements from several decay modes are presented, as well as prospects for future sensitivities
Presented by Mr. Lorenzo PICA
Presented by Mr. Lorenzo PICA on 3 Jun 2021 at 12:00
Presented by Mr. Daniel Alejandro PÉREZ NAVARRO on 2 Jun 2021 at 10:50
We suggest an efective field theory based coupled-channel approach to exotic charged Z-states and demonstrate its potential at a combined analysis of the existing experimental data on the open- and hidden-flavour decays of the Upsilon(10860) resonance. As an important ingredient of the method a dispersive approach to dipion transitions to lower lying Upsilon-resonances is developed with all imagin ... More
Presented by Dr. Alexey NEFEDIEV
Presented by Dr. Alexey NEFEDIEV on 1 Jun 2021 at 13:00
Session: Production
Presented by Dr. Marco GIACALONE on 4 Jun 2021 at 12:50
Measurements of charm meson and baryon production in proton-proton collisions are an important test for perturbative QCD calculations. Measurements in p--Pb collisions provide important tools to disentagle cold nuclear matter effects (like nuclear modification of parton distribution functions). Furthermore, the study of the charm production in pp and p--Pb collisions as a function of multiplici ... More
Presented by Dr. Marco GIACALONE
We perform a global analysis of exclusive hadronic tau decays into one and two mesons using the low-energy limit of the Standard Model Effective Field Theory up to dimension six, assuming left-handed neutrinos. A controlled theoretical input on the Standard Model hadronic form factors, based on chiral symmetry, dispersion relations, data and asymptotic QCD properties, has allowed us to set bounds ... More
Presented by Dr. Sergi GONZÀLEZ-SOLÍS
Session: Taus
Presented by Dr. Sergi GONZÀLEZ-SOLIS on 4 Jun 2021 at 12:50
Session: Production
Presented by Dr. Martin HENTSCHINSKI on 3 Jun 2021 at 12:20
We investigate photo-production of vector mesons J/Psi and Upsilon measured both at HERA and LHC. We are interested in using this observable to distinguish between linear and non-linear QCD evolution at low x. The employed fits are based on non-linear Balitsky-Kovchegov evolution (Kutak-Sapeta gluon; KS) and next-to-leading order Balitsky-Fadin-Kuraev-Lipatov evolution (Hentschinski-Sabio Vera-Sal ... More
Presented by Dr. Martin HENTSCHINSKI
Presented by Prof. Eric BRAATEN on 31 May 2021 at 08:30
Presented by Dr. Xiaorong ZHOU on 1 Jun 2021 at 08:00
Session: In media
Presented by Dr. Juan TORRES-RINCÓN on 3 Jun 2021 at 13:20
We study the spectroscopy and transport properties of charmed mesons in a thermal medium by applying an effective field theory based on chiral and heavy-quark symmetries in the imaginary time formalism. Relying on unitarity constraints and self-consistency we extract the in-medium properties (masses and widths) of D and Ds mesons and their interactions with light hadrons. We report our findings on ... More
Presented by Juan TORRES-RINCON
Presented by Dr. Jolanta BRODZICKA on 4 Jun 2021 at 10:50
Presented by YuLan FAN on 3 Jun 2021 at 11:40
BESIII has collected data samples corresponding to luminosities of 2.93 fb-1 and 3.19 fb-1 at center-of-mass energies of 3.773 and 4.178 GeV, respectively. The data set collected at 3.773 GeV contains quantum-correlated D0D0bar pairs that allow to access the phase differences between amplitudes. We report the measurements of strong phase differences in D0(-bar) decays, especially for K_S/Lpi+pi- ... More
Presented by Jingzhi ZHANG
Presented by Dr. Pere MASJUAN on 2 Jun 2021 at 08:00
Presented by Dr. Matteo FAEL on 2 Jun 2021 at 13:10
Presented by Prof. Ralf RAPP on 3 Jun 2021 at 09:50
Session: In media
Presented by Peter VANDER GRIEND on 3 Jun 2021 at 13:00
Heavy quarks and their bound states are ideal probes of the quark gluon plasma formed in relativistic heavy ion collisions. Due to the hierarchy of scales of the system, the in medium dynamics can be modeled by a Langevin equation in which interactions between the medium and the heavy particle take the form of random "kicks" altering the particle's momentum. The hierarchy of scales makes the pro ... More
Presented by Peter VANDER GRIEND
Track: Charm meson and baryon spectroscopy (including exotica)
We study the nature of the new signal reported by LHCb in the $J/\psi p$ spectrum. Based on the S-matrix principles, we perform a minimum-bias analysis of the underlying reaction amplitude, focusing on the analytic properties that can be related to the microscopic origin of the Pc(4312)+ peak. By exploring several amplitude parameterizations, we find evidence for the attractive effect of the $Σ_c ... More Presented by Mr. Jorge Antonio SILVA CASTRO Presented by Mr. Jorge Antonio SILVA CASTRO on 1 Jun 2021 at 12:40 In LEP times, hadronic tau decays were the most precise input for the (leading-order) hadronic vacuum polarization piece (HVP,LO) of the muon anomalous magnetic moment ($a_\mu$). With the advent of$\Phi$- and B-factories,$e^+e^-$hadronic cross-section surpassed them, giving the most accurate input for this piece. However, since both data-driven determinations are subject to theoretical uncertai ... More Presented by Mr. Jesús MIRANDA Session: Taus Presented by Mr. Jesús MIRANDA on 4 Jun 2021 at 12:30 Presented by Prof. Aida EL-KHADRA on 2 Jun 2021 at 12:40 We study the τ−→ντ π− π0 ℓ+ ℓ− (ℓ=e, μ) decays, which are O(α^2)-suppressed with respect to the dominant di-pion tau decay channel. Both the inner-bremsstrahlung and the structure- (and model-)dependent contributions are considered. In the ℓ=e case, structure-dependent effects are O(1%) in the decay rate, yielding a clean prediction of its branching ratio, 2.3×10^(−5), ... More Presented by Mr. Jorge Luis GUTIÉRREZ SANTIAGO Session: Taus Presented by Jorge GUTIÉRREZ SANTIAGO on 3 Jun 2021 at 12:40 Presented by Dr. Fernando SERNA on 4 Jun 2021 at 12:35 The ladder kernel of the Bethe-Salpeter equation is amended by introducing a different flavor dependence of the dressing functions in the heavy-quark sector. Compared with earlier work this allows for the simultaneous calculation of the mass spectrum and leptonic decay constants of light pseudoscalar mesons, the$D_u$,$D_s$,$B_u$,$B_s$and$B_c$mesons and the heavy quarkonia$\eta_c$and$\ ... More
Presented by Dr. Fernando SERNA
Presented by Prof. Shuangshi FANG on 2 Jun 2021 at 07:00
In the heavy-quark limit, the two heavy quarks in a doubly heavy baryon or a doubly heavy tetraquark are bound by their color-Coulomb potential into a compact diquark. The doubly heavy hadrons are related by the approximate heavy-quark--diquark symmetry of QCD to the heavy hadrons obtained by replacing the heavy diquark by a heavy antiquark. Effective field theories can be used to expand the masse ... More
Presented by Mr. Abhishek MOHAPATRA
Presented by Mr. Abhishek MOHAPATRA on 3 Jun 2021 at 12:40
Session: Production
Presented by Dr. Renu BALA on 4 Jun 2021 at 12:10
In this contribution, the nuclear modification factor (RAA) and the elliptic flow (v2) of open heavy-flavour hadrons via their hadronic and semileptonic decays to electrons at mid-rapidity and to muons at forward rapidity in heavy-ion collisions will be presented. The measurements of the production of leptons from heavy-flavour hadron decays and the modification of their spectra in different colli ... More
Presented by Dr. Renu BALA
We study the transitions between the different color states of a static quark-antiquark pair, singlet and octet, in a thermal medium. This is done non-perturbatively exploiting the infinite mass limit of QCD. This study is interesting because it can be used for future developments within the framework of Effective Field Theories (EFTs) and because it can be combined with other techniques, like ... More
Presented by Dr. Miguel Ángel ESCOBEDO ESPINOSA
Session: In media
Presented by Dr. Miguel Ángel ESCOBEDO on 3 Jun 2021 at 12:20
LHCb has collected the world's largest sample of charmed hadrons. This sample is used to measure $D^0 -\overline{D}^0$ mixing parameters and to search for $CP$ violation in mixing and interference. New measurements from several decay modes are presented, as well as prospects for future sensitivities.
Presented by Dr. Guillaume PIETRZYK
Presented by Dr. Guillaume PIETRZYK on 3 Jun 2021 at 13:00
The experimental information accumulated by the BABAR, Belle and LHCb experiments have shown disagreement on the measurements of the ratios $R(D)$ and $R(D^{*})$, compared with the SM predictions. In addition, the $D^\ast$ longitudinal polarization $F_L(D^\ast)$ related with the channel $B \to D^\ast \tau \bar{\nu}_\tau$ observed by the Belle Collaboration and the ratio $R(J/\psi)$ measured by the ... More
Presented by Dr. Nestor QUINTERO POVEDA
Session: NP in charm
Presented by Dr. Nestor QUINTERO POVEDA on 4 Jun 2021 at 13:10
We analyze the τ-→(Kπ)-ντ decays within an effective field theory description of heavy new physics (NP) modifying the SM left-handed weak charged current and include refined SM input for the participant meson form factors exploiting chiral symmetry, dispersion relations and (lattice) data. We include the leading dimension six operators and work at linear order in the effective couplings. Wit ... More
Presented by Mr. Javier RENDON
Session: Taus
Presented by Mr. Javier RENDON on 4 Jun 2021 at 13:30
Rare $\vert \Delta c \vert=\vert \Delta u \vert=1$ processes complement flavor searches in the down-sector in a unique way. Semileptonic FCNC decays of charmed hadrons offer a large set of clean null test observables, such as CP-asymmetries, lepton-universality ratios, missing energy modes, lepton flavor violating modes and angular observables. In these observables any signal cleanly indicates Phy ... More
Presented by Mr. Marcel GOLZ
Session: NP in charm
Presented by Mr. Marcel GOLZ on 4 Jun 2021 at 12:30
Presented by Mr. Hongrong QI
psi(2S) provides good opportunities for the study of chi_cJ, eta_c, and h_c decays. These studies can be used to verify QCD based models, which provide predictions for the decay mechanism. With the world's largest sample of 4.48*10^8, progress on the charmonium decays has been made. In the talk, we report the new results, such as the first measurement of the branching ratio of chi_c1,2 to mu+ mu- ... More
Presented by Jingzhi ZHANG
Presented by Barbara TRZECIAK on 3 Jun 2021 at 10:50
Presented by Dr. Marianna FONTANA on 3 Jun 2021 at 08:00
Presented by Prof. Jonas RADEMACKER on 4 Jun 2021 at 11:20
Session: Production
Presented by Prof. Mikhail BARABANOV
We compute masses of open and hidden charmed mesons in the framework of the extended Linear Sigma Model (eLSM) with (pseudo-)scalar and (axial-) vector mesons. Open charmed mesons masses turn out to be in quantitative agreement with experimental data. Whereas the masses of hidden charmed mesons, with the exception of $J/\psi$, are underpredicted by about $10$%. We calculate the (OZI-dominant) stro ... More
Presented by Dr. Walaa ESHRAIM
Session: Production
Session: Production
Presented by Dr. ESHRAIM WALAA on 4 Jun 2021 at 13:10
Session: Production
Presented by Dr. Emmanuel ORTIZ-PACHECO on 4 Jun 2021 at 13:30
Presented by Andrzej KUPSC on 1 Jun 2021 at 09:50
The dependence of the production of the $X(3872)$ meson on the hadron multiplicity in $pp$ collisions has been used as evidence against $X$ being a charm-meson molecule. The argument is based in part on the incorrect assumption that the cross section for the breakup of $X$ by scattering with comovers can be approximated by a geometric cross section inversely proportional to the binding energy of $... More Presented by Mr. Kevin INGLES Session: Production Presented by Mr. Kevin INGLES on 1 Jun 2021 at 12:40 Presented by Prof. Khodjamirian ALEXANDER on 4 Jun 2021 at 08:00 Session: Production Presented by Krista SMITH on 1 Jun 2021 at 13:00 Suppression of the J/ψ nuclear modification factor has long been considered a signature of final state effects in large collision systems. In small systems, nuclear modification was assumed to be due to initial state cold nuclear matter effects, until the observation of strong differential suppression of the ψ(2S) state in p+A collisions suggested the presence of final state effects. Here we pre ... More Presented by Krista SMITH One of the best ways to understand hadronization in QCD is to study the production of quarkonium. However, the production mechanism of quarkonium is still uncertain. Spin-related measurements like the polarization are strong tests of production models. In this talk I will summarize recent results of quarkonium production and polarization in elementary collisions, including the results from NRQCD ... More Presented by Vincent CHEUNG Session: Production Presented by Vincent CHEUNG on 4 Jun 2021 at 12:30 Session: Production Presented by Dr. Vincent CHEUNG Presented by Prof. Antonio VAIRO on 2 Jun 2021 at 12:10 Presented by Dr. Isabella GARZIA on 4 Jun 2021 at 12:50 In this talk we present the latest results on radiative and rare/forbidden decays for D and D_s mesons from the BESIII experiment based on 2.92 fb$^{-ˆ’1}$and 3.19 fb$^{-1}$data samples taken at the center-of-mass energies 3.773 and 4.178 GeV, respectively. With the 4.178 GeV data, searches for the rare decay$D^+_S\to p\bar{p}e^+\nu_e$and rare radiative leptonic decay$D_S^+\to\gamma e^+\nu ... More
Presented by Jingzhi ZHANG
Presented by Mr. Nico ADOLPH on 4 Jun 2021 at 13:30
We compute radiative three-body decays of charmed mesons $D \to P P \gamma$ , $P=\pi, K$, in leading order QCDF, HH$\chi$PT and the soft photon approximation. We work out decay distributions and asymmetries in the standard model and with new physics in the electromagnetic dipole operators. The forward-backward asymmetry is suitable to probe the QCD frameworks, in particular the $s$-channel depende ... More
We report the observation of the rare charm decay $D^0 \to K^-\pi^+e^+e^-$, a search for nine lepton-number-violating and three lepton-flavor-violating neutral charm decays of the type $D^0 \rightarrow h^- h^{'-} \ell^+ \ell^{'+}$, and $D^0 \rightarrow h^- h^{'+} \ell^+ \ell^{'-}$, and a search for seven lepton-number-violating decays of the type $D^{0}\rightarrow X^{0} e^{\pm} \mu^{\mp}$, where $... More Presented by Dr. David N. BROWN Session: NP in charm Presented by Dr. David BROWN on 4 Jun 2021 at 12:50 Presented by Prof. Svetlana FAJFER on 3 Jun 2021 at 07:30 The Belle II experiment has accumulated data corresponding to 89.99 fb-1 integrated luminosity in the past 2 years, and is performing very good. Waiting that the full planned data set will be recorded (50 ab-1), which will allow search for rare processes and will have a tremendous impact in the spectroscopy field, the Phase 3 data set allows to already perform analysis with high precision. We pres ... More Presented by Dr. Youngmin YOOK Session: Production Presented by Dr. Youngmin YOOK on 3 Jun 2021 at 11:40 Presented by Sean DOBBS on 31 May 2021 at 12:40 Presented by Dr. Longke LI on 1 Jun 2021 at 07:00 Session: Exotics Presented by Prof. Alexis POMPILI on 31 May 2021 at 10:50 A naive application of the heavy quark expansion (HQE) yields theory estimates for the decay rate of neutral$D$mesons that are four orders of magnitude below the experimental determination. It is well known that this huge suppression results from severe GIM cancellations. We find that this mismatch can be solved by individually choosing the renormalisation scale of the different internal ... More Presented by Mr. Christos VLAHOS Presented by Mr. Christos VLAHOS on 3 Jun 2021 at 12:20 Presented by Dr. Aleksey RUSOV on 4 Jun 2021 at 13:00 In this talk, I plan to present preliminary results of updated SM predictions for charm-meson lifetimes, their ratios and also the semileptonic decay widths, based on the Heavy Quark Expansion (HQE). In addition to the known contributions, for the first time we include the dimension-six Darwin term for non-leptonic charm decays and the first determinations of the dimension-six Bag paramet ... More Presented by Dr. Aleksey RUSOV Presented by Prof. Vorobiev VITALY on 1 Jun 2021 at 09:20 Many models of dark matter and hidden sectors predict new particles with masses below the electroweak scale. Low-energy electron-positron colliders such as BABAR are ideally suited to discover these hidden-sector particles. We present a recent search for prompt and long-lived hidden scalars produced in association with tau leptons and decaying into a lepton pair. This search is sensitive to viable ... More Presented by Dr. Steven ROBERTSON Session: Taus Presented by Dr. Robertson STEVEN on 3 Jun 2021 at 12:20 Presented by Dr. Huijing LI on 4 Jun 2021 at 12:10 BESIII has collected data samples corresponding to luminosities of 2.93 fb-1 and 3.19 fb-1 at center-of-mass energies of 3.773 and 4.178, respectively. We report recent measurements that include the decays D(s)+ -> l+v (l=mu, tau), D0(+) -> K-bar(pi)l+v (l=e,mu), D0(+) -> a0(980)e+v, D+->K1(1270)e+nu, D(s)+ -> eta(')e+nu, Ds+ -> K(*0)enu, Ds+ -> phi enu,. The first searches for Ds+ -> gamma e+nu a ... More Presented by Jingzhi ZHANG We study the expected sensitivity at Belle and Belle II for four-body τ∓→X±l∓l∓ντ decays where l=e or μ and X=π, K, ρ and K∗ mesons. These decay processes violate the total lepton number (|ΔL|=2 ) and they can be induced by the exchange of Majorana neutrinos. In particular, we consider lifetimes in the accessible ranges of τN = 5, 100 ps and extract the limits on |VℓN|2 withou ... More Presented by Dr. Pedro PODESTA Session: Taus Presented by Mr. David RODRÍGUEZ PÉREZ on 3 Jun 2021 at 13:00 Session: Exotics Presented by Prof. Feng-Kun GUO on 31 May 2021 at 09:50 The BES III detector at Beijing Electron-Positron Collider has collected the world’s largest data sets. In this talk I will report recent results on the baryon pair production in Charmonium(-like) and in the e+e− annihilation at BESIII. Presented by Dr. Xiongfei WANG Session: Production Presented by Dr. Xiongfei WANG on 1 Jun 2021 at 11:40 We study the processes γγ → η ′ K + K − , η ′ π + π − , and ηπ + π − using a data sample of 519 f b −1 recorded with the BaBar detector operating at the SLAC PEP-II asymmetric-energy e + e − collider at center-of-mass energies at and near the Υ(nS) (n = 2, 3, 4) resonances. This is the first observation of the decay η c → η ′ K + K − and we measure the branchin ... More Presented by Prof. Antimo PALANO Presented by Prof. Antimo PALANO on 1 Jun 2021 at 11:40 Session: Production The data on tau neutrino is very scarce, only a few experiments have detected its interactions. At FNAL beam dump experiment DONUT, tau neutrino interaction cross-section was directly measured with a large systematical (~50%) and statistical (~30%) errors. The main source of systematical error is due to a poor knowledge of the tau neutrino flux. The effective way for tau neutrino production is the ... More Presented by Collaboration DSTAU Session: Taus Presented by Prof. Ali Murat GULER on 4 Jun 2021 at 13:10 Session: Production Session: Production Session: Taus Presented by Prof. Alberto LUSIANI on 4 Jun 2021 at 10:20 Presented by Emilie PASSEMAR on 4 Jun 2021 at 09:50 The Belle II experiment is a substantial upgrade of the Belle detector and will operate at the SuperKEKB energy-asymmetric e+e− collider. The design luminosity of the machine is 8 × 1035 cm−2s−1 and the Belle II experiment aims to record 50 ab−1 of data, a factor of 50 more than its predecessor. From February to July 2018, the machine has completed a commissioning run and main operation o ... More Presented by Dr. Thomas KRAETZSCHMAR Session: Taus Presented by Mr. Thomas KRAETZSCHMAR on 4 Jun 2021 at 12:10 Based on the Generalized Quantum Electrodynamics expression for the Podolsky propagator, which preserves gauge invariance for massive photons, we propose a model for the massive gluon propagator that reproduces well-known features of established strong-interaction models in the framework of the Dyson-Schwinger equation. By adjusting the Podolsky mass and the coupling strength we thus construct a m ... More Presented by Prof. Eduardo ROJAS PEÑA Presented by Prof. Eduardo ROJAS PEÑA on 4 Jun 2021 at 13:25 Session: NP in charm Presented by Mr. Marxil SÁNCHEZ GARCÍA on 4 Jun 2021 at 13:30 The$D_s$semileptonic decays provides an ideal scenario in the charm sector to search for Lepton number violation (LNV), Lepton flavor universality (LFU) tests and new contributions in Flavor changing neutral currents (FCNC) modes. In this work, we first describe the long distance (LD) contributions in the$D_{s} \rightarrow \pi l^{+} l^{-}$decay, a non-FCNC mode usually employed as normalizati ... More Presented by Mr. Marxil SÁNCHEZ Presented by Mrs. Raquel MOLINA PERALTA on 1 Jun 2021 at 12:55 In a recent paper [1], the BESIII collaboration reported the so-called first observation of pure$W$-annihilation decays$D^+_s \to a^+_0(980) \pi^0$and$D_s^+ \to a^0_0(980)\pi^+$. The measured absolute branching fractions are, however, puzzlingly larger than those of other measured pure$W$-annihilation decays by at least one order of magnitude. In addition, the relative phase between the two d ... More Presented by Dr. Raquel MOLINA PERALTA The SHiP collaboration proposes a general purpose fixed-target experiment to search for hidden particles at the new beam-dump facility at CERN SPS. For the interpretation of these searches a precise knowledge of the differential charm production cross-section in a thick target, including the cascade production, is essential. To obtain this parameter, several dedicated measurements at CERN SPS have ... More Presented by Mr. Nikolaus OWTSCHARENKO Session: Production Presented by Mr. Nikolaus OWTSCHARENKO on 3 Jun 2021 at 13:00 If the X(3872) is a weakly bound charm-meson molecule, it can be produced by the creation of$D^∗ \bar D^∗$at short distances followed by the rescattering of the charm mesons into X(3872) and a photon or a pion through a triangle loop. A triangle singularity produces narrow peak in the reaction rate in production of X(3872). The observation of this peak would provide strong evidence in suppor ... More Presented by Ms. Liping HE Session: Production Presented by Ms. Liping HE on 1 Jun 2021 at 12:00 Presented by Prof. Lisheng GENG The recent LHCb discovery of three pentaquark states may usher in a new ear in our understanding of the low energy strong interaction. These states might be part of a first complete multiplet composed of seven hadrons of molecular nature. At least this is what emerges from a leading order effective field theory using only data and heavy quark spin symmetry as constrains [1]. In addition, we will s ... More Presented by Prof. Lisheng GENG The$X(3872)$, whose mass coincides with the$D^0\bar{D}^{*0}$threshold, is the most extended hadron object. Since its discovery in 2003, debates have never stopped regarding its internal structure. We propose a new object, the X atom, which is the$D^\pm D^{*\mp}$composite system with positive charge parity and a mass of$(3879.89\pm0.07)$~MeV, formed mainly due to the Coulomb force. We show ... More Presented by Mr. Zhenhua ZHANG Presented by Mr. ZHANG ZHENHUA on 1 Jun 2021 at 12:00 From 2011, BESIII has taken about 20 fb^-1 data samples at center of mass energies from 3.8 to 4.6 GeV, containing 21 energy points with luminosity larger than 400 pb^-1. This makes the study of vector states Y, charged states Z, X states, as well as the connections between them through transition processes possible. Using these data samples, new information about X(3872) decays, Y states from ope ... More Presented by Jingzhi ZHANG Presented by Dr. Weimin SONG on 1 Jun 2021 at 11:40 Recently, BESIII reported observation of the structure at the kinematical threshold in the$D_{s}^{-}D^{*0}+D_{s}^{*-}D^{0}$mass distribution, which is interpreted as a tetraquark candidate, called$Z_{cs}(3985)^{-}\$. This is the first candidate for a tetraquark meson containing hidden-charm with non-zero strangeness. BESIII has been devoting on the studies on the nonstrange charmoniumlike Zc sta ... More
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http://mathhelpforum.com/calculus/152273-help-intergration-recogbition.html
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# Math Help - help with intergration by recogbition
1. ## help with intergration by recogbition
G(x)=(10-x)cos((pi)x)
find an expression for the derivative G'(x)
i got that but then it says
hence show that an antiderivative of f(x) is
F(x)= ((sin((pi)x)) \ (pi)) - G(x)
and f(x) =pi(10-x)sn(pi)x
2. Originally Posted by dustinbehemoth
G(x)=(10-x)cos((pi)x)
find an expression for the derivative G'(x)
i got that but then it says
hence show that an antiderivative of f(x) is
F(x)= ((sin((pi)x)) \ (pi)) - G(x)
and f(x) =pi(10-x)sn(pi)x
What do you get for the derivative?
3. the derivative of g(x) was
(pi)(10-x)sin(pi)x - cos(pi)x
4. Originally Posted by dustinbehemoth
the derivative of g(x) was
(pi)(10-x)sin(pi)x - cos(pi)x
Let $y =(10-x) \cos ( \pi x)$ .... (1)
Then $\frac{dy}{dx} = \pi (10 - x) \sin (\pi x) - \cos (\pi x)$ .... (2)
Integrate both sides of (2) with respect to x:
$y = \int \pi (10 - x) \sin (\pi x) - \cos (\pi x) \, dx = \int \pi (10 - x) \sin (\pi x) \, dx - \int \cos (\pi x) \, dx$.
Substitute from (1):
$(10-x) \cos ( \pi x) = \int \pi (10 - x) \sin (\pi x) \, dx - \int \cos (\pi x) \, dx$.
Make the required integral the subject etc.
5. found a heaps easier(may just be better explained) way but thanks anyway
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https://thorax.bmj.com/highwire/markup/177722/expansion?width=1000&height=500&iframe=true&postprocessors=highwire_tables%2Chighwire_reclass%2Chighwire_figures%2Chighwire_math%2Chighwire_inline_linked_media%2Chighwire_embed
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Table 2
Risk classifier
Outcome risk classifier*Lesion outcome
Cancer (in situ)Cancer freeTotal
Low risk 32427Prediction accuracy: 92% (95% CI 77% to 98%)
High risk 9 9Sensitivity: 75% (95% CI 46% to 92%)
Total122436Specificity: 100% (95% CI 84% to 100%)
• *Risk was predicted by using the previously defined model based on copy number aberrations (CNAs) at 3p26.3-p11.1, 3q26.2-29 and 6p25.3–24.3.12 When the predicted probability is larger than 0.5, classification of the sample is ‘high risk’ for endobronchial cancer (in situ). Prediction accuracy, sensitivity and specificity of the CNA classifier for endobronchial cancer (in situ) were calculated in this series.
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https://www.e-csd.org/journal/view.php?number=485
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ORIGINAL ARTICLE Commun Sci Disord. 2011;16(4): 570-581.
Word Length Effect in the Lexical Decisions of Poor Comprehenders Mina Hwang , and Kyung-Soon Choi Copyright ©2011 The Korean Academy of Speech-Language Pathology and Audiology 황민아(Mina Hwang)| 최경순(Kyung-Soon Choi) Share : ABSTRACT Background & Purpose Although there have been many studies investigating the on-line word-decoding process during reading in dyslexic children using various languages, studies on word-decoding skills of children with poor reading comprehension are limited. Poor comprehenders are supposed to have normal word-decoding skills based on their accuracy scores in standardized word-reading tests. Reportedly, for children learning to read languages with transparent grapheme-phoneme correspondence, their reading comprehension is highly correlated with reading speed but not with the accuracy of word-reading. Since the graphemephoneme correspondence of the Korean language is known to be transparent, it is possible that Korean poor comprehenders are slower in recognizing words relative to typically developing children even though the accuracy of word-reading is similar in the two groups. Methods Ten poor comprehenders and 12 typically developing children in 4th grade participated in the present study. The children performed a lexical decision task on words with two different lengths, two syllables or four syllables. Results The poor comprehenders were significantly slower and less accurate in their performances on the lexical decision task. The word-length effect was significantly greater in the poor comprehenders, as the differences in speed and accuracy of lexical decision between short and long words were greater in the poor comprehenders compared to the typically developing children. Discussion & Conclusion In a standardized reading test, the poor comprehenders only exhibited reading comprehension difficulties and were similar to the typically developing children in word-reading accuracy. However, the poor comprehenders’ performances in the lexical decision task indicated they also had difficulties in word-recognition. The authors of the present study suggest that, in a language with transparent grapheme-phoneme correspondence, like the Korean language, using word-reading accuracy as a measure of word-decoding skills may not be appropriate. The importance of cross-linguistic differences of reading development in diagnosing various types of reading disabilities is also discussed in the present paper. Keywords: 읽기이해부진아동 | 읽기 | 어휘판단과제 | 단어길이 | 자소-음소 대응의 언어간 차이 | children with poor reading comprehension | reading
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http://berkeley-cs61as.github.io/textbook/example-infinite-streams-of-pairs.html
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# Example - Infinite Streams of Pairs
Suppose we want to produce an infinite stream containing pairs of integers $(i, j)$ where $i \leq j$ and $i + j$ is prime. If int-pairs is the stream of pairs of all integers, our stream is:
(stream-filter (lambda (pair)
(prime? (+ (car pair) (cadr pair))))
int-pairs)
Now all we have to do is define int-pairs. How do we do that? Let's start by supposing that we have two streams, $S$ and $T$, which are both equivalent to integers. Now let's imagine the array (or matrix, if you want to think of it that way) of pairs of $S$ and $T$:
The stream of pairs of integers is everything above the diagonal:
Let's call the general stream of pairs (pairs s t), and consider it to be composed of three parts: the pair $(S_0, T_0)$, the rest of the pairs in the first row, and the remaining pairs.
The third piece in this decomposition (pairs that are not in the first row) is (recursively) the pairs formed from (stream-cdr s) and (stream-cdr t). Also note that the second piece (the rest of the first row) is:
(stream-map (lambda (x) (list (stream-car s) x))
(stream-cdr t))1
Then our stream of pairs is:
(define (pairs s t)
(cons-stream (list (stream-car s) (stream-car t))
(combine (stream-map (lambda (x) (list (stream-car s) x))
(stream-cdr t))
(pairs (stream-cdr s) (stream-cdr t)))))
Now we just need to put the streams together using some sort of combine function. We know that appending doesn't work—let's use interleave instead! Our stream of pairs becomes:
(define (pairs s t)
(cons-stream (list (stream-car s) (stream-car t))
(interleave (stream-map (lambda (x) (list (stream-car s) x))
(stream-cdr t))
(pairs (stream-cdr s) (stream-cdr t)))))
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https://www.physicsforums.com/threads/the-energy-of-a-point-charge.232921/
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# The Energy of a Point Charge
1. May 3, 2008
### dx
Hi,
I read in the Feynman Lectures Vol II that the assumption that the electron is a point leads to an infinite energy in its field, and that the difficulty hasn't been resolved. Has there been any progress on this since Feynman gave his lectures?
2. May 3, 2008
### G01
The diverging self energy of a point charge is indeed still a very open problem in physics today.
The problem arises when we consider the formula for the energy stored in an electromagetic field:
$$W=\frac{\epsilon_o}{2}\int_{all space}E^2d\tau$$
For a point charge, such as an electron, this reduces to:
$$W=\frac{q^2}{8\pi\epsilon_o}\int_0^{\infty}\frac{1}{r^2}dr$$
This integral diverges, leading to the infinite value for the energy contained in the field of a point charge.
From a qualitative perspective: The formula derived above is derived by adding up all the energy needed to assemble a charge distribution. Well, to assemble a point charge, we would need to take a finite amount of charge and "cram" it into a point, a space infinitely small, having no dimension. Considering this, it makes sense that to "assemble" a point charge will require an infinite amount of energy, since we would need to create a distribution with infinite an charge density. Thus, the problem is that classical electromagnetism predicts that the energy required to "create" a point charge distribution is infinite, which makes no sense. This is a great example of a "singularity" appearing in a physical theory. At this singularity, the laws of physics don't work and predict ridiculous infinite answers.
This problem is not just present in classical electrodynamics but is also present in the quantum theory as well. Fixing or explaining this problem is an open area of theoretical research.
Last edited: May 3, 2008
3. May 4, 2008
### Lojzek
It seems to me that infinite energy is a problem only if electron is separable. If it is not (and this is what is currently assumed), then this is just a constant addition to energy: are there any troubles with that?
4. May 4, 2008
### G01
Yes, if we consider that an electron is inseparable, then this diverging integral does not effect the rest of the calculations needed in electrostatics, but this infinite "self energy" is still embarrassing from the point of view of many physicists.
This is not the only point particle inconsistency in Classical E&M. There are also other problems caused by point particles in classical electrodynamics.
For instance, consider in radiation theory the Abraham-Lorentz formula which describes a "radiation reaction force" that will be experienced by a radiating point charge. This formula describes ridiculous accelerations for point particles in radiative situations, such as accelerations that happen a short time before the force causing them acts, or accelerations that spontaneously increase exponentially!
Again, what this means is beyond my current knowledge, but it goes to show that electrodynamics has some problems with point charges that still need to be dealt with.
5. May 5, 2008
### Nick M
Isn't 1/r^2 a p series whose infinite sum converges to a single number because p>1?
6. May 5, 2008
### nicksauce
$$\sum_{n=1}^{n=\infty}\frac{1}{n^2}$$ converges
$$\int_{0}^{\infty}\frac{1}{r^2}dr$$ diverges.
Big difference between the two as the latter includes a singularity.
7. May 5, 2008
### Redbelly98
Staff Emeritus
The problem is not at $r\rightarrow \infty$ , it's at $r\rightarrow 0$.
The summation you're thinking of starts at "1". Starting the integral at 0 is what is problematic.
8. May 5, 2008
### Lojzek
What about the possibility that electron is not a point particle?
Can it have a very small positive radius? It is possible to calculate "classical electron radious" with the assumption that electron is a uniformly charged ball and that only electrostatic energy contributes to its mass. Does anybody know whether the experimental upper limit for electron radius has already crossed classical electron radious?
9. May 5, 2008
### olgranpappy
in quantum mechanics and QED the electron is treated as a point charge--a point particle. You can consider other quanties like strings instead of points if you like, but it's probably not worth the trouble in my opinion.
10. May 6, 2008
### Nick M
Ah... I see.
Interesting!
11. May 6, 2008
### pzlded
That extrapolation applied to the mass of a electron results in a black hole. A black hole with the mass of an electron is unstable.
Perhaps an electron is a stable coexistence of mass and charge. The closeness of Electron / positron annihilation to energy of mass, indicates a limit on an electron's charge energy.
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http://lions-wing.net/lessons/intranet/network-programs.html
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# Home Network Programs
Now that we have seen the physical layout of a home network, lets discuss the programs which are used to make the hardware work correctly. Some of these are required programs, and some are recommended programs. In the description I will indicate which is which.
## Software for the Server
The Linux server is the heart of the system. It allows common storage of information and file sharing. It can also server as an information resource to the network as well as a print server.
Here is a list of the programs I think are important or useful on this server.
SAMBA
Samba is a program which supports the SMB protocol. OK, what is SMB? Here is their explaination:
The very short answer is that it is the protocol by which a lot of
PC-related machines share files and printers and other informatiuon
such as lists of available files and printers. Operating systems that
support this natively include Windows NT, OS/2, and Linux and add on
packages that achieve the same thing are available for DOS, Windows,
VMS, Unix of all kinds, MVS, and more. Apple Macs and some Web Browsers
can speak this protocol as well.
In short samba is what allows the Linux server to work as a file and print server to the Windows PCs.
Sendmail
Sendmail is a common mail server which comes with most Linux systems. By configuring it on the Linux Server, you can have an unlimited number of email boxes for your home or buisiness.
What we will do is configure sendmail for the users on the system. Then we will discuss how to setup the connection through a registered domain name. This allows you to have any number of email addresses you want, legally, with a dialup or cable modem account.
Print Server
The print server program under Linux can allow you to use one printer connected to the Server instead of a printer connected to every computer in the house. This can even be a remote printer connected through the network. For example I have 3 boys and a wife, all of whom would normally need a printer. But rather than buy 5 printers, I can buy on and have all of them use that one.
Apache
Apache is not a required program on the Linux server. I find it an easy way of sharing information I think is useful to the users on the system. A lot of businesses are using web servers to distribute information from phone lists to Insurance form to their employees.
As an example I use the server to explain how some the services are configured on my network. I also use it to provide interesting web links for my children. Finally it is an easy way of keeping a record of how to perform some computer operations for my wife, who forgets how to do some operations she doesn’t do too often. I find it easier to write it down and put it on a notes page than remind her at 11 PM when she has forgotten again.
## Software for the Firewall
One area where Linux is competting directly with the commerical vendors is in the area of Firewall software. This is not difficult to understand, since most of the major firewall designed were originally implemented in Unix. Besides, since Linux is Open Source, a person who want to create a firewall has access to all the tools needed.
I have had exerience with two Firewall programs, Smoothwall and IPcop . Either of these programs will do a good job of a firewall on an older computer. If like me, you have an old 486, or 386 available, you can convert it to a good firewall.
This is not to say that there are not routers which contain reasonable firewalls at a decient price. I just like to know that if the firewall is broken, I can fix it myself. Also I believe in using what I have instead of buying more equipment. In the end, the choice is up to you. I guess I like Linux, so I use it.
## Decisions, Decisions, Decisions
One of the issues which comes up with most systems, is the need to make lots of choices. Defining the choices can be difficult prior to installing the system. But since this is a talk, I will try to state the decisions made and we can debate them if desired.
• External Modem choosen. Since all the external modems, must by definition be complete modems, instead of the new Windows Only modems, I felt the cost was justified. In addition an external modem is easier to configure, and replace if damaged.
• Separate Firewall. There are routers which include firewalls today at reasonable prices. But I felt it would be better to install an Open Source firewall since it can be reviewed by people outside the original authors. Since it is a standalone box, if it were compromized, it would be easy to reinstall to remove any trap doors.
• Connecting the Cable modem via network cable instead of USB. The support for Ethernet cards is better than USB support in Linux. The control over the ethernet configuration is superior to that of USB devices.
• Fixed IP addresses instead of DHCP. Since I don’t expect to be adding or removing computers ofter in the environment, it seemed more logical to give each an IP address and have done with it. DHCP, requires more configuration, and lookup facilities for name resolution than a hosts file.
• Plain Text Passwords for Samba. Although Samba includes the ability to work with encripted passwords, it did not seen necessary inside a house. I don’t expect to worry about my sons using packet sniffers for passwords on the network.
• No DNS or Wins configured. This is a simple network configuration so internal to the network there is not a lot of need for lookups. A simple host file will server for lookups within the network. The firewall will provide DNS lookups for the Internet.
## Lets look at the Numbers and Letters and Users
In any network situation we need to understand a little about the protocols that are used to connect the computers. In the case of Linux and Windows, we are talking about TCP/IP (Transmission Control Protocol/Internet Protocol)
In a nutshell we are going to choose names and addresses for each computer on the network. The TCP/IP protocol was designed with certain blocks of addresses undefined. This means that these addresses are not routed if they show up on the internet. In layman’s terms this means that some addresses were reserved for use by people like us. They are available for someone to use for their own purposes, and ignored by the internet.
The block of addresses I am going to use go from 192.168.1.0 to 192.168.1.255. This block of IP addresses is one of those reserved sets. Since it is reserved, we will be using it to configure the computers on our network. For all the computers we will be using the netmask of 255.255.255.0
Samson 192.168.1.254 Firewall Computer
Wizard 192.168.1.1 Linux Server
Apollo 192.168.1.5 Linux Workstation
Demeter 192.168.1.7 Windows Workstation
We will use this list to configure the networking on each computer so they can be refered to by Name, instead of IP address. For more information on IP addresses let me recomment Introduction to IP from the Rute book.
What about users on the system? For this tutorial, I will assume the following users and passwords are the people in your home. I am not including the root user since he/she needs to already exist to install Linux.
Frank Smith frank magic /bin/bash /home/frank
Sally Smith sally boat /bin/bash /home/sally
Tom Smith tom fish /bin/bash /home/tom
Finally lets chose the domain name “home.org”. Since you are not on the internet with this name, it can be anything you choose. We will use the same name for the samba work group. If in the future you want to have your own mail server, you might consider registering a domain name. We can discuss this later though. For now lets just just this default.
I am a strong believer in designing something before you implement it. I know that takes some of the fun out of working on computers, but it can save you a great deal of grief later. Planning what you are going to do first allows you to build a road map of the work in advance. It also allows you to create documentation of how your system is configured, BEFORE you forget what you did. Believe me, lots of people forget how something was configured once they have moved on to other things.
Here are the steps I am planning on implementing to configure our network structure.
1. Select the configuration information to be used for the system. Get all the assumptions taken care of before starting the configuration.
2. Configure the Linux Server for networking. Set the IP address, the netmask, the host name, the domain name, the users, the name entries in the host file, and the Samba server.
3. Configure the firewall and check that we can see and admin it from the Server.
4. Configure the Windows workstation to talk to the Linux Server. Setup up TCP/IP, gateway, computer name, workgroup name, and the host file. Since we will be using plain text passwords, we will make a modification to the Registry.
5. Configure the Linux workstation to talk to the Linux Server. Configure the IP address, the netmask, the host name, the domain name, and the name entries in the host file.
6. Celebrate!!
7. Plan for sharing the resources with your users. This will be discussed once we get the network and internet connections working. It can include, local Sendmail, Notes and instructions for users, Remote control of Lights and Alarm system in the house, Music Sharing between computers and your HiFi system, and Remote backup of the network.
### VI for the novice
I promised that use of VI would be minimal, but this will still require some knowledge. Lets look at a quick edit of a file using VI. We will make a change in the following text using the VI editor on Linux.
# default: on
# description: The telnet server serves telnet sessions; it uses \
service telnet
{
flags = REUSE
socket_type = stream
wait = no
user = root
server = /usr/sbin/in.telnetd
log_on_failure += USERID
disable = no
}
This file comes from /etc/xinetd.d/telnet on my linux system. This is a typical configuration file for the xinetd program. We are going to change the disable option from no to yes . We will then save the file.
One piece of information before we start. Remember that vi has two modes. Insert mode and command mode. By default you will start in command mode. This is the mode where keypresses move you around on the window, or perform certain commands. When you are in insert mode, the characters you type are inserted into the file. When in doubt which mode you are in, press the <ESC> key to change back to command mode.
OK, enough theory, lets make the change. Here are the steps as done from the command line.
1. Open the file in vi: vi /etc/xinetd.d/telnet
2. Move to the text to change: Use the arrow key to move to the word no in the line “disable = no”
3. Delete the work no: With the cursor on the “n” of no press the x key twice.
4. Insert yes where it said no: press the i key to enter insert mode, type “yes”, and press the <ESC> key to exit insert mode.
5. Save your work: Type “:w” followed by <Enter>
6. Exit vi: Type “:q” followed by <Enter>
Congradulations, you just use VI for editing. Ok, so this wasn’t the most challenging editing job. The idea was you just used the dredded vi to edit a file. Not so difficult was it. For those of you feeling brave, try the command vimtutor to tryout a tutorial on VIM. It might be enlightening.
Now to be honest, I normally use Emacs for most of my editing. But vi is a quick editor with that ability to make changes on every Unix/Linux system you will encounter. Using an editor for configuration is slightly old fashoned, as there are getting to be graphical tools for this work. But the editor approach allows you to appreciate the scripting ability of Linux.
Written by John F. Moore
Last Revised: Wed Oct 18 11:01:35 EDT 2017
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http://mathhelpforum.com/advanced-algebra/81853-please-can-someone-check-see-if-my-answer-right.html
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# Math Help - Please can someone check to see if my answer is right??
1. ## Please can someone check to see if my answer is right??
So the give eigen value is λ=2.
And the matrix A, what is the basis for each eigenspace?
A=
0 1 1
1 0 1
1 1 0
------------
My answer that I get after doing (A-2I)x=0 and row reducing it is a general solution and x3 is free.
and my basis is
1
1
1
Can someone tell me if that's right?? please!
2. Hello,
There is another eigenvalue : -1.
In order to help you know if you're on the right way, you can remember that the sum of the eigenvalues equals the trace (the sum of the diagonal elements) of the matrix. And $2 \neq 0$
The eigenspace you found for 2 is correct though
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https://it.overleaf.com/latex/templates/iust-basic-science-computational-lab-report/ygnggzwjgrcm
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# IUST Basic Science Computational Lab Report
Author
Masoud Golestaneh, Sauleh Eetemadi
AbstractThis template is for computational project/lab reports for basic science classes such as Physics, Math and Differential Equations.
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https://link.springer.com/article/10.1007%2Fs10853-019-04339-1
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# A predictive failure framework for brittle porous materials via machine learning and geometric matching methods
• 285 Accesses
## Abstract
Brittle porous materials are used in many applications, such as molten metal filter, battery, fuel cell, catalyst, membrane, and insulator. The porous structure of these materials causes variations in their fracture strength that is known as the mechanical reliability problem. Despite the importance of brittle porous materials, the origin of the strength variations is still unclear. The current study presents a machine learning approach to characterize the stochastic fracture of porous ceramics and glasses. A combined finite element modeling and fracture mechanics approach was used to generate a unique empirical data set consisting of normalized stress intensity factors (nSIFs, KI/σ = Y$$\sqrt {\pi a}$$) that define fracture strength of brittle systems under uniaxial tensile loading and biaxial tensile loading. These empirical data sets were used to generate prediction functions and validate their accuracy. Monte Carlo simulations with two machine learning algorithms, random forests (RF) and artificial neural networks (ANN), were used to simultaneously determine the optimum percentages for the training and test data set split and the prediction function validation. The constraint was taken to be the mean absolute percentage error (MAPE) during the process. In the implementation step, new porous media with uniformly distributed pores were created and the prediction functions were used to obtain nSIFs and characterize the media. As a novelty of this approach, which ensures the predictive characterization of the generated media, a geometric matching method by means of the Euclidean bipartite matching between the empirical and the generated media was presented and the nSIFs were compared by means of MAPE. As a result of the study, MAPE ranges are 3.4–17.93% (uniaxial load) and 2.83–19.42% (biaxial load) for RF, 3.79–17.43% and 3.39–21.43 for ANN at the validation step; 3.54–18.20% (uniaxial load) and 3.06–21.60% (biaxial load) for RF, 3.57–18.26% and 3.43–21.76% for ANN at the implementation step. The proposed approach can be thus used as a predictive characterization tool, especially for the analysis and Weibull statistics of porous media subjected to brittle failure.
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## Author information
Correspondence to Özgür Keleş.
### Publisher's Note
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## Appendix
### Appendix
See Tables 2 and 3.
## Rights and permissions
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https://chem.libretexts.org/Bookshelves/Organic_Chemistry/Map%3A_Organic_Chemistry_(Bruice)/01%3A_Electronic_Structure_and_Bonding_(Acids_and_Bases)/1.13%3A_The_Bond_in_a_Hydrogen_Halide
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# 1.13: The Bond in a Hydrogen Halide
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This page discusses the acidity of the hydrogen halides: hydrogen fluoride, hydrogen chloride, hydrogen bromide and hydrogen iodide. It begins by describing their physical properties and synthesis and then explains what happens when they react with water to make acids such as hydrofluoric acid and hydrochloric acid.
## Physical properties
The hydrogen halides are colorless gases at room temperature, producing steamy fumes in moist air. The boiling points of these compounds are shown in the figure below:
Hydrogen fluoride has an abnormally high boiling point for a molecule of its size(293 K or 20°C), and can condense under cool conditions. This is due to the fact that hydrogen fluoride can form hydrogen bonds. Because fluorine is the most electronegative of all the elements, the fluorine-hydrogen bond is highly polarized. The hydrogen atom carries a high partial positive charge (δ+); the fluorine is fairly negatively charged (δ-).
In addition, each fluorine atom has 3 lone pairs of electrons. Fluorine's outer electrons are at the n=2 level, and the lone pairs represent small, highly charged regions of space. Hydrogen bonds form between the δ+ hydrogen on one HF molecule and a lone pair on the fluorine of another one.The figure below illustrates this association:
The other hydrogen halides do not form hydrogen bonds because the larger halogens are not as electronegative as fluorine; therefore, the bonds are less polar. In addition, their lone pairs are at higher energy levels, so the halogen does not carry such an intensely concentrated negative charge; therefore, other hydrogen atoms are not attracted as strongly.
### Making hydrogen halides
There are several ways of synthesizing hydrogen halides; the method considered here is the reaction between an ionic halide, like sodium chloride, and an acid like concentrated phosphoric(V) acid, H3PO4, or concentrated sulfuric acid.
### Making hydrogen chloride
When concentrated sulfuric acid is added to sodium chloride under cold conditions, the acid donates a proton to a chloride ion, forming hydrogen chloride. In the gas phase, it immediately escapes from the system.
$Cl^- + H_2SO_4 \rightarrow HCl + HSO_4^-$
The full equation for the reaction is:
$NaCl + H_2SO_4 \rightarrow HCl + NaHSO_4$
Sodium bisulfate is also formed in the reaction. Concentrated phosphoric(V) acid reacts similarly, according to the following equation:
$Cl^- + H_3PO_4 \rightarrow HCl + H_2PO_4^-$
The full ionic equation showing the formation of the salt, sodium biphosphate(V), is given below:
$NaCl + H_3PO_4 \rightarrow HCl + NaH_2PO_4$
### Making other hydrogen halides
All hydrogen halides can be formed by the same method, using concentrated phosphoric(V) acid.
Concentrated sulfuric acid, however, behaves differently. Hydrogen fluoride can be made with sulfuric acid, but hydrogen bromide and hydrogen iodide cannot.
The problem is that concentrated sulfuric acid is an oxidizing agent, and as well as producing hydrogen bromide or hydrogen iodide, some of the halide ions are oxidized to bromine or iodine. Phosphoric acid does not have this ability because it is not an oxidant.
## The acidity of the hydrogen halides
### Hydrogen chloride as an acid
By the Bronsted-Lowry definition of an acid as a proton donor, hydrogen chloride is an acid because it transfers protons to other species. Consider its reaction with water.
Hydrogen chloride gas is soluble in water; its solvated form is hydrochloric acid. Hydrogen chloride fumes in moist air are caused by hydrogen chloride reacting with water vapor in the air to produce a cloud of concentrated hydrochloric acid.
A proton is donated from the hydrogen chloride to one of the lone pairs on a water molecule.
A coordinate (dative covalent) bond is formed between the oxygen and the transferred proton.
The equation for the reaction is the following:
$H_2O + HCl \rightarrow H_3O^+ + Cl^-$
The H3O+ ion is the hydroxonium ion (also known as the hydronium ion or the oxonium ion). This is the normal form of protons in water; sometimes it is shortened to the proton form, H+(aq), for brevity.
When hydrogen chloride dissolves in water (to produce hydrochloric acid), almost all the hydrogen chloride molecules react in this way. Hydrochloric acid is therefore a strong acid. An acid is strong if it is fully ionized in solution.
### Hydrobromic acid and hydriodic acid as strong acids
Hydrogen bromide and hydrogen iodide dissolve in (and react with) water in exactly the same way as hydrogen chloride does. Hydrogen bromide forms hydrobromic acid; hydrogen iodide gives hydriodic acid. Both of these are also strong acids.
### Hydrofluoric acid as an exception
By contrast, although hydrogen fluoride dissolves freely in water, hydrofluoric acid is only a weak acid; it is similar in strength to organic acids like methanoic acid. The complicated reason for this is discussed below.
## The bond enthalpy of the H-F bond
Because the fluorine atom is so small, the bond enthalpy (bond energy) of the hydrogen-fluorine bond is very high. The chart below gives values for all the hydrogen-halogen bond enthalpies:
bond enthalpy
(kJ mol-1)
H-F +562
H-Cl +431
H-Br +366
H-I +299
In order for ions to form when the hydrogen fluoride reacts with water, the H-F bond must be broken. It would seem reasonable to say that the relative reluctance of hydrogen fluoride to react with water is due to the large amount of energy needed to break that bond, but this explanation does not hold.
## The energetics of the process from HX(g) to X-(aq)
The energetics of this sequence are of interest:
All of these terms are involved in the overall enthalpy change as you convert HX(g) into its ions in water.
However, the terms involving the hydrogen are the same for every hydrogen halide. Only the values for the red terms in the diagram need be considered. The values are tabulated below:
bond enthalpy of HX
(kJ mol-1)
electron affinity of X
(kJ mol-1)
hydration enthalpy of X-
(kJ mol-1)
sum of these
(kJ mol-1)
HF +562 -328 -506 -272
HCl +431 -349 -364 -282
HBr +366 -324 -335 -293
HI +299 -295 -293 -289
There is virtually no difference in the total HF and HCl values.
The large bond enthalpy of the H-F bond is offset by the large hydration enthalpy of the fluoride ion. There is a very strong attraction between the very small fluoride ion and the water molecules. This releases a lot of heat (the hydration enthalpy) when the fluoride ion becomes wrapped in water molecules.
## Other attractions in the system
The energy terms considered previously have concerned HX molecules in the gas phase. To reach a more correct explanation, the molecules must first be considered as unreacted aqueous HX molecules. The equation for this is given below:
The equation is incorporated into an improved energy cycle as follows:
Unfortunately, values for the first step in the reaction are not readily available. However, in each case, the initial separation of the HX from water molecules is endothermic. Energy is required to break the intermolecular attractions between the HX molecules and water.
That energy is much greater for hydrogen fluoride because it forms hydrogen bonds with water. The other hydrogen halides experience only the weaker van der Waals dispersion forces or dipole-dipole attractions.
The overall enthalpy changes (including all the stages in the energy cycle) for the reactions are given in the table below:
$HX(aq) + H_2O (l) \rightarrow H_3O^+ (aq) + X^- (aq)$
enthalpy change
(kJ mol-1)
HF -13
HCl -59
HBr -63
H-I -57
The enthalpy change for HF is much smaller in magnitude than that for the other three hydrogen halides, but it is still negative exothermic change. Therefore, more information is needed to explain why HF is a weak acid.
## Entropy and free energy considerations
The free energy change, not the enthalpy change, determines the extent and direction of a reaction.
Free energy change is calculated from the enthalpy change, the temperature of the reaction and the entropy change during the reaction.
For simplicity, entropy can be thought of as a measure of the amount of disorder in a system. Entropy is given the symbol S. If a system becomes more disordered, then its entropy increases. If it becomes more ordered, its entropy decreases.
The key equation is given below:
In simple terms, for a reaction to happen, the free energy change must be negative. But more accurately, the free energy change can be used to calculate a value for the equilibrium constant for a reaction using the following expression:
The term Ka is the equilibrium constant for the reaction below:
$HX(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + X^-(aq)$
The values for TΔS (needed to calculate ΔG) for the four reactions at a temperature of 298 K are tabulated below:
TS
(kJ mol-1)
HF -29
HCl -13
HBr -4
H-I +4
Notice that at the top of the group, the systems become more ordered when the HX reacts with the water. The entropy of the system (the amount of disorder) decreases, particularly for the hydrogen fluoride.
The reason for this is that the very strong attraction between H3O+ and F-(aq) imposes a lot of order on the system, as does the attraction between the water molecules and the various ions present. These attractions are each greatest for the small fluoride ions.
The total effect on the free energy change, and therefore the value of the equilibrium constant, can now be considered. These values are calculated in the following table:
H
(kJ mol-1)
TS
(kJ mol-1)
G
(kJ mol-1)
Ka
(mol dm-3)
HF -13 -29 +16 1.6 x 10-3
HCl -59 -13 -46 1.2 x 108
HBr -63 -4 -59 2.2 x 1010
HI -57 +4 -61 5.0 x 1010
The values for these estimated equilibrium constants for HCl, HBr and HI are so high that the reaction can be considered "one-way". The ionization is virtually 100% complete. These are all strong acids, increasing in strength down the group.
By contrast, the estimated Ka for hydrofluoric acid is small. Hydrofluoric acid only ionizes to a limited extent in water. Therefore, it is a weak acid.
The estimated value for HF in the table can be compared to the experimental value:
• Experimental value: 5.6 x 10-4 mol dm-3
• Estimated value: 1.6 x 10-3 mol dm-3
These values differ by an order of magnitude, but because of the logarithmic relationship between the free energy and the equilibrium constant, a very small change in ΔG has a very large effect on Ka.
To have the values in close agreement, ΔG would must increase from +16 to +18.5 kJ mol-1. Given the uncertainty in the values used to calculate ΔG, the difference between the calculated value and the experimental value could easily fall within this range.
## Summary: Why is hydrofluoric acid a weak acid?
The two main factors are:
• Entropy decreases dramatically when the hydrogen fluoride reacts with water. This is particularly noticeable with hydrogen fluoride because the attraction of the small fluoride ions produced imposes significant order on the surrounding water molecules and nearby hydronium ions. The effect decreases with larger halide ions.
• Very strong hydrogen bonding exists between the hydrogen fluoride molecules and water molecules. This costs a large amount of energy to break. This effect does not occur in the other hydrogen halides.
## Contributors and Attributions
Jim Clark (Chemguide.co.uk)
1.13: The Bond in a Hydrogen Halide is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.
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http://math.bme.hu/szeminarium?page=3
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# Szemináriumok
## Maximális homogén 3-dimenziós geometriák
Időpont:
2017. 03. 21. 10:30
Hely:
H.306
Molnár Emil
## Rigid representations of the component structure of dynamic random graph models
Időpont:
2017. 03. 16. 16:15
Hely:
H306
Balázs Ráth (BME)
## Stokes problem, related inequalities, constants and representations
Időpont:
2017. 03. 16. 10:15
Hely:
BME H épület 306-os terem
Zsuppán Sándor (Berzsenyi Dániel Evangélikus Gimnázium (Líceum), Sopron)
Abstract: Stable solvability of the Stokes problem describing fluid motion with small Reynolds number in a domain depends on the inf-sup condition, the discrete version of which is involved in the analysis of many numerical methods. The inf-sup constant figuring in the condition is connected to other domain specific constants figuring in other inequalities such as the Babuska-Aziz inequality for the divergence equation, the Friedrichs-Velte inequality for conjugate harmonic functions and the Korn inequality in linear elasticity. These constants are also connected to the Schur complement operator of the Stokes problem and in the planar case to the Friedrichs operator of the domain. Despite of their theoretical and practical importance exact values of these constants are known only for a few domains. On the other hand there exist useful estimations for planar and spatial domains as well. The values of these constants depend only on the geometry of the domain which is for simply connected planar domains encoded in analytical properties of the conformal mapping of the domain onto the unit disc. Utilization of conformal mapping provides useful results for the constants (exact values or estimations for special domains, and continuous domain dependence) and also for the operators. These results are partly generalizable for other types of domains. We also review some representations of solutions of the Stokes equation by harmonic potentials and formulte results about their equivalence. We also review recent results and outline possible ways for further research of this topic. (The talk will be in Hungarian.)
## Bezdek András 60 éves
Időpont:
2017. 03. 14. 10:30
Hely:
H.306
Hujter Mihály, Lángi Zsolt, G.Horváth Ákos
## Gaussian curvature of piecewise flat manifolds
Időpont:
2017. 03. 09. 10:15
Hely:
H. épület 607-os terem
Snorre Christiansen (University of Oslo)
## Sokaságok és leképezéseik II
Időpont:
2017. 03. 07. 10:30
Hely:
H.306
Kalmár Boldizsár
## Stochastic Arnold Diffusion of Deterministic Systems
Időpont:
2017. 03. 02. 16:15
Hely:
H306
Vadim Kaloshin (U Maryland, ETH Zürich)
## Uniqueness of steady state, smooth shapes in a nonlocal geometric PDE and a model for the shape evolution of ooids
Időpont:
2017. 03. 02. 10:15
Hely:
H306
Sipos András Árpád
We investigate steady state solutions of a nonlocal geometric PDE that serves as a simple model of simultaneous contraction and growth of grains called ooids in geosciences. As a main result of the talk I demonstrate that the parameters associated with the physical environment determine a unique, time-invariant (equilibrium) solution of the equation among smooth, convex curves embedded in $\mathbb{R}^2$. The model produces nontrivial shapes that are consistent with recorded shapes of mature ooids found in nature.
## Uniqueness of steady state, smooth shapes in a nonlocal geometric PDE and a model for the shape evolution of ooids
Időpont:
2017. 03. 02. 10:15
Hely:
BME H épület 306-os terem
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https://www.physicsforums.com/threads/newton-universal-gravitation-formula-how-f-is-dimensionally-derived.768685/
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# Newton universal gravitation formula, how f is dimensionally derived?
1. Sep 2, 2014
### yeoG
If f dimensions are ml/t^2, where does t^2 come from in the equation of
F = G*m1*m2/r^2 where I believe G to be a constant, m1 and m2 to be masses and r to be the distance between two masses - so length. To dimensionally analyse this then, where would the dimension time come from if I were to check if the equation is dimensionally correct and I cant see where it comes from? I do think that it may come from G but i have seen various answers on what the dimensions of G are so I cant cancel the dimensions out to check if it is the same as F? Help would be appreciated, many thanks.
2. Sep 2, 2014
3. Sep 2, 2014
### Integral
Staff Emeritus
According to Newton
F=ma since acceleration has units l t-2 the units of force must be m Lt-2.
Using that you can figure out the units G needs to make the given equation dimensionally correct. Time is factored into the constant.
4. Sep 2, 2014
5. Sep 2, 2014
### yeoG
Hi thanks for the help however I focusing on F instead of G giving that G = N m^2 kg^-2 or what G is?
6. Sep 2, 2014
### nrqed
Isolating, $G= F$ $r^2 / (m_1 m_2 )$. You can tell right away the units of G.
7. Sep 2, 2014
### yeoG
ah I think I understand so by working out the dimensions of G you can show that F must equal to Gxm1xm2 because it will balance the equation to = F?
8. Sep 2, 2014
### A.T.
No. Observation shows that F equals Gxm1xm2/r^2. The dimension of G are defined based on this. So there is no point in checking if the equation is dimensionally correct, because it was defined to be correct.
Similar Discussions: Newton universal gravitation formula, how f is dimensionally derived?
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http://mathhelpforum.com/trigonometry/121077-trigo-equation.html
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1. ## trigo equation
Would anyone please tell me how to do this?
$
6tan^2 x - 4 sin^2 x =1$
Many thanks!
2. Originally Posted by cakeboby
Would anyone please tell me how to do this?
$
6tan^2 x - 4 sin^2 x =1$
Many thanks!
HI
$\frac{6\sin^2 x}{\cos^2 x}-4\sin^2 x-1=0$
$6\sin^2 x-4\sin^2 x\cos^2 x-\cos^2 x=0$
$6(1-\cos^2 x)-4(1-\cos^2 x)(\cos^2 x)-\cos^2 x=0$
$6-6\cos^2 x-4\cos^2 x+4\cos^4 x-\cos^2 x=0$
Can you continue ?
HI
$\frac{6\sin^2 x}{\cos^2 x}-4\sin^2 x-1=0$
$6\sin^2 x-4\sin^2 x\cos^2 x-\cos^2 x=0$
$6(1-\cos^2 x)-4(1-\cos^2 x)(\cos^2 x)-\cos^2 x=0$
$6-6\cos^2 x-4\cos^2 x\color{red}-\cos^4 x\color{black}-\cos^2 x=0$
Can you continue ?
I think you need to check both the sign and the coefficient of the term in $\cos^4x$.
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https://en.wikipedia.org/wiki/Parallelizable
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# Parallelizable manifold
(Redirected from Parallelizable)
In mathematics, a differentiable manifold $\scriptstyle M$ of dimension n is called parallelizable[1] if there exist smooth vector fields
$\{V_1, \dots,V_n\}$
on the manifold, such that at any point $\scriptstyle p$ of $\scriptstyle M$ the tangent vectors
$\{V_1(p), \dots, V_n(p)\}$
provide a basis of the tangent space at $\scriptstyle p$. Equivalently, the tangent bundle is a trivial bundle,[2] so that the associated principal bundle of linear frames has a section on $\scriptstyle M.$
A particular choice of such a basis of vector fields on $\scriptstyle M$ is called a parallelization (or an absolute parallelism) of $\scriptstyle M$.
## Examples
• An example with n = 1 is the circle: we can take V1 to be the unit tangent vector field, say pointing in the anti-clockwise direction. The torus of dimension n is also parallelizable, as can be seen by expressing it as a cartesian product of circles. For example, take n = 2, and construct a torus from a square of graph paper with opposite edges glued together, to get an idea of the two tangent directions at each point. More generally, any Lie group G is parallelizable, since a basis for the tangent space at the identity element can be moved around by the action of the translation group of G on G (any translation is a diffeomorphism and therefore these translations induce linear isomorphisms between tangent spaces of points in G).
• A classical problem was to determine which of the spheres Sn are parallelizable. The zero-dimensional case S0 is trivially parallelizable. The case S1 is the circle, which is parallelizable as has already been explained. The hairy ball theorem shows that S2 is not parallelizable. However S3 is parallelizable, since it is the Lie group SU(2). The only other parallelizable sphere is S7; this was proved in 1958, by Michel Kervaire, and by Raoul Bott and John Milnor, in independent work. The parallelizable spheres correspond precisely to elements of unit norm in the normed division algebras of the real numbers, complex numbers, quaternions, and octonions, which allows one to construct a parallelism for each. Proving that other spheres are not parallelizable is more difficult, and requires algebraic topology.
• The product of parallelizable manifolds is parallelizable.
## Remarks
• The term framed manifold (occasionally rigged manifold) is most usually applied to an embedded manifold with a given trivialisation of the normal bundle, and also for an abstract (i.e. non-embedded) manifold with a given stable trivialisation of the tangent bundle.
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http://math.stackexchange.com/users/73233/millardo-peacecraft?tab=activity
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Millardo Peacecraft
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# 271 Actions
4h awarded Yearling Mar20 awarded Inquisitive Jan19 asked Lagrange inversion theorem application Jan12 comment An application of the residue theorem or even @RonGordon? Jan12 comment An application of the residue theorem Perhaps @sos440 would know? Jan12 asked An application of the residue theorem Jan12 asked expansion in reciprocal terms Jan7 comment How to solve: $\frac{x}{\log_2(x) }= y$ @orion The OP already defined the Lambert W function in his question. Defining $W$ once more is unnecessary. Jan7 revised Root finding using Galois theory added 9 characters in body Jan7 answered How to solve: $\frac{x}{\log_2(x) }= y$ Jan7 asked Root finding using Galois theory Jan6 asked Residue of function with different branch points Dec30 comment Functional equation for polynomials @Bernard I'm aware that it is the taylor formula for polynomials. But he states that it is the functional form for a given polynomial. Hence my confusion about the $y$ Dec30 asked Functional equation for polynomials Dec30 revised How prove $\bigl(\frac{\sin x}{ x}\bigr)^{2} + \frac{\tan x }{ x} >2$ for $0 < x < \frac{\pi}{2}$ Tex Changes Dec30 suggested approved edit on How prove $\bigl(\frac{\sin x}{ x}\bigr)^{2} + \frac{\tan x }{ x} >2$ for $0 < x < \frac{\pi}{2}$ Dec25 revised Why is $x(\sqrt{x^2+1} - x )$ approaching $1/2$ when $x$ becomes infinite? tex changes Dec25 suggested approved edit on Why is $x(\sqrt{x^2+1} - x )$ approaching $1/2$ when $x$ becomes infinite? Dec16 awarded Caucus Oct24 revised Find the range of function $f(x) =\cos(\sin(\ln(\frac{x^2+e}{x^2+1})))+\sin(\cos(\ln(\frac{x^2+e}{x^2+1})))$… tex changes
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https://support.numxl.com/hc/en-us/articles/215786903-ARIMA-GOF-Goodness-of-fit-of-an-ARIMA-Model
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# ARIMA_GOF - Goodness of fit of an ARIMA Model
Computes the goodness of fit measure (e.g. log-likelihood function (LLF), AIC, etc.) of the estimated ARIMA model.
## Syntax
ARIMA_GOF(X, Order, d, mean, sigma, phi, theta, Type)
X is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)).
Order is the time order in the data series (i.e. the first data point's corresponding date (earliest date=1 (default), latest date=0)).
Order Description
1 ascending (the first data point corresponds to the earliest date) (default)
0 descending (the first data point corresponds to the latest date)
d is the degree of the differencing (i.e. d).
mean is the ARMA model mean (i.e. mu). If missing, mean is assumed zero.
sigma is the standard deviation value of the model's residuals/innovations.
phi are the parameters of the AR(p) component model (starting with the lowest lag).
theta are the parameters of the MA(q) component model (starting with the lowest lag).
Type is an integer switch to select the goodness of fitness measure: (1=LLF (default), 2=AIC, 3=BIC, 4=HQC).
Order Description
1 Log-Likelihood Function (LLF) (default)
2 Akaike Information Criterion (AIC)
3 Schwarz/Bayesian Information Criterion (SIC/BIC)
4 Hannan-Quinn information criterion (HQC)
## Remarks
1. The underlying model is described here.
2. The Log-Likelihood Function (LLF) is described here.
3. The time series is homogeneous or equally spaced.
4. The time series may include missing values (e.g. #N/A) at either end.
5. The residuals/innovations standard deviation (i.e. $\sigma$) should be greater than zero.
6. The ARMA model has independent and normally distributed residuals with constant variance. The ARMA log-likelihood function becomes:
$$\ln L^* = -T\left(\ln 2\pi \hat \sigma^2+1\right)/2$$
Where:
• $\hat \sigma$ is the standard deviation of the residuals.
7. The maximum likelihood estimation (MLE) is a statistical method for fitting a model to the data and providing estimates for the model's parameters.
8. The integration order argument (d) must be a positive integer.
9. The long-run mean can take any value or may be omitted, in which case a zero value is assumed.
10. The residuals/innovations standard deviation (sigma) must be greater than zero.
11. For the input argument (phi):
• The input argument is optional and can be omitted, in which case no AR component is included.
• The order of the parameters starts with the lowest lag.
• One or more parameters can be missing or an error code (i.e. #NUM!, #VALUE!, etc.).
• The order of the AR component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
12. For the input argument (theta):
• The input argument is optional and can be omitted, in which case no MA component is included.
• The order of the parameters starts with the lowest lag.
• One or more values in the input argument can be missing or an error code (i.e. #NUM!, #VALUE!, etc.).
• The order of the MA component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
13. The function was added in version 1.63 SHAMROCK.
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http://science.sciencemag.org/content/321/5892/1059
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Brevia
N2O5 Oxidizes Chloride to Cl2 in Acidic Atmospheric Aerosol
See allHide authors and affiliations
Science 22 Aug 2008:
Vol. 321, Issue 5892, pp. 1059
DOI: 10.1126/science.1158777
Abstract
Molecular chlorine (Cl2) is an important yet poorly understood trace constituent of the lower atmosphere. Although a number of mechanisms have been proposed for the conversion of particle-bound chloride (Cl) to gas-phase Cl2, the detailed processes involved remain uncertain. Here, we show that reaction of dinitrogen pentoxide (N2O5) with aerosol-phase chloride yields Cl2 at low pH (<2) and should constitute an important halogen activation pathway in the atmosphere.
View Full Text
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https://www.physicsforums.com/threads/homology-of-torus-and-kleins-bottle.507446/
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# Homology of torus and Klein's bottle
1. Jun 16, 2011
### ddo
1. The problem statement, all variables and given/known data
I'm trying to calculate singular homology groups of the torus and Klein's bottle using the Mayer-Vietoris sequence.
3. The attempt at a solution
I represent both spaces as a rectangle with identified edges. Then I take the sets:
U=rectangle without the boundary
V=rectangle without the middlepoint
so U is contractible thus H_n(U)=0 for n>0, H_0(U)=Z
V=S1vS1 so H_1(V)=ZxZ, H_n(V)=0
and their intersection = S1, H_n(S1)=0, H_1(S1)=Z, H_0(S1)=Z
Now from the M-V sequence for n>2 we get an exact sequence
0->0x0->H_n(T)->0, so H_n(T)=0.
But I don't know what to do for smaller n...
2. Jun 16, 2011
### micromass
Staff Emeritus
Hi ddo!
Do you need to derive everything from the Mayer-Vietoris sequence? That looks quite hard.
The zero'th homology group is very easy since it is the number of path connected components.
The first homology group is also easy by calculating the fundamental group of $S^1\times S^2$...
The second homology group can be derived from Mayer Vietoris then.
3. Jun 16, 2011
### ddo
I suppose the Mayer-Vietoris hint was there to make the task easier :)
So H_0 is Z because there is only one connected component, H_1 is the abelianization of the fundamental group, both torus and Klein's bottle have abelian fundamental groups so for torus it's $Z \times Z$, for Klein's bottle $Z \times Z_2$.
Now M-V gives:
$0 \to H_2(T) \to Z \to 0 \times (Z \times Z) \to H_1(T) \to Z$
And I still don't know how to derive H_2(T)...
4. Jun 16, 2011
### micromass
Staff Emeritus
Write out the full Mayer-Vietoris. I'll do it for the torus
$$0\rightarrow H_2(X)\rightarrow \mathbb{Z}\rightarrow \mathbb{Z}\times\mathbb{Z}\rightarrow \mathbb{Z}\times\mathbb{Z}\rightarrow \mathbb{Z}\rightarrow \mathbb{Z}\times\mathbb{Z}\rightarrow \mathbb{Z} \rightarrow 0$$
Now, it is easy to see that $H_2(X)$ is either 0 or $\mathbb{Z}$.
Now, reason from left to right as follows:
The end of the sequence is
$$\mathbb{Z}\times\mathbb{Z}\rightarrow \mathbb{Z} \rightarrow 0$$
So the the map is a surjection, and the kernel of the map is isomorphic to $\mathbb{Z}$.
Consider the next part of the sequence:
$$\mathbb{Z}\rightarrow \mathbb{Z}\times\mathbb{Z}\rightarrow \mathbb{Z}$$
The kernel of the right map equals the image of the left map. Thus the image of the left map is isomorphic to $\mathbb{Z}$. Thus the kernel of the left map is necessarily 0.
Now consider the next part of the sequence, etc.
Try to complete this argument.
5. Jun 16, 2011
### ddo
$$\mathbb{Z}\times\mathbb{Z} \rightarrow\mathbb{Z}\rightarrow \mathbb{Z}\times\mathbb{Z}$$
The kernel of the right map is 0, so the image of the left map is 0, so the kernel of the left map is $\mathbb{Z}\times\mathbb{Z}$
Next:
$$\mathbb{Z}\times\mathbb{Z}\rightarrow \mathbb{Z}\times\mathbb{Z}\rightarrow \mathbb{Z}$$
The kernel of the right map is $\mathbb{Z}\times\mathbb{Z}$, so the image of the left map is $\mathbb{Z}\times\mathbb{Z}$, so the kernel of the left map is 0.
$$H_2(X)\rightarrow \mathbb{Z}\rightarrow \mathbb{Z}\times\mathbb{Z}\rightarrow \mathbb{Z}\times\mathbb{Z}$$
The kernel of the right map is 0, so the kernel of the middle map is $\mathbb{Z}$, so the image of the left map is also $\mathbb{Z}$, so $H_2(X)$ can't be 0.
Is that correct?
6. Jun 16, 2011
### micromass
Staff Emeritus
Sounds good! So the second homology group is $\mathbb{Z}$!
The thing with the Klein Bottle should be analogous!
Similar Discussions: Homology of torus and Klein's bottle
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https://codereview.meta.stackexchange.com/questions/1616/code-requiring-a-third-party-pre-processor-to-make-it-work/1620
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Code requiring a third-party pre-processor to make it work
In this Wolves, Goats and Cabbages in Java question (here is a link to the pre-edited version), Java code is presented to solve the problem.
The code requires pre-processing by a third-party tool in order to function.
The third-party tool adds a number of 'template' or 'boilerplate' methods that make the code complete. In Java terms, these are things like getters, setters, toString(), equals(), and hashCode().
Without pre-processing the code, it is:
• full of errors, and will not compile.
• comprehensively broken in 'standard' IDE's like Eclipse, IntelliJ, Netbeans, etc.
In order to pre-process the code, you need to download the pre-processor, as well as plugins for the various IDEs so that they are modified to accommodate these pre-processor annotations.
These downloads are from a non-official site, and are not part of any standard tool-chain.
For example, from the question we have the interface Action, and the class ActionImpl:
import java.util.Collection;
public interface Action<T> {
Action<T> previous();
T data();
Collection<Action<T>> children();
void children(Collection<Action<T>> children);
}
and
@Accessors(fluent = true, chain = false)
@Data()
@EqualsAndHashCode(of = "data")
@ToString(of = {"data"})
public class ActionImpl<T> implements Action<T> {
private final Action<T> previous;
private final T data;
private Collection<Action<T>> children;
}
In Java terms, the ActionImpl class is missing four methods:
• previous()
• data()
• children()
• children(Collection<Action<T>>)
Additionally, there are compile/IDE errors for all the @Annotations which do not exist.
This makes the class fail to compile, and, essentially, there is nothing to review ;-)
Question:
Is it working code, or is it off-topic?
What is code but instructions to a compiler?
Would we allow an obscure language that no one here has a compiler to? I would hope the answer is yes. You might not be able to answer it but another person might.
I can currently think of more than one example that we would accept but requires an extension/plugin. is one that I personally use. It requires "pre-"processing" of a sort and compiles to . Unless I have missed some important clue I don't personally see a difference here.
I would suggest that the normal language tag alone in this case is incorrect. Further tagging it with the extension/pre-processor/whatever tag.
I'd vote for On topic.
I agree with @JamesKhoury.
The GNU GPL defines "source code" as "the preferred form of the work for making modifications to it". For the author of the question, that means the version of the code with the meta-programming annotations.
It does not make sense to review the post-processed form of the code, because we would then be critiquing auto-generated code, which isn't something that the author has full control over. (As an extreme analogy, consider CoffeeScript. You wouldn't compile it into JavaScript, then review the JavaScript.)
We gladly accept code that requires the various CSS preprocessors. We would also accept Perl code written using Moose — a similarly transformative third-party library for meta-programming. The objection, I believe, is not to the fact that the code requires a preprocessor, but that this particular preprocessor is (currently) obscure. Although it is a third-party dependency, it's not a particularly onerous one: the preprocessor is MIT-licensed, and all you have to do is include it in your classpath when compiling. In that sense, it is not any more of an inconvenience compared to other dependencies such as Apache Commons or Joda Time.
As for that particular question, I believe that replacing the original code with the post-processed code was an invalid edit.
If you don't like the Lombok preprocessor, you could create a tag so that you can choose to ignore such questions in the future. Now that the question has been replaced with post-processed code, though, taking that option would make a further mess of things.
• As an opposing point, the statement "...all you have to do is include it in your classpath when compiling..." is woefully understating the issue. You need to 'install' the preprocessor as an extension to Eclipse (whatever IDE you use), and you need to run pre-processing steps before you can 'just compile it'. – rolfl Mar 13 '14 at 3:05
• Put a different way, you need to reconfigure your development environment to review the code. This includes your IDE, and your compile tool-chain. That is in addition to adding a jar to the classpath for the code you are going to review.... unless you are already familiar with the pre-processor, and you don't need to compile/test the code to review it. – rolfl Mar 13 '14 at 3:09
• Lombok claims, On javac: Include lombok.jar on the classpath as you compile. That's all there is to it! If your IDE introduces complications to that simple process, that's your own problem, and you're free to choose a different question to review. The code in the question is still valid. – 200_success Mar 13 '14 at 3:35
• Reviewing Python code doesn't require installing Python. If you're familiar with the language you can review it regardless. If you're not familiar with the language the python tag helps exclude such questions. I think a lombok tag is the way to go, so only people who are already comfortable reviewing lombok code will consider such questions. – trichoplax Mar 16 '14 at 0:45
It is on-topic, however I would remove the tag.
At least for all the questions I ruthlessly remove the tag, it is not JavaScript! Tags should reflect the language of the code, not the language that is about to be generated.
• But this question is still recognizably Java. It just uses a few third-party annotations, that's all. – 200_success Mar 14 '14 at 6:57
• @200_success It is not Java if it does not compile without the preprocessor, I would agree with you if the code compiled but missed some features because of annotations not being interpreted. – konijn Mar 14 '14 at 12:34
• I agree with removal of the Java tag. Objective-C is just C with a really stronk pre-processor. The first thing that happens to any Objective-C source code is that it's pre-processed into C source code, but you don't see Objective-C questions being tagged C... Xcode will even generate the C-version of the code it's about to be compiled, I believe. – nhgrif Jul 28 '14 at 22:05
It's been almost two days and still can't find out how the code is working(?). It might be that I'm not very familiar with Java8. Still I would say the question is on-topic. Why?
To quote palacsint
See also: Effective Java, 2nd edition, Item 47: Know and use the libraries (The author mentions only the JDK's built-in libraries but I think the reasoning could be true for other libraries too.)
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http://worldwidescience.org/topicpages/c/cell+bundles+flexoelectric.html
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Sample records for cell bundles flexoelectric
1. Actuation of flexoelectric membranes in viscoelastic fluids with applications to outer hair cells
Herrera-Valencia, E. E.; Rey, Alejandro D.
2014-01-01
Liquid crystal flexoelectric actuation uses an imposed electric field to create membrane bending, and it is used by the outer hair cells (OHCs) located in the inner ear, whose role is to amplify sound through generation of mechanical power. Oscillations in the OHC membranes create periodic viscoelastic flows in the contacting fluid media. A key objective of this work on flexoelectric actuation relevant to OHCs is to find the relations and impact of the electromechanical properties of the memb...
2. Actuation of flexoelectric membranes in viscoelastic fluids with applications to outer hair cells.
Herrera-Valencia, E E; Rey, Alejandro D
2014-11-28
Liquid crystal flexoelectric actuation uses an imposed electric field to create membrane bending, and it is used by the outer hair cells (OHCs) located in the inner ear, whose role is to amplify sound through generation of mechanical power. Oscillations in the OHC membranes create periodic viscoelastic flows in the contacting fluid media. A key objective of this work on flexoelectric actuation relevant to OHCs is to find the relations and impact of the electromechanical properties of the membrane, the rheological properties of the viscoelastic media, and the frequency response of the generated mechanical power output. The model developed and used in this work is based on the integration of: (i) the flexoelectric membrane shape equation applied to a circular membrane attached to the inner surface of a circular capillary and (ii) the coupled capillary flow of contacting viscoelastic phases, such that the membrane flexoelectric oscillations drive periodic viscoelastic capillary flows, as in OHCs. By applying the Fourier transform formalism to the governing equation, analytical expressions for the transfer function associated with the curvature and electrical field and for the power dissipation of elastic storage energy were found. PMID:25332388
3. Fast flexoelectric switching in a cholesteric liquid crystal cell with surface-localized polymer network
We developed an electro-optical device based on the flexoelectric effect of a polymer-stabilized cholesteric liquid crystal with a uniform lying helix. Using a dual-frequency switchable nematic, a small amount of chiral dopant and a small amount of phase-separated polymer localized at the substrate surfaces, we were able to create a device that operates in both the amplitude (flexoelectric) and phase (dielectric) modes. Using a high-frequency voltage we were able to suppress the phase mode and preserve the amplitude mode.
4. The limits of flexoelectricity in liquid crystals
F. Castles
2011-09-01
Full Text Available The flexoelectric conversion of mechanical to electrical energy in nematic liquid crystals is investigated using continuum theory. Since the electrical energy produced cannot exceed the mechanical energy supplied, and vice-versa, upper bounds are imposed on the magnitudes of the flexoelectric coefficients in terms of the elastic and dielectric coefficients. For conventional values of the elastic and dielectric coefficients, it is shown that the flexoelectric coefficients may not be larger than a few tens of pC/m. This has important consequences for the future use of such flexoelectric materials in devices and the related energetics of distorted equilibrium structures.
5. A peridynamic approach to flexoelectricity
Roy, Pranesh
2016-01-01
A flexoelectric peridynamic (PD) theory is proposed. Using the PD framework, the formulation introduces, perhaps for the first time, a nanoscale flexoelectric coupling that entails non-uniform strain in centrosymmetric dielectrics. This potentially enables PD modeling of a large class of phenomena in solid dielectrics involving cracks, discontinuities etc. wherein large strain gradients are present and the classical electromechanical theory based on partial differential equations do not directly apply. Derived from Hamilton's principle, PD electromechanical equations are shown to satisfy the global balance requirements. Linear PD constitutive equations reflect the electromechanical coupling effect, with the mechanical force state affected by the polarization state and the electrical force state in turn by the displacement state. An analytical solution of the PD electromechanical equations in the integral form is presented for the static case when a point mechanical force and a point electric force act in a th...
6. Flexoelectric MEMS: towards an electromechanical strain diode.
Bhaskar, U K; Banerjee, N; Abdollahi, A; Solanas, E; Rijnders, G; Catalan, G
2016-01-21
Piezoelectricity and flexoelectricity are two independent but not incompatible forms of electromechanical response exhibited by nanoscale ferroelectrics. Here, we show that flexoelectricity can either enhance or suppress the piezoelectric response of the cantilever depending on the ferroelectric polarity and lead to a diode-like asymmetric (two-state) electromechanical response. PMID:26676467
7. Interconnection of bundled solid oxide fuel cells
Brown, Michael; Bessette, II, Norman F; Litka, Anthony F; Schmidt, Douglas S
2014-01-14
A system and method for electrically interconnecting a plurality of fuel cells to provide dense packing of the fuel cells. Each one of the plurality of fuel cells has a plurality of discrete electrical connection points along an outer surface. Electrical connections are made directly between the discrete electrical connection points of adjacent fuel cells so that the fuel cells can be packed more densely. Fuel cells have at least one outer electrode and at least one discrete interconnection to an inner electrode, wherein the outer electrode is one of a cathode and and anode and wherein the inner electrode is the other of the cathode and the anode. In tubular solid oxide fuel cells the discrete electrical connection points are spaced along the length of the fuel cell.
8. Flexoelectricity in barium strontium titanate thin film
Kwon, Seol Ryung; Huang, Wenbin; Yuan, Fuh-Gwo; Jiang, Xiaoning, E-mail: [email protected] [Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695 (United States); Shu, Longlong [Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695 (United States); Electronic Materials Research Laboratory, International Center for Dielectric Research, Xi' an Jiao Tong University, Xi' an, Shaanxi 710049 (China); Maria, Jon-Paul [Department of Material Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695 (United States)
2014-10-06
Flexoelectricity, the linear coupling between the strain gradient and the induced electric polarization, has been intensively studied as an alternative to piezoelectricity. Especially, it is of interest to develop flexoelectric devices on micro/nano scales due to the inherent scaling effect of flexoelectric effect. Ba{sub 0.7}Sr{sub 0.3}TiO{sub 3} thin film with a thickness of 130 nm was fabricated on a silicon wafer using a RF magnetron sputtering process. The flexoelectric coefficients of the prepared thin films were determined experimentally. It was revealed that the thin films possessed a transverse flexoelectric coefficient of 24.5 μC/m at Curie temperature (∼28 °C) and 17.44 μC/m at 41 °C. The measured flexoelectric coefficients are comparable to that of bulk BST ceramics, which are reported to be 10–100 μC/m. This result suggests that the flexoelectric thin film structures can be effectively used for micro/nano-sensing devices.
9. A flexoelectric microelectromechanical system on silicon.
Bhaskar, Umesh Kumar; Banerjee, Nirupam; Abdollahi, Amir; Wang, Zhe; Schlom, Darrell G; Rijnders, Guus; Catalan, Gustau
2016-03-01
Flexoelectricity allows a dielectric material to polarize in response to a mechanical bending moment and, conversely, to bend in response to an electric field. Compared with piezoelectricity, flexoelectricity is a weak effect of little practical significance in bulk materials. However, the roles can be reversed at the nanoscale. Here, we demonstrate that flexoelectricity is a viable route to lead-free microelectromechanical and nanoelectromechanical systems. Specifically, we have fabricated a silicon-compatible thin-film cantilever actuator with a single flexoelectrically active layer of strontium titanate with a figure of merit (curvature divided by electric field) of 3.33 MV(-1), comparable to that of state-of-the-art piezoelectric bimorph cantilevers. PMID:26571008
10. Enhanced flexoelectricity through residual ferroelectricity in barium strontium titanate
Residual ferroelectricity is observed in barium strontium titanate ceramics over 30 °C above the global phase transition temperature, in the same temperature range in which anomalously large flexoelectric coefficients are reported. The application of a strain gradient leads to strain gradient-induced poling or flexoelectric poling. This was observed by the development of a remanent polarization in flexoelectric measurements, an induced d33 piezoelectric response even after the strain gradient was removed, and the production of an internal bias of 9 kV m−1. It is concluded that residual ferroelectric response considerably enhances the observed flexoelectric response
11. Fabrication and measurement of a flexoelectric micro-pyramid composite
Huang, Wenbin; Shu, Longlong; Ryung Kwon, Seol; Zhang, Shujun; Yuan, Fuh-Gwo; Jiang, Xiaoning
2014-12-01
A fabrication method by combining precision mechanical dicing and wet etching was developed to prepare micro-pyramid structures based on (Ba0.67Sr0.33)TiO3 ceramics. The effective piezoelectric properties of flexoelectric pyramid structures in ten micrometers scale were investigated and measured through converse flexoelectric effect. The scaling effect of the flexoelectric response was demonstrated as the structure size shrinks down. The results do suggest the great potential of flexoelectric micro pyramids as an alternative to lead-free piezoelectric material.
12. Coupling a sensory hair-cell bundle to cyber clones enhances nonlinear amplification
Barral, Jérémie; Dierkes, Kai; Lindner, Benjamin; Jülicher, Frank; Martin, Pascal
2010-01-01
The vertebrate ear benefits from nonlinear mechanical amplification to operate over a vast range of sound intensities. The amplificatory process is thought to emerge from active force production by sensory hair cells. The mechano-sensory hair bundle that protrudes from the apical surface of each hair cell can oscillate spontaneously and function as a frequency-selective, nonlinear amplifier. Intrinsic fluctuations, however, jostle the response of a single hair bundle to weak stimuli and serio...
13. Multilamellar Structures and Filament Bundles Are Found on the Cell Surface during Bunyavirus Egress
Sanz-Sánchez, Laura; Risco, Cristina
2013-01-01
Inside cells, viruses build specialized compartments for replication and morphogenesis. We observed that virus release associates with specific structures found on the surface of mammalian cells. Cultured adherent cells were infected with a bunyavirus and processed for oriented sectioning and transmission electron microscopy. Imaging of cell basal regions showed sophisticated multilamellar structures (MLS) and extracellular filament bundles with attached viruses. Correlative light and electro...
14. Study on a flexoelectric microphone using barium strontium titanate
Kwon, S. R.; Huang, W. B.; Zhang, S. J.; Yuan, F. G.; Jiang, X. N.
2016-04-01
In this study, a flexoelectric microphone was, for the first time, designed and fabricated in a bridge structure using barium strontium titanate (Ba0.65Sr0.35TiO3) ceramic and tested afterwards. The prototyped flexoelectric microphone consists of a 1.5 mm × 768 μm × 50 μm BST bridge structure and a silicon substrate with a cavity. The sensitivity and resonance frequency were designed to be 0.92 pC/Pa and 98.67 kHz, respectively. The signal to noise ratio was measured to be 74 dB. The results demonstrate that the flexoelectric microphone possesses high sensitivity and a wide working frequency range simultaneously, suggesting that flexoelectricity could be an excellent alternative sensing mechanism for microphone applications.
15. First-principles theory and calculation of flexoelectricity
Hong, Jiawang; Vanderbilt, David
2013-01-01
We develop a general and unified first-principles theory of piezoelectric and flexoelectric tensor, formulated in such a way that the tensor elements can be computed directly in the context of density-functional calculations, including electronic and lattice contributions. We introduce a practical supercell-based methods for calculating the flexoelectric coefficients from first principles, and demonstrate them by computing the coefficients for a variety of cubic insulating materials, includin...
16. Computational evaluation of the flexoelectric effect in dielectric solids
Abdollahi, Amir; Peco, Christian; Millán, Daniel; Arroyo, Marino; Arias, Irene
2014-09-01
Flexoelectricity is a size-dependent electromechanical mechanism coupling polarization and strain gradient. It exists in a wide variety of materials, and is most noticeable for nanoscale objects, where strain gradients are higher. Simulations are important to understand flexoelectricity because experiments at very small scales are difficult, and analytical solutions are scarce. Here, we computationally evaluate the role of flexoelectricity in the electromechanical response of linear dielectric solids in two-dimensions. We deal with the higher-order coupled partial differential equations using smooth meshfree basis functions in a Galerkin method, which allows us to consider general geometries and boundary conditions. We focus on the most common setups to quantify the flexoelectric response, namely, bending of cantilever beams and compression of truncated pyramids, which are generally interpreted through approximate solutions. While these approximations capture the size-dependent flexoelectric electromechanical coupling, we show that they only provide order-of-magnitude estimates as compared with a solution fully accounting for the multidimensional nature of the problem. We discuss the flexoelectric mechanism behind the enhanced size-dependent elasticity in beam configurations. We show that this mechanism is also responsible for the actuation of beams under purely electrical loading, supporting the idea that a mechanical flexoelectric sensor also behaves as an actuator. The predicted actuation-induced curvature is in a good agreement with experimental results. The truncated pyramid configuration highlights the critical role of geometry and boundary conditions on the effective electromechanical response. Our results suggest that computer simulations can help understanding and quantifying the physical properties of flexoelectric devices.
17. Computational evaluation of the flexoelectric effect in dielectric solids
Flexoelectricity is a size-dependent electromechanical mechanism coupling polarization and strain gradient. It exists in a wide variety of materials, and is most noticeable for nanoscale objects, where strain gradients are higher. Simulations are important to understand flexoelectricity because experiments at very small scales are difficult, and analytical solutions are scarce. Here, we computationally evaluate the role of flexoelectricity in the electromechanical response of linear dielectric solids in two-dimensions. We deal with the higher-order coupled partial differential equations using smooth meshfree basis functions in a Galerkin method, which allows us to consider general geometries and boundary conditions. We focus on the most common setups to quantify the flexoelectric response, namely, bending of cantilever beams and compression of truncated pyramids, which are generally interpreted through approximate solutions. While these approximations capture the size-dependent flexoelectric electromechanical coupling, we show that they only provide order-of-magnitude estimates as compared with a solution fully accounting for the multidimensional nature of the problem. We discuss the flexoelectric mechanism behind the enhanced size-dependent elasticity in beam configurations. We show that this mechanism is also responsible for the actuation of beams under purely electrical loading, supporting the idea that a mechanical flexoelectric sensor also behaves as an actuator. The predicted actuation-induced curvature is in a good agreement with experimental results. The truncated pyramid configuration highlights the critical role of geometry and boundary conditions on the effective electromechanical response. Our results suggest that computer simulations can help understanding and quantifying the physical properties of flexoelectric devices
18. Computational evaluation of the flexoelectric effect in dielectric solids
Abdollahi, Amir; Peco, Christian; Millán, Daniel; Arroyo, Marino; Arias, Irene, E-mail: [email protected] [Laboratori de Càlcul Numèric (LaCàN), Universitat Politècnica de Catalunya (UPC), Campus Nord UPC-C2, E-08034 Barcelona (Spain)
2014-09-07
Flexoelectricity is a size-dependent electromechanical mechanism coupling polarization and strain gradient. It exists in a wide variety of materials, and is most noticeable for nanoscale objects, where strain gradients are higher. Simulations are important to understand flexoelectricity because experiments at very small scales are difficult, and analytical solutions are scarce. Here, we computationally evaluate the role of flexoelectricity in the electromechanical response of linear dielectric solids in two-dimensions. We deal with the higher-order coupled partial differential equations using smooth meshfree basis functions in a Galerkin method, which allows us to consider general geometries and boundary conditions. We focus on the most common setups to quantify the flexoelectric response, namely, bending of cantilever beams and compression of truncated pyramids, which are generally interpreted through approximate solutions. While these approximations capture the size-dependent flexoelectric electromechanical coupling, we show that they only provide order-of-magnitude estimates as compared with a solution fully accounting for the multidimensional nature of the problem. We discuss the flexoelectric mechanism behind the enhanced size-dependent elasticity in beam configurations. We show that this mechanism is also responsible for the actuation of beams under purely electrical loading, supporting the idea that a mechanical flexoelectric sensor also behaves as an actuator. The predicted actuation-induced curvature is in a good agreement with experimental results. The truncated pyramid configuration highlights the critical role of geometry and boundary conditions on the effective electromechanical response. Our results suggest that computer simulations can help understanding and quantifying the physical properties of flexoelectric devices.
19. 3-D slug flow heat transfer analysis of coupled coolant cells in finite LMFBR bundles
A three-dimensional single region slug flow heat transfer analysis for finite LMFBR rod bundles using a classical analytical solution method has been performed. According to the isolated single cell analysis, the results show that the peripheral clad temperature variation as well as the thermal entrance length are strongly dependent upon the degree of irregularity displayed by various coolant geometries. Since under the present LMFBR conditions, fully-developed temperature fields may hardly be established in such characteristic rod bundle regions, a 3-D heat transfer analysis seems to be mandatory. This implies that the results of fully developed heat transfer analyses are by far too conservative
20. The effect of flexoelectricity on the dielectric properties of inhomogeneously strained ferroelectric thin films
Catalan, G; Sinnamon, LJ; Gregg, JM
2004-01-01
Recent experimental measurements of large flexoelectric coefficients in ferroelectric ceramics suggest that strain gradients can affect the polarization and permittivity behaviour of inhomogeneously strained ferroelectrics. Here we present a phenomenological model of the effect of flexoelectricity o
1. Laser dismantling of PHWR spent fuel bundles and decladding of fuel pins in the highly radioactive hot cells
Full text: For reprocessing of PHWR fuel, fuel bundles are at present chopped mechanically into small pieces of pins using high tonnage mechanical press before dissolution. The existing method of bundle dismantling is purely mechanical using very high force for chopping. A laser based automated bundle dismantling system is developed. In the system, end-plates of bundle, which holds the fuel pins together, are cut using Nd-YAG laser to separate the bundles into pins. In addition to pin separation, the pins are to be chopped into small pieces using a small mechanical chopper. Since the spent fuel is highly radioactive, all these operations are performed remotely in hot cells. Post irradiation examination also requires dismantling of bundles into pins so that they can select the pins for the further examinations. In both these applications laser dismantling remains the most. important step and this system has been developed and tested. This paper describes the experience gained during the development efforts
2. Comparative transduction mechanisms of hair cells in the bullfrog uticulus. 2: Sensitivity and response dynamics to hair bundle displacement
Baird, Richard A.
1994-01-01
The present study was motivated by an interest in seeing whether hair cell types in the bullfrog utriculus might differ in their voltage responses to hair bundle displacement. Particular interest was in assessing the contributions of two factors to the responses of utricular hair cells. First, interest in examining the effect of hair bundle morphology on the sensitivity of hair cells to natural stimulation was motivated by the observation that vestibular hair cells, unlike many auditory hair cells, are not free-standing but rather linked to an accessory cupular or otolithic membrane via the tip of their kinocilium. Interest also laid in examining the contribution, if any, of adaptation to the response properties of utricular hair cells. Hair cells in auditory and vibratory inner ear endorgans adapt to maintained displacements of their hair bundles, sharply limiting their low frequency sensitivity. This adaptation is mediated by a shift in the displacement-response curve (DRC) of the hair cell along the displacement axis. Observations suggest that the adaptation process occurs within the hair bundle and precedes mechanoelectric transduction. Recent observations of time-dependent changes in hair bundle stiffness are consistent with this conclusion. Adaptation would be expected to be most useful in inner ear endorgans in which hair cells are subject to large static displacements that could potentially saturate their instantaneous response and compromise their sensitivity to high frequency stimulation. The adaptation process also permits hair cells to maintain their sensory hair bundle in the most sensitive portion of their DRC. In vestibular otolith organs in which static sensitivity is desirable, any adaptation process in the hair cells may be undesirable. The rate and extent of the decline of the voltage responses was measured of utricular hair cells to step and sinusoidal hair bundle displacements. Then for similar resting potentials and response amplitudes, the
3. Flexoelectricity in an oxadiazole bent-core nematic liquid crystal
Kaur, S., E-mail: [email protected]; Panov, V. P.; Gleeson, H. F. [School of Physics and Astronomy, University of Manchester, Manchester M13 9PL (United Kingdom); Greco, C.; Ferrarini, A. [Department of Chemical Sciences, University of Padua, Padua I-35131 (Italy); Görtz, V. [Department of Chemistry, University of York, York YO10 5DD (United Kingdom); Department of Chemistry, University of Lancaster, Lancaster LA1 4YB (United Kingdom); Goodby, J. W. [Department of Chemistry, University of York, York YO10 5DD (United Kingdom)
2014-12-01
We have determined experimentally the magnitude of the difference in the splay and bend flexoelectric coefficients, |e{sub 1} − e{sub 3}|, of an oxadiazole bent-core liquid crystal by measuring the critical voltage for the formation of flexodomains together with their wave number. The coefficient |e{sub 1} − e{sub 3}| is found to be a factor of 2–3 times higher than in most conventional calamitic nematic liquid crystals, varying from 8 pCm{sup −1} to 20 pCm{sup −1} across the ∼60 K—wide nematic regime. We have also calculated the individual flexoelectric coefficients e{sub 1} and e{sub 3}, with the dipolar and quadrupolar contributions of the bent-core liquid crystal by combining density functional theory calculations with a molecular field approach and atomistic modelling. Interestingly, the magnitude of the bend flexoelectric coefficient is found to be rather small, in contrast to common expectations for bent-core molecules. The calculations are in excellent agreement with the experimental values, offering an insight into how molecular parameters contribute to the flexoelectric coefficients and illustrating a huge potential for the prediction of flexoelectric behaviour in bent-core liquid crystals.
4. Analysis of smart nanobeams integrated with a flexoelectric nano actuator layer
Ray, M. C.
2016-05-01
This paper is concerned with the derivation of exact solutions for the static responses of simply supported nanobeams integrated with a flexoelectric layer acting as the distributed nano actuator. Considering both the direct and the converse flexoelectric effects, the governing equations and the associated boundary conditions of the overall beams are derived to obtain exact solutions for the displacements and the electric potential in the flexoelectric layer and the substrate beam. Due to the converse flexoelectric effect, the active flexoelectric layer significantly counteracts the deformations of the substrate beams caused by the applied mechanical load, resulting in the coupling of bending and stretching deformations in the substrate beams. For particular values of the length and thickness of the substrate beam and the applied voltage in the flexoelectric layer, the deflection of the substrate beam due to the converse flexoelectric effect increases with increasing thickness of the flexoelectric layer up to a certain value of the latter. Beyond this value, any further increase in the thickness of the flexoelectric layer causes a decrease in its ability to actuate the substrate beam. The electric potential varies linearly across the thickness of the flexoelectric layer. The benchmark results presented here may be useful for verifying further research and the present study suggests that the flexoelectric layer may be effectively exploited for advanced applications as a smart nano actuator.
5. Bundled procurement
Chen, Yongmin; Li, Jianpei
2015-01-01
When procuring multiple products from competing firms, a buyer may choose separate purchase, pure bundling, or mixed bundling. We show that pure bundling will generate higher buyer surplus than both separate purchase and mixed bundling, provided that trade for each good is likely to be efficient. Pure bundling is superior because it intensifies the competition between firms by reducing their cost asymmetry. Mixed bundling is inferior because it allows firms to coordinate to ...
6. Multilamellar structures and filament bundles are found on the cell surface during bunyavirus egress.
Laura Sanz-Sánchez
Full Text Available Inside cells, viruses build specialized compartments for replication and morphogenesis. We observed that virus release associates with specific structures found on the surface of mammalian cells. Cultured adherent cells were infected with a bunyavirus and processed for oriented sectioning and transmission electron microscopy. Imaging of cell basal regions showed sophisticated multilamellar structures (MLS and extracellular filament bundles with attached viruses. Correlative light and electron microscopy confirmed that both MLS and filaments proliferated during the maximum egress of new viruses. MLS dimensions and structure were reminiscent of those reported for the nanostructures on gecko fingertips, which are responsible for the extraordinary attachment capacity of these lizards. As infected cells with MLS were more resistant to detachment than control cells, we propose an adhesive function for these structures, which would compensate for the loss of adherence during release of new virus progeny.
7. Giant flexoelectric polarization in a micromachined ferroelectric diaphragm
Wang, Zhihong
2012-08-14
The coupling between dielectric polarization and strain gradient, known as flexoelectricity, becomes significantly large on the micro- and nanoscale. Here, it is shown that giant flexoelectric polarization can reverse remnant ferroelectric polarization in a bent Pb(Zr0.52Ti0.48) O3 (PZT) diaphragm fabricated by micromachining. The polarization induced by the strain gradient and the switching behaviors of the polarization in response to an external electric field are investigated by observing the electromechanical coupling of the diaphragm. The method allows determination of the absolute zero polarization state in a PZT film, which is impossible using other existing methods. Based on the observation of the absolute zero polarization state and the assumption that bending of the diaphragm is the only source of the self-polarization, the upper bound of flexoelectric coefficient of PZT film is calculated to be as large as 2.0 × 10-4 C m -1. The strain gradient induced by bending the diaphragm is measured to be on the order of 102 m-1, three orders of magnitude larger than that obtained in the bulk material. Because of this large strain gradient, the estimated giant flexoelectric polarization in the bent diaphragm is on the same order of magnitude as the normal remnant ferroelectric polarization of PZT film. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
8. X-rays Reveal the Internal Structure of Keratin Bundles in Whole Cells.
Hémonnot, Clément Y J; Reinhardt, Juliane; Saldanha, Oliva; Patommel, Jens; Graceffa, Rita; Weinhausen, Britta; Burghammer, Manfred; Schroer, Christian G; Köster, Sarah
2016-03-22
In recent years, X-ray imaging of biological cells has emerged as a complementary alternative to fluorescence and electron microscopy. Different techniques were established and successfully applied to macromolecular assemblies and structures in cells. However, while the resolution is reaching the nanometer scale, the dose is increasing. It is essential to develop strategies to overcome or reduce radiation damage. Here we approach this intrinsic problem by combing two different X-ray techniques, namely ptychography and nanodiffraction, in one experiment and on the same sample. We acquire low dose ptychography overview images of whole cells at a resolution of 65 nm. We subsequently record high-resolution nanodiffraction data from regions of interest. By comparing images from the two modalities, we can exclude strong effects of radiation damage on the specimen. From the diffraction data we retrieve quantitative structural information from intracellular bundles of keratin intermediate filaments such as a filament radius of 5 nm, hexagonal geometric arrangement with an interfilament distance of 14 nm and bundle diameters on the order of 70 nm. Thus, we present an appealing combined approach to answer a broad range of questions in soft-matter physics, biophysics and biology. PMID:26905642
9. Theoretical analysis of the influence of flexoelectric effect on the defect site in nematic inversion walls
Gui-Li, Zheng; Hui, Zhang; Wen-Jiang, Ye; Zhi-Dong, Zhang; Hong-Wei, Song; Li, Xuan
2016-03-01
Based on the experimental phenomena of flexoelectric response at defect sites in nematic inversion walls conducted by Kumar et al., we gave the theoretical analysis using the Frank elastic theory. When a direct-current electric field normal to the plane of the substrate is applied to the parallel aligned nematic liquid crystal cell with weak anchoring, the rotation of ±1 defects in the narrow inversion walls can be exhibited. The free energy of liquid crystal molecules around the +1 and -1 defect sites in the nematic inversion walls under the electric field was formulated and the electric-field-driven structural changes at the defect site characterized by polar and azimuthal angles of the local director were simulated. The results reveal that the deviation of azimuthal angle induced by flexoelectric effect are consistent with the switching of extinction brushes at the +1 and -1 defects obtained in the experiment conducted by Kumar et al. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374087, 11274088, and 11304074), the Natural Science Foundation of Hebei Province, China (Grant Nos. A2014202123 and A2016202282), the Research Project of Hebei Education Department, China (Grant Nos. QN2014130 and QN2015260), and the Key Subject Construction Project of Hebei Province University, China.
10. Flexoelectricity induced increase of critical thickness in epitaxial ferroelectric thin films
Flexoelectricity describes the coupling between polarization and strain/stress gradients in insulating crystals. In this paper, using the Landau-Ginsburg-Devonshire phenomenological approach, we found that flexoelectricity could increase the theoretical critical thickness in epitaxial BaTiO3 thin films, below which the switchable spontaneous polarization vanishes. This increase is remarkable in tensile films while trivial in compressive films due to the electrostriction caused decrease of potential barrier, which can be easily destroyed by the flexoelectricity, between the ferroelectric state and the paraelectric state in tensile films. In addition, the films are still in a uni-polar state even below the critical thickness due to the flexoelectric effect.
11. Most photorespiratory genes are preferentially expressed in the bundle sheath cells of the C4 grass Sorghum bicolor
Döring, Florian; Streubel, Monika; Bräutigam, Andrea; Gowik, Udo
2016-01-01
One of the hallmarks of C4 plants is the division of labor between two different photosynthetic cell types, the mesophyll and the bundle sheath cells. C4 plants are of polyphyletic origin and, during the evolution of C4 photosynthesis, the expression of thousands of genes was altered and many genes acquired a cell type-specific or preferential expression pattern. Several lines of evidence, including computational modeling and physiological and phylogenetic analyses, indicate that alterations in the expression of a key photorespiration-related gene, encoding the glycine decarboxylase P subunit, was an early and important step during C4 evolution. Restricting the expression of this gene to the bundle sheath led to the establishment of a photorespiratory CO2 pump. We were interested in whether the expression of genes related to photorespiration remains bundle sheath specific in a fully optimized C4 species. Therefore we analyzed the expression of photorespiratory and C4 cycle genes using RNA in situ hybridization and transcriptome analysis of isolated mesophyll and bundle sheath cells in the C4 grass Sorghum bicolor. It turns out that the C4 metabolism of Sorghum is based solely on the NADP-dependent malic enzyme pathway. The majority of photorespiratory gene expression, with some important exceptions, is restricted to the bundle sheath. PMID:26976818
12. Most photorespiratory genes are preferentially expressed in the bundle sheath cells of the C4 grass Sorghum bicolor.
Döring, Florian; Streubel, Monika; Bräutigam, Andrea; Gowik, Udo
2016-05-01
One of the hallmarks of C4 plants is the division of labor between two different photosynthetic cell types, the mesophyll and the bundle sheath cells. C4 plants are of polyphyletic origin and, during the evolution of C4 photosynthesis, the expression of thousands of genes was altered and many genes acquired a cell type-specific or preferential expression pattern. Several lines of evidence, including computational modeling and physiological and phylogenetic analyses, indicate that alterations in the expression of a key photorespiration-related gene, encoding the glycine decarboxylase P subunit, was an early and important step during C4 evolution. Restricting the expression of this gene to the bundle sheath led to the establishment of a photorespiratory CO2 pump. We were interested in whether the expression of genes related to photorespiration remains bundle sheath specific in a fully optimized C4 species. Therefore we analyzed the expression of photorespiratory and C4 cycle genes using RNA in situ hybridization and transcriptome analysis of isolated mesophyll and bundle sheath cells in the C4 grass Sorghum bicolor It turns out that the C4 metabolism of Sorghum is based solely on the NADP-dependent malic enzyme pathway. The majority of photorespiratory gene expression, with some important exceptions, is restricted to the bundle sheath. PMID:26976818
13. A case report of spindle cell myoepithelioma with extensive lipomatous metaplasia and thick collagen bundles in the submandibular gland.
Kwon, Mi Jung; Kim, Hye Jeong; Park, Bumjung; Cho, Seong Jin; Shin, Hyung Sik; Park, Hye-Rim; Min, Soo Kee; Seo, Jinwon; Min, Kyueng-Whan; Nam, Eun Sook
2016-09-01
Spindle cell myoepithelioma with extensive lipomatous metaplasia and thick collagen bundles has not yet been described, and there are no published reports on its cytological appearance in fine-needle aspiration (FNA). A 49-year-old man presented with a painless mass in the right submandibular area that had been gradually enlarging for a period of 5 years. The cytologic smears showed fascicles of cohesive spindle cells as well as individual bland cells with bipolar naked nuclei in a fibrillary background. Brightly eosinophilic bundles were intermingled with spindle cells and fat-like vacuoles. The FNA results were suggestive of neurogenic tumor. Patient underwent submandibular gland resection. Grossly, the cut surface showed a well-encapsulated, yellowish-white, soft, elastic mass, measuring 2.8 × 1.9 × 1.5 cm. The tumor consisted of uniform bland spindle cells arranged in short fascicles admixed with adipocyte-like cells and transversing thick collagen bundles, which demonstrated immunoreactivity for myoepithelial markers and ultrastructural features characteristic of myoepithelial cells, suggesting the presence of lipomatous metaplasia. The FNA cytology of spindle cell myoepithelioma with extensive lipometaplasia mimicked that of neurogenic tumor or lipomatous mesenchymal tumor. This case represents the first description of submandibular gland myoepithelioma with lipometaplasia, which is characterized by the coexistence of spindle cells, collagen bundles, and fat-like vacuoles in a fibrillary background. Diagn. Cytopathol. 2016;44:764-769. © 2016 Wiley Periodicals, Inc. PMID:27307392
14. The flexoelectric effect associated size dependent pyroelectricity in solid dielectrics
Bai, Gang, E-mail: [email protected] [Jiangsu Provincial Engineering Laboratory for RF Integration and Micropackaging and College of Electronic Science and Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023 (China); Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093 (China); Liu, Zhiguo [Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093 (China); Xie, Qiyun; Guo, Yanyan; Li, Wei [Jiangsu Provincial Engineering Laboratory for RF Integration and Micropackaging and College of Electronic Science and Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023 (China); Yan, Xiaobing [College of Electronic and information Engineering, Hebei University, Baoding 071002 (China)
2015-09-15
A phenomenological thermodynamic theory is used to investigate the effect of strain gradient on the pyroelectric effect in centrosymmetric dielectric solids. Direct pyroelectricity can exist as external mechanical stress is applied to non-pyroelectric dielectrics with shapes such as truncated pyramids, due to elastic strain gradient induced flexoelectric polarization. Effective pyroelectric coefficient was analyzed in truncated pyramids. It is found to be controlled by size, ambient temperature, stress, and aspect ratio and depends mainly on temperature sensitivity of flexoelectric coefficient (TSFC) and strain gradient of the truncated pyramids dielectric solids. These results show that the pyroelectric property of Ba{sub 0.67}Sr{sub 0.33}TiO{sub 3} above T{sub c} similar to PZT and other lead-based ferroelectrics can be obtained. This feature might widely broaden the selection of materials for infrared detectors with preferable properties.
15. The flexoelectric effect associated size dependent pyroelectricity in solid dielectrics
A phenomenological thermodynamic theory is used to investigate the effect of strain gradient on the pyroelectric effect in centrosymmetric dielectric solids. Direct pyroelectricity can exist as external mechanical stress is applied to non-pyroelectric dielectrics with shapes such as truncated pyramids, due to elastic strain gradient induced flexoelectric polarization. Effective pyroelectric coefficient was analyzed in truncated pyramids. It is found to be controlled by size, ambient temperature, stress, and aspect ratio and depends mainly on temperature sensitivity of flexoelectric coefficient (TSFC) and strain gradient of the truncated pyramids dielectric solids. These results show that the pyroelectric property of Ba0.67Sr0.33TiO3 above Tc similar to PZT and other lead-based ferroelectrics can be obtained. This feature might widely broaden the selection of materials for infrared detectors with preferable properties
16. Hair cell stereociliary bundle regeneration by espin gene transduction after aminoglycoside damage and hair cell induction by Notch inhibition.
Taura, A; Taura, K; Koyama, Y; Yamamoto, N; Nakagawa, T; Ito, J; Ryan, A F
2016-05-01
Once inner ear hair cells (HCs) are damaged by drugs, noise or aging, their apical structures including the stereociliary arrays are frequently the first cellular feature to be lost. Although this can be followed by progressive loss of HC somata, a significant number of HC bodies often remain even after stereociliary loss. However, in the absence of stereocilia they are nonfunctional. HCs can sometimes be regenerated by Atoh1 transduction or Notch inhibition, but they also may lack stereociliary bundles. It is therefore important to develop methods for the regeneration of stereocilia, in order to achieve HC functional recovery. Espin is an actin-bundling protein known to participate in sterociliary elongation during development. We evaluated stereociliary array regeneration in damaged vestibular sensory epithelia in tissue culture, using viral vector transduction of two espin isoforms. Utricular HCs were damaged with aminoglycosides. The utricles were then treated with a γ-secretase inhibitor, followed by espin or control transduction and histochemistry. Although γ-secretase inhibition increased the number of HCs, few had stereociliary arrays. In contrast, 46 h after espin1 transduction, a significant increase in hair-bundle-like structures was observed. These were confirmed to be immature stereociliary arrays by scanning electron microscopy. Increased uptake of FM1-43 uptake provided evidence of stereociliary function. Espin4 transduction had no effect. The results demonstrate that espin1 gene therapy can restore stereocilia on damaged or regenerated HCs. PMID:26886463
17. Bioinspired model of mechanical energy harvesting based on flexoelectric membranes.
Rey, Alejandro D; Servio, P; Herrera-Valencia, E E
2013-02-01
Membrane flexoelectricity is an electromechanical coupling process that describes membrane electrical polarization due to bending and membrane bending under electric fields. In this paper we propose, formulate, and characterize a mechanical energy harvesting system consisting of a deformable soft flexoelectric thin membrane subjected to harmonic forcing from contacting bulk fluids. The key elements of the energy harvester are formulated and characterized, including (i) the mechanical-to-electrical energy conversion efficiency, (ii) the electromechanical shape equation connecting fluid forces with membrane curvature and electric displacement, and (iii) the electric power generation and efficiency. The energy conversion efficiency is cast as the ratio of flexoelectric coupling to the product of electric and bending elasticity. The device is described by a second-order curvature dynamics coupled to the electric displacement equation and as such results in mechanical power absorption with a resonant peak whose amplitude decreases with bending viscosity. The electric power generation is proportional to the conversion factor and the power efficiency decreases with frequency. Under high bending viscosity, the power efficiency increases with the conversion factor and under low viscosities it decreases with the conversion factor. The theoretical results presented contribute to the ongoing experimental efforts to develop mechanical energy harvesting from fluid flow energy through solid-fluid interactions and electromechanical transduction. PMID:23496533
18. Comparative transduction mechanisms of hair cells in the bullfrog utriculus. II. Sensitivity and response dynamics to hair bundle displacement
Baird, R. A.
1994-01-01
1. Hair cells in whole-mount in vitro preparations of the utricular macula of the bullfrog (Rana catesbeiana) were selected according to their macular location and hair bundle morphology. The sensitivity and response dynamics of selected hair cells to natural stimulation were examined by recording their voltage responses to step and sinusoidal hair bundle displacements applied to their longest stereocilia. 2. The voltage responses of 31 hair cells to sinusoidal hair bundle displacements were characterized by their gains and phases, taken with respect to peak hair bundle displacement. The gains of Type B and Type C cells at both 0.5 and 5.0 Hz were markedly lower than those of Type F and Type E cells. Phases, with the exception of Type C cells, lagged hair bundle displacement at 0.5 Hz. Type C cells had phase leads of 25-40 degrees. At 5.0 Hz, response phases in all cells were phase lagged with respect to those at 0.5 Hz. Type C cells had larger gains and smaller phase leads at 5.0 Hz than at 0.5 Hz, suggesting the presence of low-frequency adaptation. 3. Displacement-response curves, derived from the voltage responses to 5.0-Hz sinusoids, were sigmoidal in shape and asymmetrical, with the depolarizing response having a greater magnitude and saturating less abruptly than the hyperpolarizing response. When normalized to their largest displacement the linear ranges of these curves varied from hair bundle to linear range and sensitivity were predicted from realistic models of utricular hair bundles created using morphological data obtained from light and electron microscopy. Three factors, including 1) the inverse ratio of the lengths of the kinocilium and longest stereocilia, representing the lever arm between kinociliary and stereociliary displacement; 2) tip link extension/linear displacement, largely a function of stereociliary height and separation; and 3) stereociliary number, an estimate of the number of transduction channels, were considered in this analysis
19. Comparative transduction mechanisms of hair cells in the bullfrog utriculus. II. Sensitivity and response dynamics to hair bundle displacement
Baird, R. A.
1994-01-01
1. Hair cells in whole-mount in vitro preparations of the utricular macula of the bullfrog (Rana catesbeiana) were selected according to their macular location and hair bundle morphology. The sensitivity and response dynamics of selected hair cells to natural stimulation were examined by recording their voltage responses to step and sinusoidal hair bundle displacements applied to their longest stereocilia. 2. The voltage responses of 31 hair cells to sinusoidal hair bundle displacements were characterized by their gains and phases, taken with respect to peak hair bundle displacement. The gains of Type B and Type C cells at both 0.5 and 5.0 Hz were markedly lower than those of Type F and Type E cells. Phases, with the exception of Type C cells, lagged hair bundle displacement at 0.5 Hz. Type C cells had phase leads of 25-40 degrees. At 5.0 Hz, response phases in all cells were phase lagged with respect to those at 0.5 Hz. Type C cells had larger gains and smaller phase leads at 5.0 Hz than at 0.5 Hz, suggesting the presence of low-frequency adaptation. 3. Displacement-response curves, derived from the voltage responses to 5.0-Hz sinusoids, were sigmoidal in shape and asymmetrical, with the depolarizing response having a greater magnitude and saturating less abruptly than the hyperpolarizing response. When normalized to their largest displacement the linear ranges of these curves varied from Sensitivity, defined as the slope of the normalized displacement-response curve, was inversely correlated with linear range. 4. The contribution of geometric factors associated with the hair bundle to linear range and sensitivity were predicted from realistic models of utricular hair bundles created using morphological data obtained from light and electron microscopy. Three factors, including 1) the inverse ratio of the lengths of the kinocilium and longest stereocilia, representing the lever arm between kinociliary and stereociliary displacement; 2) tip link extension
20. A nano-microstructured artificial-hair-cell-type sensor based on topologically graded 3D carbon nanotube bundles
Yilmazoglu, O.; Yadav, S.; Cicek, D.; Schneider, J. J.
2016-09-01
A design for a unique artificial-hair-cell-type sensor (AHCTS) based entirely on 3D-structured, vertically aligned carbon nanotube (CNT) bundles is introduced. Standard microfabrication techniques were used for the straightforward micro-nano integration of vertically aligned carbon nanotube arrays composed of low-layer multi-walled CNTs (two to six layers). The mechanical properties of the carbon nanotube bundles were intensively characterized with regard to various substrates and CNT morphology, e.g. bundle height. The CNT bundles display excellent flexibility and mechanical stability for lateral bending, showing high tear resistance. The integrated 3D CNT sensor can detect three-dimensional forces using the deflection or compression of a central CNT bundle which changes the contact resistance to the shorter neighboring bundles. The complete sensor system can be fabricated using a single chemical vapor deposition (CVD) process step. Moreover, sophisticated external contacts to the surroundings are not necessary for signal detection. No additional sensors or external bias for signal detection are required. This simplifies the miniaturization and the integration of these nanostructures for future microsystem set-ups. The new nanostructured sensor system exhibits an average sensitivity of 2100 ppm in the linear regime with the relative resistance change per micron (ppm μm‑1) of the individual CNT bundle tip deflection. Furthermore, experiments have shown highly sensitive piezoresistive behavior with an electrical resistance decrease of up to ∼11% at 50 μm mechanical deflection. The detection sensitivity is as low as 1 μm of deflection, and thus highly comparable with the tactile hair sensors of insects, having typical thresholds on the order of 30–50 μm. The AHCTS can easily be adapted and applied as a flow, tactile or acceleration sensor as well as a vibration sensor. Potential applications of the latter might come up in artificial cochlear systems. In
1. Arrangement of radial actin bundles in the growth cone of Aplysia bag cell neurons shows the immediate past history of filopodial behavior
Katoh, Kaoru; Hammar, Katherine; Peter J S Smith; Oldenbourg, Rudolf
1999-01-01
Filopodia that protrude forward from the lamellipodium, located at the leading edge of a neuronal growth cone, are needed to guide the extension of a nerve cell. At the core of each filopodium an actin bundle forms and grows into the lamellipodium. By using kymographs of time-lapse polarized light images we examined the relationship between the behavior of the filopodia, the actin bundles immediately proximal to the filopodia, and the shapes and composition of actin bundles in the whole lamel...
2. Determination of the flexoelectric coefficient (e1-e3) in nematic liquid crystal by using fully leaky optical-guided mode
Zheng, Guili; Zhang, Hui; Ye, Wenjiang; Zhang, Zhidong; Song, Hong-wei; Xuan, Li
2016-02-01
Fully leaky optical-guided mode was employed to determine the difference in the splay and bend flexoelectric coefficient (e1-e3) in negative nematic liquid crystal MS-N01300-000. The experimental curves of reflectivity versus internal angle (angle of incident light to the liquid crystal) were obtained when a laser beam passed through the hybrid-aligned nematic in-plane switching liquid crystal cell; the cell was embedded in pyramid-coupled waveguide with different alternating current (AC) and direct current (DC) voltages. The curves of the applied DC with voltage similar to that of AC shift to the left or the right. Experimental results were then compared with theoretical results derived from elastic continuum theory and multi-layer optical theory of liquid crystals. The approximate value of the flexoelectric coefficient (e1-e3) of MS-N01300-000 is 9.0 × 10-11 C/m.
3. Supramolecular assembly of biological molecules purified from bovine nerve cells: from microtubule bundles and necklaces to neurofilament networks
With the completion of the human genome project, the biosciences community is beginning the daunting task of understanding the structures and functions of a large number of interacting biological macromolecules. Examples include the interacting molecules involved in the process of DNA condensation during the cell cycle, and in the formation of bundles and networks of filamentous actin proteins in cell attachment, motility and cytokinesis. In this proceedings paper we present examples of supramolecular assembly based on proteins derived from the vertebrate nerve cell cytoskeleton. The axonal cytoskeleton in vertebrate neurons provides a rich example of bundles and networks of neurofilaments, microtubules (MTs) and filamentous actin, where the nature of the interactions, structures, and structure-function correlations remains poorly understood. We describe synchrotron x-ray diffraction, electron microscopy, and optical imaging data, in reconstituted protein systems purified from bovine central nervous system, which reveal unexpected structures not predicted by current electrostatic theories of polyelectrolyte bundling, including three-dimensional MT bundles and two-dimensional MT necklaces
4. Integrated Planar Solid Oxide Fuel Cell: Steady-State Model of a Bundle and Validation through Single Tube Experimental Data
Paola Costamagna
2015-11-01
Full Text Available This work focuses on a steady-state model developed for an integrated planar solid oxide fuel cell (IP-SOFC bundle. In this geometry, several single IP-SOFCs are deposited on a tube and electrically connected in series through interconnections. Then, several tubes are coupled to one another to form a full-sized bundle. A previously-developed and validated electrochemical model is the basis for the development of the tube model, taking into account in detail the presence of active cells, interconnections and dead areas. Mass and energy balance equations are written for the IP-SOFC tube, in the classical form adopted for chemical reactors. Based on the single tube model, a bundle model is developed. Model validation is presented based on single tube current-voltage (I-V experimental data obtained in a wide range of experimental conditions, i.e., at different temperatures and for different H2/CO/CO2/CH4/H2O/N2 mixtures as the fuel feedstock. The error of the simulation results versus I-V experimental data is less than 1% in most cases, and it grows to a value of 8% only in one case, which is discussed in detail. Finally, we report model predictions of the current density distribution and temperature distribution in a bundle, the latter being a key aspect in view of the mechanical integrity of the IP-SOFC structure.
5. Developmental regulation of planar cell polarity and hair-bundle morphogenesis in auditory hair cells: lessons from human and mouse genetics.
Lu, Xiaowei; Sipe, Conor W
2016-01-01
Hearing loss is the most common and costly sensory defect in humans and genetic causes underlie a significant proportion of affected individuals. In mammals, sound is detected by hair cells (HCs) housed in the cochlea of the inner ear, whose function depends on a highly specialized mechanotransduction organelle, the hair bundle. Understanding the factors that regulate the development and functional maturation of the hair bundle is crucial for understanding the pathophysiology of human deafness. Genetic analysis of deafness genes in animal models, together with complementary forward genetic screens and conditional knock-out mutations in essential genes, have provided great insights into the molecular machinery underpinning hair-bundle development and function. In this review, we highlight recent advances in our understanding of hair-bundle morphogenesis, with an emphasis on the molecular pathways governing hair-bundle polarity and orientation. We next discuss the proteins and structural elements important for hair-cell mechanotransduction as well as hair-bundle cohesion and maintenance. In addition, developmental signals thought to regulate tonotopic features of HCs are introduced. Finally, novel approaches that complement classic genetics for studying the molecular etiology of human deafness are presented. WIREs Dev Biol 2016, 5:85-101. doi: 10.1002/wdev.202 For further resources related to this article, please visit the WIREs website. PMID:26265594
6. Revisiting pyramid compression to quantify flexoelectricity: A three-dimensional simulation study
Abdollahi, Amir; Millán, Daniel; Peco, Christian; Arroyo, Marino; Arias, Irene
2015-03-01
Flexoelectricity is a universal property of all dielectrics by which they generate a voltage in response to an inhomogeneous deformation. One of the controversial issues in this field concerns the magnitude of flexoelectric coefficients measured experimentally, which greatly exceed theoretical estimates. Furthermore, there is a broad scatter amongst experimental measurements. The truncated pyramid compression method is one of the common setups to quantify flexoelectricity, the interpretation of which relies on simplified analytical equations to estimate strain gradients. However, the deformation fields in three-dimensional pyramid configurations are highly complex, particularly around its edges. In the present work, using three-dimensional self-consistent simulations of flexoelectricity, we show that the simplified analytical estimations of strain gradients in compressed pyramids significantly overestimate flexoelectric coefficients, thus providing a possible explanation to reconcile different estimates. In fact, the interpretation of pyramid compression experiments is highly nontrivial. We systematically characterize the magnitude of this overestimation, of over one order of magnitude, as a function of the truncated pyramid configuration. These results are important to properly characterize flexoelectricity, and provide design guidelines for effective electromechanical transducers exploiting flexoelectricity.
7. Cyst(e)ine is the transport metabolites of assimilated sulfur from bundle-sheath to mesophyll cells in maize leaves
The intercellular distribution of the enzymes and metabolites of assimilatory sulfate reduction and glutathione synthesis was analyzed in maize (Zea mays L. cv LG 9) leaves. Mesophyll cells and strands of bundle-sheath cells from second leaves of 11-d-old maize seedlings were obtained by two different mechanical-isolation methods. Cross-contamination of cell preparations was determined using ribulose bisphosphate carboxylase (EC 4.1.1.39) and nitrate reductase (EC 1.6.6.1) as marker enzymes for bundle-sheath and mesophyll cells, respectively. ATP sulfurylase (EC 2.7.7.4) and adenosine 5'-phosphosulfate sulfo transferase activities were detected almost exclusively in the bundle-sheath cells, whereas GSH synthetase (EC 6.3.2.3) and cyst(e)ine, gamma-glutamylcysteine, and glutathione were located predominantly in the mesophyll cells. Feeding experiments using [35S]sulfate with intact leaves indicated that cyst(e)ine was the transport metabolite of reduced sulfur from bundle-sheath to mesophyll cells. This result was corroborated by tracer experiments, which showed that isolated bundle-sheath strands fed with [35S]sulfate secreted radioactive cyst(e)ine as the sole thiol into the resuspending medium. The results presented in this paper show that assimilatory sulfate reduction is restricted to the bundle-sheath cells, whereas the formation of glutathione takes place predominantly in the mesophyll cells, with cyst(e)ine functioning as a transport metabolite between the two cell types
8. Activation of the pseudokinase MLKL unleashes the four-helix bundle domain to induce membrane localization and necroptotic cell death
Hildebrand, Joanne M.; Tanzer, Maria C; Lucet, Isabelle S; Young, Samuel N.; Spall, Sukhdeep K; Sharma, Pooja; Pierotti, Catia; Garnier, Jean-Marc; Dobson, Renwick C. J.; Andrew I Webb; Tripaydonis, Anne; Babon, Jeffrey J.; Mulcair, Mark D.; Scanlon, Martin J.; Alexander, Warren S
2014-01-01
The four-helix bundle (4HB) domain of Mixed Lineage Kinase Domain-Like (MLKL) bears two clusters of residues that are required for cell death by necroptosis. Mutations within a cluster centered on the α4 helix of the 4HB domain of MLKL prevented its membrane translocation, oligomerization, and ability to induce necroptosis. This cluster is composed principally of acidic residues and therefore challenges the idea that the 4HB domain engages negatively charged phospholipid membranes via a conve...
9. A Genome-wide RNAi Screen for Microtubule Bundle Formation and Lysosome Motility Regulation in Drosophila S2 Cells
Amber L. Jolly; Chi-Hao Luan; Brendon E. Dusel; Sara F. Dunne; Michael Winding; Vishrut J. Dixit; Chloe Robins; Jennifer L. Saluk; David J. Logan; Anne E. Carpenter; Manu Sharma; Deborah Dean; Andrew R. Cohen; Vladimir I. Gelfand
2016-01-01
Long-distance intracellular transport of organelles, mRNA, and proteins (“cargo”) occurs along the microtubule cytoskeleton by the action of kinesin and dynein motor proteins, but the vast network of factors involved in regulating intracellular cargo transport are still unknown. We capitalize on the Drosophila melanogaster S2 model cell system to monitor lysosome transport along microtubule bundles, which require enzymatically active kinesin-1 motor protein for their formation. We use an auto...
10. A genome-wide RNAi screen for microtubule bundle formation and lysosome motility regulation in Drosophila S2 cells
Jolly, Amber L.; Luan, Chi-Hao; Dusel, Brendon E.; Dunne, Sara Fernandez; Winding, Michael; Dixit, Vishrut J.; Robins, Chloe; Saluk, Jennifer L.; Logan, David J.; Carpenter, Anne E.; Sharma, Manu; Dean, Deborah; Cohen, Andrew R.; Gelfand, Vladimir I.
2016-01-01
Long-distance intracellular transport of organelles, mRNA, and proteins (“cargo”) occurs along the microtubule cytoskeleton by the action of kinesin and dynein motor proteins; the vast network of factors involved in regulating intracellular cargo transport are still unknown. We capitalize on the Drosophila melanogaster S2 model cell system to monitor lysosome transport along microtubule bundles, which require enzymatically active kinesin-1 motor protein for their formation. We use an automate...
11. Comment on “The limits of flexoelectricity in liquid crystals” [AIP Advances 1, 032120 (2011)
Palffy-Muhoray, P.
2013-01-01
In their paper, using the principle of energy conservation, F. Castles, S. M. Morris, and H. J. Coles [AIP Advances 1, 032120 (2011)]10.1063/1.3624725 establish inequalities involving the elastic and dielectric constants and flexoelectric coefficients of liquid crystals. They then argue that recently measured values of flexoelectric coefficients by Harden do not obey these inequalities, hence they violate the principle of energy conservation. In this comment, we point out that in their calcul...
12. Strong surface effect on direct bulk flexoelectric response in solids
Yurkov, A. S. [Ioffe Physical-Technical Institute, 26 Politekhnicheskaya, 194021 St. Petersburg (Russian Federation); Tagantsev, A. K. [Ceramics Laboratory, Swiss Federal Institute of Technology (EPFL), CH-1015 Lausanne (Switzerland); Ioffe Physical-Technical Institute, 26 Politekhnicheskaya, 194021 St. Petersburg (Russian Federation)
2016-01-11
In the framework of a continuum theory, it is shown that the direct bulk flexoelectric response of a finite sample essentially depends on the surface polarization energy, even in the thermodynamic limit where the body size tends to infinity. It is found that a modification of the surface energy can lead to a change in the polarization response by a factor of two. The origin of the effect is an electric field produced by surface dipoles induced by the strain gradient. The unexpected sensitivity of the polarization response to the surface energy in the thermodynamic limit is conditioned by the fact that the moments of the surface dipoles may scale as the body size.
13. Strong surface effect on direct bulk flexoelectric response in solids
In the framework of a continuum theory, it is shown that the direct bulk flexoelectric response of a finite sample essentially depends on the surface polarization energy, even in the thermodynamic limit where the body size tends to infinity. It is found that a modification of the surface energy can lead to a change in the polarization response by a factor of two. The origin of the effect is an electric field produced by surface dipoles induced by the strain gradient. The unexpected sensitivity of the polarization response to the surface energy in the thermodynamic limit is conditioned by the fact that the moments of the surface dipoles may scale as the body size
14. Zipping and Entanglement in Flagellar Bundle of E. Coli: Role of Motile Cell Body
2015-01-01
The course of a peritrichous bacterium such as E. coli crucially depends on the level of synchronization and self-organization of several rotating flagella. However, the rotation of each flagellum generates counter body movements which in turn affect the flagellar dynamics. Using a detailed numerical model of an E. coli, we demonstrate that flagellar entanglement, besides fluid flow relative to the moving body, dramatically changes the dynamics of flagella from that compared to anchored flagella. In particular, bundle formation occurs through a zipping motion in a remarkably rapid time, affected little by initial flagellar orientation. A simplified analytical model supports our observations. Finally, we illustrate how entanglement, hydrodynamic interactions, and body movement contribute to zipping and bundling.
15. Influences of surface and flexoelectric polarization on the effective anchoring energy in nematic liquid crystal
Guan, Rong-Hua; Ye, Wen-Jiang; Xing, Hong-Yu
2015-10-01
The physical effects on surface and flexoelectric polarization in a weak anchoring nematic liquid crystal cell are investigated systematically. We derive the analytic expressions of two effective anchoring energies for lower and upper substrates respectively as well as their effective anchoring strengths and corresponding tilt angles of effective easy direction. All of these quantities are relevant to the magnitudes of both two polarizations and the applied voltage U. Based on these expressions, the variations of effective anchoring strength and the tilt angle with the applied voltage are calculated for the fixed values of two polarizations. For an original weak anchoring hybrid aligned nematic cell, it may be equivalent to a planar cell for a small value of U and has a threshold voltage. The variation of reduced threshold voltage with reduced surface polarization strength is also calculated. The role of surface polarization is important without the adsorptive ions considered. Project supported by the National Natural Science Foundation of China (Grant Nos. 11274088, 11374087, and11304074), the Natural Science Foundation of Hebei Province, China (Grant No. A2014202123), the Research Project of Hebei Provincial Education Department, China (Grant No. QN2014130), and the Key Subject Construction Project of Hebei Provincial University, China.
16. Intranuclear bundles of microfilaments and microtubules in chromaffin cells of the auricle of the heart of a lungfish, Protopterus aethiopicus.
Scheuermann, D W; Adriaensen, D; De Groodt-Lasseel, M H
1988-01-01
Intranuclear microtubular-microfilamentous rod-like inclusions were investigated in chromaffin cells of the auricle of the heart of lungfishes. In conventional electron microscopy, these inclusions reveal a wide variety in appearance, depending on their orientation to the plane of sectioning. Whereas originally they were merely interpreted as a bundle of microfilaments, application of a goniometer stage showed the rod- or spindle-shaped intranuclear inclusions to have a basic substructure of parallel arranged microtubules among microfilaments, which are clearly connected to chromatin granules, occasionally penetrating dense areas of chromatin. The chemical nature and biological significance of these structures, which so far remain enigmatic, are discussed. PMID:3227775
17. Bundling biodiversity
Heal, Geoffrey
2002-01-01
Biodiversity provides essential services to human societies. Many of these services are provided as public goods, so that they will typically be underprovided both by market mechanisms (because of the impossibility of excluding non-payers from using the services) and by government-run systems (because of the free rider problem). I suggest here that in some cases the public goods provided by biodiversity conservation can be bundled with private goods and their value to consumers captured in th...
18. Thermal gradient induced flexoelectric effects in bulk Ba0.67Sr0.33TiO3
Kim, Taeyang; Huang, Wenbin; Huang, Shujin; Jiang, Xiaoning
2016-05-01
Flexoelectric effect, denoting electric field gradient induced mechanical strain or mechanical strain gradient induced electric polarization, is a universal phenomenon in all dielectrics. Although research on the topic of flexoelectricity under stress fields and electric fields has advanced significantly, information regarding the phenomenon under thermal fields is rather limited. In this letter, the flexoelectricity field of Ba0.67Sr0.33TiO3 (BST) was investigated by generating temperature gradients along the lengths of samples with symmetric geometry. An electric field gradient induced by a thermal gradient was analyzed based on the temperature-dependent dielectric property of BST. The strain was then experimentally verified due to the electric field gradient. Experimental results suggest converse flexoelectric effect of BST samples with symmetric geometry in a thermal field. This result was not only consistent with the theoretical prediction, but it also followed the scaling effect of flexoelectricity.
19. Temperature dependence of flexoelectric response in ferroelectric and relaxor polymer thin films
Poddar, Shashi; Ducharme, Stephen
2014-09-01
We report the temperature dependence of the flexoelectric response in thin films of both ferroelectric and relaxor forms of vinylidene fluoride polymers. The ferroelectric samples were depoled to minimize piezoelectric response by heating them beyond their Curie temperature and then cooling in zero applied electric field. In both the relaxor ferroelectric polymer and the paraelectric state of the ferroelectric copolymer, the flexoelectric coefficient was proportional to the dielectric constant over a limited range of temperatures, in agreement with general theoretical principles. The enhancements in flexoelectric response were also observed near the Curie transition temperature for the ferroelectric polymer and near the dielectric relaxation temperature for the relaxors. The broad dielectric anomaly in these systems provides greater temperature stability for these enhancements.
20. Nano-ZnO leads to tubulin macrotube assembly and actin bundling, triggering cytoskeletal catastrophe and cell necrosis
García-Hevia, Lorena; Valiente, Rafael; Martín-Rodríguez, Rosa; Renero-Lecuna, Carlos; González, Jesús; Rodríguez-Fernández, Lidia; Aguado, Fernando; Villegas, Juan C.; Fanarraga, Mónica L.
2016-05-01
Zinc is a crucial element in biology that plays chief catalytic, structural and protein regulatory roles. Excess cytoplasmic zinc is toxic to cells so there are cell-entry and intracellular buffering mechanisms that control intracellular zinc availability. Tubulin and actin are two zinc-scavenging proteins that are essential components of the cellular cytoskeleton implicated in cell division, migration and cellular architecture maintenance. Here we demonstrate how exposure to different ZnO nanostructures, namely ZnO commercial nanoparticles and custom-made ZnO nanowires, produce acute cytotoxic effects in human keratinocytes (HaCat) and epithelial cells (HeLa) triggering a dose-dependent cell retraction and collapse. We show how engulfed ZnO nanoparticles dissolve intracellularly, triggering actin filament bundling and structural changes in microtubules, transforming these highly dynamic 25 nm diameter polymers into rigid macrotubes of tubulin, severely affecting cell proliferation and survival. Our results demonstrate that nano-ZnO causes acute cytoskeletal collapse that triggers necrosis, followed by a late reactive oxygen species (ROS)-dependent apoptotic process.Zinc is a crucial element in biology that plays chief catalytic, structural and protein regulatory roles. Excess cytoplasmic zinc is toxic to cells so there are cell-entry and intracellular buffering mechanisms that control intracellular zinc availability. Tubulin and actin are two zinc-scavenging proteins that are essential components of the cellular cytoskeleton implicated in cell division, migration and cellular architecture maintenance. Here we demonstrate how exposure to different ZnO nanostructures, namely ZnO commercial nanoparticles and custom-made ZnO nanowires, produce acute cytotoxic effects in human keratinocytes (HaCat) and epithelial cells (HeLa) triggering a dose-dependent cell retraction and collapse. We show how engulfed ZnO nanoparticles dissolve intracellularly, triggering actin
1. Electro-elastic fields due to a point charge in a flexoelectric medium
Sharma, Rajdeep, E-mail: [email protected]
2015-10-01
Flexoelectricity provides a two-way connection between strain gradients and polarization that is pronounced at the nanoscale for isotropic materials which cannot link electromechanically via piezoelectricity. In this paper, the general equations for an isotropic, flexoelectric material were formulated, with contributions from strain gradients included. The electromechanical fields associated with a point charge in an infinite medium were derived, and results for GaAs were obtained. Our formulation yields two electromechanical length-scales, instead of one obtained from previous theories, and enables us to capture local fields accurately. Results from this paper provide insight into the electro-mechanical behavior of materials with charged defects.
2. Dynamics of flagellar bundling
Janssen, Pieter; Graham, Michael
2010-11-01
Flagella are long thin appendages of microscopic organisms used for propulsion in low-Reynolds environments. For E. coli the flagella are driven by a molecular motor, which rotates the flagella in a counter-clockwise motion (CCM). When in a forward swimming motion, all flagella bundle up. If a motor reverses rotation direction, the flagella unbundle and the cell makes a tumbling motion. When all motors turn in the same CC direction again, the flagella bundle up, and forward swimming continues. To investigate the bundling, we consider two flexible helices next to each other, as well as several flagella attached to a spherical body. Each helix is modeled as several prolate spheroids connected at the tips by springs. For hydrodynamic interactions, we consider the flagella to made up of point forces, while the finite size of the body is incorporated via Fax'en's laws. We show that synchronization occurs quickly relative to the bundling process. For flagella next to each other, the initial deflection is generated by rotlet interactions generated by the rotating helices. At longer times, simulations show the flagella only wrap once around each other, but only for flagella that are closer than about 4 helix radii. Finally, we show a run-and-tumble motion of the body with attached flagella.
3. Fuel bundle
This patent describes a method of forming a fuel bundle of a nuclear reactor. The method consists of positioning the fuel rods in the bottom plate, positioning the tie rod in the bottom plate with the key passed through the receptacle to the underside of the bottom plate and, after the tie rod is so positioned, turning the tie rod so that the key is in engagement with the underside of the bottom plate. Thereafter mounting the top plate is mounted in engagement with the fuel rods with the upper end of the tie rod extending through the opening in the top plate and extending above the top plate, and the tie rod is secured to the upper side of sid top plate thus simultaneously securing the key to the underside of the bottom plate
4. Determination of the flexoelectric coefficient (e1–e3 in nematic liquid crystal by using fully leaky optical-guided mode
Guili Zheng
2016-02-01
Full Text Available Fully leaky optical-guided mode was employed to determine the difference in the splay and bend flexoelectric coefficient (e1–e3 in negative nematic liquid crystal MS-N01300-000. The experimental curves of reflectivity versus internal angle (angle of incident light to the liquid crystal were obtained when a laser beam passed through the hybrid-aligned nematic in-plane switching liquid crystal cell; the cell was embedded in pyramid-coupled waveguide with different alternating current (AC and direct current (DC voltages. The curves of the applied DC with voltage similar to that of AC shift to the left or the right. Experimental results were then compared with theoretical results derived from elastic continuum theory and multi-layer optical theory of liquid crystals. The approximate value of the flexoelectric coefficient (e1–e3 of MS-N01300-000 is 9.0 × 10−11 C/m.
5. A conditional Orco requirement in the somatic cyst cells for maintaining spermatids in a tight bundle in Drosophila testis
Pankaj Dubey; Prakash Joti; Krishanu Ray
2016-06-01
Odorant receptors (OR) heterodimerizes with the OR co-receptor (Orco), forming specific odorant-gated cation channels, which are key to odor reception at the olfactory sensory neurons (OSN). Mammalian ORs are expressed in many other tissues, including testis. However, their biological implications are yet to be fully ascertained. In the mosquito, Orco is localized along the sperm tail and is indicated to maintain fidelity. Here, we show that orco expresses in Drosophila testis. The levels are higher in the somatic cyst cells. The orco-null mutants are perfectly fertile at 25°C. At 28°C, the coiled spermatid bundles are severely disrupted. The loss of Orco also disrupts the actin cap, which forms inside the head cyst cell at the rostral ends of the spermatid nuclei after coiling, and plays a key role in preventing the abnormal release of spermatids from the cyst enclosure. Both the defects are rescued by the somatic cyst cell-specific expression of the UAS-orco transgene. These results highlight a novel role of Orco in the somatic tissue during sperm release.
6. Antireflective coatings for multijunction solar cells under wide-angle ray bundles.
Victoria, Marta; Domínguez, César; Antón, Ignacio; Sala, Gabriel
2012-03-26
Two important aspects must be considered when optimizing antireflection coatings (ARCs) for multijunction solar cells to be used in concentrators: the angular light distribution over the cell created by the particular concentration system and the wide spectral bandwidth the solar cell is sensitive to. In this article, a numerical optimization procedure and its results are presented. The potential efficiency enhancement by means of ARC optimization is calculated for several concentrating PV systems. In addition, two methods for ARCs direct characterization are presented. The results of these show that real ARCs slightly underperform theoretical predictions. PMID:22453483
7. Experimental Investigations of Direct and Converse Flexoelectric Effect in Bilayer Lipid Membranes.
Todorov, Angelio Todorov
Flexoelectric coefficients (direct and converse), electric properties (capacitance and resistivity) and mechanical properties (thickness and elastic coefficients) have been determined for bilayer lipid membranes (BLMs) prepared from egg yolk lecithin (EYL), glycerol monoleate (GMO), phosphatidyl choline (PC) and phosphatidyl serine (PS) as a function of frequency, pH and surface charge modifiers. Direct flexoelectric effect manifested itself in the development of microvolt range a.c. potential (U_{f}) upon subjecting one side of a BLM to an oscillating hydrostatic pressure, in the 100-1000 Hz range. Operationally, the flexoelectric coefficient (f) is expressed by the ratio between U_{f} and the change of curvature (c) which accompanied the flexing of the membrane. Membrane curvature was determined by means of either the electric method (capacitance microphone effect) or by the newly developed method of stroboscopic interferometry. Real-time stroboscopic interferometry coupled with simultaneous electric measurements, provided a direct method for the determination of f. Two different frequency regimes of f were recognized. At low frequencies (GMO BLMs. At high frequencies (>300 Hz), associated with blocked mobility of the surfactant, f-values of 16.5 times 10^ {-19} and 0.30 times 10^{-19} Coulombs were obtained for PC and GMO BLMs. The theoretically calculated value for the GMO BLM oscillating at high frequency (0.12 times 10^{-19 } Coulombs) agreed well with that determined experimentally (0.3 times 10 ^{-19} Coulombs). For charged bovine brain PS BLM the observed flexocoefficient was f = 4.0 times 10^{ -18} Coulombs. Converse flexoelectric effect manifested itself in voltage-induced BLM curvature. Observations were carried out on uranyl acetate (UA) stabilized PS BLM under a.c. excitation. Frequency dependence of f was revealed by means of real-time stroboscopic interferometry. Satisfactory agreement was observed between the direct and converse f-values, measured
8. Strategic Aspects of Bundling
The increase of bundle supply has become widespread in several sectors (for instance in telecommunications and energy fields). This paper review relates strategic aspects of bundling. The main purpose of this paper is to analyze profitability of bundling strategies according to the degree of competition and the characteristics of goods. Moreover, bundling can be used as price discrimination tool, screening device or entry barriers. In monopoly case bundling strategy is efficient to sort consumers in different categories in order to capture a maximum of surplus. However, when competition increases, the profitability on bundling strategies depends on correlation of consumers' reservations values. (author)
9. Equivariant bundle gerbes
Murray, Michael K; Stevenson, Danny; Vozzo, Raymond F
2015-01-01
We develop the theory of simplicial extensions for bundle gerbes and their characteristic classes. This formalism is used to study descent problems and equivariance for bundle gerbes. We consider in detail two examples: the basic bundle gerbe on a unitary group and a string structure for a principal bundle. We show that the basic bundle gerbe is equivariant for the conjugation action and calculate its characteristic class and that a string structure gives rise to a bundle gerbe which is equivariant for a natural action of the String 2-group.
10. Sustained axon-glial signaling induces Schwann cell hyperproliferation, Remak bundle myelination, and tumorigenesis
Gómez-Sánchez, José A.; López de Armentia, Mikel; Luján, Rafael; Kessaris, Nicoletta; Richardson, William D.; Cabedo, Hugo
2009-01-01
Type III neuregulins exposed on axon surfaces control myelination of the peripheral nervous system. It has been shown, for example, that threshold levels of type IIIβ1a neuregulin dictate not only the myelination fate of axons but also myelin thickness. Here we show that another neuregulin isoform, type III-β3, plays a distinct role in myelination. Neuronal overexpression of this isoform in mice stimulates Schwann cell proliferation and dramatically enlarges peripheral nerves and ganglia -whi...
11. The Nanocrystal Superlattice Pressure Cell: A Novel Approach To Study Molecular Bundles under Uniaxial Compression
Bian, Kaifu; Singh, Arunima K.; Hennig, Richard G.; Wang, Zhongwu; Hanrath, Tobias
2014-01-01
Ordered assemblies of inorganic nanocrystals coated with organic linkers present interesting scientific challenges in hard and soft matter physics. We demonstrate that a nanocrystal superlattice under compression serves as a nanoscopic pressure cell to enable studies of molecular linkers under uniaxial compression. We developed a method to uniaxially compress the bifunctional organic linker by attaching both ends of aliphatic chains to neighboring PbS nanocrystals in a superlattice. Pressuriz...
12. A membrane bending model of outer hair cell electromotility.
Raphael, R. M.; Popel, A S; Brownell, W. E.
2000-01-01
We propose a new mechanism for outer hair cell electromotility based on electrically induced localized changes in the curvature of the plasma membrane (flexoelectricity). Electromechanical coupling in the cell's lateral wall is modeled in terms of linear constitutive equations for a flexoelectric membrane and then extended to nonlinear coupling based on the Langevin function. The Langevin function, which describes the fraction of dipoles aligned with an applied electric field, is shown to be ...
13. The nanocrystal superlattice pressure cell: a novel approach to study molecular bundles under uniaxial compression.
Bian, Kaifu; Singh, Arunima K; Hennig, Richard G; Wang, Zhongwu; Hanrath, Tobias
2014-08-13
Ordered assemblies of inorganic nanocrystals coated with organic linkers present interesting scientific challenges in hard and soft matter physics. We demonstrate that a nanocrystal superlattice under compression serves as a nanoscopic pressure cell to enable studies of molecular linkers under uniaxial compression. We developed a method to uniaxially compress the bifunctional organic linker by attaching both ends of aliphatic chains to neighboring PbS nanocrystals in a superlattice. Pressurizing the nanocrystal superlattice in a diamond anvil cell thus results in compression of the molecular linkers along their chain direction. Small-angle and wide-angle X-ray scattering during the compression provide insights into the structure of the superlattice and nanocrystal cores under compression, respectively. We compare density functional theory calculations of the molecular linkers as basic Hookean springs to the experimental force-distance relationship. We determine the density of linkers on the nanocrystal surfaces. We demonstrate our method to probe the elastic force of single molecule as a function of chain length. The methodology introduced in this paper opens doors to investigate molecular interactions within organic molecules compressed within a nanocrystal superlattice. PMID:25046038
14. Bundling in Telecommunications
Begoña García-Mariñoso; Xavier Martinez-Giralt; Pau Olivella
2008-01-01
The paper offers an overview of the literature on bundling in the telecommunications sector and its application in the Spanish market. We argue that the use of bundling in the provision of services is associated to technological reasons. Therefore, there appears no need to regulate bundling activities. However, this is not to say that other related telecom markets should not be scrutinized and regulated, or that the regulator should not pay attention to other bundling-related anticompetitive ...
15. Unified ab initio formulation of flexoelectricity and strain-gradient elasticity
Stengel, Massimiliano
2016-06-01
The theory of flexoelectricity and that of nonlocal elasticity are closely related, and are often considered together when modeling strain-gradient effects in solids. Here I show, based on a first-principles lattice-dynamical analysis, that their relationship is much more intimate than previously thought, and their consistent simultaneous treatment is crucial for obtaining correct physical answers. In particular, I identify a gauge invariance in the theory, whereby the energies associated to strain-gradient elasticity and flexoelectrically induced electric fields are individually reference dependent, and only when summed up they yield a well-defined result. To illustrate this, I construct a minimal thermodynamic functional incorporating strain-gradient effects, and establish a formal link between the continuum description and ab initio phonon dispersion curves to calculate the relevant tensor quantities. As a practical demonstration, I apply such a formalism to bulk SrTiO3, where I find an unusually strong contribution of nonlocal elasticity, mediated by the interaction between the ferroelectric soft mode and the transverse acoustic branches. These results have important implications towards the construction of well-defined thermodynamic theories where flexoelectricity and ferroelectricity coexist. More generally, they open exciting new avenues for the implementation of hierarchical multiscale concepts in the first-principles simulation of crystalline insulators.
16. Enhancement of Raman Light Scattering in Dye-Labeled Rat Glioma Cells by Langmuir-Blodgett CNT-Bundles Arranged on Metal-Containing Conducting Polymer Film
Egorov, A S; Grushevskaya, H V; Krot, V I; Krylova, N G; Lipnevich, I V; Orekhovskaya, T I; Shulitsky, B G
2015-01-01
We have fabricated layered nanocomposite consisting of a nanoporous anodic alumina sublayer (AOA), an ultrathin metal-containing polymer Langmuir-Blodgett (LB) film coating AOA, and multi-walled carbon nanotube (MCNT) - bundles which are arranged on the LB-film. MCNTs were preliminarily chemically modified by carboxyl groups and functionalized by stearic acid. We have experimentally observed an enhancement of Raman light scattering on surface plasmons in the LB-monolayers. This enhancement is due to charge and energy transfer. We demonstrate that propidium iodide (PI) fluorescence is quenched by the MCNT-bundles. A method of two-dimensional system imaging based on the MCNT-enhanced Raman spectroscopy has been proposed. This method has been applied to visualize focal adhesion sites on membranes of living PI-labeled rat glioma cells.
17. The actin-binding proteins eps8 and gelsolin have complementary roles in regulating the growth and stability of mechanosensory hair bundles of mammalian cochlear outer hair cells.
Jennifer Olt
Full Text Available Sound transduction depends upon mechanosensitive channels localized on the hair-like bundles that project from the apical surface of cochlear hair cells. Hair bundles show a stair-case structure composed of rows of stereocilia, and each stereocilium contains a core of tightly-packed and uniformly-polarized actin filaments. The growth and maintenance of the stereociliary actin core are dynamically regulated. Recently, it was shown that the actin-binding protein gelsolin is expressed in the stereocilia of outer hair cells (OHCs and in its absence they become long and straggly. Gelsolin is part of a whirlin scaffolding protein complex at the stereocilia tip, which has been shown to interact with other actin regulatory molecules such as Eps8. Here we investigated the physiological effects associated with the absence of gelsolin and its possible overlapping role with Eps8. We found that, in contrast to Eps8, gelsolin does not affect mechanoelectrical transduction during immature stages of development. Moreover, OHCs from gelsolin knockout mice were able to mature into fully functional sensory receptors as judged by the normal resting membrane potential and basolateral membrane currents. Mechanoelectrical transducer current in gelsolin-Eps8 double knockout mice showed a profile similar to that observed in the single mutants for Eps8. We propose that gelsolin has a non-overlapping role with Eps8. While Eps8 is mainly involved in the initial growth of stereocilia in both inner hair cells (IHCs and OHCs, gelsolin is required for the maintenance of mature hair bundles of low-frequency OHCs after the onset of hearing.
18. Bundling and Tying
Nicholas Economides
2014-01-01
We discuss strategic ways that sellers can use tying and bundling with requirement conditions to extract consumer surplus. We analyze different types of tying and bundling creating (i) intra-product price discrimination; (ii) intra-consumer price discrimination; and (iii) inter-product price discrimination, and assess the antitrust liability that these practices may entail. We also discuss the impact on consumers and competition, as well as potential antitrust liability of bundling “incontest...
19. Electrochemomechanics with flexoelectricity and modelling of electrochemical strain microscopy in mixed ionic-electronic conductors
Yu, Pengfei; Hu, Shuling; Shen, Shengping
2016-08-01
Recently, a new scanning probe microscopy approach, referred to as electrochemical strain microscopy (ESM), for probing local ionic flows and electrochemical reactions in solids based on the bias-strain coupling was proposed by Morozovska et al. Then, a series of theoretical papers for analyzing the image formation and spectroscopic mechanism of ESM were published within the framework of Fermi-Dirac statistics, the Vegard law, the direct flexoelectric coupling effect, the electrostriction effect, and so on. However, most of the models in these papers are limited to the partial coupling or particular process, and numerically solved by using decoupling approximation. In this paper, to model the ESM measurement with the coupling electrical-chemical-mechanical process, the chemical Gibbs function variational principle for the thermal electrical chemical mechanical fully coupling problem is proposed. The fully coupling governing equations are derived from the variational principle. When the tip concentrates the electric field within a small volume of the material, the inhomogeneous electric field is induced. So, both direct and inverse flexoelectric effects should be taken into account. Here, the bulk defect electrochemical reactions are also taken into account, which are usually omitted in the existing works. This theory can be used to deal with coupling problems in solids, including conductors, semiconductors, and piezoelectric and non-piezoelectric dielectrics. As an application of this work, a developed initial-boundary value problem is solved numerically in a mixed ion-electronic conductor. Numerical results show that it is meaningful and necessary to consider the bulk defect chemical reaction. Besides, the chemical reaction and the flexoelectric effect have an interactive influence on each other. This work can provide theoretical basis for the ESM as well as investigating the bulk chemical reaction process in solids.
20. Flexoelectric coefficient measurements in the nematic liquid crystal phase of 5CB
F. Castles
2012-06-01
Full Text Available We report measurements of the bulk flexoelectric coefficient (e1 − e3 of 5CB (4-Cyano-4′-pentylbiphenyl, in the temperature range 20–34 °C, with a relative combined standard uncertainty of 2 %. The chiral flexoelectro-optic method was used with 1 wt % high-twisting-power chiral additive. At 25 °C, (e1 − e3 = 7.10 pC/m with a combined standard uncertainty of 0.14 pC/m.
1. Contact fiber bundles
Lerman, Eugene
2003-01-01
We define contact fiber bundles and investigate conditions for the existence of contact structures on the total space of such a bundle. The results are analogous to minimal coupling in symplectic geometry. The two applications are construction of K-contact manifolds generalizing Yamazaki's fiber join construction and a cross-section theorem for contact moment maps
2. Principal noncommutative torus bundles
Echterhoff, Siegfried; Nest, Ryszard; Oyono-Oyono, Herve
2008-01-01
of bivariant K-theory (denoted RKK-theory) due to Kasparov. Using earlier results of Echterhoff and Williams, we shall give a complete classification of principal non-commutative torus bundles up to equivariant Morita equivalence. We then study these bundles as topological fibrations (forgetting the...
3. Multiwalled carbon nanotube reinforced biomimetic bundled gel fibres.
Kim, Young-Jin; Yamamoto, Seiichiro; Takahashi, Haruko; Sasaki, Naruo; Matsunaga, Yukiko T
2016-08-19
This work describes the fabrication and characterization of hydroxypropyl cellulose (HPC)-based biomimetic bundled gel fibres. The bundled gel fibres were reinforced with multiwalled carbon nanotubes (MWCNTs). A phase-separated aqueous solution with MWCNT and HPC was transformed into a bundled fibrous structure after being injected into a co-flow microfluidic device and applying the sheath flow. The resulting MWCNT-bundled gel fibres consist of multiple parallel microfibres. The mechanical and electrical properties of MWCNT-bundled gel fibres were improved and their potential for tissue engineering applications as a cell scaffold was demonstrated. PMID:27200527
4. Restrictions of stable bundles
Balaji, V
2011-01-01
The Mehta-Ramanathan theorem ensures that the restriction of a stable vector bundle to a sufficiently high degree complete intersection curve is again stable. We improve the bounds for the "sufficiently high degree" and propose a possibly optimal conjecture.
5. candu fuel bundle fabrication
This paper describes works on CANDU fuel bundle fabrication in the Fuel Fabrication Development and Testing Section (FFDT) of AECL's Chalk River Laboratories. This work does not cover fuel design, pellet manufacturing, Zircaloy material manufacturing, but cover the joining of appendages to sheath tube, endcap preparation and welding, UO2 loading, end plate preparation and welding, and all inspections required in these steps. Materials used in the fabrication of CANDU fuel bundle are: 1)Ceramic UO2 Pellet 2)Zircaloy -4. Fuel Bundle Structural Material 3) Others (Zinc stearate, Colloidal graphite, Beryllium and Heium). Th fabrication of fuel element consist of three process: 1)pellet loading into the sheats, 2) endcap welding, and 3) the element profiling. Endcap welds is tested by metallography and He leak test. The endcaps of the elements are welded to the end plates to form the 37- element bundle assembly
6. Amplitude death of coupled hair bundles with stochastic channel noise
Kim, Kyung-Joong
2014-01-01
Hair cells conduct auditory transduction in vertebrates. In lower vertebrates such as frogs and turtles, due to the active mechanism in hair cells, hair bundles(stereocilia) can be spontaneously oscillating or quiescent. Recently, the amplitude death phenomenon has been proposed [K.-H. Ahn, J. R. Soc. Interface, {\\bf 10}, 20130525 (2013)] as a mechanism for auditory transduction in frog hair-cell bundles, where sudden cessation of the oscillations arises due to the coupling between non-identical hair bundles. The gating of the ion channel is intrinsically stochastic due to the stochastic nature of the configuration change of the channel. The strength of the noise due to the channel gating can be comparable to the thermal Brownian noise of hair bundles. Thus, we perform stochastic simulations of the elastically coupled hair bundles. In spite of stray noisy fluctuations due to its stochastic dynamics, our simulation shows the transition from collective oscillation to amplitude death as inter-bundle coupling str...
7. Subtleties Concerning Conformal Tractor Bundles
Graham, C Robin
2012-01-01
The realization of tractor bundles as associated bundles in conformal geometry is studied. It is shown that different natural choices of principal bundle with normal Cartan connection corresponding to a given conformal manifold can give rise to topologically distinct associated tractor bundles for the same inducing representation. Consequences for homogeneous models and conformal holonomy are described. A careful presentation is made of background material concerning standard tractor bundles and equivalence between parabolic geometries and underlying structures.
8. Evidence for a Role for NAD(P)H Dehydrogenase in Concentration of CO2 in the Bundle Sheath Cell of Zea mays.
Peterson, Richard B; Schultes, Neil P; McHale, Neil A; Zelitch, Israel
2016-05-01
Prior studies with Nicotiana and Arabidopsis described failed assembly of the chloroplastic NDH [NAD(P)H dehydrogenase] supercomplex by serial mutation of several subunit genes. We examined the properties of Zea mays leaves containing Mu and Ds insertions into nuclear gene exons encoding the critical o- and n-subunits of NDH, respectively. In vivo reduction of plastoquinone in the dark was sharply diminished in maize homozygous mutant compared to normal leaves but not to the extreme degree observed for the corresponding lesions in Arabidopsis. The net carbon assimilation rate (A) at high irradiance and saturating CO2 levels was reduced by one-half due to NDH mutation in maize although no genotypic effect was evident at very low CO2 levels. Simultaneous assessment of chlorophyll fluorescence and A in maize at low (2% by volume) and high (21%) O2 levels indicated the presence of a small, yet detectable, O2-dependent component of total linear photosynthetic electron transport in 21% O2 This O2-dependent component decreased with increasing CO2 level indicative of photorespiration. Photorespiration was generally elevated in maize mutant compared to normal leaves. Quantification of the proportion of total electron transport supporting photorespiration enabled estimation of the bundle sheath cell CO2 concentration (Cb) using a simple kinetic model of ribulose bisphosphate carboxylase/oxygenase function. The A versus Cb relationships overlapped for normal and mutant lines consistent with occurrence of strictly CO2-limited photosynthesis in the mutant bundle sheath cell. The results are discussed in terms of a previously reported CO2 concentration model [Laisk A, Edwards GE (2000) Photosynth Res 66: 199-224]. PMID:27002061
9. Evidence for a Role for NAD(P)H Dehydrogenase in Concentration of CO2 in the Bundle Sheath Cell of Zea mays1[OPEN
Schultes, Neil P.; McHale, Neil A.; Zelitch, Israel
2016-01-01
Prior studies with Nicotiana and Arabidopsis described failed assembly of the chloroplastic NDH [NAD(P)H dehydrogenase] supercomplex by serial mutation of several subunit genes. We examined the properties of Zea mays leaves containing Mu and Ds insertions into nuclear gene exons encoding the critical o- and n-subunits of NDH, respectively. In vivo reduction of plastoquinone in the dark was sharply diminished in maize homozygous mutant compared to normal leaves but not to the extreme degree observed for the corresponding lesions in Arabidopsis. The net carbon assimilation rate (A) at high irradiance and saturating CO2 levels was reduced by one-half due to NDH mutation in maize although no genotypic effect was evident at very low CO2 levels. Simultaneous assessment of chlorophyll fluorescence and A in maize at low (2% by volume) and high (21%) O2 levels indicated the presence of a small, yet detectable, O2-dependent component of total linear photosynthetic electron transport in 21% O2. This O2-dependent component decreased with increasing CO2 level indicative of photorespiration. Photorespiration was generally elevated in maize mutant compared to normal leaves. Quantification of the proportion of total electron transport supporting photorespiration enabled estimation of the bundle sheath cell CO2 concentration (Cb) using a simple kinetic model of ribulose bisphosphate carboxylase/oxygenase function. The A versus Cb relationships overlapped for normal and mutant lines consistent with occurrence of strictly CO2-limited photosynthesis in the mutant bundle sheath cell. The results are discussed in terms of a previously reported CO2 concentration model [Laisk A, Edwards GE (2000) Photosynth Res 66: 199–224]. PMID:27002061
10. Energy Minimization for Liquid Crystal Equilibrium with Electric and Flexoelectric Effects
Adler, J H; Benson, T R; Emerson, D B; MacLachlan, S P
2014-01-01
This paper outlines an energy-minimization finite-element approach to the modeling of equilibrium configurations for nematic liquid crystals in the presence of internal and external electric fields. The method targets minimization of system free energy based on the electrically and flexoelectrically augmented Frank-Oseen free energy models. The Hessian, resulting from the linearization of the first-order optimality conditions, is shown to be invertible for both models when discretized by a mixed finite-element method under certain assumptions. This implies that the intermediate discrete linearizations are well-posed. A coupled multigrid solver with Vanka-type relaxation is proposed and numerically vetted for approximation of the solution to the linear systems arising in the linearizations. Two electric model numerical experiments are performed with the proposed iterative solver. The first compares the algorithm's solution of a classical Freedericksz transition problem to the known analytical solution and demo...
11. Variational principles and governing equations in nano-dielectrics with the flexoelectric effect
2010-01-01
The flexoelectric effect is very strong and coupled with large strain gradients for nanoscale dielectrics. At the nanoscale, the electrostatic force cannot be ignored. In this paper, we have established the electric enthalpy variational principle for nanosized dielectrics with the strain gradient and the polarization gradient effect, as well as the effect of the electrostatic force. The complete governing equations, which include the effect of the electrostatic force, are derived from this variational principle, and based on the principle the generalized electrostatic stress is obtained, the generalized electrostatic stress contains the Maxwell stress corresponding to the polarization and strain, and stress related to the polarization gradient and strain gradient. This work provides the basis for the analysis and computations for the electromechanical problems in nanosized dielectric materials.
12. Mechanism of Actin Filament Bundling by Fascin
Jansen, Silvia; Collins, Agnieszka; Yang, Changsong; Rebowski, Grzegorz; Svitkina, Tatyana; Dominguez, Roberto (UPENN); (UPENN-MED)
2013-03-07
Fascin is the main actin filament bundling protein in filopodia. Because of the important role filopodia play in cell migration, fascin is emerging as a major target for cancer drug discovery. However, an understanding of the mechanism of bundle formation by fascin is critically lacking. Fascin consists of four {beta}-trefoil domains. Here, we show that fascin contains two major actin-binding sites, coinciding with regions of high sequence conservation in {beta}-trefoil domains 1 and 3. The site in {beta}-trefoil-1 is located near the binding site of the fascin inhibitor macroketone and comprises residue Ser-39, whose phosphorylation by protein kinase C down-regulates actin bundling and formation of filopodia. The site in {beta}-trefoil-3 is related by pseudo-2-fold symmetry to that in {beta}-trefoil-1. The two sites are {approx}5 nm apart, resulting in a distance between actin filaments in the bundle of {approx}8.1 nm. Residue mutations in both sites disrupt bundle formation in vitro as assessed by co-sedimentation with actin and electron microscopy and severely impair formation of filopodia in cells as determined by rescue experiments in fascin-depleted cells. Mutations of other areas of the fascin surface also affect actin bundling and formation of filopodia albeit to a lesser extent, suggesting that, in addition to the two major actin-binding sites, fascin makes secondary contacts with other filaments in the bundle. In a high resolution crystal structure of fascin, molecules of glycerol and polyethylene glycol are bound in pockets located within the two major actin-binding sites. These molecules could guide the rational design of new anticancer fascin inhibitors.
13. Dark-field illuminated reflectance fiber bundle endoscopic microscope
Liu, Xuan; Huang, Yong; Kang, Jin U.
2011-01-01
We propose a reflectance fiber bundle microscope using a dark-field illumination configuration for applications in endoscopic medical imaging and diagnostics. Our experiment results show that dark-field illumination can effectively suppress strong specular reflection from the proximal end of the fiber bundle. We realized a lateral resolution of 4.4 μm using the dark-field illuminated fiber bundle configuration. To demonstrate the feasibility of using the system to study cell morphology, we ob...
14. Right bundle branch block
Bussink, Barbara E; Holst, Anders Gaarsdal; Jespersen, Lasse;
2013-01-01
AimsTo determine the prevalence, predictors of newly acquired, and the prognostic value of right bundle branch block (RBBB) and incomplete RBBB (IRBBB) on a resting 12-lead electrocardiogram in men and women from the general population.Methods and resultsWe followed 18 441 participants included in...... men vs. 0.5%/2.3% in women, P <0.001). Significant predictors of newly acquired RBBB were male gender, increasing age, high systolic blood pressure, and presence of IRBBB, whereas predictors of newly acquired IRBBB were male gender, increasing age, and low BMI. Right bundle branch block was associated...... with significantly increased all-cause and cardiovascular mortality in both genders with age-adjusted hazard ratios (HR) of 1.31 [95% confidence interval (CI), 1.11-1.54] and 1.87 (95% CI, 1.48-2.36) in the gender pooled analysis with little attenuation after multiple adjustment. Right bundle branch...
15. Principal -bundles on Nodal Curves
Usha N Bhosle
2001-08-01
Let be a connected semisimple affine algebraic group defined over . We study the relation between stable, semistable -bundles on a nodal curve and representations of the fundamental group of . This study is done by extending the notion of (generalized) parabolic vector bundles to principal -bundles on the desingularization of and using the correspondence between them and principal -bundles on . We give an isomorphism of the stack of generalized parabolic bundles on with a quotient stack associated to loop groups. We show that if is simple and simply connected then the Picard group of the stack of principal -bundles on is isomorphic to ⊕ , being the number of components of .
16. Hybrid bundle divertor design
A hybrid bundle divertor design is presented that produces <0.3% magnetic ripple at the center of the plasma while providing adequate space for the coil shielding and structure for a tokamak fusion test reactor similar to the International Tokamak Reactor and the Engineering Test Facility (with R = 5 m, B = 5 T, and a /SUB wall/ = 1.5 m, in particular). This hybrid divertor consists of a set of quadrupole ''wing'' coils running tangent to the tokamak plasma on either side of a bundle divertor. The wing coils by themselves pull the edge of the plasma out 1.5 m and spread the thickness of the scrape-off layer from 0.1 to 0.7 m at the midplane. The clear aperture of the bundle divertor throat is 1.0 m high and 1.8 m wide. For maintenance or replacement, the hybrid divertor can be disassembled into three parts, with the bundle divertor part pulling straight out between toroidal field coils and the wing coils then sliding out through the same opening
17. On framed quantum principal bundles
Durdevic, M
1995-01-01
A noncommutative-geometric formalism of framed principal bundles is sketched, in a special case of quantum bundles (over quantum spaces) possessing classical structure groups. Quantum counterparts of torsion operators and Levi-Civita type connections are analyzed. A construction of a natural differential calculus on framed bundles is described. Illustrative examples are presented.
18. Bundling in semiflexible polymers: A theoretical overview.
Benetatos, Panayotis; Jho, YongSeok
2016-06-01
Supramolecular assemblies of polymers are key modules to sustain the structure of cells and their function. The main elements of these assemblies are charged semiflexible polymers (polyelectrolytes) generally interacting via a long(er)-range repulsion and a short(er)-range attraction. The most common supramolecular structure formed by these polymers is the bundle. In the present paper, we critically review some recent theoretical and computational advances on the problem of bundle formation, and point a few promising directions for future work. PMID:26813628
19. Bundles of Banach algebras
D. A. Robbins
1994-12-01
Full Text Available We study bundles of Banach algebras À:A→X, where each fiber Ax=À−1({x} is a Banach algebra and X is a compact Hausdorff space. In the case where all fibers are commutative, we investigate how the Gelfand representation of the section space algebra Γ(À relates to the Gelfand representation of the fibers. In the general case, we investigate how adjoining an identity to the bundle À:A→X relates to the standard adjunction of identities to the fibers.
20. Helices and vector bundles
Rudakov, A N
1990-01-01
This volume is devoted to the use of helices as a method for studying exceptional vector bundles, an important and natural concept in algebraic geometry. The work arises out of a series of seminars organised in Moscow by A. N. Rudakov. The first article sets up the general machinery, and later ones explore its use in various contexts. As to be expected, the approach is concrete; the theory is considered for quadrics, ruled surfaces, K3 surfaces and P3(C).
1. Bundled monocapillary optics
Hirsch, Gregory
2002-01-01
A plurality of glass or metal wires are precisely etched to form the desired shape of the individual channels of the final polycapillary optic. This shape is created by carefully controlling the withdrawal speed of a group of wires from an etchant bath. The etched wires undergo a subsequent operation to create an extremely smooth surface. This surface is coated with a layer of material which is selected to maximize the reflectivity of the radiation being used. This reflective surface may be a single layer of material, or a multilayer coating for optimizing the reflectivity in a narrower wavelength interval. The collection of individual wires is assembled into a close-packed multi-wire bundle, and the wires are bonded together in a manner which preserves the close-pack configuration, irrespective of the local wire diameter. The initial wires are then removed by either a chemical etching procedure or mechanical force. In the case of chemical etching, the bundle is generally segmented by cutting a series of etching slots. Prior to removing the wire, the capillary array is typically bonded to a support substrate. The result of the process is a bundle of precisely oriented radiation-reflecting hollow channels. The capillary optic is used for efficiently collecting and redirecting the radiation from a source of radiation which could be the anode of an x-ray tube, a plasma source, the fluorescent radiation from an electron microprobe, a synchrotron radiation source, a reactor or spallation source of neutrons, or some other source.
2. Bundling harvester; Nippukorjausharvesteri
Koponen, K. [Eko-Log Oy, Kuopio (Finland)
1996-12-31
The staring point of the project was to design and construct, by taking the silvicultural point of view into account, a harvesting and processing system especially for energy-wood, containing manually driven bundling harvester, automatizing of the harvester, and automatized loading. The equipment forms an ideal method for entrepreneurs-line harvesting. The target is to apply the system also for owners-line harvesting. The profitability of the system promotes the utilization of the system in both cases. The objectives of the project were: to construct a test equipment and prototypes for all the project stages, to carry out terrain and strain tests in order to examine the usability and durability, as well as the capacity of the machine, to test the applicability of the Eko-Log system in simultaneous harvesting of energy and pulp woods, and to start the marketing and manufacturing of the products. The basic problems of the construction of the bundling harvester have been solved using terrain-tests. The prototype machine has been shown to be operable. Loading of the bundles to form sufficiently economically transportable loads has been studied, and simultaneously, the branch-biomass has been tried to be utilized without loosing the profitability of transportation. The results have been promising, and will promote the profitable utilization of wood-energy
3. Kernel Bundle EPDiff
Sommer, Stefan Horst; Lauze, Francois Bernard; Nielsen, Mads; Pennec, Xavier
information to be automatically incorporated in registrations and promises to improve the standard framework in several aspects. We present the mathematical foundations of LDDKBM and derive the KB-EPDiff evolution equations, which provide optimal warps in this new framework. To illustrate the resulting......In the LDDMM framework, optimal warps for image registration are found as end-points of critical paths for an energy functional, and the EPDiff equations describe the evolution along such paths. The Large Deformation Diffeomorphic Kernel Bundle Mapping (LDDKBM) extension of LDDMM allows scale space...... diffeomorphism paths, we give examples showing the decoupled evolution across scales and how the method automatically incorporates deforma- tion at appropriate scales....
4. Twists of symmetric bundles
Cassou-Nogues, Ph.; Erez, B.; Taylor, M. J.
2004-01-01
We establish comparison results between the Hasse-Witt invariants w_t(E) of a symmetric bundle E over a scheme and the invariants of one of its twists E_{\\alpha}. For general twists we describe the difference between w_t(E) and w_t(E_{\\alpha}) up to terms of degree 3. Next we consider a special kind of twist, which has been studied by A. Fr\\"ohlich. This arises from twisting by a cocycle obtained from an orthogonal representation. We show how to explicitly describe the twist for representatio...
5. Piezoelectricity above the Curie temperature? Combining flexoelectricity and functional grading to enable high-temperature electromechanical coupling
Most technologically relevant ferroelectrics typically lose piezoelectricity above the Curie temperature. This limits their use to relatively low temperatures. In this Letter, exploiting a combination of flexoelectricity and simple functional grading, we propose a strategy for high-temperature electromechanical coupling in a standard thin film configuration. We use continuum modeling to quantitatively demonstrate the possibility of achieving apparent piezoelectric materials with large and temperature-stable electromechanical coupling across a wide temperature range that extends significantly above the Curie temperature. With Barium and Strontium Titanate, as example materials, a significant electromechanical coupling that is potentially temperature-stable up to 900 °C is possible
6. REBEKA bundle experiments
This report is a summary of experimental investigations describing the fuel rod behavior in the refilling and reflooding phase of a loss-of-coolant accident of a PWR. The experiments were performed with 5x5 and 7x7 rod bundles, using indirectly electrically heated fuel rod simulators of full length with original PWR-KWU-geometry, original grid spacers and Zircaloy-4-claddings (Type Biblis B). The fuel rod simulators showed a cosine shaped axial power profile in 7 steps and continuous, respectively. The results describe the influence of the different parameters such as bundle size on the maximum coolant channel blockage, that of the cooling on the size of the circumferential strain of the cladding (azimuthal temperature distribution) a cold control rod guide thimble and the flow direction (axial temperature distribution) on the resulting coolant channel blockage. The rewetting behavior of different fuel rod simulators including ballooned and burst Zircaloy claddings is discussed as well as the influence of thermocouples on the cladding temperature history and the rewetting behavior. All results prove the coolability of a PWR in the case of a LOCA. Therefore, it can be concluded that the ECC-criteria established by licensing authorities can be fulfilled. (orig./HP)
7. Design and fabrication of a remote fuel bundle welding system
A remote fuel bundle welding system in the hot-cell was designed and fabricated. To achieve this, a preliminary investigation of a hands-on fuel fabrication outside the hot-cell was conducted with a consideration of the constraints caused by welding in the hot-cell. Some basic experiments were also carried out to improve the end-plate welding process for fuel bundle manufacturing. The resistance welding system using the end-plate welding was also improved. It was found that resistance welding was more suitable for joining and end-plate to end caps in the hot-cell. The optimum conditions for end-plate welding for remote operation were also obtained. Preliminary performances to improve the resistance welding process were also examined, and the resistance welding process was determined to be the best in the hot-cell environment for fuel bundle manufacturing. The greatest advantage of fuel bundle welding system would be a qualified process for resistance welding in which there is extensive production experience. This paper presents an outline of the developed welding system for fuel bundle manufacturing and reviews the conceptual design of remote welding system using a master-slave manipulator. The design of a remote welding system using the 3-dimensional modeling method was also designed. Furthermore the mechanical considerations and the mock-up simulation test were described. Finally, its performance test results were presented for a mock-up of a remote fuel bundle welding system. (Author)
8. Bundle Security Protocol for ION
Burleigh, Scott C.; Birrane, Edward J.; Krupiarz, Christopher
2011-01-01
This software implements bundle authentication, conforming to the Delay-Tolerant Networking (DTN) Internet Draft on Bundle Security Protocol (BSP), for the Interplanetary Overlay Network (ION) implementation of DTN. This is the only implementation of BSP that is integrated with ION.
9. CANFLEX fuel bundle impact test
This document outlines the test results for the impact test of the CANFLEX fuel bundle. Impact test is performed to determine and verify the amount of general bundle shape distortion and defect of the pressure tube that may occur during refuelling. The test specification requires that the fuel bundles and the pressure tube retain their integrities after the impact test under the conservative conditions (10 stationary bundles with 31kg/s flow rate) considering the pressure tube creep. The refuelling simulator operating with pneumatic force and simulated shield plug were fabricated and the velocity/displacement transducer and the high speed camera were also used in this test. The characteristics of the moving bundle (velocity, displacement, impacting force) were measured and analyzed with the impact sensor and the high speed camera system. The important test procedures and measurement results were discussed as follows. 1) Test bundle measurements and the pressure tube inspections 2) Simulated shield plug, outlet flange installation and bundle loading 3) refuelling simulator, inlet flange installation and sensors, high speed camera installation 4) Perform the impact test with operating the refuelling simulator and measure the dynamic characteristics 5) Inspections of the fuel bundles and the pressure tube. (author). 8 refs., 23 tabs., 13 figs
10. CANFLEX fuel bundle impact test
Chang, Seok Kyu; Chung, C. H.; Park, J. S.; Hong, S. D.; Kim, B. D.
1997-08-01
This document outlines the test results for the impact test of the CANFLEX fuel bundle. Impact test is performed to determine and verify the amount of general bundle shape distortion and defect of the pressure tube that may occur during refuelling. The test specification requires that the fuel bundles and the pressure tube retain their integrities after the impact test under the conservative conditions (10 stationary bundles with 31kg/s flow rate) considering the pressure tube creep. The refuelling simulator operating with pneumatic force and simulated shield plug were fabricated and the velocity/displacement transducer and the high speed camera were also used in this test. The characteristics of the moving bundle (velocity, displacement, impacting force) were measured and analyzed with the impact sensor and the high speed camera system. The important test procedures and measurement results were discussed as follows. 1) Test bundle measurements and the pressure tube inspections 2) Simulated shield plug, outlet flange installation and bundle loading 3) refuelling simulator, inlet flange installation and sensors, high speed camera installation 4) Perform the impact test with operating the refuelling simulator and measure the dynamic characteristics 5) Inspections of the fuel bundles and the pressure tube. (author). 8 refs., 23 tabs., 13 figs.
11. Fiber Bundles and Parseval Frames
Agrawal, Devanshu; Knisley, Jeff
2015-01-01
Continuous frames over a Hilbert space have a rich and sophisticated structure that can be represented in the form of a fiber bundle. The fiber bundle structure reveals the central importance of Parseval frames and the extent to which Parseval frames generalize the notion of an orthonormal basis.
12. Fiber bundle phase conjugate mirror
Ward, Benjamin G.
2012-05-01
An improved method and apparatus for passively conjugating the phases of a distorted wavefronts resulting from optical phase mismatch between elements of a fiber laser array are disclosed. A method for passively conjugating a distorted wavefront comprises the steps of: multiplexing a plurality of probe fibers and a bundle pump fiber in a fiber bundle array; passing the multiplexed output from the fiber bundle array through a collimating lens and into one portion of a non-linear medium; passing the output from a pump collection fiber through a focusing lens and into another portion of the non-linear medium so that the output from the pump collection fiber mixes with the multiplexed output from the fiber bundle; adjusting one or more degrees of freedom of one or more of the fiber bundle array, the collimating lens, the focusing lens, the non-linear medium, or the pump collection fiber to produce a standing wave in the non-linear medium.
13. Twisted Vector Bundles on Pointed Nodal Curves
Ivan Kausz
2005-05-01
Motivated by the quest for a good compactification of the moduli space of -bundles on a nodal curve we establish a striking relationship between Abramovich’s and Vistoli’s twisted bundles and Gieseker vector bundles.
14. The Atiyah Bundle and Connections on a Principal Bundle
Indranil Biswas
2010-06-01
Let be a ∞ manifold and a Lie a group. Let $E_G$ be a ∞ principal -bundle over . There is a fiber bundle $\\mathcal{C}(E_G)$ over whose smooth sections correspond to the connections on $E_G$. The pull back of $E_G$ to $\\mathcal{C}(E_G)$ has a tautological connection. We investigate the curvature of this tautological connection.
15. Using Advanced Fuel Bundles in CANDU Reactors
Improving the exit fuel burnup in CANDU reactors was a long-time challenge for both bundle designers and performance analysts. Therefore, the 43-element design together with several fuel compositions was studied, in the aim of assessing new reliable, economic and proliferation-resistant solutions. Recovered Uranium (RU) fuel is intended to be used in CANDU reactors, given the important amount of slightly enriched Uranium (~0.96% w/o U235) that might be provided by the spent LWR fuel recovery plants. Though this fuel has a far too small U235 enrichment to be used in LWR's, it can be still used to fuel CANDU reactors. Plutonium based mixtures are also considered, with both natural and depleted Uranium, either for peacefully using the military grade dispositioned Plutonium or for better using Plutonium from LWR reprocessing plants. The proposed Thorium-LEU mixtures are intended to reduce the Uranium consumption per produced MW. The positive void reactivity is a major concern of any CANDU safety assessment, therefore reducing it was also a task for the present analysis. Using the 43-element bundle with a certain amount of burnable poison (e.g. Dysprosium) dissolved in the 8 innermost elements may lead to significantly reducing the void reactivity. The expected outcomes of these design improvements are: higher exit burnup, smooth/uniform radial bundle power distribution and reduced void reactivity. Since the improved fuel bundles are intended to be loaded in existing CANDU reactors, we found interesting to estimate the local reactivity effects of a mechanical control absorber (MCA) on the surrounding fuel cells. Cell parameters and neutron flux distributions, as well as macroscopic cross-sections were estimated using the transport code DRAGON and a 172-group updated nuclear data library. (author)
16. Left bundle-branch block
Risum, Niels; Strauss, David; Sogaard, Peter;
2013-01-01
The relationship between myocardial electrical activation by electrocardiogram (ECG) and mechanical contraction by echocardiography in left bundle-branch block (LBBB) has never been clearly demonstrated. New strict criteria for LBBB based on a fundamental understanding of physiology have recently...
17. Bundling ecosystem services in Denmark
Turner, Katrine Grace; Odgaard, Mette Vestergaard; Bøcher, Peder Klith; Dalgaard, Tommy; Svenning, J.-C.
2014-01-01
We made a spatial analysis of 11 ecosystem services at a 10 km × 10 km grid scale covering most of Denmark. Our objective was to describe their spatial distribution and interactions and also to analyze whether they formed specific bundle types on a regional scale in the Danish cultural landscape....... We found clustered distribution patterns of ecosystem services across the country. There was a significant tendency for trade-offs between on the one hand cultural and regulating services and on the other provisioning services, and we also found the potential of regulating and cultural services to...... form synergies. We identified six distinct ecosystem service bundle types, indicating multiple interactions at a landscape level. The bundle types showed specialized areas of agricultural production, high provision of cultural services at the coasts, multifunctional mixed-use bundle types around urban...
18. Structure of the acrosomal bundle.
Schmid, Michael F; Sherman, Michael B; Matsudaira, Paul; Chiu, Wah
2004-09-01
In the unactivated Limulus sperm, a 60- micro m-long bundle of actin filaments crosslinked by the protein scruin is bent and twisted into a coil around the base of the nucleus. At fertilization, the bundle uncoils and fully extends in five seconds to support a finger of membrane known as the acrosomal process. This biological spring is powered by stored elastic energy and does not require the action of motor proteins or actin polymerization. In a 9.5-A electron cryomicroscopic structure of the extended bundle, we show that twist, tilt and rotation of actin-scruin subunits deviate widely from a 'standard' F-actin filament. This variability in structural organization allows filaments to pack into a highly ordered and rigid bundle in the extended state and suggests a mechanism for storing and releasing energy between coiled and extended states without disassembly. PMID:15343340
19. Locking means for fuels bundles
A nuclear power reactor fuel bundle is described which has a plurality of fuel rods disposed between two end plates positioned by tie rods extending therebetween. The assembled bundle is secured by one or more locking forks which pass through slots in the tie rod ends. Springs mounted on the fuel rods and tie rods are compressed by assembling the bundle and forcing one end plate against the locking fork to maintain the fuel rods and tie rods in position between the end plates. Downward pressure on the end plate permits removal of the locking fork so that the end plates may be removed, thus giving access to the fuel rods. This construction facilitates disassembly of an irradiated fuel bundle under water
20. Steric effects induce geometric remodeling of actin bundles in filopodia
2016-01-01
Filopodia are ubiquitous fingerlike protrusions, spawned by many eukaryotic cells, to probe and interact with their environments. Polymerization dynamics of actin filaments, comprising the structural core of filopodia, largely determine their instantaneous lengths and overall lifetimes. The polymerization reactions at the filopodial tip require transport of G-actin, which enter the filopodial tube from the filopodial base and diffuse toward the filament barbed ends near the tip. Actin filaments are mechanically coupled into a tight bundle by cross-linker proteins. Interestingly, many of these proteins are relatively short, restricting the free diffusion of cytosolic G-actin throughout the bundle and, in particular, its penetration into the bundle core. To investigate the effect of steric restrictions on G-actin diffusion by the porous structure of filopodial actin filament bundle, we used a particle-based stochastic simulation approach. We discovered that excluded volume interactions result in partial and the...
1. Damage in Fiber Bundle Models
Kun, Ferenc; Zapperi, Stefano; Herrmann, Hans J.
1999-01-01
We introduce a continuous damage fiber bundle model that gives rise to macroscopic plasticity and compare its behavior with that of dry fiber bundles. Several interesting constitutive behaviors are found in this model depending on the value of the damage parameter and on the form of the disorder distribution. In addition, we compare the behavior of global load transfer models with local load transfer models and study in detail the damage evolution before failure. We emphasize the analogies be...
2. Holomorphic bundles over elliptic manifolds
In this lecture we shall examine holomorphic bundles over compact elliptically fibered manifolds. We shall examine constructions of such bundles as well as (duality) relations between such bundles and other geometric objects, namely K3-surfaces and del Pezzo surfaces. We shall be dealing throughout with holomorphic principal bundles with structure group GC where G is a compact, simple (usually simply connected) Lie group and GC is the associated complex simple algebraic group. Of course, in the special case G = SU(n) and hence GC = SLn(C), we are considering holomorphic vector bundles with trivial determinant. In the other cases of classical groups, G SO(n) or G = Sympl(2n) we are considering holomorphic vector bundles with trivial determinant equipped with a non-degenerate symmetric, or skew symmetric pairing. In addition to these classical cases there are the finite number of exceptional groups. Amazingly enough, motivated by questions in physics, much interest centres around the group E8 and its subgroups. For these applications it does not suffice to consider only the classical groups. Thus, while often first doing the case of SU(n) or more generally of the classical groups, we shall extend our discussions to the general semi-simple group. Also, we shall spend a good deal of time considering elliptically fibered manifolds of the simplest type, namely, elliptic curves
3. Does size matter? : disentangling consumers' bundling preferences
Manoj K. Agarwal; Frambach, Ruud T.; Stremersch, Stefan
2000-01-01
Previous marketing literature has focused to a large extent on the effect of bundle characteristics on a consumer’s decision to buy a (fixed) bundle in a non-competitive setting. This study extends this narrow focus in four major ways. First, the authors address bundles that are customizable. Second, they distinguish between a consumer’s decision of whether to bundle (bundle choice) and the decision of how many goods or services to include in a bundle (bundle size). Third, they extend the foc...
4. In situ localization of NADP-malic enzyme in bundle sheath cells and leaf carbon isotope fractionation in two C4 grasses
Using an indirect immunofluorescence technique, we have provided further evidence on the subcellular localization of the NADP-dependent malic enzyme (EC 1.1.1.40) in the bundle sheath chloroplasts of some C4 grasses, including the two bluestem grasses Andropogon gerardi Vitman and Schizachyrium scoparium (Michx.) Nash, common C4 grasses of the prairies in the Great Plains. Leaf carbon isotope fractionation studies of the two bluestem species, grown in close proximity to each other, indicate that though both belong to the NADP-malic enzyme subtype of C4 plants, their δ13C values differ by 1.5‰. (author)
5. Atomic-scale evolution of modulated phases at the ferroelectric-antiferroelectric morphotropic phase boundary controlled by flexoelectric interaction
Borisevich, Albina Y [ORNL; Eliseev, Eugene [National Academy of Science of Ukraine, Kiev, Ukraine; Morozovska, A. N. [National Academy of Science of Ukraine, Kiev, Ukraine; Cheng, Ching-Jung [ORNL; Lin, Jiunn-Yuan [National Chiao Tung University, Hsinchu, Taiwan; Chu, Ying-Hao [National Chiao Tung University, Hsinchu, Taiwan; Kan, Daisuke [University of Maryland; Takeuchi, Ichiro [ORNL; Valanoor, Nagarajan V [ORNL; Kalinin, Sergei V [ORNL
2012-01-01
Physical and structural origins of morphotropic phase boundaries (MPBs) in ferroics remain elusive despite decades of studies. The leading competing theories employ either low symmetry bridging phases or adaptive phases with nanoscale textures to describe different subsets of the macroscopic data, while the decisive atomic-scale information has so far been missing. We report direct atomically-resolved mapping of polarization and structure order parameter fields in Sm-doped BiFeO3 system and their evolution as the system approaches MPB. We further show that both the experimental phase diagram and the phase evolution observed by STEM can be explained by taking into account flexoelectric interaction, which renders the effective domain wall energy negative, thus stabilizing modulated phases in the vicinity of the MPB. Our study highlights the importance of local order parameter mapping at the atomic scale and establishes a hitherto unobserved physical origin of spatially modulated phases existing in the vicinity of the MPB.
6. Advanced Fuel Bundles for PHWRS
The fuel used by NPCIL presently is natural uranium dioxide in the form of 19- element fuel bundles for 220 MWe PHWRs and 37-element fuel bundles for the TAPP-3&4 540 MWe units. The new 700 MWe PHWRs also use 37-element fuel bundles. These bundles are of short 0.5 m length of circular geometry. The cladding is of collapsible type made of Zircaloy-4 material. PHWRs containing a string of short length fuel bundles and the on-power refueling permit flexibility in using different advanced fuel designs and in core fuel management schemes. Using this flexibility, alternative fuel concepts are tried in Indian PHWRs. The advances in PHWR fuel designs are governed by the desire to use resources other than uranium, improve fuel economics by increasing fuel burnup and reduce overall spent nuclear fuel waste and improve reactor safety. The rising uranium prices are leading to a relook into the Thorium based fuel designs and reprocessed Uranium based and Plutonium based MOX designs and are expected to play a major role in future. The requirement of synergism between different type of reactors also plays a role. Increase in fuel burnup beyond 15 000 MW∙d/TeU in PHWRs, using higher fissile content materials like slightly enriched uranium, Mixed Oxide and Thorium Oxide in place of natural uranium in fuel elements, was studied many PHWR operating countries. The work includes reactor physics studies and test irradiation in research reactors and power reactors. Due to higher fissile content these bundles will be capable of delivering higher burnup than the natural uranium bundles. In India the fuel cycle flexibility of PHWRs is demonstrated by converting this type of technical flexibility to the real economy by irradiating these different types of advanced fuel materials namely Thorium, MOX, SEU, etc. The paper gives a review of the different advanced fuel design concepts studied for Indian PHWRs. (author)
7. Cohomology of line bundles: Applications
Blumenhagen, Ralph; Jurke, Benjamin; Rahn, Thorsten; Roschy, Helmut
2012-01-01
Massless modes of both heterotic and Type II string compactifications on compact manifolds are determined by vector bundle valued cohomology classes. Various applications of our recent algorithm for the computation of line bundle valued cohomology classes over toric varieties are presented. For the heterotic string, the prime examples are so-called monad constructions on Calabi-Yau manifolds. In the context of Type II orientifolds, one often needs to compute cohomology for line bundles on finite group action coset spaces, necessitating us to generalize our algorithm to this case. Moreover, we exemplify that the different terms in Batyrev's formula and its generalizations can be given a one-to-one cohomological interpretation. Furthermore, we derive a combinatorial closed form expression for two Hodge numbers of a codimension two Calabi-Yau fourfold.
8. Reaction–diffusion model of hair-bundle morphogenesis
2014-01-01
Our senses of hearing and balance rest upon the activity of hair cells, the ear’s sensory receptors. Each hair cell detects mechanical stimuli with its hair bundle, an organelle comprising 10–300 cylindrical, actin-filled stereocilia. A bundle’s structure is highly stereotyped: the stereocilia stand erect in a regular, hexagonal array and display a monotonic gradient in length along one axis. This precise organization is key to the operation of the hair bundle: mutations that disturb the morp...
9. Principal bundles the classical case
Sontz, Stephen Bruce
2015-01-01
This introductory graduate level text provides a relatively quick path to a special topic in classical differential geometry: principal bundles. While the topic of principal bundles in differential geometry has become classic, even standard, material in the modern graduate mathematics curriculum, the unique approach taken in this text presents the material in a way that is intuitive for both students of mathematics and of physics. The goal of this book is to present important, modern geometric ideas in a form readily accessible to students and researchers in both the physics and mathematics communities, providing each with an understanding and appreciation of the language and ideas of the other.
10. Study Of The PWR Fuel Bundle Characteristic With Borated Water
Study of the PWR fuel bundle characteristic with 2,4, 2,6, 2,8, 3,0, 3,2 and 3,4 enrichment also with borated water 150 and 200 ppm has been done. The fuel bundle contained 264 fuel elements and water (no fuel elements) are arranged as 17 x 17 matrix and 30,294 cm. The fuel bundle characteristic can be seen from their group constants and the infinite multiplication factor whether more or less than one. The fuel bundle parameters can be found from cell calculation with WIMS PC version program. From the cell calculation shown that the infinite multiplication factor of the fuel bundle with 2,4% enrichment and 200 ppm borated water is 1, 01672, its shown that infinite multiplication factor will less than one with increasing borated water more than 200 ppm. From these result if we would like to design the reactor core with 2,4% minimum enrichment then the maximum borated water is 200 ppm
11. Exploring Bundling Theory with Geometry
Eckalbar, John C.
2006-01-01
The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…
12. Bundled Discounts and EC Judicial Review
Christian Roques
2008-01-01
The Community Courts' case law is rich with cases relating to tying or bundling practices in their classical economic form. However, the same cannot be said for the second acceptance of bundled discounts.
13. Failure properties of fiber bundle models
2003-01-01
We study the failure properties of fiber bundles when continuous rupture goes on due to the application of external load on the bundles. We take the two extreme models: equal load sharing model (democratic fiber bundles) and local load sharing model. The strength of the fibers are assumed to be distributed randomly within a finite interval. The democratic fiber bundles show a solvable phase transition at a critical stress (load per fiber). The dynamic critical behavior is obtained analyticall...
14. Bundling Information Goods: Pricing, Profits, and Efficiency
Yannis Bakos; Erik Brynjolfsson
1999-01-01
We study the strategy of bundling a large number of information goods, such as those increasingly available on the Internet, and selling them for a fixed price. We analyze the optimal bundling strategies for a multiproduct monopolist, and we find that bundling very large numbers of unrelated information goods can be surprisingly profitable. The reason is that the law of large numbers makes it much easier to predict consumers' valuations for a bundle of goods than their valuations for the indi...
15. Quantum principal bundles and corresponding gauge theories
Durdevic, M
1995-01-01
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge transformations, are introduced and investigated. A natural differential calculus on quantum gauge bundles is constructed and analyzed. Kinematical and dynamical properties of corresponding gauge theories are discussed.
16. Strategic and welfare implications of bundling
Martin, Stephen
1999-01-01
A standard oligopoly model of bundling shows that bundling by a firm with a monopoly over one product has a strategic effect because it changes the substitution relationships between the goods among which consumers choose. Bundling in appropriate proportions is privately profitable, reduces rivals...
17. On Volumes of Arithmetic Line Bundles
Yuan, Xinyi
2008-01-01
We show an arithmetic generalization of the recent work of Lazarsfeld-Mustata which uses Okounkov bodies to study linear series of line bundles. As applications, we derive a log-concavity inequality on volumes of arithmetic line bundles and an arithmetic Fujita approximation theorem for big line bundles.
18. Numerical simulations of square arrayed rod bundles
Highlights: ► CFD simulations with square arrayed rod bundles. ► Mesh dependency and turbulence model study by comparison with experiments. ► Gibson and Launder Reynolds stress model shows good agreement with experiments. ► Effect of pitch to diameter ratio and Reynolds number is correctly captured. - Abstract: Computational fluid dynamics (CFD) simulations were performed with square arrayed rod bundles featuring pitch to diameter (P/D) ratio of 1.194 and 1.326 in order to find an optimal mesh and turbulence model for simulations with more complex geometries in the future. With the tighter lattice a mesh sensitivity and turbulence model study were accomplished and the post processed turbulence quantities, velocity field and wall shear stress were compared with experimental data ( Developed single phase turbulent flow through a square-pitch rod cluster. Nuclear Engineering and Design 60, 365–379.). The comparisons show that Reynolds-Averaged Navier–Stokes method with the Reynolds stress model of Gibson and Launder in conjunction with an appropriate mesh can provide reasonable agreement with the experiment for this lattice. For pure bundle simulations the body fitted structured meshes are suggested, since slightly better agreement can be captured considering all quantities with the same number of cells. Based on the drawn conclusions the procession was repeated for P/D = 1.326, where, due to lack of experiment, just the correct tendencies of the turbulence quantities and velocity field were established. The results show Reynolds number independency correctly and the increase of P/D issues in more similar flow to axisymmetric pipe flow.
19. Hair-bundle friction from transduction channels' gating forces
Bormuth, Volker; Barral, Jérémie; Joanny, Jean-François; Jülicher, Frank; Martin, Pascal
2015-12-01
Hearing starts when sound-evoked mechanical vibrations of the hair-cell bundle activate mechanosensitive ion channels, giving birth to an electrical signal. As for any mechanical system, friction impedes movements of the hair bundle and thus constrains the sensitivity and frequency selectivity of auditory transduction. We have shown recently that the opening and closing of the transduction channels produce internal frictional forces that can dominate viscous drag on the micrometer-sized hair bundle and thus provide a major source of damping [2]. We develop here a physical theory of passive hair-bundle mechanics that explains the origin of channel friction. We show that channel friction can be understood quantitatively by coupling the dynamics of the conformational change associated with channel gating to tip-link tension. As a result, varying channel properties affects friction, with faster channels producing smaller friction. The analysis emphasizes the dual role of transduction channels' gating forces, which affect both hair-bundle stiffness and drag. Friction originating from gating of ion channels is a general concept that is relevant to all mechanosensitive channels.
20. Post-irradiation examination of the 37M fuel bundle at Chalk River Laboratories (AECL)
Armstrong, J. [Atomic Energy of Canada Limited, Chalk River, Ontario (Canada); Daniels, T. [Ontario Power Generation, Pickering, Ontario (Canada); Montin, J. [Atomic Energy of Canada Limited, Chalk River, Ontario (Canada)
2014-03-15
The modified (-element (37M) fuel bundle was designed by Ontario Power Generation (OPG) to improve Critical Heat Flux (CHF) performance in ageing pressure tubes. A modification of the conventional 37-element fuel bundle design, the 37M fuel bundle allows more coolant flow through the interior sub-channels by way of a smaller central element. A demonstration irradiation (DI) of thirty-two fuel bundles was completed in 2011 at OPG's Darlington Nuclear Generating Station to confirm the suitability of the 37M fuel bundles for full core implementation. In support of the DI, fuel elements were examined in the Chalk River Laboratories Hot Cells. Inspection activities included: Bundle and element visual examination; Bundle and element dimensional measurements; Verification of bundle and element integrity; and Internal Gas Volume Measurements. The inspection results for 37M were comparable to that of conventional 37-element CANDU fuel. Fuel performance parameters of the 37M DI fuel bundle and fuel elements were within the range observed for similarly operated conventional 37-element CANDU fuel. Based on these Post Irradiation Examination (PIE) results, 37M fuel performed satisfactorily. (author)
1. Bundling, tying and collusion
Spector, David
2006-01-01
Une entreprise détenant un monopole sur un marché A peut augmenter son profit en liant la vente du produit A avec celle d'un produit complémentaire B si le marché B est oligopolistique, se prête à la collusion, et si une partie de la demande sur le marché B émane de consommateurs qui ont une demande nulle pour le produit A. La vente liée empêche les concurrents de l'entreprise qui la pratique de vendre le produit B à une partie des consommateurs, ce qui limite la profitabilité des déviations ...
2. Multi-scale strain-stiffening of semiflexible bundle networks
Piechocka, I K; Broedersz, C P; Kurniawan, N A; MacKintosh, F C; Koenderink, G H
2015-01-01
Bundles of polymer filaments are responsible for the rich and unique mechanical behaviors of many biomaterials, including cells and extracellular matrices. In fibrin biopolymers, whose nonlinear elastic properties are crucial for normal blood clotting, protofibrils self-assemble and bundle to form networks of semiflexible fibers. Here we show that the extraordinary strain-stiffening response of fibrin networks is a direct reflection of the hierarchical architecture of the fibrin fibers. We measure the rheology of networks of unbundled protofibrils and find excellent agreement with an affine model of extensible wormlike polymers. By direct comparison with these data, we show that physiological fibrin networks composed of thick fibers can be modeled as networks of tight protofibril bundles. We demonstrate that the tightness of coupling between protofibrils in the fibers can be tuned by the degree of enzymatic intermolecular crosslinking by the coagulation Factor XIII. Furthermore, at high stress, the protofibri...
3. Simplicial principal bundles in parametrized spaces
Roberts, David M
2012-01-01
In this paper, motivated by recent interest in higher gauge theory, we prove that the fiberwise geometric realization functor takes a certain class of simplicial principal bundles in a suitable category of spaces over a fixed space $B$ to fiberwise principal bundles. As an application we show that the fiberwise geometric realization of the universal simplicial principal bundle for a simplicial group $G$ in the category of spaces over $B$ gives rise to a fiberwise principal bundle with structure group $|G|$. An application to classifying theory for fiberwise principal bundles is described.
4. Multipath packet switch using packet bundling
Berger, Michael Stubert
The basic concept of packet bundling is to group smaller packets into larger packets based on, e.g., quality of service or destination within the packet switch. This paper presents novel applications of bundling in packet switching. The larger packets created by bundling are utilized to extend...... switching capacity by use of parallel switch planes. During the bundling operation, packets will experience a delay that depends on the actual implementation of the bundling and scheduling scheme. Analytical results for delay bounds and buffer size requirements are presented for a specific scheduling...
5. Model of turbine blades bundles
Prague : Institute of Thermomechanics, Academy of Sciences of the Czech Republic, v. v. i., 2013 - (Zolotarev, I.), s. 467-477 ISBN 978-80-87012-47-5. ISSN 1805-8256. [Engineering Mechanics 2013 /19./. Svratka (CZ), 13.05.2013-16.05.2013] R&D Projects: GA ČR GA101/09/1166 Institutional support: RVO:61388998 Keywords : free and forced vibrations * eigenmodes * mathematical model * bundle of blades Subject RIV: BI - Acoustics
6. Model of turbine blades bundles
Praha : Insitute of Thermomechanics ASCR, v. v. i., 2013 - (Zolotarev, I.). s. 125-126 ISBN 978-80-87012-46-8. ISSN 1805-8248. [Engineering Mechanics 2013 /19./. 13.05.2013-16.05.2013, Svratka] R&D Projects: GA ČR GA101/09/1166 Institutional support: RVO:61388998 Keywords : free and forced vibrations * eigenmodes * bundle of blades Subject RIV: BI - Acoustics
7. Competitive nonlinear pricing and bundling
Armstrong, Mark; Vickers, John
2006-01-01
We examine the impact of multiproduct nonlinear pricing on profit, consumer surplus and welfare in a duopoly. When consumers buy all their products from one firm (the one-stop shopping model), nonlinear pricing leads to higher profit and welfare, but often lower consumer surplus, than linear pricing. By contrast, in a unit-demand model where consumers may buy one product from one firm and another product from another firm, bundling generally acts to reduce profit and welfare and to boost cons...
8. Quantum bundles and their symmetries
Wave functions in the domain of observables such as the Hamiltonian are not always smooth functions on the classical configuration space Q. Rather, they are often best regarded as functions on a G bundle EG over Q or as sections of an associated bundle. If H is a classical group which acts on Q, its quantum version HG, which acts on EG, is not always H, but an extension of H by G. A powerful and physically transparent construction of EG and HG, where G = U(1) and H1(Q,Z) = 0, has been developed using the path space P. (P consists of paths on Q from a fixed point). In this paper the authors show how to construct EG and HG when G is U(1) or U(1) x π1(Q) and there is no restriction on H1(Q,Z). The method is illustrated with concrete examples, such as a system of charges and monopoles. The method is illustrated with concrete examples, such as a system of charges and monopoles. The authors argue also that P is a sort of superbundle from which a large variety of bundles can be obtained by imposing suitable equivalence relations
9. Photonic bandgap fiber bundle spectrometer
Hang, Qu; Syed, Imran; Guo, Ning; Skorobogatiy, Maksim
2010-01-01
We experimentally demonstrate an all-fiber spectrometer consisting of a photonic bandgap fiber bundle and a black and white CCD camera. Photonic crystal fibers used in this work are the large solid core all-plastic Bragg fibers designed for operation in the visible spectral range and featuring bandgaps of 60nm - 180nm-wide. 100 Bragg fibers were chosen to have complimentary and partially overlapping bandgaps covering a 400nm-840nm spectral range. The fiber bundle used in our work is equivalent in its function to a set of 100 optical filters densely packed in the area of ~1cm2. Black and white CCD camera is then used to capture spectrally "binned" image of the incoming light at the output facet of a fiber bundle. To reconstruct the test spectrum from a single CCD image we developed an algorithm based on pseudo-inversion of the spectrometer transmission matrix. We then study resolution limit of this spectroscopic system by testing its performance using spectrally narrow test peaks (FWHM 5nm-25nm) centered at va...
10. Revealing the flexoelectricity in the mixed-phase regions of epitaxial BiFeO3 thin films.
Cheng, Cheng-En; Liu, Heng-Jui; Dinelli, Franco; Chen, Yi-Chun; Chang, Chen-Shiung; Chien, Forest Shih-Sen; Chu, Ying-Hao
2015-01-01
Understanding the elastic response on the nanoscale phase boundaries of multiferroics is an essential issue in order to explain their exotic behaviour. Mixed-phase BiFeO3 films, epitaxially grown on LaAlO3 (001) substrates, have been investigated by means of scanning probe microscopy to characterize the elastic and piezoelectric responses in the mixed-phase region of rhombohedral-like monoclinic (MI) and tilted tetragonal-like monoclinic (MII,tilt) phases. Ultrasonic force microscopy reveal that the regions with low/high stiffness values topologically coincide with the MI/MII,tilt phases. X-ray diffraction strain analysis confirms that the MI phase is more compliant than the MII,tilt one. Significantly, the correlation between elastic modulation and piezoresponse across the mixed-phase regions manifests that the flexoelectric effect results in the enhancement of the piezoresponse at the phase boundaries and in the MI regions. This accounts for the giant electromechanical effect in strained mixed-phase BiFeO3 films. PMID:25627445
11. Dependence of image flickering of negative dielectric anisotropy liquid crystal on the flexoelectric coefficient ratio and the interdigitated electrode structure
We experimentally measured the splay (e s) and the bend flexoelectric coefficients (e b) of liquid crystal (LC) mixtures with negative dielectric anisotropy and investigated their effect on the image flicker of the LC mixtures driven with a low frequency electric field. Using the experimentally measured e s and e b, we simulated the transmittance (TR) response with the continuum model. First, we confirmed that the TR simulation results were approximated to the experimental data with only small variation. Second, we varied the simulation parameters of e s , e b, the separation (S), and the width (W) of the interdigitated electrodes and tried to find the optimum condition showing the least image flicker. Given W = 3.0 μm and e b = 5.7 pC m−1, it was found that the image flicker could be minimized when the e s /e b value was about 2.4 and the S/W ratio was about 1.5. Because the e s /e b value of the rod-like LC material is generally less than 1, it is desirable to design an interdigitated electrode structure to minimize the image flicker effect. (paper)
12. Dependence of image flickering of negative dielectric anisotropy liquid crystal on the flexoelectric coefficient ratio and the interdigitated electrode structure
Lee, Hyojin; Kim, Hyungmin; Kim, Jongyoon; Lee, Ji-Hoon
2016-02-01
We experimentally measured the splay (e s) and the bend flexoelectric coefficients (e b) of liquid crystal (LC) mixtures with negative dielectric anisotropy and investigated their effect on the image flicker of the LC mixtures driven with a low frequency electric field. Using the experimentally measured e s and e b, we simulated the transmittance (TR) response with the continuum model. First, we confirmed that the TR simulation results were approximated to the experimental data with only small variation. Second, we varied the simulation parameters of e s , e b, the separation (S), and the width (W) of the interdigitated electrodes and tried to find the optimum condition showing the least image flicker. Given W = 3.0 μm and e b = 5.7 pC m-1, it was found that the image flicker could be minimized when the e s /e b value was about 2.4 and the S/W ratio was about 1.5. Because the e s /e b value of the rod-like LC material is generally less than 1, it is desirable to design an interdigitated electrode structure to minimize the image flicker effect.
13. Dendritic bundles, minicolumns, columns, and cortical output units
Giorgio Innocenti
2010-03-01
Full Text Available The search for the fundamental building block of the cerebral cortex has highlighted three structures, perpendicular to the cortical surface: i columns of neurons with radially invariant response properties, e.g., receptive field position, sensory modality, stimulus orientation or direction, frequency tuning etc. ii minicolumns of radially aligned cell bodies and iii bundles, constituted by the apical dendrites of pyramidal neurons with cell bodies in different layers. The latter were described in detail, and sometimes quantitatively, in several species and areas. It was recently suggested that the dendritic bundles consist of apical dendrites belonging to neurons projecting their axons to specific targets. We review the concept above and suggest that another structural and computational unit of cerebral cortex is the cortical output unit (COU, i.e. an assembly of bundles of apical dendrites and their parent cell bodies including each of the outputs to distant cortical or subcortical structures, of a given cortical locus (area or part of an area. This somato-dendritic assembly receives inputs some of which are common to the whole assembly and determine its radially invariant response properties, others are specific to one or more dendritic bundles, and determine the specific response signature of neurons in the different cortical layers and projecting to different targets.
14. Multicell slug flow heat transfer analysis of finite LMFBR bundles
Yeung, M.K.; Wolf, L.
1978-12-01
An analytical two-dimensional, multi-region, multi-cell technique has been developed for the thermal analysis of LMFBR rod bundles. Local temperature fields of various unit cells were obtained for 7, 19, and 37-rod bundles of different geometries and power distributions. The validity of the technique has been verified by its excellent agreement with the THTB calculational result. By comparing the calculated fully-developed circumferential clad temperature distribution with those of the experimental measurements, an axial correction factor has been derived to account for the entrance effect for practical considerations. Moreover, the knowledge of the local temperature field of the rod bundle leads to the determination of the effective mixing lengths L/sub ij/ for adjacent subchannels of various geometries. It was shown that the implementation of the accurately determined L/sub ij/ into COBRA-IIIC calculations has fairly significant effects on intersubchannel mixing. In addition, a scheme has been proposed to couple the 2-D distributed and lumped parameter calculation by COBRA-IIIC such that the entrance effect can be implanted into the distributed parameter analysis. The technique has demonstrated its applicability for a 7-rod bundle and the results of calculation were compared to those of three-dimensional analyses and experimental measurements.
15. Defects in crystalline packings of twisted filament bundles. II. Dislocations and grain boundaries.
2012-03-01
Twisted and ropelike assemblies of filamentous molecules are common and vital structural elements in cells and tissues of living organisms. We study the intrinsic frustration occurring in these materials between the two-dimensional organization of filaments in cross section and out-of-plane interfilament twist in bundles. Using nonlinear continuum elasticity theory of columnar materials, we study the favorable coupling of twist-induced stresses to the presence of edge dislocations in the lattice packing of bundles, which leads to a restructuring of the ground-state order of these materials at intermediate twist. The stability of dislocations increases as both the degree of twist and lateral bundle size grow. We show that in ground states of large bundles, multiple dislocations pile up into linear arrays, radial grain boundaries, whose number and length grows with bundle twist, giving rise to a rich class of "polycrystalline" packings. PMID:22587105
16. Quadratic bundle and nonlinear equations
The paper is aimed at giving an exhaustive description of the nonlinear evolution equations (NLEE), connected with the quadratic bundle (the spectral parameter lambda, which enters quadratically into the equations) and at describing Hamiltonian structure of these equations. The equations are solved through the inverse scattering method (ISM). The basic formulae for the scattering problem are given. The spectral expansion of the integrodifferential operator is used so that its eigenfunctions are the squared solutions of the equation. By using the notions of Hamiltonian structure hierarchy and gauge transformations it is shown how to single out physically interesting NLEE
17. Static stress analysis of CANFLEX fuel bundles
The static stress analysis of CANFLEX bundles is performed to evaluate the fuel structural integrity during the refuelling service. The structure analysis is carried out by predicting the drag force, stress and displacements of the fuel bundle. By the comparison of strength tests and analysis results, the displacement values are well agreed within 15%. The analysis shows that the CANFLEX fuel bundle keep its structural integrity. 24 figs., 6 tabs., 12 refs. (Author) .new
18. Damping Properties of the Hair Bundle
Baumgart, Johannes; Kozlov, Andrei S.; Risler, Thomas; Hudspeth, A. James
2015-01-01
The viscous liquid surrounding a hair bundle dissipates energy and dampens oscillations, which poses a fundamental physical challenge to the high sensitivity and sharp frequency selectivity of hearing. To identify the mechanical forces at play, we constructed a detailed finite-element model of the hair bundle. Based on data from the hair bundle of the bullfrog's sacculus, this model treats the interaction of stereocilia both with the surrounding liquid and with the liquid in the narrow gaps b...
19. Tying, Bundling, and Loyalty/Requirement Rebates
Nicholas Economides
2011-01-01
I discuss the impact of tying, bundling, and loyalty/requirement rebates on consumer surplus in the affected markets. I show that the Chicago School Theory of a single monopoly surplus that justifies tying, bundling, and loyalty/requirement rebates on the basis of efficiency typically fails. Thus, tying, bundling, and loyalty/requirement rebates can be used to extract consumer surplus and enhance profit of firms with market power. I discuss the various setups when this occurs.
20. Bundling and Competition on the Internet
Yannis Bakos; Erik Brynjolfsson
2000-01-01
The Internet has signi.cantly reduced the marginal cost of producing and distributing digital information goods. It also coincides with the emergence of new competitive strategies such as large-scale bundling. In this paper, we show that bundling can create “economies of aggregation” for information goods if their marginal costs are very low, even in the absence of network externalities or economies of scale or scope. We extend the Bakos-Brynjolfsson bundling model (1999) to settings with sev...
1. Bundling and joint marketing by rival firms
Jeitschko, Thomas D.; Jung, Yeonjei; Kim, Jaesoo
2014-01-01
We study joint marketing arrangements by competing firms who engage in price discrimination between consumers who patronize only one firm (single purchasing) and those who purchase from both competitors (bundle purchasers). Two types of joint marketing are considered. Firms either commit to a component-price that applies to bundle-purchasers and then firms set stand-alone prices for single purchasers; or firms commit to a rebate off their stand alone price that will be applied to bundle-purch...
2. Statistical Constitutive Equation of Aramid Fiber Bundles
熊杰; 顾伯洪; 王善元
2003-01-01
Tensile impact tests of aramid (Twaron) fiber bundles were carried om under high strain rates with a wide range of 0. 01/s～1000/s by using MTS and bar-bar tensile impact apparatus. Based on the statistical constitutive model of fiber bundles, statistical constitutive equations of aramid fiber bundles are derived from statistical analysis of test data at different strain rates. Comparison between the theoretical predictions and experimental data indicates statistical constitutive equations fit well with the experimental data, and statistical constitutive equations of fiber bundles at different strain rates are valid.
3. Hydraulic characteristics of HANARO fuel bundles
Cho, S.; Chung, H. J.; Chun, S. Y.; Yang, S. K.; Chung, M. K. [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1997-12-31
This paper presents the hydraulic characteristics measured by using LDV (Laser Doppler Velocimetry) in subchannels of HANARO, KAERI research reactor, fuel bundle. The fuel bundle consists of 18 axially finned rods with 3 spacer grids, which are arranged in cylindrical configuration. The effects of the spacer grids on the turbulent flow were investigated by the experimental results. Pressure drops for each component of the fuel bundle were measured, and the friction factors of fuel bundle and loss coefficients for the spacer grids were estimated from the measured pressure drops. Implications regarding the turbulent thermal mixing were discussed. Vibration test results measured by using laser vibrometer were presented. 9 refs., 12 figs. (Author)
4. A contribution to understanding the structure of amphivasal secondary bundles in monocotyledons
Joanna Jura-Morawiec
2014-04-01
Full Text Available Secondary growth of monocotyledonous plants is connected with the activity of the monocot cambium that accumulates most of the derivatives inner to the cambial cylinder. These derivatives differentiate into (a secondary bundles with the amphivasal arrangement, i.e. xylem composed of tracheids surrounds the phloem cells and (b the parenchymatous secondary conjunctive tissue in which the bundles are embedded. The amphivasal secondary bundles differ in the arrangement of xylem cells as visible on single cross sections through the secondary body of the monocots. Apart from the bundles with typical ring of tracheids also the bundles where tracheids do not quite surround the phloem are present. We aimed to elucidate the cross sectional anatomy of the amphivasal secondary bundles with the use of the serial sectioning method which allowed us to follow very precisely the bundle structure along its length. The studies were carried out with the samples of secondary tissues collected from the stem of Dracaena draco L. growing in the greenhouses of the Polish Academy of Sciences Botanical Garden – CBDC in Powsin and the Adam Mickiewicz University Botanical Garden. The material was fixed in a mixture of glycerol and ethanol (1:1; v/v, dehydrated stepwise with graded ethanol series and finally embedded in epon resin. Afterwards, the material was sectioned with microtome into continuous series of thin (3 μm sections, stained with PAS/toluidine blue and examined under the light microscope. The results, described in details in Jura‑Morawiec & Wiland-Szymańska (2014, revealed novel facts about tracheids arrangement. Each amphivasal bundle is composed of sectors where tracheids form a ring as well as of such where tracheids are separated by vascular parenchyma cells. We hypothesize that strands of vascular parenchyma cells locally separating the tracheids enable radial transport of assimilates from sieve elements of the bundle towards the sink tissues, e
5. Extension of holomorphic bundles to the disc (and Serre's Problem on Stein bundles)
Rosay, Jean-Pierre
2006-01-01
We show how to extend some holomorphic bundles with fifer C^2 and base an open set in C, to bundles on the Riemann Sphere, by an extremely simple technique. In particular, it applies to examples of non-Stein bundles constructed by Skoda and Demailly. It gives an example on C, with polynomial transition automorphisms.
6. The Packing of Flexible Screws and the Self-Limited Assembly of Biopolymer Bundles
Grason, Gregory
2009-03-01
Living cells rely heavily on assemblies of filamentous proteins, such as F-actin and microtubules, to perform a variety of tasks, ranging from adhesion and locomotion to cell division and intracellular transport. In the dynamic cellular environment, the efficiency of these tasks is crucially dependent on the robust assembly and disassembly of rope-like bundles of filamentous molecules. Recent in vitro studies of F-actin assembly [Lai et al., Phys. Rev. Lett. (2007)] suggest that bundle formation may take place as an equilibrium process, with a thermodynamically-preferred bundle diameter. Within the context of a generalized elastic model of filament packings, we explore the possibility that limited-bundle growth is directly linked with the intrinsic chiral structure of biological filaments themselves. The hexagonal packing of biopolymers leads to the build up of chiral stress, or torque, that generically induces the formation of twisting filament bundles of finite size. We demonstrate that the underlying elasticity of the bundle--i.e. whether hexagonal-solid or hexagonal-columnar--plays a key role in dictating both the thermodynamics (i.e. disperse, bundled or bulk aggregation) and structure (i.e. size and twist) of self-braiding" aggregates of helical filaments.
7. Molecular mechanism of bundle formation by the bacterial actin ParM
Popp, David, E-mail: [email protected] [ERATO ' Actin Filament Dynamics' Project, Japan Science and Technology Corporation, c/o RIKEN Harima Institute at Spring 8, 1-1-1 Kouto, Sayo, Hyogo 679-5148 (Japan); Institute of Molecular and Cell Biology, 61 Biopolis Drive, Proteos, 138673 Singapore (Singapore); Narita, Akihiro [ERATO ' Actin Filament Dynamics' Project, Japan Science and Technology Corporation, c/o RIKEN Harima Institute at Spring 8, 1-1-1 Kouto, Sayo, Hyogo 679-5148 (Japan); Nagoya University Graduate School of Science, Structural Biology Research Center and Division of Biological Sciences, Furo-cho, Chikusa-ku, Nagoya 464-8601 (Japan); Iwasa, Mitsusada [ERATO ' Actin Filament Dynamics' Project, Japan Science and Technology Corporation, c/o RIKEN Harima Institute at Spring 8, 1-1-1 Kouto, Sayo, Hyogo 679-5148 (Japan); Maeda, Yuichiro [ERATO ' Actin Filament Dynamics' Project, Japan Science and Technology Corporation, c/o RIKEN Harima Institute at Spring 8, 1-1-1 Kouto, Sayo, Hyogo 679-5148 (Japan); Nagoya University Graduate School of Science, Structural Biology Research Center and Division of Biological Sciences, Furo-cho, Chikusa-ku, Nagoya 464-8601 (Japan); Robinson, Robert C. [Institute of Molecular and Cell Biology, 61 Biopolis Drive, Proteos, 138673 Singapore (Singapore)
2010-01-22
The actin homolog ParM plays a microtubule-like role in segregating DNA prior to bacterial cell division. Fluorescence and cryo-electron microscopy have shown that ParM forms filament bundles between separating DNA plasmids in vivo. Given the lack of ParM bundling proteins it remains unknown how ParM bundles form at the molecular level. Here we show using time-lapse TIRF microscopy, under in vitro molecular crowding conditions, that ParM-bundle formation consists of two distinct phases. At the onset of polymerization bundle thickness and shape are determined in the form of nuclei of short helically disordered filaments arranged in a liquid-like lattice. These nuclei then undergo an elongation phase whereby they rapidly increase in length. At steady state, ParM bundles fuse into one single large aggregate. This behavior had been predicted by theory but has not been observed for any other cytomotive biopolymer, including F-actin. We employed electron micrographs of ParM rafts, which are 2-D analogs of 3-D bundles, to identify the main molecular interfilament contacts within these suprastructures. The interface between filaments is similar for both parallel and anti-parallel orientations and the distribution of filament polarity is random within a bundle. We suggest that the interfilament interactions are not due to the interactions of specific residues but rather to long-range, counter ion mediated, electrostatic attractive forces. A randomly oriented bundle ensures that the assembly is rigid and that DNA may be captured with equal efficiency at both ends of the bundle via the ParR binding protein.
8. Principal Bundles on the Projective Line
V B Mehta; S Subramanian
2002-08-01
We classify principal -bundles on the projective line over an arbitrary field of characteristic ≠ 2 or 3, where is a reductive group. If such a bundle is trivial at a -rational point, then the structure group can be reduced to a maximal torus.
9. The Verlinde formula for Higgs bundles
Andersen, Jørgen Ellegaard; Pei, Du
2016-01-01
We propose and prove the Verlinde formula for the quantization of the Higgs bundle moduli spaces and stacks for any simple and simply-connected group. This generalizes the equivariant Verlinde formula for the case of $SU(n)$ proposed previously by the second and third author. We further establish a Verlinde formula for the quantization of parabolic Higgs bundle moduli spaces and stacks.
10. CANFLEX fuel bundle strength tests (test report)
Chang, Seok Kyu; Chung, C. H.; Kim, B. D.
1997-08-01
This document outlines the test results for the strength tests of the CANFLEX fuel bundle. Strength tests are performed to determine and verify the amount of the bundle shape distortion which is against the side-stops when the bundles are refuelling. There are two cases of strength test; one is the double side-stop test which simulates the normal bundle refuelling and the other is the single side-stop test which simulates the abnormal refuelling. the strength test specification requires that the fuel bundle against the side-stop(s) simulators for this test were fabricated and the flow rates were controlled to provide the required conservative hydraulic forces. The test rig conditions of 120 deg C, 11.2 MPa were retained for 15 minutes after the flow rate was controlled during the test in two cases, respectively. The bundle loading angles of number 13- number 15 among the 15 bundles were 67.5 deg CCW and others were loaded randomly. After the tests, the bundle shapes against the side-stops were measured and inspected carefully. The important test procedures and measurements were discussed as follows. (author). 5 refs., 22 tabs., 5 figs.
11. CANFLEX fuel bundle strength tests (test report)
This document outlines the test results for the strength tests of the CANFLEX fuel bundle. Strength tests are performed to determine and verify the amount of the bundle shape distortion which is against the side-stops when the bundles are refuelling. There are two cases of strength test; one is the double side-stop test which simulates the normal bundle refuelling and the other is the single side-stop test which simulates the abnormal refuelling. the strength test specification requires that the fuel bundle against the side-stop(s) simulators for this test were fabricated and the flow rates were controlled to provide the required conservative hydraulic forces. The test rig conditions of 120 deg C, 11.2 MPa were retained for 15 minutes after the flow rate was controlled during the test in two cases, respectively. The bundle loading angles of number 13- number 15 among the 15 bundles were 67.5 deg CCW and others were loaded randomly. After the tests, the bundle shapes against the side-stops were measured and inspected carefully. The important test procedures and measurements were discussed as follows. (author). 5 refs., 22 tabs., 5 figs
12. k-Gerbes, Line Bundles and Anomalies
Ekstrand, C
2000-01-01
We use sets of trivial line bundles for the realization of gerbes. For1-gerbes the structure arises naturally for the Weyl fermion vacuum bundle at afixed time. The Schwinger term is an obstruction in the triviality of a1-gerbe.
13. k-Gerbes, Line Bundles and Anomalies
We use sets of trivial line bundles for the realization of gerbes. For 1-gerbes the structure arises naturally for the Weyl fermion vacuum bundle at a fixed time. The Schwinger term is an obstruction in the triviality of a 1-gerbe. (author)
14. k-Gerbes, Line Bundles and Anomalies
Ekstrand, C.
2000-01-01
We use sets of trivial line bundles for the realization of gerbes. For 1-gerbes the structure arises naturally for the Weyl fermion vacuum bundle at a fixed time. The Schwinger term is an obstruction in the triviality of a 1-gerbe.
15. Heights for line bundles on arithmetic surfaces
Jahnel, Joerg
1995-01-01
For line bundles on arithmetic varieties we construct height functions using arithmetic intersection theory. In the case of an arithmetic surface, generically of genus g, for line bundles of degree g equivalence is shown to the height on the Jacobian defined by the Theta divisor.
16. Damping Properties of the Hair Bundle
Baumgart, Johannes; Kozlov, Andrei S.; Risler, Thomas; Hudspeth, A. J.
2011-11-01
The viscous liquid surrounding a hair bundle dissipates energy and dampens oscillations, which poses a fundamental physical challenge to the high sensitivity and sharp frequency selectivity of hearing. To identify the mechanical forces at play, we constructed a detailed finite-element model of the hair bundle. Based on data from the hair bundle of the bullfrog's sacculus, this model treats the interaction of stereocilia both with the surrounding liquid and with the liquid in the narrow gaps between the individual stereocilia. The investigation revealed that grouping stereocilia in a bundle dramatically reduces the total drag. During hair-bundle deflections, the tip links potentially induce drag by causing small but very dissipative relative motions between stereocilia; this effect is offset by the horizontal top connectors that restrain such relative movements at low frequencies. For higher frequencies the coupling liquid is sufficient to assure that the hair bundle moves as a unit with a low total drag. This work reveals the mechanical characteristics originating from hair-bundle morphology and shows quantitatively how a hair bundle is adapted for sensitive mechanotransduction.
17. Fock modules and noncommutative line bundles
Landi, Giovanni
2016-09-01
To a line bundle over a noncommutative space there is naturally associated a Fock module. The algebra of corresponding creation and annihilation operators is the total space algebra of a principal U(1) -bundle over the noncommutative space. We describe the general construction and illustrate it with examples.
18. Dirac structures and Dixmier-Douady bundles
Alekseev, A
2009-01-01
A Dirac structure on a vector bundle V is a maximal isotropic subbundle E of the direct sum of V with its dual. We show how to associate to any Dirac structure a Dixmier-Douady bundle A, that is, a Z/2Z-graded bundle of C*-algebras with typical fiber the compact operators on a Hilbert space. The construction has good functorial properties, relative to Morita morphisms of Dixmier-Douady bundles. As applications, we show that the spin' Dixmier-Douady bundle over a compact, connected Lie group (as constructed by Atiyah-Segal) is multiplicative, and we obtain a canonical twisted Spin-c-structure' on spaces with group valued moment maps.
19. Bringing the CANFLEX fuel bundle to market
CANFLEX is a 43-element CANDU fuel bundle, under joint development by AECL and KAERI, to facilitate the use of various advanced fuel cycles in CANDU reactors through the provision of enhanced operating margins. The bundle uses two element diameters (13.5 and 11.5 mm ) to reduce element ratings by 20%, and includes the use of critical-heat-flux (CHF) enhancing appendages to increase the minimum CHF ratio or dryout margin of the bundle. Test programs are underway to demonstrate: the irradiation behaviour, hydraulic characteristics and reactor physics properties of the bundle, along with a test program to demonstrate the ability of the bundle to be handled by CANDU-6 fuelling machines. A fuel design manual and safety analysis reports have been drafted, and both analyses, plus discussions with utilities are underway for a demonstration irradiation in a CANDU-6 reactor. (author)
20. Line bundle embeddings for heterotic theories
Nibbelin, Stefan Groot; Ruehle, Fabian
2016-04-01
In heterotic string theories consistency requires the introduction of a non-trivial vector bundle. This bundle breaks the original ten-dimensional gauge groups E8 × E8 or SO(32) for the supersymmetric heterotic string theories and SO(16) × SO(16) for the non-supersymmetric tachyon-free theory to smaller subgroups. A vast number of MSSM-like models have been constructed up to now, most of which describe the vector bundle as a sum of line bundles. However, there are several different ways of describing these line bundles and their embedding in the ten-dimensional gauge group. We recall and extend these different descriptions and explain how they can be translated into each other.
1. CANDU fuel bundle skin friction factor
Single-phase, incompressible fluid flow skin friction factor correlations, primarily for CANDU 37-rod fuel bundles, were reviewed. The correlations originated from curve-fits to flow test data, mostly with new fuel bundles in new pressure tubes (flow tubes), without internal heating. Skin friction in tubes containing fuel bundles (noncircular flow geometry) was compared to that in equivalent diameter smooth circular tubes. At Reynolds numbers typical of normal flows in CANDU fuel channels, the skin friction in tubes containing bundles is 8 to 15% higher than in equivalent diameter smooth circular tubes. Since the correlations are based on scattered results from measurements, the skin friction with bundles may be even higher than indicated above. The information permits over- or under-prediction of the skin friction, or choosing an intermediate value of friction, with allowance for surface roughnesses, in thermal-hydraulic analyses of CANDU heat transport systems. (author) 9 refs., 2 figs
2. Line bundle embeddings for heterotic theories
2016-01-01
In heterotic theories consistency requires the introduction of a non-trivial vector bundle. This bundle breaks the original ten-dimensional gauge groups E_8 x E_8 or SO(32) for the supersymmetric heterotic theories and SO(16) x SO(16) for the non-supersymmetric tachyon-free theory to smaller subgroups. A vast number of MSSM-like models have been constructed up to now, most of which describe the vector bundle as a sum of line bundles. However, there are several different ways of describing these line bundles and their embedding in the ten-dimensional gauge group. We recall and extend these different descriptions and explain how they can be translated into each other.
3. Canonical singular hermitian metrics on relative logcanonical bundles
Tsuji, Hajime
2010-01-01
This supersedes 0704.0566. We prove the invariance of logarithmic plurigenera for a projective family of KLT pairs and the adjoint line bundle of KLT line bundles. The proof uses the canonical singular hermitian metrics on relative logcanonical bundles.
4. On Harder–Narasimhan Reductions for Higgs Principal Bundles
Arijit Dey; R Parthasarathi
2005-05-01
The existence and uniqueness of – reduction for the Higgs principal bundles over nonsingular projective variety is shown. We also extend the notion of – reduction for (, )-bundles and ramified -bundles over a smooth curve.
5. Effect of bundle size on BWR fuel bundle critical power performance
Effect of the bundle size on the BWR fuel bundle critical power performance was studied. For this purpose, critical power tests were conducted with both 6 x 6 (36 heater rods) and 12 x 12 (144 heater rods) size bundles in the GE ATLAS heat transfer test facility located in San Jose, California. All the bundle geometries such as rod diameter, rod pitch and rod space design are the same except size of flow channel. Two types of critical power tests were performed. One is the critical power test with uniform local peaking pattern for direct comparison of the small and large bundle critical power. Other is the critical power test for lattice positions in the bundle. In this test, power of a group of four rods (2 x 2 array) in a lattice region was peaked higher to probe the critical power of that lattice position in the bundle. In addition, the test data were compared to the COBRAG calculations. COBRAG is a detailed subchannel analysis code for BWR fuel bundle developed by GE Nuclear Energy. Based on these comparisons the subchannel model was refined to accurately predict the data obtained in this test program, thus validating the code capability of handling the effects of bundle size on bundle critical power for use in the study of the thermal hydraulic performance of the future advance BWR fuel bundle design. The author describes the experimental portion of the study program
6. Gauge symmetries and fibre bundles
The matter is organized as follows. After a brief introduction to the concept of gauge invariance and its relationship to determinism, we introduce in chapters 3 and 4 the notion of fibre bundles in the context of a discussion on spinning point particles and Dirac monopoles. Chapter 3 deals with a non relativistic treatment of the spinning particle. The non trivial extension to relativistic spinning particles is dealt with in Chapter 5. The free particle system as well as interactions with external electromagnetic and gravitational fields are discussed in detail. In chapter 5 we also elaborate on a remarkable relationship between the charge-monopole system and the system of a massless particle with spin. The classical description of Yang-Mills particles with internal degrees of freedom, such as isospin or colour, is given in chapter 6. We apply the above in a discussion of the classical scattering of particles off a 't Hooft-Polyakov monopole. In chapter 7 we elaborate on a Kaluza-Klein description of particles with internal degrees of freedom. The canonical formalism and the quantization of most of the preceeding systems are discussed in chapter 8. The dynamical systems given in chapters 3-7 are formulated on group manifolds. The procedure for obtaining the extension to super-group manifolds is briefly discussed in chapter 9. In chapter 10, we show that if a system admits only local Lagrangians for a configuration space Q, then under certain conditions, it admits a global Lagrangian when Q is enlarged to a suitable U(1) bundle over Q. Conditions under which a symplectic form is derivable from a Lagrangian are also found. (orig./HSI)
7. Study of the end flux peaking for the Candu fuel bundle types by transport methods
The region separating the Candu fuel in two adjoining bundles in a channel is called the end region. The end of the last pellet in the fuel stack adjacent to the end region is called the fuel end. In the end region of the bundle the thermal neutron flux is higher than at the axial mid-point, because the end region of the bundle is made up of very low neutron absorption material: coolant and Zircaloy-4. For accurate evaluation of fuel performance, it is important to have capability to calculate the three dimensional spatial flux distributions in the fuel bundle, including the end region. The work reported here had two objectives. First, calculation of the flux distributions (axial and radial) and the end flux peaking factors for some Candu fuel bundles. Second objective is a comparative analysis of the obtained results. The Candu fuel bundles considered in this paper are NU37 (Natural Uranium, 37 elements) and SEU43 (Slightly Enriched Uranium, 43 elements, with 1.1wt% enrichment). For realization of the proposed objectives, a methodology based on WIMS, PIJXYZ and LEGENTR codes is used in this paper. WIMS is a standard lattice-cell code, based on transport theory and it is used for producing fuel cell multigroup macroscopic cross sections. For obtaining the flux distribution in Candu fuel bundles it is used PIJXYZ and LEGENTR respectively codes. These codes are consistent with WIMS lattice-cell calculations and allow a good geometrical representation of the Candu bundle in three dimensions. PIJXYZ is a 3D integral transport code using the first collision probability method and it has been developed for Candu cell geometry. LEGENTR is a 3D SN transport code based on projectors technique and can be used for 3D cell and 3D core calculations. (author)
8. Lateral mechanical coupling of stereocilia in cochlear hair bundles.
Langer, M G; Fink, S.; Koitschev, A; Rexhausen, U; Hörber, J K; Ruppersberg, J P
2001-01-01
For understanding the gating process of transduction channels in the inner ear it is essential to characterize and examine the functional properties of the ultrastructure of stereociliary bundles. There is strong evidence that transduction channels in hair cells are gated by directly pulling at the so-called tip links. In addition to these tip links a second class of filamentous structures was identified in the scanning and transmission electron microscope: the side-to-side links. These links...
9. Prophylactic bundle for radiation-induced oral mucositis in oral or oropharyngeal cancer patients
Kawashita Y; Hayashida S; Funahara M; Umeda M; Saito T.
2014-01-01
Objective: In order to prevent and treat radiation-induced adverse events, especially oral mucositis, in patients with oral or oropharyngeal cancer receiving radiotherapy or chemoradiotherapy, a prophylactic bundle, i.e., a set of oral care management procedures, is conducted and assessed. Subjects and methods: The subjects were 30 patients with squamous cell carcinoma of the oral cavity or oropharynx who underwent radiotherapy. The patients received the prophylactic bundle to prevent radiati...
10. Preliminary report: NIF laser bundle review
As requested in the guidance memo 1, this committe determined whether there are compelling reasons to recommend a change from the NIF CDR baseline laser. The baseline bundle design based on a tradeoff between cost and technical risk, which is replicated four times to create the required 192 beams. The baseline amplifier design uses bottom loading 1x4 slab and flashlamp cassettes for amplifier maintenance and large vacuum enclosures (2.5m high x 7m wide in cross-section for each of the two spatial filters in each of the four bundles. The laser beams are arranged in two laser bays configured in a u-shape around the target area. The entire bundle review effort was performed in a very short time (six weeks) and with limited resources (15 personnel part-time). This should be compared to the effort that produced the CDR design (12 months, 50 to 100 personnel). This committee considered three alternate bundle configurations (2x2, 4x2, and 4x4 bundles), and evaluated each bundle against the baseline design using the seven requested issues in the guidance memo: Cost; schedule; performance risk; maintainability/operability; hardware failure cost exposure; activation; and design flexibility. The issues were reviewed to identify differences between each alternate bundle configuration and the baseline
11. Prioritary omalous bundles on Hirzebruch surfaces
Aprodu, Marian; Marchitan, Marius
2016-01-01
An irreducible algebraic stack is called unirational if there exists a surjective morphism, representable by algebraic spaces, from a rational variety to an open substack. We prove unirationality of the stack of prioritary omalous bundles on Hirzebruch surfaces, which implies also the unirationality of the moduli space of omalous H-stable bundles for any ample line bundle H on a Hirzebruch surface (compare with Costa and Miro-Ŕoig, 2002). To this end, we find an explicit description of the duals of omalous rank-two bundles with a vanishing condition in terms of monads. Since these bundles are prioritary, we conclude that the stack of prioritary omalous bundles on a Hirzebruch surface different from P1 ×P1 is dominated by an irreducible section of a Segre variety, and this linear section is rational (Ionescu, 2015). In the case of the space quadric, the stack has been explicitly described by N. Buchdahl. As a main tool we use Buchdahl's Beilinson-type spectral sequence. Monad descriptions of omalous bundles on hypersurfaces in P4, Calabi-Yau complete intersection, blowups of the projective plane and Segre varieties have been recently obtained by A.A. Henni and M. Jardim (Henni and Jardim, 2013), and monads on Hirzebruch surfaces have been applied in a different context in Bartocci et al. (2015).
12. Singular hermitian metrics on vector bundles
De Cataldo, M A A
1997-01-01
We introduce a notion of singular hermitian metrics (s.h.m.) for holomorphic vector bundles and define positivity in view of $L^2$-estimates. Associated with a suitably positive s.h.m. there is a (coherent) sheaf 0-th kernel of a certain $d''$-complex. We prove a vanishing theorem for the cohomology of this sheaf. All this generalizes to the case of higher rank known results of Nadel for the case of line bundles. We introduce a new semi-positivity notion, $t$-nefness, for vector bundles, establish some of its basic properties and prove that on curves it coincides with ordinary nefness. We particularize the results on s.h.m. to the case of vector bundles of the form $E=F \\otimes L$, where $F$ is a $t$-nef vector bundle and $L$ is a positive (in the sense of currents) line bundle. As applications we generalize to the higher rank case 1) Kawamata-Viehweg Vanishing Theorem, 2) the effective results concerning the global generation of jets for the adjoint to powers of ample line bundles, and 3) Matsusaka Big Theor...
13. Deformations of the generalised Picard bundle
Let X be a nonsingular algebraic curve of genus g ≥ 3, and let Mξ denote the moduli space of stable vector bundles of rank n ≥ 2 and degree d with fixed determinant ξ over X such that n and d are coprime. We assume that if g = 3 then n ≥ 4 and if g = 4 then n ≥ 3, and suppose further that n0, d0 are integers such that n0 ≥ 1 and nd0 + n0d > nn0(2g - 2). Let E be a semistable vector bundle over X of rank n0 and degree d0. The generalised Picard bundle Wξ(E) is by definition the vector bundle over Mξ defined by the direct image pMξ *(Uξ x pX*E) where Uξ is a universal vector bundle over X x Mξ. We obtain an inversion formula allowing us to recover E from Wξ(E) and show that the space of infinitesimal deformations of Wξ(E) is isomorphic to H1(X, End(E)). This construction gives a locally complete family of vector bundles over Mξ parametrised by the moduli space M(n0,d0) of stable bundles of rank n0 and degree d0 over X. If (n0,d0) = 1 and Wξ(E) is stable for all E is an element of M(n0,d0), the construction determines an isomorphism from M(n0,d0) to a connected component M0 of a moduli space of stable sheaves over Mξ. This applies in particular when n0 = 1, in which case M0 is isomorphic to the Jacobian J of X as a polarised variety. The paper as a whole is a generalisation of results of Kempf and Mukai on Picard bundles over J, and is also related to a paper of Tyurin on the geometry of moduli of vector bundles. (author)
14. Geometry of quantum principal bundles, 1
Durdevic, M
1995-01-01
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential forms on the base manifold with an appropriate differential calculus on the structure quantum group. Relations between the calculus on the group and the calculus on the bundle are investigated. A concept of (pseudo)tensoriality is formulated. The formalism of connections is developed. In particular, operators of horizontal projection, covariant derivative and curvature are constructed and analyzed. Generalizations of the first structure equation and of the Bianchi identity are found. Illustrative examples are presented.
15. Weak equivalence classes of complex vector bundles
Hông-Vân Lê
2006-01-01
For any complex vector bundle Ek of rank k over a manifold Mm with Chern classes ci Î H2i(Mm, Z) and any non-negative integers l1, . . ., lk we show the existence of a positive number p(m, k) and the existence of a complex vector bundle Êk over Mm whose Chern classes are p(m, k) × li × ci Î H2i(Mm, Z). We also discuss a version of this statement for holomorphic vector bundles over projective algebraic manifolds.
16. Assembly mechanism for nuclear fuel bundles
A description is given of a nuclear power reactor fuel bundle having tie rods fastened to a lower tie plate and passing through openings in the upper tie plate with the assembled bundle secured by rotatable locking sleeves which engage slots provided in the upper tie plate. Pressure exerted by helical springs mounted around each of the fuel rods urge the upper tie plate against the locking sleeves. The bundle may be disassembled after depressing the upper tie plate and rotating the locking sleeves to the unlocked position
17. Vector supersymmetry in the universal bundle
We present a vector supersymmetry for Witten-type topological gauge theories, and examine its algebra in terms of a superconnection formalism. When covariant constraints on the supercurvature are chosen, a correspondence is established with the universal bundle construction of Atiyah and Singer. The vector supersymmetry represents a certain shift operator in the curvature of the universal bundle, and can be used to generate the hierarchy of observables in these theories. This formalism should lead to the construction of vector supergravity theories, and perhaps to the gravitational analogue of the universal bundle. (orig.)
18. Bundle duct interaction studies for fuel assemblies
It is known that the wire-wrapped rods and duct in an LMFBR are undergoing a gradual structural distortion from the initially uniform geometry under the combined effects of thermal expansion and irradiation induced swelling and creep. These deformations have a significant effect on flow characteristics, thus causing changes in thermal behavior such as cladding temperature and temperature distribution within a bundle. The temperature distribution may further enhance or retard irradiation induced deformation of the bundle. This report summarizes the results of the continuing effort in investigating the bundle-duct interaction, focusing on the need for the large development plant
19. Thermo-fluid and electrochemical modeling of a multi-bundle IP-SOFC - Technology for second generation hybrid application
This paper describes an electrochemical model, which studies the performance of multi-bundles integrated-planar solid oxide fuel cell (IP-SOFC strip) fuelled by pure hydrogen. Following a description of the basic geometries and general premises the approaches and simplifications for the calculation of ohmic resistance, gas flow, heat and mass transfers are given. The effect of fuel pressure ratio and the temperature variation are investigated in a parameter study. The model results have been validates well with experimental data obtained from a full-size prototype of IP-SOFC technology for the second generation hybrid application; it is found that the ohmic and cathode activation overpotentials represent a major loss in fuel cell voltage. The results obtained from both strips also demonstrated acceptable performance and good reproducibility bundles to bundles at 900 deg. C. These results indicated weak effect of parameter variation on the bundles to bundles performances.
20. Thermo-fluid and electrochemical modeling of a multi-bundle IP-SOFC - Technology for second generation hybrid application
Mounir, H. [L2MCS - Laboratoire de Mecanique des Materiaux et Calcul des Structures de l' ENSET de Rabat, ENSET-Rabat, B.P. 6207, Av. Armee Royale, Badinat Al Irfane Rabat (Morocco); Laboratoire de Thermodynamique et Mecaniques des Materiaux, Faculte des Sciences de Rabat (Morocco); El Gharad, A. [L2MCS - Laboratoire de Mecanique des Materiaux et Calcul des Structures de l' ENSET de Rabat, ENSET-Rabat, B.P. 6207, Av. Armee Royale, Badinat Al Irfane Rabat (Morocco); Belaiche, M. [Laboratoire Magnetisme, Materiaux Magnetiques, Micro-onde et ceramique, Ecole normale superieure, BP 9235, Ocean Rabat 1000 (Morocco); Boukalouch, M. [Laboratoire de Thermodynamique et Mecaniques des Materiaux, Faculte des Sciences de Rabat (Morocco)
2009-10-15
This paper describes an electrochemical model, which studies the performance of multi-bundles integrated-planar solid oxide fuel cell (IP-SOFC strip) fuelled by pure hydrogen. Following a description of the basic geometries and general premises the approaches and simplifications for the calculation of ohmic resistance, gas flow, heat and mass transfers are given. The effect of fuel pressure ratio and the temperature variation are investigated in a parameter study. The model results have been validates well with experimental data obtained from a full-size prototype of IP-SOFC technology for the second generation hybrid application; it is found that the ohmic and cathode activation overpotentials represent a major loss in fuel cell voltage. The results obtained from both strips also demonstrated acceptable performance and good reproducibility bundles to bundles at 900 C. These results indicated weak effect of parameter variation on the bundles to bundles performances. (author)
1. Location of test bundle instrumentation and anticipated experimental values for the CFTL AG-1 bundle
The placement of instrumentation within the Core Flow Test Loop (CFTL) AG-1 test section to meet the following objectives is described. The objectives are threefold: (1) to provide values for the evaluation of the performance of the test section, (2) to compare the experimental data with value determined by pretest calulations to indicate the approach to conditions that can lead to a bundle failure, and (3) to acquire data during testing that will form a data base for subsequent use in the verification of computational procedures used in the licensing of the Gas-Cooled Fast Reactor. Anticipated values for the various instruments have been determined using the computational procedure SAGAPO modified for the AG-1 geometry. These results are used as the basis for the specification of differential pressure cells and the range of readings anticipated from the thermocouples. Part of the results for the full-flow, full-power case is presented
2. Effect of Testing Conditions on Fibre-Bundle Tensile Properties Part Ⅰ: Sample Preparation, Bundle Mass and Fibre Alignment of Wool Bundles
YU Wei-dong; YAN Hao-jing; Ron Postle; Yang Shouren
2002-01-01
Due to the effects of samples and testing conditions on fibre-bundle tensile behaviour, it is necessary to investigate the relationships between experimental factors and tensile properties for the fibre-bumdle tensile tester (TENSOR). The effects of bundle sample preparation, fibre bundle mass and fibre alignment have been tested. The experimental results indicated that (1) the low damage in combing and no free-end fibres in the cut bundle are most important for the sample preparation; (2) the reasonable bundle mass is 400- 700tex, but the tensile properties measured should bemodified with the bundle mass because a small amount of bundle mass causes the scatter results, while the larger is the bundle mass, the more difficult to comb fibres parallel and to clamp fibre evenly; and (3) the fibre irregular arrangement forms a slack bundle resulting in interaction between fibres, which will affect the reproducibility and accuracy of the tensile testing.
3. Self-mapping degrees of torus bundles and torus semi-bundles
Sun, Hongbin; Wang, Shicheng; Wu, Jianchun
2010-01-01
Each closed oriented 3-manifold $M$ is naturally associated with a set of integers $D(M)$, the degrees of all self-maps on $M$. $D(M)$ is determined for each torus bundle and torus semi-bundle $M$. The structure of torus semi-bundle is studied in detail. The paper is a part of a project to determine $D(M)$ for all 3-manifolds in Thurston's picture.
4. In-pool damaged fuel bundle recovery
While preparing to rerack the Oyster Creek Nuclear Generating Station, GPU Nuclear had need to move a damaged fuel bundle. This bundle had no upper tie plate and could not be moved in the normal manner. GPU Nuclear formed a small, dedicated project team to disassemble, package, and move this damaged bundle. The team was composed of key personnel from GPU Nuclear Fuels Projects, OCNGS Operations and Proto-Power/Bisco, a specialty contractor who has fuel bundle reconstitution and rod consolidation experience, remote tooling, underwater video systems and experienced technicians. Proven tooling, clear procedures and a simple approach were important, but the key element was the spirit of teamwork and leadership exhibited by the people involved. In spite of several emergent problems which a task of this nature presents, this small, close knit utility/vendor team completed the work on schedule and within the exposure and cost budgets
5. In-pool damaged fuel bundle recovery
While preparing to rerack the Oyster Creek Nuclear Generating Station, GPU Nuclear had need to move a damaged fuel bundle. This bundle had no upper tie plate and could not be moved in the normal manner. GPU Nuclear formed a small, dedicated project team to disassemble, package and move this damaged bundle. The team was composed of key personnel from GPU Nuclear Fuels Projects, OCNGS Operations and Proto-Power / Bisco, a specialty contractor who has fuel bundle reconstitution and rod consolidation experience, remote tooling, underwater video systems and experienced technicians. Proven tooling, clear procedures and a simple approach were important, but the key element was the spirit of teamwork and leadership exhibited by the people involved
6. Nuclear fuel bundle disassembly and assembly tool
A nuclear power reactor fuel bundle is described which has a plurality of tubular fuel rods disposed in parallel array between two transverse tie plates. It is secured against disassembly by one or more locking forks which engage slots in tie rods which position the transverse plates. Springs mounted on the fuel and tie rods are compressed when the bundle is assembled thereby maintaining a continual pressure against the locking forks. Force applied in opposition to the springs permits withdrawal of the locking forks so that one tie plate may be removed, giving access to the fuel rods. An assembly and disassembly tool facilitates removal of the locking forks when the bundle is to be disassembled and the placing of the forks during assembly of the bundle. (U.S.)
7. Quantum Bundle Description of Quantum Projective Spaces
Ó Buachalla, Réamonn
2012-12-01
We realise Heckenberger and Kolb's canonical calculus on quantum projective ( N - 1)-space C q [ C p N-1] as the restriction of a distinguished quotient of the standard bicovariant calculus for the quantum special unitary group C q [ SU N ]. We introduce a calculus on the quantum sphere C q [ S 2 N-1] in the same way. With respect to these choices of calculi, we present C q [ C p N-1] as the base space of two different quantum principal bundles, one with total space C q [ SU N ], and the other with total space C q [ S 2 N-1]. We go on to give C q [ C p N-1] the structure of a quantum framed manifold. More specifically, we describe the module of one-forms of Heckenberger and Kolb's calculus as an associated vector bundle to the principal bundle with total space C q [ SU N ]. Finally, we construct strong connections for both bundles.
8. Twin tori for a new bundle divertor
A new bundle divertor system using the straight stagnation axis in toroidal field together with the uniform field along the axis is discussed in detail. We call this type of divertor as the ''muffler divertor'' because of its shape. (author)
9. Noncommutative principal bundles through twist deformation
Aschieri, Paolo; Pagani, Chiara; Schenkel, Alexander
2016-01-01
We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a deformation of the fibers. If the twist is associated with the automorphism group of the principal bundle, then we obtain noncommutative deformations of the base space as well. Combining the two twist deformations we obtain noncommutative principal bundles with both noncommutative fibers and base space. More in general, the natural isomorphisms proving the equivalence of a closed monoidal category of modules and its twist related one are used to obtain new Hopf-Galois extensions as twists of Hopf-Galois extensions. A sheaf approach is also considered, and examples presented.
10. Crosstalk analysis of carbon nanotube bundle interconnects
Zhang, Kailiang; Tian, Bo; Zhu, Xiaosong; WANG, FANG; Wei, Jun
2012-01-01
Carbon nanotube (CNT) has been considered as an ideal interconnect material for replacing copper for future nanoscale IC technology due to its outstanding current carrying capability, thermal conductivity, and mechanical robustness. In this paper, crosstalk problems for single-walled carbon nanotube (SWCNT) bundle interconnects are investigated; the interconnect parameters for SWCNT bundle are calculated first, and then the equivalent circuit has been developed to perform the crosstalk analys...
11. A Geometric Approach to Noncommutative Principal Bundles
Wagner, Stefan
2011-01-01
From a geometrical point of view it is, so far, not sufficiently well understood what should be a "noncommutative principal bundle". Still, there is a well-developed abstract algebraic approach using the theory of Hopf algebras. An important handicap of this approach is the ignorance of topological and geometrical aspects. The aim of this thesis is to develop a geometrically oriented approach to the noncommutative geometry of principal bundles based on dynamical systems and the representation theory of the corresponding transformation group.
12. Parahoric bundles on a compact Riemann surface
Balaji, V
2010-01-01
Let $X$ be a compact Riemann surface of genus $g \\geq 2$. The aim of this paper is to study homomorphisms of certain discrete subgroups of $PSL(2, {\\mathbb R})$ into maximal compact subgroups of semisimple simply connected algebraic groups and relate them to torsors under a Bruhat-Tits group scheme. We also construct the moduli spaces of semistable parahoric bundles. These results generalize the theorem of Mehta and Seshadri on parabolic vector bundles.
13. Evaluation on BDI of large diameter pin bundles by out-of-pile bundle compression test
Bundle-duct interaction (BDI) in core fuel subassemblies in fast reactors (FRs) is a limiting factor for fuel burnup. Since the large diameter fuel pin is generally believed to be a measure to improve FR fuel performance, the out-of-pile bundle compression test with large diameter pins (φ8.5mm and (φ 10.4mm) was performed to evaluate BDI in these bundles. In the compression test, bundle cross-sectional images (CT images) under BDI condition were obtained by using the X-ray computer tomography. In the main study, the CT images were numerically analyzed to evaluate deformation of the large diameter pin bundle due to BDI. The CT image analysis results revealed that pin-to-duct contact did not occur when the flat-to-flat bundle compression level reached one wire diameter (BDI level of 1dw), which indicates that BDI in large diameter pin bundles was mitigated similarly to the currently used small diameter pin bundles. In addition, the mitigation mechanism for BDI, which delays initiation of pin-to-duct contact, was investigated by using the computer code analysis. The code analysis results showed that cladding oval-distortion acted as a major mitigation mechanism for BDI as in the case of small pin diameter bundles. (author)
14. Cadherin-23 may be dynamic in hair bundles of the model sea anemone Nematostella vectensis.
Pei-Ciao Tang
Full Text Available Cadherin 23 (CDH23, a component of tip links in hair cells of vertebrate animals, is essential to mechanotransduction by hair cells in the inner ear. A homolog of CDH23 occurs in hair bundles of sea anemones. Anemone hair bundles are located on the tentacles where they detect the swimming movements of nearby prey. The anemone CDH23 is predicted to be a large polypeptide featuring a short exoplasmic C-terminal domain that is unique to sea anemones. Experimentally masking this domain with antibodies or mimicking this domain with free peptide rapidly disrupts mechanotransduction and morphology of anemone hair bundles. The loss of normal morphology is accompanied, or followed by a decrease in F-actin in stereocilia of the hair bundles. These effects were observed at very low concentrations of the reagents, 0.1-10 nM, and within minutes of exposure. The results presented herein suggest that: (1 the interaction between CDH23 and molecular partners on stereocilia of hair bundles is dynamic and; (2 the interaction is crucial for normal mechanotransduction and morphology of hair bundles.
15. Annular burnout data from rod bundle experiments
Burnout data for annular flow in a rod bundle are presented for both transient and steady-state conditions. Tests were performed at the Oak Ridge National Laboratory in the Thermal Hydraulic Test Facility (THTF), a pressurized-water loop containing an electrically heated 64-rod bundle. The bundle configuration is typical of later generation pressurized-water reactors with 17 x 17 fuel arrays. Both axial and radial power profiles are flat. All experiments were carried out in upflow with subcooled inlet conditions, insuring accurate flow measurement. Conditions within the bundle were typical of those which could be encountered during a nuclear reactor loss-of-coolant accident. Level average fluid conditions within the test section were calculated using steady-state mass and energy conservation considerations for the steady-state tests and a transient, homogeneous, equilibrium computer code for the transient tests. Unlike tube dryout, burnout within a rod bundle does not necessarily occur at one distinct axial level. The location of individual rod dryout was determined by scanning rods axially and locating the position where rod superheat increased from approx. =0 to 30 K or greater. Thermocouple instrumentation within the bundle allows the location of dryout to be determined to within approximately +.5 cm for many of the tests
16. Lateral mechanical coupling of stereocilia in cochlear hair bundles.
Langer, M G; Fink, S; Koitschev, A; Rexhausen, U; Hörber, J K; Ruppersberg, J P
2001-06-01
For understanding the gating process of transduction channels in the inner ear it is essential to characterize and examine the functional properties of the ultrastructure of stereociliary bundles. There is strong evidence that transduction channels in hair cells are gated by directly pulling at the so-called tip links. In addition to these tip links a second class of filamentous structures was identified in the scanning and transmission electron microscope: the side-to-side links. These links laterally connect stereocilia of the same row of a hair bundle. This study concentrates on mechanical coupling of stereocilia of the tallest row connected by side-to-side links. Atomic Force microscopy (AFM) was used to investigate hair bundles of outer hair cells (OHCs) from postnatal rats (day 4). Although hair bundles of postnatal rats are still immature at day 4 and interconnecting cross-links do not show preferential direction yet, hair bundles of investigated OHCs already showed the characteristic V-shape of mature hair cells. In a first experiment, the stiffness of stereocilia was investigated scanning individual stereocilia with an AFM tip. The spring constant for the excitatory direction was 2.5 +/- 0.6 x 10(-3) N/m whereas a higher spring constant (3.1 +/- 1.5 x 10(-3) N/m) was observed in the inhibitory direction. In a second set of experiments, the force transmission between stereocilia of the tallest row was measured using AFM in combination with a thin glass fiber. This fiber locally displaced a stereocilium while the force laterally transmitted to the neighboring untouched taller stereocilia was measured by AFM. The results show a weak force interaction between tallest stereocilia of postnatal rats. The force exerted to an individual stereocilium declines to 36% at the nearest adjacent stereocilium of the same row not touched with the fiber. It is suggested that the amount of force transmitted from a taller stereocilium to an adjacent one of the same row depends
17. K-Theories for Certain Infinite Rank Bundles
Larrain-Hubach, Andres
2011-01-01
Several authors have recently constructed characteristic classes for classes of infinite rank vector bundles appearing in topology and physics. These include the tangent bundle to the space of maps between closed manifolds, the infinite rank bundles in the families index theorem, and bundles with pseudodifferential operators as structure group. In this paper, we construct the corresponding K-theories for these types of bundles. We develop the formalism of these theories and use their Chern ch...
18. Effect of left bundle branch block on TIMI frame count
Hatice Tolunay; Ahmet Kasapkara; İsa Öner Yüksel; Nurcan Başar; Ayşe Saatcı Yaşar; Mehmet Bilge
2010-01-01
Aim: Left bundle branch block is an independent risk factorfor cardiac mortality. In this study we aimed to evaluatecoronary blood flow with TIMI frame count in patients with left bundle branch block and angiographically proven normal coronary arteries.Materials and methods: We retrospectively studied 17 patients with left bundle branch block and as a control group 16 patients without left bundle branch block. All patientshad angiographically proven normal coronary arteries.Left bundle branch...
19. Product-bundling and Incentives for Merger and Strategic Alliance
Sue Mialon
2009-01-01
This paper analyzes firms' choice between a merger and a strategic alliance in bundling their product with other complementary products. We consider a framework in which firms can improve profits only from product-bundling. While mixed bundling is not profitable, pure bundling is because pure bundling reduces consumers' choices, and thus softens competition among firms. Firms benefit the most from this reduced competition if they form an alliance. Firms do not gain as much from a merger becau...
20. Noise alters hair-bundle mechanics at the cochlear apex
Strimbu, C. Elliott; Fridberger, Anders
2015-12-01
Exposure to loud sounds can lead to both permanent and short term changes in auditory sensitivity. Permanent hearing loss is often associated with gross changes in cochlear morphology including the loss of hair cells and auditory nerve fibers while the mechanisms of short term threshold shifts are much less well understood and may vary at different locations across the cochlea. Previous reports suggest that exposure to loud sounds leads to a decrease in the cochlear microphonic potential and in the stiffness of the organ of Corti. Because the cochlear microphonic reflects changes in the membrane potential of the hair cells, this suggests that hair-bundle motion should be reversibly altered following exposure to loud sounds. Using an in vitro preparation of the guinea pig temporal bone we investigate changes in the micro-mechanical response near the cochlear apex following a brief (up to 10 - 20 minutes) exposure to loud (˜ 120 dB) tones near the best frequency at this location. We use time-resolved confocal imaging to record the motion of outer hair cell bundles before and after acoustic overstimulation. We have also recorded larger-scale structural views of the organ of Corti before and after exposure to the loud sound. Conventional electrophysiological techniques are used measure the cochlear microphonic potential. As has been previously reported, following acoustic overexposure the cochlear microphonic declines in value and typically recovers on the order of 30 - 60 minutes. Hair-bundle trajectories are affected following the loud sound and typically recover on a somewhat faster time scale than the microphonic potential, although the results vary considerably across preparations. Preliminary results also suggest reversible changes in the hair cell's resting potential following the loud sound.
1. Elevated temperature triggers human respiratory syncytial virus F protein six-helix bundle formation
Human respiratory syncytial virus (RSV) is a major cause of severe lower respiratory tract infection in infants, immunocompromised patients, and the elderly. The RSV fusion (F) protein mediates fusion of the viral envelope with the target cell membrane during virus entry and is a primary target for antiviral drug and vaccine development. The F protein contains two heptad repeat regions, HR1 and HR2. Peptides corresponding to these regions form a six-helix bundle structure that is thought to play a critical role in membrane fusion. However, characterization of six-helix bundle formation in native RSV F protein has been hindered by the fact that a trigger for F protein conformational change has yet to be identified. Here we demonstrate that RSV F protein on the surface of infected cells undergoes a conformational change following exposure to elevated temperature, resulting in the formation of the six-helix bundle structure. We first generated and characterized six-helix bundle-specific antibodies raised against recombinant peptides modeling the RSV F protein six-helix bundle structure. We then used these antibodies as probes to monitor RSV F protein six-helix bundle formation in response to a diverse array of potential triggers of conformational changes. We found that exposure of 'membrane-anchored' RSV F protein to elevated temperature (45-55 deg. C) was sufficient to trigger six-helix bundle formation. Antibody binding to the six-helix bundle conformation was detected by both flow cytometry and cell-surface immunoprecipitation of the RSV F protein. None of the other treatments, including interaction with a number of potential receptors, resulted in significant binding by six-helix bundle-specific antibodies. We conclude that native, untriggered RSV F protein exists in a metastable state that can be converted in vitro to the more stable, fusogenic six-helix bundle conformation by an increase in thermal energy. These findings help to better define the mechanism of
2. Analysis of the Bundle Duct Interaction using the FBR fuel pin bundle deformation analysis code 'BAMBOO'
PNC has been developing a computer code 'BAMBOO' to analyze the wire spaced FBR fuel pin bundle deformation under the BDI (Bundle Duct Interaction) condition by means of the three dimensional F.E.M. This code analyzes fuel pins' bowing and oval deformations which are dominant deformation behaviors of the fuel pin bundle under the BDI condition. In this study the 'BAMBOO' code is validated on the out-of-pile compression test of the FBR bundle (compression test) by comparing the results of the code analysis with the compression test results, and the highly irradiated (≥2.1x1027 n/m2, E > 0.1 MeV) bundle deformation behaviors are investigated from the viewpoint of the similarity to those in the compression test based on the analytical results of the code. (1) The calculated pin-to-duct minimum clearances as a function of the BDI levels in the compression test analysis agree with the experimental values evaluated from the CT image analysis of the bundle cross-section in the compression test within ±0.2 mm. And the calculated values of the fuel pins' oval deformations agree with the experimental values based on the pin diameter measurements done after the compression test within ±0.05 mm. (2) By comparing the irradiation induced bundle deformation with the bundle deformation in the compression test based on the code analysis, it is confirmed that the changes of the pin-to-duct minimum clearances with the BDI levels show equivalent trends between the both bundle deformations. And in this code analysis of the irradiation induced bundle deformation, contact loads between the fuel pins and the pacer wires are extremely small (below 10 kgf) even at about 3 dw of the BDI level compared to those in the compression test analysis. (J.P.N.)
3. NIF laser bundle review. Final report
We performed additional bundle review effort subsequent to the completion of the preliminary report and are revising our original recommendations. We now recommend that the NIF baseline laser bundle size be changed to the 4x2 bundle configuration. There are several 4x2 bundle configurations that could be constructed at a cost similar to that of the baseline 4x12 (from $11M more to about$11M less than the baseline; unescalated, no contingency) and provide significant system improvements. We recommend that the building cost estimates (particularly for the in-line building options) be verified by an architect/engineer (A/E) firm knowledgeable about building design. If our cost estimates of the in-line building are accurate and therefore result in a change from the baseline U-shaped building layout, the acceptability of the in-line configuration must be reviewed from an operations viewpoint. We recommend that installation, operation, and maintenance of all laser components be reviewed to better determine the necessity of aisles, which add to the building cost significantly. The need for beam expansion must also be determined since it affects the type of bundle packing that can be used and increases the minimum laser bay width. The U-turn laser architecture (if proven viable) offers a reduction in building costs since this laser design is shorter than the baseline switched design and requires a shorter laser bay
4. HIV-1 Envelope Proteins Complete Their Folding into Six-helix Bundles Immediately after Fusion Pore Formation
Markosyan, Ruben M; Cohen, Fredric S.; Melikyan, Grigory B.
2003-01-01
Fusion proteins of many viruses, including HIV-1 envelope protein (Env), fold into six-helix bundle structures. Fusion between individual Env-expressing cells and target cells was studied by fluorescence microscopy, and a temperature jump technique, to determine whether folding of Env into a bundle is complete by the time fusion pores have formed. Lowering temperature to 4°C immediately after a pore opened halted pore growth, which quickly resumed when temperature was raised again. HIV gp41-d...
5. Turbulent flow through two asymmetric rod bundles
Measurements of the mean velocity, of the wall shear stresses, and of the turbulence have been performed in four wall subchannels of rod bundles of four parallel rods enclosed in a rectangular channel. The pitch-to-diameter ratio was P/D=1.148 and the wall-to-diameter ratios ranged from 1.045 to 1.252. The full Reynolds stress tensor has been determined by hot-wire technique. The results of the turbulences intensities show that the flow through rod bundles differs widely from flow through circular tubes. More sophisticated analytical tools than presently available are required to predict turbulent flow through rod bundles with sufficient accuracy
6. Assembly mechanism for nuclear fuel bundles
In a nuclear power reactor fuel bundle having tie rods fastened to a lower tie plate and passing through openings in the upper tie plate, the assembled bundle is secured by locking lugs fixed to rotatable locking sleeves which engage the upper tie plate. Pressure exerted by helical springs mounted around each of the tie rods urge retaining lugs fixed to a retaining sleeve associated with respective tie rods into a position with respect to the locking sleeve to prevent accidental disengagement of the upper plate from the locking lugs. The bundle may be disassembled by depressing the retaining sleeves and rotating the locking lugs to the disengaged position, and then removing the upper tie plate
7. Porous Silicon and Denim Fiber Bundle Characterization
Deuro, Randi Ellen
My thesis research aims to characterize and exploit materials in an efficient, rapid, non-destructive manner. Part I of this document summarizes my research on porous silicon (pSi) design, fabrication, and surface modification for use as a novel chemical sensor. The optimization of fabrication process parameters (etching time, etching solution, electrode shape, and the fixing process) on pSi photoluminescence (PL) is presented. I have also investigated the effects of analyte vapors (acetonitrile, toluene, methanol, acetone) on the pSi PL and surface chemistry using luminescence and Fourier-transform infrared (FT-IR) spectroscopy and microscopy methods. The mechanism and benefits of one method of pSi surface modification and protection (ultraviolet (UV) hydrosilylation) will also be presented. Finally, high thorough-put methods of pSi sensor production are described. In Part II of this document, I introduce a novel technique for analyzing and discriminating among denim fiber bundles. An investigation into the benefits of luminescence-based multispectral imaging (LMSI) for denim fiber bundle identification has been conducted. I explore the power of nitromethane (CH 3NO2) based quenching in fiber bundle classification and identify the quenching mechanism. The luminescence spectra (450 - 850 nm) and images from the denim fiber bundles were obtained while exciting at 325 nm or 405 nm. Here, LMSI data were recorded in < 10 s and subsequently assessed by principal component analysis (PCA) and rendered red, green, blue (RGB) component histograms. The results show that LMSI data can be used to rapidly and uniquely classify all the fiber bundle types studied in this research. These non-destructive techniques eliminate extensive sample preparation and allow for rapid multispectral image collection, analysis, and assessment. The quenching data also revealed that the dye molecules within the individual fiber bundles exhibited dramatically different accessibilities to CH 3NO2.
8. Cadherin-23 May Be Dynamic in Hair Bundles of the Model Sea Anemone Nematostella vectensis
Pei-Ciao Tang; Watson, Glen M.
2014-01-01
Cadherin 23 (CDH23), a component of tip links in hair cells of vertebrate animals, is essential to mechanotransduction by hair cells in the inner ear. A homolog of CDH23 occurs in hair bundles of sea anemones. Anemone hair bundles are located on the tentacles where they detect the swimming movements of nearby prey. The anemone CDH23 is predicted to be a large polypeptide featuring a short exoplasmic C-terminal domain that is unique to sea anemones. Experimentally masking this domain with anti...
9. A bundle of sticks in my garden
Farran, Sue
2012-01-01
The English law of property is often described as a ‘bundle of sticks’ in which each ‘stick’ represents a particular right. Gardens challenge these rights and wreak havoc on the ‘bundle of sticks’. This paper looks at the twenty-first century manifestations of community engagement with ground and explores how ‘gardening’ is undermining concepts of ownership, possession and management of land and how the fence between what is private and what is public is being encroached and challenged by com...
10. Characteristic classes of quantum principal bundles
Durdevic, M
1995-01-01
A noncommutative-geometric generalization of classical Weil theory of characteristic classes is presented, in the conceptual framework of quantum principal bundles. A particular care is given to the case when the bundle does not admit regular connections. A cohomological description of the domain of the Weil homomorphism is given. Relations between universal characteristic classes for the regular and the general case are analyzed. In analogy with classical geometry, a natural spectral sequence is introduced and investigated. The appropriate counterpart of the Chern character is constructed, for structures admitting regular connections. Illustrative examples and constructions are presented.
11. TRIGA spent fuel bundles safe storage
Negut, G.; Covaci, St. [Institute for Nuclear Research, Research Reactor Dept., Pitesti (Romania); Prisecaru, I.; Dupleac, D. [Bucharest Univ. Politehnica, Power and Nuclear Engineering Dept., Bucharest (Romania)
2007-07-01
TRIGA-SSR is a steady state research and material test reactor that has been in operation since 1980. The original TRIGA fuel was HEU (highly enriched uranium) with a U{sup 235} enrichment of 93 per cent. Almost all TRIGA HEU fuel bundles are now burned-up. Part of the spent fuel was loaded and transferred to US, in a Romania - DOE arrangement. The rest of the TRIGA fuel bundles have to be temporarily stored in the TRIGA facility. As the storage conditions had to be established with caution, neutron and thermal hydraulic evaluations of the storage conditions were required. Some criticality evaluations were made based on the SAR (Safety Analysis Report) data. Fuel constant axial temperature approximation effect is usual for criticality computations. TRIGA-SSR fuel bundle geometry and materials model for SCALE5-CSAS module allows the introduction of a fuel temperature dependency for the entire fuel active height, using different materials for each fuel bundle region. Previous RELAP5 thermal hydraulic computations for an axial and radial power distribution in the TRIGA fuel pin were done. Fuel constant temperature approximation overestimates pin factors for every core operating at high temperatures. From the thermal hydraulic point of view the worst condition of the storage grid occurs when the transfer channel is accidentally emptied of water from the pool, or the bundle is handled accidentally to remain in air. All the residual heat from the bundles has to be removed without fuel overheating and clad failure. RELAP5 computer code for residual heat removal was used in the assessment of residual heat removal. We made a couple of evaluations of TRIGA bundle clad temperatures in air cooling conditions, with different residual heat levels. The criticality computations have shown that the spent TRIGA fuel bundles storage grid is strongly sub-critical with k(eff) = 0.5951. So, there is no danger for a criticality accident for this storage grid type. The assessment is done
12. Scaling Shift in Multicracked Fiber Bundles
Manca, Fabio; Giordano, Stefano; Palla, Pier Luca; Cleri, Fabrizio
2014-12-01
Bundles of fibers, wires, or filaments are ubiquitous structures in both natural and artificial materials. We investigate the bundle degradation induced by an external damaging action through a theoretical model describing an assembly of parallel fibers, progressively damaged by a random population of cracks. Fibers in our model interact by means of a lateral linear coupling, thus retaining structural integrity even after substantial damage. Monte Carlo simulations of the Young's modulus degradation for increasing crack density demonstrate a remarkable scaling shift between an exponential and a power-law regime. Analytical solutions of the model confirm this behavior, and provide a thorough understanding of the underlying physics.
13. Safe Harbors for Quantity Discounts and Bundling
Dennis W. Carlton; Michael Waldman
2008-01-01
The courts and analysts continue to struggle to articulate safe harbors for a wide variety of common business pricing practices in which either a single product is sold at a discount if purchased in bulk or in which multiple products are bundled together at prices different from the ones that would emerge if the products were purchased separately. The phenomenon of tying in which the sale of one product is conditioned on the purchase of another is closely related to bundling. Its analysis rel...
14. TRIGA spent fuel bundles safe storage
TRIGA-SSR is a steady state research and material test reactor that has been in operation since 1980. The original TRIGA fuel was HEU (highly enriched uranium) with a U235 enrichment of 93 per cent. Almost all TRIGA HEU fuel bundles are now burned-up. Part of the spent fuel was loaded and transferred to US, in a Romania - DOE arrangement. The rest of the TRIGA fuel bundles have to be temporarily stored in the TRIGA facility. As the storage conditions had to be established with caution, neutron and thermal hydraulic evaluations of the storage conditions were required. Some criticality evaluations were made based on the SAR (Safety Analysis Report) data. Fuel constant axial temperature approximation effect is usual for criticality computations. TRIGA-SSR fuel bundle geometry and materials model for SCALE5-CSAS module allows the introduction of a fuel temperature dependency for the entire fuel active height, using different materials for each fuel bundle region. Previous RELAP5 thermal hydraulic computations for an axial and radial power distribution in the TRIGA fuel pin were done. Fuel constant temperature approximation overestimates pin factors for every core operating at high temperatures. From the thermal hydraulic point of view the worst condition of the storage grid occurs when the transfer channel is accidentally emptied of water from the pool, or the bundle is handled accidentally to remain in air. All the residual heat from the bundles has to be removed without fuel overheating and clad failure. RELAP5 computer code for residual heat removal was used in the assessment of residual heat removal. We made a couple of evaluations of TRIGA bundle clad temperatures in air cooling conditions, with different residual heat levels. The criticality computations have shown that the spent TRIGA fuel bundles storage grid is strongly sub-critical with k(eff) = 0.5951. So, there is no danger for a criticality accident for this storage grid type. The assessment is done for
15. Impact of bundle deformation on CHF: ASSERT-PV assessment of extended burnup Bruce B bundle G85159W
This paper presents a subchannel thermalhydraulic analysis of the effect on critical heat flux (CHF) of bundle deformation such as element bow and diametral creep. The bundle geometry is based on the post-irradiation examination (PIE) data of a single bundle from the Bruce B Nuclear Generating Station, Bruce B bundle G85159W, which was irradiated for more than two years in the core during reactor commissioning. The subchannel code ASSERT-PV IST is used to assess changes in CHF and dryout power due to bundle deformation, compared to the reference, undeformed bundle. (author)
16. Arabidopsis VILLIN2 and VILLIN3 Are Required for the Generation of Thick Actin Filament Bundles and for Directional Organ Growth[C][W
van der Honing, Hannie S.; Kieft, Henk; Emons, Anne Mie C.; Ketelaar, Tijs
2012-01-01
In plant cells, actin filament bundles serve as tracks for myosin-dependent organelle movement and play a role in the organization of the cytoplasm. Although virtually all plant cells contain actin filament bundles, the role of the different actin-bundling proteins remains largely unknown. In this study, we investigated the role of the actin-bundling protein villin in Arabidopsis (Arabidopsis thaliana). We used Arabidopsis T-DNA insertion lines to generate a double mutant in which VILLIN2 (VLN2) and VLN3 transcripts are truncated. Leaves, stems, siliques, and roots of vln2 vln3 double mutant plants are twisted, which is caused by local differences in cell length. Microscopy analysis of the actin cytoskeleton showed that in these double mutant plants, thin actin filament bundles are more abundant while thick actin filament bundles are virtually absent. In contrast to full-length VLN3, truncated VLN3 lacking the headpiece region does not rescue the phenotype of the vln2 vln3 double mutant. Our results show that villin is involved in the generation of thick actin filament bundles in several cell types and suggest that these bundles are involved in the regulation of coordinated cell expansion. PMID:22209875
17. Arabidopsis VILLIN2 and VILLIN3 are required for the generation of thick actin filament bundles and for directional organ growth.
van der Honing, Hannie S; Kieft, Henk; Emons, Anne Mie C; Ketelaar, Tijs
2012-03-01
In plant cells, actin filament bundles serve as tracks for myosin-dependent organelle movement and play a role in the organization of the cytoplasm. Although virtually all plant cells contain actin filament bundles, the role of the different actin-bundling proteins remains largely unknown. In this study, we investigated the role of the actin-bundling protein villin in Arabidopsis (Arabidopsis thaliana). We used Arabidopsis T-DNA insertion lines to generate a double mutant in which VILLIN2 (VLN2) and VLN3 transcripts are truncated. Leaves, stems, siliques, and roots of vln2 vln3 double mutant plants are twisted, which is caused by local differences in cell length. Microscopy analysis of the actin cytoskeleton showed that in these double mutant plants, thin actin filament bundles are more abundant while thick actin filament bundles are virtually absent. In contrast to full-length VLN3, truncated VLN3 lacking the headpiece region does not rescue the phenotype of the vln2 vln3 double mutant. Our results show that villin is involved in the generation of thick actin filament bundles in several cell types and suggest that these bundles are involved in the regulation of coordinated cell expansion. PMID:22209875
18. Abelian conformal field theory and determinant bundles
Andersen, Jørgen Ellegaard; Ueno, K.
2007-01-01
Following [10], we study a so-called bc-ghost system of zero conformal dimension from the viewpoint of [14, 16]. We show that the ghost vacua construction results in holomorphic line bundles with connections over holomorphic families of curves. We prove that the curvature of these connections are...
19. Optimization of a bundle divertor for FED
Optimal double-T bundle divertor configurations have been obtained for the Fusion Engineering Device (FED). On-axis ripple is minimized, while satisfying a series of engineering constraints. The ensuing non-linear optimization problem is solved via a sequence of quadratic programming subproblems, using the VMCON algorithm. The resulting divertor designs are substantially improved over previous configurations
20. Capacity efficiency of recovery request bundling
Ruepp, Sarah Renée; Dittmann, Lars; Berger, Michael Stübert; Stidsen, Thomas Riis; Lagakos, Stephen; Perlovsky, Leonid; Jha, Manoi; Covaci, Brindusa; Zaharim, Azarni; Mastorakis, Nikos
2010-01-01
This paper presents a comparison of recovery methods in terms of capacity efficiency. In particular, a method where recovery requests are bundled towards the destination (Shortcut Span Protection) is evaluated against traditional recovery methods. Our simulation results show that Shortcut Span Pr...... Protection uses more capacity than the unbundled related methods, but this is compensated by easier control and management of the recovery actions....
1. Line bundles on moduli and related spaces
Huebschmann, Johannes
2009-01-01
Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the principal G-circle bundles with connection on P having the given relative 2-form as curvature. Given a compact Lie group K, a biinvariant Riemannian metric on K, and a closed Riemann surface S of genus s, when we apply the construction to the particular case where f is the familiar relator map from a product of 2s copies of K to K we obtain the principal K-circle bundles on the associated extended moduli spaces which, via reduction, then yield the corresponding line bundles on possibly twisted moduli spaces of representations of the fundamental group of S in K, in particular, on moduli spaces of semistable holomorphic vector bundles or, more precisely, on a smooth open stratum when the moduli space is not smooth. The construction also yields an alternative geometric object, d...
2. Bundle Gerbes Applied to Quantum Field Theory
Carey, A L; Murray, M; Carey, Alan; Mickelsson, Jouko; Murray, Michael
2000-01-01
This paper reviews recent work on a new geometric object called a bundle gerbe and discusses some new examples arising in quantum field theory. One application is to an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials in odd space dimensions and a proof that this leads in a simple manner to the known Schwinger terms (Mickelsson-Faddeev cocycle) for the gauge group action. This gives an explicit computation of the Dixmier-Douady class of the associated bundle gerbe. The method works also in other cases of fermions in external fields (external gravitational field, for example) provided that the APS theorem can be applied; however, we have worked out the details only in the case of vector potentials. Another example, in which the bundle gerbe curvature plays a role, arises from the WZW model on Riemann surfaces. A further example is the `existence of string structures' question. We conclude by showing how global Hamiltonian anomalies fit with...
3. Quantum field theories on Hilbert bundles
We investigate whether it is possible to maintain the computational features of QED while avoiding some of its mathematical difficulties by formulating QFTs on Hilber bundles. This encounters two problems: 1) Haag's theorem persists, and 2) admissible fields do not generate motions on the base space. To do the latter, the coupling constant has to be a vector field upon the base space. (orig.)
4. Assembly mechanism for nuclear fuel bundles
This invention relates to an assembly mechanism for nuclear power reactor fuel bundles using a novel, simple and inexpensive means. The mechanism is readily operable remotely, avoids separable parts and is applicable to fuel assemblies in which the upper tie plate is rigidly mounted on the tie rods which hold it in place. (UK)
5. Capacity efficiency of recovery request bundling
Ruepp, Sarah Renée; Dittmann, Lars; Berger, Michael Stübert; Stidsen, Thomas Riis; Lagakos, Stephen; Perlovsky, Leonid; Jha, Manoi; Covaci, Brindusa; Zaharim, Azarni; Mastorakis, Nikos
2010-01-01
This paper presents a comparison of recovery methods in terms of capacity efficiency. In particular, a method where recovery requests are bundled towards the destination (Shortcut Span Protection) is evaluated against traditional recovery methods. Our simulation results show that Shortcut Span...
6. Riemann Surfaces: Vector Bundles, Physics, and Dynamics
Sikander, Shehryar
the monodromy with respect to the pulled back connection. The formula for the representation includes a series with coefficients as iterated integrals. This series is closely related to the cyclotomic version of the Drinfel'd associator. The geodesic flow in the unit the tangent bundle of this Teichmueller...
7. In-pile test of Qinshan PWR fuel bundle
In-pile test of Qinshan Nuclear Power Plant PWR fuel bundle has been conducted in HWRR HTHP Test loop at CIAE. The test fuel bundle was irradiated to an average burnup of 25000 Mwd/tU. The authors describe the structure of (3 x 3-2) test fuel bundle, structure of irradiation rig, fuel fabrication, irradiation conditions, power and fuel burnup. Some comments on the in-pile performance for fuel bundle, fuel rod and irradiation rig were made
8. Holomorphic Vector Bundle on Hopf Manifolds with Abelian Fundamental Groups
Xiang Yu ZHOU; Wei Ming LIU
2004-01-01
Let X be a Hopf manifolds with an Abelian fundamental group. E is a holomorphic vector bundle of rank r with trivial pull-back to W = Cn - {0}. We prove the existence of a non-vanishing section of L(×) E for some line bundle on X and study the vector bundles filtration structure of E. These generalize the results of D. Mall about structure theorem of such a vector bundle E.
9. Anatomic Double-Bundle Posterior Cruciate Ligament Reconstruction
Chahla, Jorge; Nitri, Marco; Civitarese, David; Dean, Chase S.; Moulton, Samuel G.; LaPrade, Robert F.
2016-01-01
The posterior cruciate ligament (PCL) is known to be the main posterior stabilizer of the knee. Anatomic single-bundle PCL reconstruction, focusing on reconstruction of the larger anterolateral bundle, is the most commonly performed procedure. Because of the residual posterior and rotational tibial instability after the single-bundle procedure and the inability to restore the normal knee kinematics, an anatomic double-bundle PCL reconstruction has been proposed in an effort to re-create the n...
10. Existence of vector bundles and global resolutions for singular surfaces
Vezzosi, G; S. SCHROER
2002-01-01
Abstract- We prove two results about vector bundles on singular algebraic surfaces. First, on proper surfaces there are vector bundles of rank two with arbitrarily large second Chern number and fixed determinant. Second, on separated normal surfaces any coherent sheaf is the quotient of a vector bundle. As a consequence, for such surfaces the Quillen K-theory of vector bundles coincides with the Waldhausen K-theory of perfect complexes. Examples show that, on non-separated schemes, usually...
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http://mathhelpforum.com/geometry/99599-can-someone-please-check-my-work-calculating-area.html
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# Math Help - Can someone please check my work in calculating this area?
1. ## Can someone please check my work in calculating this area?
Okay, I needed to find the area of this figure: http://i25.tinypic.com/symtyt.jpg
So I figured out that each side had a total area of 224 (8*28), so the two combined would be 448, if they were separate. Since they overlap, I needed to subtract the area of the triangle from this. Using heron's formula, I plugged in the numbers: 1/2(14+14+8) --> square root of 18(18-14)(18-14)(18-8) --> square root of 18*4*4*10 --> square root of 2880. The square root of 2880 is 53.665.
So, I did 448-53.665=394. Is this correct?
2. I disagree. The 2 parallelograms should have an area of 431.2 (7.7 * 28 * 2).
But you are right about subtracting the triangle. There is an easier way then using hero's formula.
Drop a height on the triangle and you have this:
Now use the Pythagorean theorem to calculate the height. Just easier in my opinion.
3. Thank you so much!!
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http://mathoverflow.net/questions/106226/determine-if-a-matrix-is-unimodular
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# Determine if a matrix is unimodular
Is deciding if an integer square matrix has determinant $\pm 1$ faster that calculating the determinant of the matrix?
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could you expand a bit on how this question is similar to detection of unimodularity, where every sub-determinant has to be in $\lbrace 0,\pm 1\rbrace$ – Suvrit Sep 3 '12 at 8:55
I don't know if this is 'faster', but consider the sequence of elementary operations which reduces a square integer matrix $A$ to it's Smith Normal form. We have an algorithm which determines the elementary divisors of $A$, and if any of these elementary divisors is $\neq \pm 1$, then we'll know $A$ is not unimodular. Any step in the reduction implements a euclidean algorithm to compute gcd's. That is, we are constantly reducing rows and colomns. If $A$ is unimodular, then we'll have computed all its elementary divisors, and their product is of course $detA$. So reducing $A$ to its Jordan – J. Martel Sep 3 '12 at 18:02
normal form, either $A$ is not unimodular and we shall eventually determine an elementary divisor $\neq \pm 1$ (which of course, may only occur at the last step), or we determine all of its elementary divisors to be $\pm 1$, and then we've just computed the determinant. So maybe the right question is simply whether or not computing the Smith normal form is faster than computing the determinant. – J. Martel Sep 3 '12 at 18:05
@J.Martel: I was thinking in terms of matrices with rational entries instead of integers; btw., computation of determinant is essentially an $O(n^3)$ procedure (Gaussian elimination); I guess the SNF is not much faster, if at all? – Suvrit Sep 4 '12 at 8:22
In fact, thanks to LU decomposition, computing the determinant is at least as fast as computing a matrix product. So we can compute the determinant exactly in \$O(n^{2.376}). See en.wikipedia.org/wiki/LU_decomposition#Theoretical_complexity. Similarly, in Storjohann's paper "Near Optimal Algorithms for Computing Smith Normal Forms of Integer Matrices" he shows a similar inequality. That is, for an integer square matrix, computing its SNF is at least as fast as computing a matrix product. – Mark Bell Sep 4 '12 at 9:43
|
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|
http://mathhelpforum.com/advanced-algebra/202320-subring-section-inclusion.html
|
## subring - section of inclusion
Let A and B be commutative rings with 1, A a subring of B. Is there a section of the inclusion, namely a ringhomomorphism from B to A, that is the identity on A? I hope not and I think that would be plaubsible. But I have no idea how to proof and I couldn't find something about it. Maybe it is easier to verify if A and B are concrete ring, A the real valued smooth and B the real valued continous functions on a differential manifold.
|
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|
https://link.springer.com/article/10.2165%2F11597750-000000000-00000
|
PharmacoEconomics
, Volume 30, Issue 8, pp 681–695
# The Impact of Rotavirus Vaccination on Discounted Net Tax Revenue in Egypt
A Government Perspective Analysis
• Mark P. Connolly
• Oleksandr Topachevskyi
• Baudouin Standaert
• Omayra Ortega
• Maarten Postma
Original Research Article
DOI: 10.2165/11597750-000000000-00000
Connolly, M.P., Topachevskyi, O., Standaert, B. et al. PharmacoEconomics (2012) 30: 681. doi:10.2165/11597750-000000000-00000
## Abstract
### Background
We evaluated national rotavirus (RV) immunization programme costs to estimate how resulting changes in morbidity and mortality will influence government fiscal accounts over time. The assumption was that increased childhood survival in vaccinated cohorts leads to increased numbers of children consuming government resource, and an increased number of future tax payers.
### Objective
Our objective was to evaluate the difference in lifetime discounted net tax revenue generated by RV vaccinated and unvaccinated cohorts from the Egyptian government perspective.
### Methods
The model framework adopts the Egyptian government perspective for RV immunization costs (year 2009 values) and all government transfers (e.g. education costs, health costs, pensions). To reflect the government tax revenue, we applied a fixed income tax burden to earnings over the lifetime of vaccinated and unvaccinated cohorts. At each year of the model, we derive net taxes (gross taxes less transfers) discounted to the immunization year to reflect the present value of RV vaccination investment costs.
### Results
Projected incremental net present values of the vaccinated cohort versus the unvaccinated cohort are $US6.1 million,$US58.1 million and \$US55.7 million at 25-, 50- and 72-year time horizons, respectively. The internal rate of return for the government based on RV vaccination at years 25, 50 and 72 was 10.8%, 15.1% and 14.9, respectively. Within the first 5 years of vaccination, 76% of vaccine acquisition costs were offset due to direct and indirect cost savings attributed to a reduction in RV-related disease burden. Investments in RV vaccination in a single year are entirely offset when the vaccinated cohort of newborns reach 22 years of age.
### Conclusion
The government perspective is useful for evaluating investments in RV vaccination because of ongoing government transfers and tax receipts attributed to changes in RV-attributed morbidity and mortality. The analysis described here illustrates that investing in RV offers tangible long-term fiscal benefits for government over many generations that would not ordinarily be captured in economic evaluations typically applied to healthcare interventions.
© Springer International Publishing AG 2012
## Authors and Affiliations
• Mark P. Connolly
• 1
• 2
• Oleksandr Topachevskyi
• 3
• Baudouin Standaert
• 3
• Omayra Ortega
• 4
• Maarten Postma
• 1
1. 1.PharmacoEpidemiology and PharmacoEconomics, Department of PharmacyUniversity of GroningenGroningenThe Netherlands
2. 2.Global Market Access SolutionsSaint-PrexSwitzerland
3. 3.GlaxoSmithKline BiologicalsWavreBelgium
4. 4.Department of Mathematical and Natural SciencesArizona State UniversityPhoenixUSA
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|
https://tex.stackexchange.com/questions/41043/macro-to-draw-a-parabola-with-pgf-tikz
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# Macro to draw a parabola with pgf/TikZ
I have been trying to build a macro \parabola{...} to draw a parabola passing through 3 coordinates with TikZ but without success.
For example
\parabola{A}{B}{C}
would draw the parabola interpolating the (x,y) coordinates (A), (B) and (C). I would like also to specify the style of the curve, the plot domain, etc.
The main problem I found is that I cannot figure out how to obtain the value of a given coordinate in dimensionless form (given a certain unit).
• Did you try the parabola path option already? There are some examples on page 146 in the manual. What is the obstacle that prevents you to achieve what you want with parabola? – percusse Jan 13 '12 at 22:05
• Welcome to TeX.SE. It would be helpful to post a compilable MWE that illustrates what you done so far so those trying to help can have something to start with. – Peter Grill Jan 13 '12 at 22:10
• As far as I know, the parabola path operation allows to draw the parabola passing through 3 given points only if one of them is the bend. I want a way to draw a parabola using three arbitrary TikZ coordinates. – maeshtro Jan 13 '12 at 22:47
# Introduction
This is an old question, but all previous answers have limitations: the main one is that all use plot. And plot command produce multiple cubic curves. But to draw a parabola a single quadratic (cubic) curve is enough.
# Some explanations
Any parabola can be drawn by a quadratic Bézier curve, and so by a cubic Bézier curve.
(A cubic curve with control points A,B,C,D draws a quadratic one iff AD=3BC.)
The "standard" parabola t(1-t) over [0,1] can be drawn by \draw (0,0) .. controls (1/3,1/3) and (2/3,1/3) .. (1,0);.
Every parabola between two points can be obtained by an affine transform from this "standard one". Using this we can define a style parabola through that use a single Bézier curve to draw the desired parabola. This style can be used with to or edge in the following way (A) to[parabola through={(B)}] (C).
# The code
The definition of the parabola through is:
\makeatletter
\def\pt@get#1#2{
\tikz@scan@one@point\pgfutil@firstofone#2\relax%
\csname pgf@x#1\endcsname=\pgf@x%
\csname pgf@y#1\endcsname=\pgf@y%
}
\tikzset{
parabola through/.style={
to path={{[x={(\pgf@xc,\pgf@yc)}, y=\parabola@y, shift=(\tikztostart)]
-- (0,0) .. controls (1/3,1/3) and (2/3,1/3) .. (1,0) \tikztonodes}--(\tikztotarget)}
},
parabola through/.prefix code={
\pt@get{a}{(\tikztostart)}\pt@get{b}{#1}\pt@get{c}{(\tikztotarget)}%
\advance\pgf@xb by-\pgf@xa\advance\pgf@yb by-\pgf@ya%
\advance\pgf@xc by-\pgf@xa\advance\pgf@yc by-\pgf@ya%
\pgfmathsetmacro\parabola@y{(\pgf@yc-\pgf@xc/\pgf@xb*\pgf@yb)%
/(\pgf@xb-\pgf@xc)*\pgf@xc}%
}
}
\makeatother
Note: We can avoid \makeatletter/\makeatother and all @s by using let from the calc library.
We can use (A) to[parabola through={(B)}] (C):
• in every case where the parabola exists, so when the three x-coordinates are different,
• the point B can be outside the drawn are,
• this can be part of a general path with nodes positioned on it.
Example 1:
\tikz\draw[help lines] (0,0) grid (4,3)
(0,0) edge[parabola through={(3,2)},
red,thick,fill=blue,fill opacity=.21] (4,1);
Example 2 (Full MWE):
\documentclass[tikz,border=7pt]{standalone}
\makeatletter
\def\pt@get#1#2{
\tikz@scan@one@point\pgfutil@firstofone#2\relax%
\csname pgf@x#1\endcsname=\pgf@x%
\csname pgf@y#1\endcsname=\pgf@y%
}
\tikzset{
parabola through/.style={
to path={{[x={(\pgf@xc,\pgf@yc)}, y=\parabola@y, shift=(\tikztostart)]
-- (0,0) .. controls (1/3,1/3) and (2/3,1/3) .. (1,0) \tikztonodes}--(\tikztotarget)}
},
parabola through/.prefix code={
\pt@get{a}{(\tikztostart)}\pt@get{b}{#1}\pt@get{c}{(\tikztotarget)}%
\advance\pgf@xb by-\pgf@xa\advance\pgf@yb by-\pgf@ya%
\advance\pgf@xc by-\pgf@xa\advance\pgf@yc by-\pgf@ya%
\pgfmathsetmacro\parabola@y{(\pgf@yc-\pgf@xc/\pgf@xb*\pgf@yb)%
/(\pgf@xb-\pgf@xc)*\pgf@xc}%
}
}
\makeatother
\begin{document}
\begin{tikzpicture}
\draw[help lines] (-1,-1) grid (3,3);
% variations of the point "through"
\foreach \y in {-1,-.9,...,1}
\draw[green] (-1,1) node[black]{.}
to[parabola through={(0,\y)}] node[black]{.}
node[black,at end]{.} (1,.5);
% variations of a boundary point
\foreach \y in {1.5,1.7,...,3}
\draw[purple] (-1,2) node[black]{.}
to[parabola through={(0,2)}] node[black]{.}
node[black,at end]{.} (1,\y);
% variations of a point "trough" outside the drawn part
\foreach \y in {-1,-0.5,...,3}{
\draw[red,thick] (.5,1) node[black]{.}
to[parabola through={(3,\y)}] node[black]{.}
node[black,at end]{.} (2,1);
\draw[dashed,blue] (.5,1) node[black]{.}
to[parabola through={(2,1)}] node[black]{.}
node[black,at end]{.} (3,\y);
}
\end{tikzpicture}
\end{document}
# Compared to the built in parabola operation
TikZ provide a parabola path operation. But it is not very well designed :
• the (0,0) parabola (1,1) is supposed to draw the parabola t^2 between 0 and 1. It draws a cubic curve that is close to this parabola but it is not exactly the same, actually it draws (0,0) .. controls (.5,0) and (0.8875,0.775) .. (1,1), but the exact curve is (0,0) .. controls (1/3,0) and (2/3,1/3) .. (1,1) (not clear why this curve is not used),
• when used with bend option, it use two cubic curves to approximate the parabola, but only one is enough to draw the exact one,
• when used with bend=<point> option, if you do not choose well the point the curve is not a parabola.
There is a situation where the original parabola is simpler to use (even if not exactly a parabola is drawn), when the bend (the extremal point) is at the start or at the end : (0,0) parabola (2,4) is simpler than (0,0) to[parabola through={(1,1)}] (2,4).
• @PaulGaborit Thanks ! I changed the code following your advise putting the order "division, multiplication,division, multiplication" in the formula of\parabola@y. – Kpym May 5 '18 at 14:42
• Nice. Any idea why these can't be concatenated like other types of edges though? (E.g.,\tikz\draw (0,2) to[parabola through={(1,0)}] (2,4) to[parabola through={(3,3)}] (4,3); has a gap.) – Circumscribe Jul 3 '18 at 17:16
• @Circumscribe I have no idea why. But it is easy to correct : I have added --(\tikztotarget) to the end of to path and now it works as expected. Thank you for reporting this inconsistency. – Kpym Jul 3 '18 at 21:02
1) A variant with fp :
\documentclass{article}
\usepackage{tikz,fp}
\FPmessagesfalse
\FPdebugfalse
\makeatletter
\tikzset{%
parabola through/.style={
to path={%
\pgfextra{%
\tikz@scan@one@point\pgfutil@firstofone(\tikztostart)\relax
\FPeval\xa{\pgf@sys@tonumber{\pgf@x}/28.45274}
\FPeval\ya{\pgf@sys@tonumber{\pgf@y}/28.45274}
\tikz@scan@one@point\pgfutil@firstofone#1\relax
\FPeval\xb{\pgf@sys@tonumber{\pgf@x}/28.45274}
\FPeval\yb{\pgf@sys@tonumber{\pgf@y}/28.45274}
\tikz@scan@one@point\pgfutil@firstofone(\tikztotarget)\relax
\FPeval\xc{\pgf@sys@tonumber{\pgf@x}/28.45274}
\FPeval\yc{\pgf@sys@tonumber{\pgf@y}/28.45274}
\FPeval\pb@a{(\ya*(\xb-\xc)+\yb*(\xc-\xa)+\yc*(\xa-\xb))/%
((\xa-\xb)*(\xa-\xc)*(\xb-\xc))}
\FPeval\pb@b{(\ya*(\xc+\xb)*(\xc-\xb)+\yb*(\xa+\xc)*(\xa-\xc)+\yc*(\xb+\xa)*(\xb-\xa))/((\xa-\xb)*(\xa-\xc)*(\xb-\xc))}
\FPeval\pb@c{(\ya*\xb*\xc*(\xb-\xc)+\yb*\xa*\xc*(\xc-\xa)+\yc*\xa*\xb*(\xa-\xb))/((\xa-\xb)*(\xa-\xc)*(\xb-\xc))}
\draw plot[domain=\xa:\xc] (\x,{\pb@a*(\x*\x)+\pb@b*\x+\pb@c}) ;
}(\tikztotarget)
}
}
}
\makeatother
\begin{document}
\begin{tikzpicture}
\draw [help lines] (-3,-1) grid (7,4);
\draw (-3,0) to[parabola through={(-2,2)}]%
(0,-1) to[parabola through={(2,4)}] (4,0) to[parabola through={(5,3)}] (7,0);
\end{tikzpicture}
\end{document}
2) From maeshtro's answer with gnuplot
\documentclass{article}
\usepackage{tikz}
\makeatletter
\tikzset{%
parabola through/.style={
to path={%
\pgfextra{%
\tikz@scan@one@point\pgfutil@firstofone(\tikztostart)\relax
\edef\xa{\pgf@sys@tonumber{\pgf@x}}
\edef\ya{\pgf@sys@tonumber{\pgf@y}}
\tikz@scan@one@point\pgfutil@firstofone#1\relax
\edef\xb{\pgf@sys@tonumber{\pgf@x}}
\edef\yb{\pgf@sys@tonumber{\pgf@y}}
\tikz@scan@one@point\pgfutil@firstofone(\tikztotarget)\relax
\edef\xc{\pgf@sys@tonumber{\pgf@x}}
\edef\yc{\pgf@sys@tonumber{\pgf@y}}
\draw plot[domain=\xa/28.45274:\xc/28.45274] function{
\ya/28.45274*((x*28.45274-\xb)*(x*28.45274-\xc))/((\xa-\xb)*(\xa-\xc))+
\yb/28.45274*((x*28.45274-\xa)*(x*28.45274-\xc))/((\xb-\xa)*(\xb-\xc))+
\yc/28.45274*((x*28.45274-\xa)*(x*28.45274-\xb))/((\xc-\xa)*(\xc-\xb))
};
}(\tikztotarget)
}
}
}
\makeatother
\begin{document}
\begin{tikzpicture}
\draw [help lines] (-3,-1) grid (7,4);
\draw (-3,0) to[parabola through={(-2,2)}] (0,-1) to[parabola through={(2,4)}] (4,0) to[parabola through={(5,3)}] (7,0);
\end{tikzpicture}
\end{document}
Here is one solution. It essentially solves the linear equation obtained from quadratic interpolation. It is important to note however that it is far from perfect. In particular there are strong constraints on possible points because of tikz computations limitations: the numbers in the computations must be small enough. This is clearly not what tikz is made for. Using other ways to obtain the coefficients would be better (sagetex or asymptote or others).
At least it is a nice example of the use of letin a tikz path.
I hope the computations are clear enough. The coefficients A, B and C are the coefficients of the quadratic polynomial Ax^2 + Bx + C.
The points must be entered in increasing order of the x coordinates for the code to work correctly.
The code is
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
\coordinate (1) at (0.1,0.2);
\coordinate (2) at (0.2,0.7);
\coordinate (3) at (0.4,-0.3);
\draw let \p1 = (1),
\p2 = (2),
\p3 = (3),
\n{denom} = {(\x1 - \x2)*(\x1 - \x3)*(\x2-\x3)},
\n{A} = {(\x3*(\y2-\y1) + \x2*(\y1-\y3) + \x1*(\y3-\y2))/\n{denom}},
\n{B} = {(\x3*\x3*(\y1-\y2) + \x2*\x2*(\y3-\y1)+\x1*\x1*(\y2-\y3))/\n{denom}},
\n{C} = {(\x2*\x3*(\x2-\x3)*\y1 + \x3*\x1*(\x3-\x1)*\y2 + \x1*\x2*(\x1-\x2)*\y3)/\n{denom}} in
plot[domain=\x1:\x3] (\x,{\n{A}*\x*\x+\n{B}*\x + \n{C}});
\end{tikzpicture}
\end{document}
• \coordinate (1) at (-3,0); \coordinate (2) at (-2,2); \coordinate (3) at (0,0); gives dimension too large – Alain Matthes Jan 14 '12 at 22:40
• @Altermundus: As I mentioned in my answer, there are (major) limitations on what my answer can do. That is why I used points that are close together. – Frédéric Jan 15 '12 at 4:24
Here is a solution inspired by this answer.
\documentclass{standalone}
\usepackage{tikz}
\makeatletter
\def\parabola@save@target#1{%
\def\parabola@target{#1}}
\def\parabola@save@start#1{%
\def\parabola@start{#1}}
\def\parabola@save@midpoint#1{%
\def\parabola@midpoint{#1}}
\tikzset{
parabola through/.style={
to path={%
\pgfextra{%
\edef\parabola@@target{(\tikztotarget)}%
\tikz@scan@one@point\parabola@save@target\parabola@@target\relax
\edef\parabola@@start{(\tikztostart)}%
\tikz@scan@one@point\parabola@save@start\parabola@@start\relax
\edef\parabola@@midpoint{(#1)}%
\tikz@scan@one@point\parabola@save@midpoint\parabola@@midpoint\relax
\parabola@start
\pgfmathsetmacro{\parabola@xa}{\the\pgf@x/1cm}
\pgfmathsetmacro{\parabola@ya}{\the\pgf@y/1cm}
\parabola@midpoint
\pgfmathsetmacro{\parabola@xb}{\the\pgf@x/1cm}
\pgfmathsetmacro{\parabola@yb}{\the\pgf@y/1cm}
\parabola@target
\pgfmathsetmacro{\parabola@xc}{\the\pgf@x/1cm}
\pgfmathsetmacro{\parabola@yc}{\the\pgf@y/1cm}
% f(x) = ax^2 + bx + c
% a=-(-x1*y3+x3*y1+x2*y3+x1*y2-x2*y1-x3*y2)/(x1*x3^2-x2*x3^2+x2*x1^2-x3*x1^2+x3*x2^2-x1*x2^2)
% b=(-x1^2*y3+x1^2*y2+y1*x3^2-y2*x3^2+x2^2*y3-y1*x2^2)/((x1-x2)*(-x1*x3+x1*x2+x3^2-x2*x3))
% c=(x1^2*x2*y3-x1^2*x3*y2-x2^2*x1*y3+y2*x1*x3^2+x2^2*x3*y1-y1*x2*x3^2)/((x1-x2)*(-x1*x3+x1*x2+x3^2-x2*x3))
\pgfmathsetmacro{\parabola@a}{-(-\parabola@xa*\parabola@yc+\parabola@xc*\parabola@ya+\parabola@xb*\parabola@yc+\parabola@xa*\parabola@yb-\parabola@xb*\parabola@ya-\parabola@xc*\parabola@yb)/(\parabola@xa*\parabola@xc^2-\parabola@xb*\parabola@xc^2+\parabola@xb*\parabola@xa^2-\parabola@xc*\parabola@xa^2+\parabola@xc*\parabola@xb^2-\parabola@xa*\parabola@xb^2)}
\pgfmathsetmacro{\parabola@b}{(-\parabola@xa^2*\parabola@yc+\parabola@xa^2*\parabola@yb+\parabola@ya*\parabola@xc^2-\parabola@yb*\parabola@xc^2+\parabola@xb^2*\parabola@yc-\parabola@ya*\parabola@xb^2)/((\parabola@xa-\parabola@xb)*(-\parabola@xa*\parabola@xc+\parabola@xa*\parabola@xb+\parabola@xc^2-\parabola@xb*\parabola@xc))}
\pgfmathsetmacro{\parabola@c}{(\parabola@xa^2*\parabola@xb*\parabola@yc-\parabola@xa^2*\parabola@xc*\parabola@yb-\parabola@xb^2*\parabola@xa*\parabola@yc+\parabola@yb*\parabola@xa*\parabola@xc^2+\parabola@xb^2*\parabola@xc*\parabola@ya-\parabola@ya*\parabola@xb*\parabola@xc^2)/((\parabola@xa-\parabola@xb)*(-\parabola@xa*\parabola@xc+\parabola@xa*\parabola@xb+\parabola@xc^2-\parabola@xb*\parabola@xc))}
\draw plot[samples=100,domain=\parabola@xa:\parabola@xc] function {\parabola@a*(x**2)+\parabola@b*x+\parabola@c};
}
}
}
}
\makeatother
\begin{document}
\begin{tikzpicture}
\node[circle,fill=red] at (0,0) {};
\node[circle,fill=blue] at (2,2) {};
\node[circle,fill=green] at (4,0) {};
\draw (0,0) to[parabola through={(2,2)}] (4,0);
\end{tikzpicture}
\end{document}
• \draw (-3,0) to[parabola through={(-2,2)}] (0,0); is incorrect – Alain Matthes Jan 14 '12 at 22:43
• @Altermundus You're right. maple gave me this solution. Maybe some operator precedence issue? The use of Lagrange polynomials is much better here. – cjorssen Jan 15 '12 at 21:38
You can rely on \pgfmathparse to always return any given length in pt. Take a look at the output of:
\pgfmathparse{12cm+1pt}
\pgfmathresult
\pgfmathparse{1pt}
\pgfmathresult
which will output as:
342.43306
1.0
With this you can pretty much do all your calculation by transferring to the (now dimensionless) unit pt. However you should be weary of very large numbers.
To circumvent this you could rely on the fpu unit of pgf.
% Preamble
\usepgflibrary{fpu}
\begin{document}
\pgfkeys{/pgf/fpu,/pgf/fpu/output format=fixed}
\pgfmathparse{12cm+1pt}
\pgfmathresult
\pgfmathparse{1pt}
\pgfmathresult
342.43306000000000
1.0000000000
Then you have access to numbers which are always in one specific unit!
Thank you all for your answers. They helped me a lot. Finally I chose the following approach which uses gnuplot. It is not very elegant but it meets my needs.
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\newcommand\parabola[3]{%
\path[draw]
let
\p1=#1,\p2=#2,\p3=#3
in
\pgfextra
\pgfmathsetmacro{\xa}{\x1/1cm}
\pgfmathsetmacro{\ya}{\y1/1cm}
\pgfmathsetmacro{\xb}{\x2/1cm}
\pgfmathsetmacro{\yb}{\y2/1cm}
\pgfmathsetmacro{\xc}{\x3/1cm}
\pgfmathsetmacro{\yc}{\y3/1cm}
\endpgfextra
plot[domain=\xa:\xc] function{
\ya*((x-\xb)*(x-\xc))/((\xa-\xb)*(\xa-\xc))+
\yb*((x-\xa)*(x-\xc))/((\xb-\xa)*(\xb-\xc))+
\yc*((x-\xa)*(x-\xb))/((\xc-\xa)*(\xc-\xb))
};}
\begin{document}
\begin{tikzpicture}
\coordinate (A) at (1,0);
\coordinate (B) at (3,8);
\coordinate (C) at (4,-1);
\fill[red] (A) circle (2pt) (B) circle (2pt) (C) circle (2pt);
\parabola{(A)}{(B)}{(C)}
\end{tikzpicture}
\end{document}
• Fine idea to use the Lagrange polynomial without develop it but you can develop the idea and gnuplot can divide for you. I update my answer. – Alain Matthes Jan 15 '12 at 7:05
• @Altermundus and Maeshtro I've tried this but my system spits this at me: Package pgf Warning: Plot data file <file name> no foundo n input line any idea why? – Pureferret Feb 11 '12 at 17:02
• It's difficult to answer with so few elements. First you need to test gnuplot, then you need to authorize TeX to launch gnuplot and to verify your path. – Alain Matthes Feb 11 '12 at 18:17
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http://princeton.universitypressscholarship.com/view/10.23943/princeton/9780691157122.001.0001/upso-9780691157122-chapter-004
|
Users without a subscription are not able to see the full content.
## Charles L. Epstein and Rafe Mazzeo
Print publication date: 2013
Print ISBN-13: 9780691157122
Published to Princeton Scholarship Online: October 2017
DOI: 10.23943/princeton/9780691157122.001.0001
Show Summary Details
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PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in HSO for personal use (for details see http://www.universitypressscholarship.com/page/privacy-policy).date: 17 August 2018
# The Model Solution Operators
Chapter:
(p.51) Chapter Four The Model Solution Operators
Source:
Degenerate Diffusion Operators Arising in Population Biology (AM-185)
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691157122.003.0004
This chapter introduces the model problems and the solution operator for the associated heat equations. These operators give a good approximation for the behavior of the heat kernel in neighborhoods of different types of boundary points. The chapter states and proves the elementary features of these operators and shows that the model heat operators have an analytic continuation to the right half plane. It first considers the model problem in 1-dimension and in higher dimensions before discussing the solution to the homogeneous Cauchy problem. It then describes the first steps toward perturbation theory and constructs the solution operator for generalized Kimura diffusions on a suitable scale of Hölder spaces. It also defines the resolvent families and explains why the estimates obtained here are not adequate for the perturbation theoretic arguments needed to construct the solution operator for generalized Kimura diffusions.
Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
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https://sciencehouse.wordpress.com/category/physics/page/2/
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# Talk in Göttingen
I’m currently in Göttingen, Germany at the Bernstein Sparks Workshop: Beyond mean field theory in the neurosciences, a topic near and dear to my heart. The slides for my talk are here. Of course no trip to Göttingen would be complete without a visit to Gauss’s grave and Max Born’s house. Photos below.
# New paper on path integrals
Carson C. Chow and Michael A. Buice. Path Integral Methods for Stochastic Differential Equations. The Journal of Mathematical Neuroscience, 5:8 2015.
Abstract: Stochastic differential equations (SDEs) have multiple applications in mathematical neuroscience and are notoriously difficult. Here, we give a self-contained pedagogical review of perturbative field theoretic and path integral methods to calculate moments of the probability density function of SDEs. The methods can be extended to high dimensional systems such as networks of coupled neurons and even deterministic systems with quenched disorder.
This paper is a modified version of our arXiv paper of the same title. We added an example of the stochastically forced FitzHugh-Nagumo equation and fixed the typos.
# Talk at Jackfest
I’m currently in Banff, Alberta for a Festschrift for Jack Cowan (webpage here). Jack is one of the founders of theoretical neuroscience and has infused many important ideas into the field. The Wilson-Cowan equations that he and Hugh Wilson developed in the early seventies form a foundation for both modeling neural systems and machine learning. My talk will summarize my work on deriving “generalized Wilson-Cowan equations” that include both neural activity and correlations. The slides can be found here. References and a summary of the work can be found here. All videos of the talks can be found here.
Addendum: 17:44. Some typos in the talk were fixed.
Addendum: 18:25. I just realized I said something silly in my talk. The Legendre transform is an involution because the transform of the transform is the inverse. I said something completely inane instead.
# Analytic continuation continued
As I promised in my previous post, here is a derivation of the analytic continuation of the Riemann zeta function to negative integer values. There are several ways of doing this but a particularly simple way is given by Graham Everest, Christian Rottger, and Tom Ward at this link. It starts with the observation that you can write
$\int_1^\infty x^{-s} dx = \frac{1}{s-1}$
if the real part of $s>0$. You can then break the integral into pieces with
$\frac{1}{s-1}=\int_1^\infty x^{-s} dx =\sum_{n=1}^\infty\int_n^{n+1} x^{-s} dx$
$=\sum_{n=1}^\infty \int_0^1(n+x)^{-s} dx=\sum_{n=1}^\infty\int_0^1 \frac{1}{n^s}\left(1+\frac{x}{n}\right)^{-s} dx$ (1)
For $x\in [0,1]$, you can expand the integrand in a binomial expansion
$\left(1+\frac{x}{n}\right)^{-s} = 1 +\frac{sx}{n}+sO\left(\frac{1}{n^2}\right)$ (2)
Now substitute (2) into (1) to obtain
$\frac{1}{s-1}=\zeta(s) -\frac{s}{2}\zeta(s+1) - sR(s)$ (3)
or
$\zeta(s) =\frac{1}{s-1}+\frac{s}{2}\zeta(s+1) +sR(s)$ (3′)
where the remainder $R$ is an analytic function when $Re s > -1$ because the resulting series is absolutely convergent. Since the zeta function is analytic for $Re s >1$, the right hand side is a new definition of $\zeta$ that is analytic for $s >0$ aside from a simple pole at $s=1$. Now multiply (3) by $s-1$ and take the limit as $s\rightarrow 1$ to obtain
$\lim_{s\rightarrow 1} (s-1)\zeta(s)=1$
which implies that
$\lim_{s\rightarrow 0} s\zeta(s+1)=1$ (4)
Taking the limit of $s$ going to zero from the right of (3′) gives
$\zeta(0^+)=-1+\frac{1}{2}=-\frac{1}{2}$
Hence, the analytic continuation of the zeta function to zero is -1/2.
The analytic domain of $\zeta$ can be pushed further into the left hand plane by extending the binomial expansion in (2) to
$\left(1+\frac{x}{n}\right)^{-s} = \sum_{r=0}^{k+1} \left(\begin{array}{c} -s\\r\end{array}\right)\left(\frac{x}{n}\right)^r + (s+k)O\left(\frac{1}{n^{k+2}}\right)$
Inserting into (1) yields
$\frac{1}{s-1}=\zeta(s)+\sum_{r=1}^{k+1} \left(\begin{array}{c} -s\\r\end{array}\right)\frac{1}{r+1}\zeta(r+s) + (s+k)R_{k+1}(s)$
where $R_{k+1}(s)$ is analytic for $Re s>-(k+1)$. Now let $s\rightarrow -k^+$ and extract out the last term of the sum with (4) to obtain
$\frac{1}{-k-1}=\zeta(-k)+\sum_{r=1}^{k} \left(\begin{array}{c} k\\r\end{array}\right)\frac{1}{r+1}\zeta(r-k) - \frac{1}{(k+1)(k+2)}$ (5)
Rearranging (5) gives
$\zeta(-k)=-\sum_{r=1}^{k} \left(\begin{array}{c} k\\r\end{array}\right)\frac{1}{r+1}\zeta(r-k) -\frac{1}{k+2}$ (6)
where I have used
$\left( \begin{array}{c} -s\\r\end{array}\right) = (-1)^r \left(\begin{array}{c} s+r -1\\r\end{array}\right)$
The righthand side of (6) is now defined for $Re s > -k$. Rewrite (6) as
$\zeta(-k)=-\sum_{r=1}^{k} \frac{k!}{r!(k-r)!} \frac{\zeta(r-k)(k-r+1)}{(r+1)(k-r+1)}-\frac{1}{k+2}$
$=-\sum_{r=1}^{k} \left(\begin{array}{c} k+2\\ k-r+1\end{array}\right) \frac{\zeta(r-k)(k-r+1)}{(k+1)(k+2)}-\frac{1}{k+2}$
$=-\sum_{r=1}^{k-1} \left(\begin{array}{c} k+2\\ k-r+1\end{array}\right) \frac{\zeta(r-k)(k-r+1)}{(k+1)(k+2)}-\frac{1}{k+2} - \frac{\zeta(0)}{k+1}$
Collecting terms, substituting for $\zeta(0)$ and multiplying by $(k+1)(k+2)$ gives
$(k+1)(k+2)\zeta(-k)=-\sum_{r=1}^{k-1} \left(\begin{array}{c} k+2\\ k-r+1\end{array}\right) \zeta(r-k)(k-r+1) - \frac{k}{2}$
Reindexing gives
$(k+1)(k+2)\zeta(-k)=-\sum_{r'=2}^{k} \left(\begin{array}{c} k+2\\ r'\end{array}\right) \zeta(-r'+1)r'-\frac{k}{2}$
Now, note that the Bernoulli numbers satisfy the condition $\sum_{r=0}^{N-1} B_r = 0$. Hence, let $\zeta(-r'+1)=-\frac{B_r'}{r'}$
and obtain
$(k+1)(k+2)\zeta(-k)=\sum_{r'=0}^{k+1} \left(\begin{array}{c} k+2\\ r'\end{array}\right) B_{r'}-B_0-(k+2)B_1-(k+2)B_{k+1}-\frac{k}{2}$
which using $B_0=1$ and $B_1=-1/2$ gives the self-consistent condition
$\zeta(-k)=-\frac{B_{k+1}}{k+1}$,
which is the analytic continuation of the zeta function for integers $k\ge 1$.
# Analytic continuation
I have received some skepticism that there are possibly other ways of assigning the sum of the natural numbers to a number other than -1/12 so I will try to be more precise. I thought it would be also useful to derive the analytic continuation of the zeta function, which I will do in a future post. I will first give a simpler example to motivate the notion of analytic continuation. Consider the geometric series $1+s+s^2+s^3+\dots$. If $|s| < 1$ then we know that this series is equal to
$\frac{1}{1-s}$ (1)
Now, while the geometric series is only convergent and thus analytic inside the unit circle, (1) is defined everywhere in the complex plane except at $s=1$. So even though the sum doesn’t really exist outside of the domain of convergence, we can assign a number to it based on (1). For example, if we set $s=2$ we can make the assignment of $1 + 2 + 4 + 8 + \dots = -1$. So again, the sum of the powers of two doesn’t really equal -1, only (1) is defined at s=2. It’s just that the geometric series and (1) are the same function inside the domain of convergence. Now, it is true that the analytic continuation of a function is unique. However, although the value of -1 for $s=-1$ is the only value for the analytic continuation of the geometric series, that doesn’t mean that the sum of the powers of 2 needs to be uniquely assigned to negative one because the sum of the powers of 2 is not an analytic function. So if you could find some other series that is a function of some parameter $z$ that is analytic in some domain of convergence and happens to look like the sum of the powers of two for some $z$ value, and you can analytically continue the series to that value, then you would have another assignment.
Now consider my example from the previous post. Consider the series
$\sum_{n=1}^\infty \frac{n-1}{n^{s+1}}$ (2)
This series is absolutely convergent for $s>1$. Also note that if I set s=-1, I get
$\sum_{n=1}^\infty (n-1) = 0 +\sum_{n'=1}^\infty n' = 1 + 2 + 3 + \dots$
which is the sum of then natural numbers. Now, I can write (2) as
$\sum_{n=1}^\infty\left( \frac{1}{n^s}-\frac{1}{n^{s+1}}\right)$
and when the real part of s is greater than 1, I can further write this as
$\sum_{n=1}^\infty\frac{1}{n^s}-\sum_{n=1}^\infty\frac{1}{n^{s+1}}=\zeta(s)-\zeta(s+1)$ (3)
All of these operations are perfectly fine as long as I’m in the domain of absolute convergence. Now, as I will show in the next post, the analytic continuation of the zeta function to the negative integers is given by
$\zeta (-k) = -\frac{B_{k+1}}{k+1}$
where $B_k$ are the Bernoulli numbers, which is given by the Taylor expansion of
$\frac{x}{e^x-1} = \sum B_n \frac{x^n}{n!}$ (4)
The first few Bernoulli numbers are $B_0=1, B_1=-1/2, B_2 = 1/6$. Thus using this in (4) gives $\zeta(-1)=-1/12$. A similar proof will give $\zeta(0)=-1/2$. Using this in (3) then gives the desired result that the sum of the natural numbers is (also) 5/12.
Now this is not to say that all assignments have the same physical value. I don’t know the details of how -1/12 is used in bosonic string theory but it is likely that the zeta function is crucial to the calculation.
# Nonuniqueness of -1/12
I’ve been asked to give an example of how the sum of the natural numbers could lead to another value in the comments to my previous post so I thought it may be of general interest to more people. Consider again $S=1+2+3+4\dots$ to be the sum of the natural numbers. The video in the previous slide gives a simple proof by combining divergent sums. In essence, the manipulation is doing renormalization by subtracting away infinities and the left over of this renormalization is -1/12. There is another video that gives the proof through analytic continuation of the Riemann zeta function
$\zeta(s)=\sum_{n=1}^\infty \frac{1}{n^s}$
The zeta function is only strictly convergent when the real part of s is greater than 1. However, you can use analytic continuation to extract values of the zeta function to values where the sum is divergent. What this means is that the zeta function is no longer the “same sum” per se, but a version of the sum taken to a domain where it was not originally defined but smoothly (analytically) connected to the sum. Hence, the sum of the natural numbers is given by $\zeta(-1)$ and $\zeta(0)=\sum_{n=1}^\infty 1$, (infinite sum over ones). By analytic continuation, we obtain the values $\zeta(-1)=-1/12$ and $\zeta(0)=-1/2$.
Now notice that if I subtract the sum over ones from the sum over the natural numbers I still get the sum over the natural numbers, e.g.
$1+2+3+4\dots - (1+1+1+1\dots)=0+1+2+3+4\dots$.
Now, let me define a new function $\xi(s)=\zeta(s)-\zeta(s+1)$ so $\xi(-1)$ is the sum over the natural numbers and by analytic continuation $\xi(-1)=-1/12+1/2=5/12$ and thus the sum over the natural numbers is now 5/12. Again, if you try to do arithmetic with infinity, you can get almost anything. A fun exercise is to create some other examples.
# The sum of the natural numbers is -1/12?
This wonderfully entertaining video giving a proof for why the sum of the natural numbers is -1/12 has been viewed over 1.5 million times. It just shows that there is a hunger for interesting and well explained math and science content out there. Now, we all know that the sum of all the natural numbers is infinite but the beauty (insidiousness) of infinite numbers is that they can be assigned to virtually anything. The proof for this particular assignment considers the subtraction of the divergent oscillating sum $S_1=1-2+3-4+5 \dots$ from the divergent sum of the natural numbers $S = 1 + 2 + 3+4+5\dots$ to obtain $4S$. Then by similar trickery it assigns $S_1=1/4$. Solving for $S$ gives you the result $S = -1/12$. Hence, what you are essentially doing is dividing infinity by infinity and that as any school child should know, can be anything you want. The most astounding thing to me about the video was learning that this assignment was used in string theory, which makes me wonder if the calculations would differ if I chose a different assignment.
Addendum: Terence Tao has a nice blog post on evaluating such sums. In a “smoothed” version of the sum, it can be thought of as the “constant” in front of an asymptotic divergent term. This constant is equivalent to the analytic continuation of the Riemann zeta function. Anyway, the -1/12 seems to be a natural way to assign a value to the divergent sum of the natural numbers.
|
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|
https://en.m.wikipedia.org/wiki/Greedy_algorithm
|
# Greedy algorithm
Greedy algorithms determine minimum number of coins to give while making change. These are the steps a human would take to emulate a greedy algorithm to represent 36 cents using only coins with values {1, 5, 10, 20}. The coin of the highest value, less than the remaining change owed, is the local optimum. (In general the change-making problem requires dynamic programming to find an optimal solution; however, most currency systems, including the Euro and US Dollar, are special cases where the greedy strategy does find an optimal solution.)
A greedy algorithm is an algorithmic paradigm that follows the problem solving heuristic of making the locally optimal choice at each stage[1] with the intent of finding a global optimum. In many problems, a greedy strategy does not usually produce an optimal solution, but nonetheless a greedy heuristic may yield locally optimal solutions that approximate a globally optimal solution in a reasonable amount of time.
For example, a greedy strategy for the traveling salesman problem (which is of a high computational complexity) is the following heuristic: "At each step of the journey, visit the nearest unvisited city." This heuristic does not intend to find a best solution, but it terminates in a reasonable number of steps; finding an optimal solution to such a complex problem typically requires unreasonably many steps. In mathematical optimization, greedy algorithms optimally solve combinatorial problems having the properties of matroids, and give constant-factor approximations to optimization problems with submodular structure.
## Specifics
In general, greedy algorithms have five components:
1. A candidate set, from which a solution is created
2. A selection function, which chooses the best candidate to be added to the solution
3. A feasibility function, that is used to determine if a candidate can be used to contribute to a solution
4. An objective function, which assigns a value to a solution, or a partial solution, and
5. A solution function, which will indicate when we have discovered a complete solution
Greedy algorithms produce good solutions on some mathematical problems, but not on others. Most problems for which they work will have two properties:
Greedy choice property
We can make whatever choice seems best at the moment and then solve the subproblems that arise later. The choice made by a greedy algorithm may depend on choices made so far, but not on future choices or all the solutions to the subproblem. It iteratively makes one greedy choice after another, reducing each given problem into a smaller one. In other words, a greedy algorithm never reconsiders its choices. This is the main difference from dynamic programming, which is exhaustive and is guaranteed to find the solution. After every stage, dynamic programming makes decisions based on all the decisions made in the previous stage, and may reconsider the previous stage's algorithmic path to solution.
Optimal substructure
"A problem exhibits optimal substructure if an optimal solution to the problem contains optimal solutions to the sub-problems."[2]
### Cases of failure
Examples on how a greedy algorithm may fail to achieve the optimal solution.
Starting from A, a greedy algorithm that tries to find the maximum by following the greatest slope will find the local maximum at "m", oblivious to the global maximum at "M".
With a goal of reaching the largest-sum, at each step, the greedy algorithm will choose what appears to be the optimal immediate choice, so it will choose 12 instead of 3 at the second step, and will not reach the best solution, which contains 99.
For many other problems, greedy algorithms fail to produce the optimal solution, and may even produce the unique worst possible solution. One example is the traveling salesman problem mentioned above: for each number of cities, there is an assignment of distances between the cities for which the nearest-neighbor heuristic produces the unique worst possible tour.[3]
## Types
Greedy algorithms can be characterized as being 'short sighted', and also as 'non-recoverable'. They are ideal only for problems which have 'optimal substructure'. Despite this, for many simple problems, the best suited algorithms are greedy algorithms. It is important, however, to note that the greedy algorithm can be used as a selection algorithm to prioritize options within a search, or branch-and-bound algorithm. There are a few variations to the greedy algorithm:
• Pure greedy algorithms
• Orthogonal greedy algorithms
• Relaxed greedy algorithms
## Theory
Greedy algorithms have a long history of study in combinatorial optimization and theoretical computer science. Greedy heuristics are known to produce suboptimal results on many problems,[4] and so natural questions are:
• For which problems do greedy algorithms perform optimally?
• For which problems do greedy algorithms guarantee an approximately optimal solution?
• For which problems is the greedy algorithm guaranteed not to produce an optimal solution?
A large body of literature exists answering these questions for general classes of problems, such as matroids, as well as for specific problems, such as set cover.
### Matroids
A matroid is a mathematical structure that generalizes the notion of linear independence from vector spaces to arbitrary sets. If an optimization problem has the structure of a matroid, then the appropriate greedy algorithm will solve it optimally.[5]
### Submodular functions
A function ${\displaystyle f}$ defined on subsets of a set ${\displaystyle \Omega }$ is called submodular if for every ${\displaystyle S,T\subseteq \Omega }$ we have that ${\displaystyle f(S)+f(T)\geq f(S\cup T)+f(S\cap T)}$ .
Suppose one wants to find a set ${\displaystyle S}$ which maximizes ${\displaystyle f}$ . The greedy algorithm, which builds up a set ${\displaystyle S}$ by incrementally adding the element which increases ${\displaystyle f}$ the most at each step, produces as output a set that is at least ${\displaystyle (1-1/e)\max _{X\subseteq \Omega }f(X)}$ .[6] That is, greedy performs within a constant factor of ${\displaystyle (1-1/e)\approx 0.63}$ as good as the optimal solution.
Similar guarantees are provable when additional constraints, such as cardinality constraints,[7] are imposed on the output, though often slight variations on the greedy algorithm are required. See [8] for an overview.
### Other problems with guarantees
Other problems for which the greedy algorithm gives a strong guarantee, but not an optimal solution, include
Many of these problems have matching lower bounds; i.e., the greedy algorithm does not perform better, in the worst case, than the guarantee.
## Applications
Greedy algorithms mostly (but not always) fail to find the globally optimal solution because they usually do not operate exhaustively on all the data. They can make commitments to certain choices too early which prevent them from finding the best overall solution later. For example, all known greedy coloring algorithms for the graph coloring problem and all other NP-complete problems do not consistently find optimum solutions. Nevertheless, they are useful because they are quick to think up and often give good approximations to the optimum.
If a greedy algorithm can be proven to yield the global optimum for a given problem class, it typically becomes the method of choice because it is faster than other optimization methods like dynamic programming. Examples of such greedy algorithms are Kruskal's algorithm and Prim's algorithm for finding minimum spanning trees, and the algorithm for finding optimum Huffman trees.
Greedy algorithms appear in network routing as well. Using greedy routing, a message is forwarded to the neighboring node which is "closest" to the destination. The notion of a node's location (and hence "closeness") may be determined by its physical location, as in geographic routing used by ad hoc networks. Location may also be an entirely artificial construct as in small world routing and distributed hash table.
## Notes
1. ^ Black, Paul E. (2 February 2005). "greedy algorithm". Dictionary of Algorithms and Data Structures. U.S. National Institute of Standards and Technology (NIST). Retrieved 17 August 2012.
2. ^ Introduction to Algorithms (Cormen, Leiserson, Rivest, and Stein) 2001, Chapter 16 "Greedy Algorithms".
3. ^ Gutin, Gregory; Yeo, Anders; Zverovich, Alexey (2002). "Traveling salesman should not be greedy: Domination analysis of greedy-type heuristics for the TSP". Discrete Applied Mathematics. 117 (1–3): 81–86. doi:10.1016/S0166-218X(01)00195-0.
4. ^ U. Feige. A threshold of ln n for approximating set cover. Journal of the ACM (JACM), 45(4):634–652, 1998.
5. ^ Papadimitriou, Christos H., and Kenneth Steiglitz. Combinatorial optimization: algorithms and complexity. Courier Corporation, 1998.
6. ^ G. Nemhauser, L.A. Wolsey, and M.L. Fisher. "An analysis of approximations for maximizing submodular set functions—I." Mathematical Programming 14.1 (1978): 265-294.
7. ^ N. Buchbinder, et al. "Submodular maximization with cardinality constraints." Proceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms. Society for Industrial and Applied Mathematics, 2014.
8. ^ Krause, Andreas, and Daniel Golovin. "Submodular function maximization." (2014): 71-104.
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https://www.physicsforums.com/threads/integration-calc-work-what-did-i-do-wrong.90844/
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# Integration/calc work? what did i do wrong
1. Sep 25, 2005
Int[1/(x^2+4)^2]
let x= 2 tan(q)
i get 1/(4 tan^2(q) + 4)^2
I get 1/ (16 tan ^4(q) + 32 (1-sec^2(q) + 16)
and now i think about doing a u-substituition with tan x=u, du =sec^2 (x) can i do that!??!?!?! :surprised
2. Sep 25, 2005
do you just dont like my topics i want help in?
3. Sep 25, 2005
### whozum
$$\frac{1}{(4\tan(q)+4)^2} = \frac{1}{16\sec^4q}$$
Similar Discussions: Integration/calc work? what did i do wrong
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https://www.toppr.com/guides/chemistry/chemical-bonding-and-molecular-structure/ferrous-sulphate/
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# Ferrous Sulphate
Iron(II) sulfate or ferrous sulfate signifies a variety of salts with the formula $${FeSO_4 \cdot xH_2O}$$. These compounds are most commonly known as heptahydrate (x = 7) but are also known for several x values. Hydrated form is medically used for the treatment of iron deficiency, as well as for industrial applications. It is well known since ancient times as copperas and green vitriol (vitriol is an archaic term for the sulfate), blue-green heptahydrate (hydrate with “7” water molecules) is the most common type of this material. Learn ferrous sulphate in this article.
Ferrous Sulphate
## What is Ferrous Sulphate?
Ferrous sulfate is an iron salt that is also known as green vitriol. Ferrous Sulfate signifies a variety of salts with the formula $${FeSO_4 \cdot xH_2O}$$. The Other names of Iron(II) sulphate include; Ferrous sulfate, Green vitriol, Iron vitriol, Copperas, Melanterite, Szomolnokite. Blue-green heptahydrate (hydrate with “7” water molecules) is the most common type of this material. All Iron(II) sulfates dissolve in water to produce the same aquo complex $${[Fe(H_2O)_6]^{2+}}$$, which is paramagnetic and has the octahedral molecular geometry.
The term copperas goes back to the time period when copper(II) sulfate was known as blue copperas, and perhaps, by contrast, iron(II) and zinc sulfate were known as green and white copperas. It forms when iron filings mix into a copper sulfate solution, iron pushes the copper because it is more reactive and takes its place leading to the formation of iron sulfate.
It is present on the World Health Organization’s list of essential medicines as the safest and effective drugs necessary in the health sector. In 2018, with more than 8 million prescriptions, it was the 94th most widely prescribed drug in the United States.
### Properties of Ferrous Sulphate
• The chemical formula of the ferrous sulphate is $$-{FeSO_4}$$
• Its Molar mass is – 151.908 g/mol.
• The density of ferrous sulphate is $${2.84 g/cm^3}$$
• Colour/Appearance of ferrous sulphate –
Anhydrous – White crystals
Monohydrate – Yellowish white crystals
Heptahydrate – Bluish-green crystals.
• Odour – It is odourless
• The Melting point of ferrous sulphate is 56-64\degree C.
• The Boiling point of the ferrous sulphate is >300\degree C.
• Covalently-Bonded Unit – 2
• Hydrogen Bond Acceptor – 4
• It is soluble in water.
### Hydrates of Ferrous Sulphate
Iron(II) sulfate is available in several states of hydrations, and some of these types occur in nature. Such as;
$${FeSO_4 \cdot H_2O}$$ (Szomolnokite, relatively rare)
$${FeSO_4 \cdot 4H_2O}$$ (Rozenite, white, relatively common, maybe dehydration product of melanterite)
$${FeSO_4 \cdot 5H_2O}$$ (Siderotil, relatively rare)
$${FeSO_4 \cdot 6H_2O}$$ (Ferrohexahydrite, relatively rare)
$${FeSO_4 \cdot 7H_2O}$$ (Melanterite, blue-green, very common)
Tetrahydrate is stable when the temperature of the aqueous solution exceeds $${56.6 \degree C} {(133.9 \degree F)}$$. The solution forms both tetrahydrate and monohydrate at $${64.8 \degree C} {(148.6 \degree F)}$$.
All of the mineral types listed link with the oxidation zones of iron-bearing ore beds(marcasite) and related environment (like coal fire sites). Many undergo accelerated dehydration and occasionally oxidation. Numerous other, more complex (either simple, hydrated and with additional cations) Fe(II)-sulphate-bearing sulphates occur in these environments, with copiapite being a good and usual example.
### Production of Ferrous Sulphate
When steel finishing before plating or coating, the steel sheet or rod passes through the sulphuric acid pickling baths. It generates a significant amount of iron(II) sulfate as a by-product.
$${Fe + H_2SO_4 \longrightarrow FeSO_4 + H_2}$$
Another source of production of large amounts is the production of titanium dioxide from ilmenite by the sulfate process.
Ferrous sulfate is also produced commercially by the oxidation process of pyrite:
$${2 FeS_2 + 7 O_2 + 2 H_2O \longrightarrow 2 FeSO_4 + 2 H_2SO_4}$$
Displacing metals that are less reactive than iron from the solutions of their sulfate can also produce ferrous sulphate:
$${CuSO_4 + Fe \longrightarrow FeSO_4 + Cu}$$
### Uses
Industrially, ferrous sulfate is mostly useful as a precursor to other iron compounds. It is a reducing agent and is also for the reduction of chromate in cement to a less toxic Cr(III) substance. Historically, ferrous sulfate has been in use as a dye fixative in the textile industry for centuries. And for blackening the leather and as a source of ink. The processing of sulphuric acid by the distillation of green vitriol (Iron(II) sulfate) is a well-known method for more than 700 years.
### Medical Use
Iron is an essential heavy metal that is useful in several over-the-counter multi-vitamin and mineral supplements. It is also in use therapeutically at higher doses to cure or avoid iron-deficiency anaemia. When consumed at the usual prescribed daily intake or at the replacement dosage, iron has little or no adverse effect on the liver. In high doses and intentional or unintentional overdosages, iron causes severe toxicity, one such factor of which is acute liver failure.
Impheron and iron dextran are injectable iron supplements. Ferrous fumarate, ferrous gluconate and ferrous sulphate are the most common oral iron supplements. Ferrous sulfate is by far the safest and cheapest supplement for iron.
### Plants Growth
Iron (II) sulfate or ferrous sulfate, is a soil alteration to lower the pH of high alkaline soil so that plants can absorb soil’s nutrients. It is useful for treating iron chlorosis in horticulture. Though not as fast-acting as ferric EDTA, its effects are longer-lasting. It can be combined with compost and dug into the soil to create a store that can last for years.
### Other Uses
1. Ferrous sulfate introduction into the cooling water running through the turbine condenser tubes to create a corrosion-resistant protective layer.
2. It is useful in gold refining for precipitating metallic gold from auric chloride solutions (gold dissolved in solution with aqua regia).
3. It has been in use for the purification of water by flocculation and for the elimination of phosphates in municipal and industrial sewage treatment plants to avoid the eutrophication of water bodies.
4. Useful as a traditional way of treating wood panelling on houses, either individually, dissolved in water or as an element of water-based paint.
5. Green vitriol is also a useful reagent for the detection of mushrooms.
6. It is useful as an iron catalyst element of the Fenton reagent.
7. It’s one of the most necessary ingredients in the ink of iron gall.
Question.1. What are the benefits of ferrous sulfate?
Answer. Myoglobin allows storing oxygen in the muscle cells. Ferrous sulfate is a mineral that is essential to the body. Ferrous sulfate is useful in curing iron deficiency anaemia, which is the lack of red blood cells triggered by the less iron content in the body. It can also be useful for uses other than those listed here.
Question.2. Why is iron called ferrous?
Answer. Usually, “ferrous” means “containing iron” the expression comes from the Latin word Ferrum (‘iron’). Ferrous metals involve steel and pig iron (with a carbon content of a few per cent) and iron alloys with many other metals (such as stainless steel).
Question.3. What are the benefits of ferrous sulphate?
Answer. The primary benefit of using ferrous sulfate supplement is to maintain normal iron levels in the body.
• It helps in maintaining normal iron levels in the blood.
• It may even prevent symptoms of iron deficiency.
• Also, it is useful in treating iron-deficiency anaemia.
Question.4. What are the side effects of overdosage of ferrous sulphate?
Answer. The most common side effects reported by people include different types of gastrointestinal distress, including nausea, diarrhoea, vomiting, stomach pain, constipation, and black or discoloured stools.
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http://mathhelpforum.com/advanced-statistics/592-some-random-variable-confusion.html
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# Math Help - Some random variable confusion!
1. ## Any help here would be stupendous!!!
Hello,
I was a bit confused by this problem that appeared in my prob and stat textbook:
"Suppose that X had a uniform distribution on the interval [0,5] and that the random variable Y is defined by Y = 0 if X <= 1, Y = 5 if X >= 3, and
Y = X otherwise. Sketch the d.f. of Y"
I wanted to solve this problem by first finding the mixed probability function of Y, f_Y. To do this I first found the probability function of X, f_X:
f_X(x) = { 0 if x < 0; 1/5 if 0 <= x <= 5; 0 if x > 5 } by the fact that X has uniform distribution on [0,5].
Then to find f_Y, the mixed probability function of Y:
Pr(Y = 0) = Pr(X <= 1) = 1/5
Also, it's given that Y = 5 if X >= 3 which means that
Pr(Y = 5) = Pr(X >= 3) = 2/5
The only solution I could think of was that after summing the places of non-zero probability mass at Y = 0 and Y = 5 to get 1/5 + 2/5 = 3/5, that then it forces Pr(0 < Y < 5) = 2/5. Then maybe would I interpret "Y = X otherwise" to mean that simply Y distrubutes the probability 2/5 uniformly over the interval (0,5)? In that case I would have:
f_Y(y) = { 0 if y < 0; 1/5 if y = 0; 2/25 if 0 < y < 5; 2/5 if y = 5; 0 if y > 5 }
And then the Pr(Y = 0) + Pr(0 < Y < 5) + Pr(Y = 5) = 1/5 + 10/25 + 2/5 =
25/25 = 1 as needed. But I'm not sure that that's what is meant by "Y = X otherwise" Oh well, I'd really appreciate any help on determining the correct formulas for the mixed probability function of Y. Thanks in advance for any help,
2. Originally Posted by epv
Hello,
I was a bit confused by this problem that appeared in my prob and stat textbook:
"Suppose that X had a uniform distribution on the interval [0,5] and that the random variable Y is defined by Y = 0 if X <= 1, Y = 5 if X >= 3, and
Y = X otherwise. Sketch the d.f. of Y"
Try this:
$
F_Y(x) = \begin{cases} 0 \quad (x < 0})
\\ \frac15 \quad(0 \le x < 1) \\
\frac{x}{5} \quad (1 \le x < 3)
\\ \frac35 \quad(3 \le x < 5)\\
|
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https://www.tutorialspoint.com/what-is-the-difference-between-erroractionpreference-and-erroraction-cmdlet-in-powershell
|
# What is the difference between $ErrorActionPreference and$ErrorAction cmdlet in PowerShell ?
PowerShellMicrosoft TechnologiesSoftware & Coding
As we know $ErrorActionPreference and$ErrorAction both have the same functionality and both are used to handle terminating errors by converting Non-Terminating errors to Terminating errors. But when both the variables are used, we need to know which takes precedence.
$ErrorActionPreference variable is used at the start of the script while the$erroraction variable is a common parameter and used with the cmdlet. In some cases, we might need the script to be terminated as soon as an error occurs but inside the script, we have some cmdlets which need to be ignored or continued if the error occurs. In that situation, we -ErrorAction is important and it takes precedence.
## Example
$ErrorActionPreference = "Stop" try{ Get-Service -Name ABC Get-Process powershell Get-Process chromesds Get-Service Spooler } catch{$_.Exception.Message
}
## Output
Cannot find any service with service name 'ABC'.
In the above example, the script is terminated because the ABC service name doesn’t exist and because of it, the next commands can’t execute as the $ErrorActionPreference value is set to Stop. Once we add the -ErrorAction in the Get-Service command, it will take the precedence. $ErrorActionPreference = "Stop"
try{
Get-Service -Name ABC -ErrorAction Continue
Get-Process powershell
Get-Process chromesds
Get-Service Spooler
}
catch{
\$_.Exception.Message
}
## Output
Line |
4 | Get-Service -Name ABC -ErrorAction Continue
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
| Cannot find any service with service name 'ABC'.
NPM(K) PM(M) WS(M) CPU(s) Id SI ProcessName
------ ----- ----- ------ -- -- -----------
43 234.39 11.33 49.17 7668 1 powershell
Cannot find a process with the name "chromesds". Verify the process name and call
the cmdlet again.
Once we add the -ErrorAction parameter with Continue value, execution moves to the next command as shown in the above output and stops when it can’t find process name “Chromesds” and can’t execute next command as -ErrorAction is not mentioned in that command.
Updated on 03-Sep-2020 10:58:31
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https://gankochavim.com/ghrkqx/archive.php?page=231d92-is-the-inverse-of-a-covariance-matrix-symmetric
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We consider multivariate Gaussian models as a set of concentration matrices in the cone, and focus on linear models that are homogeneous (i.e. Hot Network Questions In 19th century France, were police able to send people to jail without a trial, as presented in "Les Misérables"? The eigenvalues still represent the variance magnitude in the direction of the largest spread of the data, and the variance components of the covariance matrix still represent the variance magnitude in the direction of the x-axis and y-axis. Earlier, Erik Ivar Fredholm had introduced the concept of a pseudoinverse of integral operators in 1903. That is, if you would compute the covariance matrix as. Both matrices lie in the cone of n×n positive definite matrices. This can almost be done in-place (you only need temporary storage for the diagonal elements, an accumulator and some integer iterators). The fact that the inverse of a block diagonal matrix has a simple, diagonal form will help you a lot. The easiest thing to do is to use numpy.linalg.pinv to perform a pseudo-inverse which will only use the singular-values that are well-conditioned to compute the inverse. (2) There are some very common algorithms for matrix inversion. In practice, is best to keep the inverse factored. Is it the reason why a covariance matrix is a symmetric n by n matrix? We discuss the implications of these properties both theoretically and empirically. if some concentration matrix is in the model, then so are its scalar … I tried SVD but the problem it does not go very well on GPU. Every such distribution is described by the covariance matrix or, its inverse, the concentration matrix. sample covariance matrix while the second part covers the case when the sample covariance matrix is a centered one. When we see a unit covariance matrix we really do not know, whether it is the “originally symmetric” distribution, or a “rotated symmetric distribution”. Well, for a 2x2 matrix the inverse is: In other words: swap the positions of a and d, put negatives in front of b and c, and divide everything by the determinant (ad-bc). Standard results on partitioned matrix inversion indicate that the in- 2x2 Matrix. Do players know if a hit from a monster is a critical hit? The three-dimensional covariance matrix is shown as . Start with a Correlation Matrix. A symmetric matrix can be formed by multiplying a matrix A with its transpose — AᵀA or AAᵀ (usually AᵀA ≠ AAᵀ). In machine learning, the covariance matrix with zero-centered data is in this form. Which direction should axle lock nuts face? \end{align} Lower indices are rows, upper indices are columns and L^{-\top} is the transpose of L^{-1}, My Cholesky algorithm (probably from Numerical Recipes or Wikipedia), L_i^j = \frac{M_i^j - M_i \cdot M_j}{M_i^i - M_i \cdot M_i}. Some factorization that can come in handy? For AR (p) processes the Yule-Walker equations allow the Again, this is because we never had to form the covariance matrix directly to compute the Cholesky factor. Has anyone had this issue? Estimating inverse covariance matrix 1 We consider the problem of finding a good estimator for inverse covariance matrix 1 with a constraint that certain given pairs of variables are conditionally independent. The simplest example, and a cousin of a covariance matrix, is a correlation matrix. Tags: diagonal entry inverse matrix inverse matrix of a 2 by 2 matrix linear algebra symmetric matrix Next story Find an Orthonormal Basis of \R^3 Containing a Given Vector Previous story If Every Proper Ideal of a Commutative Ring is a Prime Ideal, then It is a Field. Hence the matrix has to be symmetric. I'm new to R and portfolio optimization. Also, Variance-Covariance matrices are always square matrices of size n, where n is the number of variables in your experiment. The matrix of correlation coefficients and the matrix of variances-covariances are square and symmetric. This equation doesn't change if you switch the positions of x and y. Positive Definite Matrix. : Actually, just check the Numerical Recipes example. We prove a positive-definite symmetric matrix A is invertible, and its inverse is positive definite symmetric. Nevertheless, +1 for getting the ball rolling. Hi all, As far as I know, the inverse of symmetric matrix is always symmetric. Where does the expression "dialled in" come from? The covariance matrix is a symmetric positive semi-definite matrix. Efficient computation of the matrix square root inverse. Use MathJax to format equations. norm(F_inv*F) using Cholesky is around 1.2, and F_inv*F is close to the identity matrix, but not accurate enough. I did this for the first time recently, using suggestions from mathSE. The inverse covariance matrix, commonly referred to as the precision matrix displays information about the partial correlations of variables. From this, I can quickly calculate M^{-1} = \left(L L^\top\right)^{-1} = L^{-\top}L^{-1}. MIT Linear Algebra Exam problem and solution. [1] Generalization of the variance. With a matrix which is close to being singular these can be surprisingly large sometimes. I also tried to use Cholesky decomposition to get the inverse matrix instead of build-in inv. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Thanks for contributing an answer to Computational Science Stack Exchange! square and symmetric -- X(i,j) = X(j,i). I don't know of a way to exploit the fact that the matrices are symmetric and positive definite. Since A − 1 A = I, ( A − 1 A) T = I T, or ( A T) ( A − 1) T = I. 2x2 Matrix. Is it more efficient to send a fleet of generation ships or one massive one? My back-substitution algorithm (from Numerical Recipes, check their version as I may have made a mistake with the LaTeX markup), \left(L^{-1}\right)_i^j = \left\{\begin{array}{11} The algorithm in this paper can be applied to any problem where the inverse of the symmetric positive-definite covariance (or correlation) matrix of a stochastic process is required to be accurately tracked with time. OK, how do we calculate the inverse? On the Inverse of the Covariance Matrix 1823 matrix of the covariance matrix C formed by eliminating its first row and column; finally, ZN-1 and inN-[- are the N - 1 column vectors made up of all but the first elements of the original z and imn vectors, respectively. go from (a) to (b). This finding has important implications in high dimensional statistics where it is important to exploit structure in order to construct consistent estimators in non-trivial norms. \left(-L_i \cdot \left(L^{-T}\right)_j\right) / L_i^i & \mbox{otherwise} is the statistical expectation operator. These identities are in The Matrix Cookbook. Eigendecomposition when the matrix is symmetric; The decomposed matrix with eigenvectors are now orthogonal matrix. The remainder of this paper is organized as follows. Given the qualities of this matrix, and the intended uses, I wonder: What is the best, in terms of numerical stability, way to go about computing or using (let's say for quadratic forms or matrix-vector multiplication in general) this inverse? Why is the TV show "Tehran" filmed in Athens? \end{array}\right.. Computational Science Stack Exchange is a question and answer site for scientists using computers to solve scientific problems. The formula for variance is given byσ2x=1n−1n∑i=1(xi–ˉx)2where n is the number of samples (e.g. The auto-covariance matrix{\displaystyle \operatorname {K} _{\mathbf {X} \mathbf {X} }}$$is related to the autocorrelation matrix$${\displaystyle \operatorname {R} _{\mathbf {X} \mathbf {X} }} by Yes, it's roundoff error. Instead of 'isequal' which demands exact equality, try displaying the difference invC-invC' to see if the differences fall within the range of what you would regard as reasonable round off errors. 11 speed shifter levers on my 10 speed drivetrain. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Again, we see that the covariant matrix is real and symmetric. The covariance matrix is a symmetric positive semi-definite matrix. The following formula is used for covariance determination. Variance-Covariance matrices are always symmetric, as it can be proven from the actual equation to calculate each term of said matrix. The Cholesky factorization $C=R^TR$ leads to a Cholesky-like factorization of the inverse $C^{-1}=SS^T$ with the upper triangular matrix $S=R^{-1}$. Later videos will build on this for a discussion of a Least Square solution to a system of equations. Since is a symmetric matrix, it can be eigen-decomposed as , where is the matrix whose columns are eigenvectors of , and is the diagonal matrix whose entries are eigenvalues of . I then use backsubstitution or forwardsubstitution (depending on whether I choose L to be upper or lower triangular), to invert $L$, such that I have $L^{-1}$. How does steel deteriorate in translunar space? If the covariance matrix is positive definite, then the distribution of X is non-degenerate; otherwise it is degenerate. One property of rotation matrices is that their transpose is the same as the inverse matrix. But A T = A, so ( A − 1) T is the inverse of A. The distributions tightens with large peak value of p(x), as the variance terms decrease. Determinant of variance-covariance matrix Of great interest in statistics is the determinant of a square symmetric matrix $${\bf D}$$ whose diagonal elements are sample variances and whose off-diagonal elements are sample covariances. , a symmetric positive semi-definite matrix following format to as the inverse factored block diagonal is. We need to have three-dimensional data the concentration matrix to the problem it does along side. '' filmed in Athens integer iterators ) is presented: how do we know this the. T = a, or by the covariance matrix, is called the inverse of a block matrix. Matrix with the use of linear transformations and eigendecomposition a toilet ring fell into the drain, how do do! I am demotivated by unprofessionalism that has affected me personally at the difference between covariance and variance I demotivated! Statements based on opinion ; back them up with references or personal experience estimator exploiting the structure of proposed... The case when the matrix Cookbook in characteristic different from 2, each diagonal element of positive. Size n, where $M$ is non-degenerate ; otherwise it is and..., since all off-diagonal elements are zero site for scientists using computers to solve scientific problems scientific problems accurancy reduced... Is N. the tracee of the covariance matrix, do yourself a favor with large peak of... Or more variables are zero be proved by simply looking at the cofactors of a. Following is the covariance matrix, do yourself a favor, if you would compute the matrix... Said matrix the top as it can be surprisingly large sometimes answer to computational Science Stack is... Σ−1 by different methods has been given by [ 5 & 6 ] properties theoretically! Fredholm had introduced the concept of covariance matrices TV show Tehran filmed! The distribution of X is non-degenerate ; otherwise it is easy and useful to show covariance. And negative values where n is the covariance matrix is always symmetric, as far as I know the. Cone of n×n positive definite matrices '' filmed in Athens and.. Every square diagonal matrix has simple... Bjerhammar in 1951, and Roger Penrose in 1955 service, privacy policy and cookie policy boy off with! $( a − 1 ) why do you need more constraints on sparseness etc the. Is even better since you do n't know of a covariance matrix are the same it... Fleet of generation ships or one massive one two variables will …,... I do n't know of a pseudoinverse of integral operators in 1903 a skew-symmetric must. From$ ( 1 ) why do you need more constraints on sparseness etc difference between and. The use of linear transformations and eigendecomposition variable decreases, other variable increases, and Roger Penrose in 1955 X... Numerically stable on nasty problems, how do we know this is because we never had form. And an inverse matrix matrix equality theoretically and empirically very desirable in linear algebra ; back them up references. Should not really care - those two are identical exists, is the! Hard drives for PCs cost scientists using computers to solve scientific problems 10 speed drivetrain zero-centered is. As it does along the side variable increases, and Roger Penrose in.! An inverse relationship exist between them a skew-symmetric matrix must be zero, since all off-diagonal elements zero... Of data based on the concept of covariance matrices positive semi-definite matrix is implicitly and! Accumulator and some integer iterators ) ) matrix '' come from accumulator and some integer )! Only need temporary storage for the random vector X the covariance matrix is a critical?! Contributing an answer to computational Science Stack Exchange as well be proven from the actual equation calculate... Create the 3×3 square covariance matrix and the way it describes the shape a! M = a, if it exists, is best to keep the inverse of block! Vector X the covariance matrix of variances-covariances are square and symmetric of rotation is!, then the distribution of X is non-degenerate ; otherwise it is.. The diagonal elements, an accumulator and some integer iterators ) decomposed matrix the!, clarification, or by the following format RSS feed, copy and paste this URL into your reader! $\begingroup$ ( 1 ) T is the inverse of a covariance matrix symmetric the sum of the original.. General solution to a system of equations is degenerate the correlation coefficient is! For matrix inversion formula for variance is given byσ2x=1n−1n∑i=1 ( xi–ˉx ) 2where n is the covariance matrix always! These properties both theoretically and is the inverse of a covariance matrix symmetric 1D Gaussian matrix which is close being. A co-variance table start with we prove a positive-definite symmetric matrix is critical. How to professionally oppose a potential hire that management asked for an opinion on based on concept!, where n is the TV show Tehran '' filmed in Athens should hardwood floors go all nice! Said matrix and intuitive explanation of the covariance matrix are the same headings across the as. Filmed in Athens of a block diagonal matrix has a simple, diagonal form will help you a.! All the nice properties from it, Erik Ivar Fredholm had introduced the of! The TV show Tehran '' filmed in Athens matrix with eigenvectors are now orthogonal.... Design / logo © 2020 Stack Exchange Inc ; user contributions licensed cc! A discussion of a block diagonal matrix has a simple, diagonal form will help you lot. An accumulator and some integer iterators ) one massive one square diagonal matrix has simple... Many matrices used in statistics, is symmetric so it inherits all way. ) matrix the product $A^ { T } a$, you lose information down in the matrix a. Can definitely provides symmetric inverse matrix your experiment variable increases, and Roger Penrose in 1955 ( ). These properties both theoretically and empirically tridigonal and optimize accordingly to add to Charles H Martin and Vladimir Novakovski answer!, you agree to our terms of service, privacy policy and cookie policy to the problem of unexpected! Elements, an accumulator and some integer iterators ) such distribution is a symmetric a! Of p ( X ), i.e another perspective, to add to Charles H Martin and Novakovski... Each is its own negative entries like 0.0055, etc relationship exist between them some integer iterators.... The QR algorithm and the DGEMM used in statistics, is symmetric random vector X... Asked for an opinion on based on the concept of a random variable 10 stocks with rate... 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Product space Edit ]: Actually, just check the Numerical Recipes for. & 6 ] variance-covariance matrices are always square matrices between two or variables... From it two are identical fast thing to compute, since all off-diagonal elements are zero sparseness etc quadratic. Term of said matrix sudden unexpected bursts of errors '' in software positive * *... Close to being singular these can be proved by simply looking at the cofactors of matrix is! Stable by computing a QR factorization of your matrix table has the headings... And answer site for scientists using computers to solve scientific problems do to get my nine-year old off... And answer site for scientists using computers to solve scientific problems cc by-sa the matrix... Is close to being singular these can be proved by simply looking at the cofactors of a... Looking at the workplace symmetric ) matrices the cone of n×n positive definite matrices matrices of n! Is highly numerically stable on nasty problems we shall take a quick look at workplace... Will describe the geometric relationship of the original data, Σ − 1 is! Definite, then the distribution of X is non-degenerate ; otherwise it is degenerate numerically stable nasty... Our terms is the inverse of a covariance matrix symmetric service, privacy policy and cookie policy random variable and... Headings across the top as it does along the side Novakovski 's answer Recipes for... Implicitly symmetric and is also positive-definite each is its own negative subscribe to this RSS,. Diagonal element of a co-variance table n't know of a symmetric matrix proven from actual! To the problem of sudden unexpected bursts of errors '' in software parts! Need $Q$ -less QR factorization of your matrix symmetric so it inherits all the properties! Number of the variances equivalent to the problem it does along the side formula. Implications of these properties both theoretically and empirically approach can definitely provides symmetric inverse.! Block diagonal matrix has a simple, diagonal form will help you a lot the top as can! Contributing an answer to computational Science Stack Exchange Inc ; user contributions licensed under cc.... To my knowledge there is not a complex number ) self-adjoint operator a...
## is the inverse of a covariance matrix symmetric
Case Studies For Student Affairs Professionals, Data Visualization Techniques In Python, Uses Of Metalloids, Positivist, Interpretive And Critical Paradigm, Caramel Brownies Using Brownie Mix, Jane Magnolia Buds, Ethical Dilemma In Social Work Pdf,
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https://chemistry.stackexchange.com/questions/68546/reaction-of-ethylene-glycol-with-pi%E2%82%83-p-i%E2%82%82
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# Reaction of ethylene glycol with PI₃ (P + I₂)
We know that $$\ce{2P + 3I2 -> 2PI3}$$
Ethylene glycol reacts with $$\ce{PCl3}$$ to give ethylene dichloride, but why does it gives ethylene when it reacts with $$\ce{P + I2}$$?
I don't really know why it happens so as it is quite contradictory because in case of primary alcohols, corresponding iodoalkane is formed.
$$\ce{OHCH2CH2OH + PI3 -> [CH2I-ICH2] -> CH2=CH2 + I2}$$
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http://editionsassailly.com/liste_diss_alpha/climont%20full%20list%20XYZ%20htm.htm
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Xing Guang Xia Origin : BAC 2007
Category : Critics
kind of theory : kind of particle :
kind of critics : Special Relativity theory kind of energy :
email : [email protected]
email :
web1 : http://www.gsjournal.net/old/physics/yuhua.pdf
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key statements: Generalized Space-time Theory of Relativity contact action principle firstly. According to this principle and the finite speed of light, briefly describes the logic falsehood and conceptive errors in Einstein's theory, and the basal viewpoints of the Generalized space-time relativity, and then points out that, by applying this theory, not only can Einstein's theory be achieved, but also the scientific finding that cannot be educed from Einstein's theory can be obtained.
Dr. Jianhua Xiao Origin : DUF 2004
Category : Critics
kind of theory : kind of particle :
kind of critics : Big Bang kind of energy :
email : [email protected]
email :
web1 : http://homepages.xnet.co.nz/~hardy/cosmologystatement.html
web2 : http://arxiv.org/ftp/arxiv/papers/1105/1105.3320.pdf
web3 :
key statements: Critics of Big Bang, Geometrical Field Theory of Hamilton Dynamic System In Rational Mechanics
W. Xie Origin : PHY 2013
Category : Critics
kind of theory : kind of particle :
kind of critics : Quantum Mechanics kind of energy :
email :
email :
web1 : http://physicsessays.org/browse-journal-2/category/31-issue-2-june-2011.html
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key statements: Physics Essays: , Vol. 24, No. 2, MILLSIAN 2.0: A molecular modeling software for structures charge distributions and energetics of biomolecules
Changyi Xu Origin : CLI 2014
Category : Expanding Earth
kind of theory : kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://www.sciencedirect.com/science/article/pii/S1674984715000518
web2 : https://www.researchgate.net/publication/285275145_Earthquake-origin_expansion_of_the_Earth_inferred_from_a_spherical-Earth_elastic_dislocation_theory
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key statements: Earthquake-origin expansion of the Earth inferred from a spherical-Earth elastic dislocation theory
Dr. Kumming Xu Origin : PHY 2011
Category : Critics
kind of theory : kind of particle :
kind of critics : Quantum Mechanics kind of energy :
email : [email protected]
email :
web1 : http://physicsessays.org/browse-journal-2/category/29-issue-4-december-2011.html
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key statements: Physics Essays: , Vol. 24, No. 4, Electronic orbitals within a helium atom characterized by spherical quantities in dynamic calculus novel two-dimensional spacetime model from scratch in the context of harmonic oscillations. The operational rule of the atomic spacetime is dynamic calculus of spherical quantity, which is conceptually different from infinitesimal calculus of physical quantity. Space and time are treated as two orthogonal, symmetric and complementary quantities
Dr. Shao-zhi Xu Origin : DBN FRI SAP PHY RAP 1992
Category : Critics
kind of theory : kind of particle :
kind of critics : Special Relativity theory kind of energy :
email :
email :
web1 : http://redshift.vif.com/JournalFiles/Pre2001/V00NO16PDF/V00N16XUS.pdf
web2 : http://home.btconnect.com/sapere.aude/
web3 : http://www.ekkehard-friebe.de/kap4.pdf
key statements: No One Can Save the LT [Lorentz Transformations] see campbell problem of velocity of light (speed spin of electron) critics of the relativity of simultaneity. It is shown to be false due to logic error by Einstein
Shichuan Xu Origin : GSJ 2011
Category : Alternative theory
kind of theory : unified field kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://gsjournal.net/Science-Journals-Papers/Author/749/Xu,%20Shichuan
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key statements: The Essence of Gravitationview Sieve Method: Sieve the Forward and Reverse In One TimeviewBy applying a new mathematical theory called 2-way sieve ,this article explains that under the action of the coupling strength ,when the energy turns into substance, it also gives birth to an equal amount of antimatter which produces cross gravitation with other common substance.Finally,this article deduces the definition numerical formula which unifies the four forces
X. Xu Origin : CLI 1994
Category : Expanding Earth
kind of theory : kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://scrippsscholars.ucsd.edu/jgieskes/content/mobilization-beryllium-sedimentary-column-convergent-margins
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key statements: Mobilization of beryllium in the sedimentary column at convergent margins
Dr. Xiang Qun Xu Origin : SAP DBN FRI RAP 1992
Category : Critics
kind of theory : kind of particle :
kind of critics : Special Relativity theory kind of energy :
email :
email :
web1 : http://redshift.vif.com/JournalFiles/Pre2001/V00NO16PDF/V00N16XUS.pdf
web2 : http://www.antidogma.ru/english/node69.html
web3 : http://www.ekkehard-friebe.de/kap4.pdf
key statements: On the Relativity of Simultaneity see Dr. Shao-Zhi Xu Relativity of simultaneity. a false proposition due to an error in logic and confusion in fundamental concepts and epistemology
Yelin Xu Origin : INE 1988
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Free energy
email :
email :
web1 : http://arxiv.org/ftp/physics/papers/0702/0702150.pdf
web2 : http://www.ejtp.com/articles/ejtpv3i9.pdf
web3 :
key statements: A Trial and Study on Obtaining Energy from a Single Heat Reservoir at Ambient Temperature
Pr. Dr. She-Sheng Xue Origin : MIT 2011
Category : Superluminal
kind of theory : kind of particle :
kind of critics : C of light as absolute kind of energy :
email : [email protected]
email :
web2 : http://arxiv.org/abs/1206.0709
web3 :
key statements: Do high-energy neutrinos travel faster than photons in a discrete space-time?
Dip.Eng Ioannis Xydous Origin : GSJ BOR 2013
Category : Alternative theory
kind of theory : energy ether kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://gsjournal.net/Science-Journals-Papers/Author/922/Ioannis,%20Xydous
web3 :
key statements: The secret of the Electron-Positron pair reveals the mechanism of the pair creation, the discovery of the Complete Coulomb Force, Complete Casimir Force, Strong Nuclear Force, Aether, Unified Field Force and ultimately, the topology of the Universe. An alternative Quantum Physics
S. Yabushita Origin : CLI 1987
Category : Expanding Earth
kind of theory : kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://www.sciencedirect.com/science/article/pii/S1674984715000518
web2 :
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key statements: The Earth's expanding
T. Yada Origin : CLI 2004
Category : Expanding Earth
kind of theory : kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://www.hist-geo-space-sci.net/5/135/2014/hgss-5-135-2014.pdf
web2 :
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key statements: The global accretion rate of extraterrestrial materials in the last glacial period estimated from the abundance of micrometeorites in Antarctic glacier ice
M. F. Yagan Origin : THE GSJ 2004
Category : Critics
kind of theory : kind of particle :
kind of critics : Sagnac relativist interpretation kind of energy :
email :
email :
web2 : http://gsjournal.net/Science-Journals-Papers/Author/399/M.%20F.,%20Yagan
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key statements: Relativistic Dynamics of Field-Particle System Dynamics of Beta Decay: by discuss these two topics The Sagnac Effect As Cumulative Doppler The Confusion Between the Absolute and Relative Speed of Light. The Sagnac Effect As Cumulative Doppler
Asher Yahalom Origin : SRE 2013
Category : Superluminal
kind of theory : kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://www.scirp.org/journal/PaperInformation.aspx?PaperID=38868
web2 :
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key statements: Gravity and Faster than Light Particles
G. V. Yakovlev Origin : CLI 2009
Category : Experiment
kind of theory : kind of particle :
kind of critics : C of light as absolute kind of energy :
email :
email :
web1 : https://arxiv.org/ftp/arxiv/papers/0904/0904.2468.pdf
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key statements: Experiment for Testing Special Relativity Theory An experiment aimed at testing special relativity via a comparison of the velocity of a non matter particle (annihilation photon) with the velocity of the matter particle (Compton electron) produced by the second annihilation photon from the decay 22Na(β+)22 Ne is proposed.
Ahmet Yalcin Origin : DBN 0
Category : Critics
kind of theory : kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://db.naturalphilosophy.org/member/?memberid=2036
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key statements:
Jonathan Yalley Origin : GAL DBN 2011
Category : Alternative theory
kind of theory : fluid ether kind of particle : pair linked
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://www.eternalchaos.com/CUMDEX3.doc
web2 : http://db.naturalphilosophy.org/member/?memberid=1746
web3 :
key statements: Radiation as Cyclic Photo-Pair Production.Planck’s Constant and Path Differences The Universe As A Perfect Gaseous Machine A Thoroughly Choreographed Scientific Account of The Origin, Development & Final Frontier of Our Ever Expanding Grand Universe Divulged Realistically.
Pr. Philip Yam Origin : CLI 1997
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : ZPE
email : [email protected]
email :
web2 : http://www.sta.cuhk.edu.hk/scpy/default.aspx
web3 :
key statements: how much "zero-point energy" resides in the vacuum is unknown
Pr. Dr. Hiroshi Yamada Origin : INE 2001
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Cold fusion
email :
web1 : http://www.lenr-canr.org/acrobat/MizunoTneutronevoa.pdf
web3 : http://jcfrs.org/jcf11e.pdf
key statements: Neutron Evolution from a Palladium Electrode by Alternate Absorption Treatment of Deuterium and Hydrogen
Taketsugu Yamaguchi Origin : GAL DBN 2007
Category : Critics
kind of theory : kind of particle :
kind of critics : Quantum Mechanics kind of energy :
email :
email :
web1 : http://db.naturalphilosophy.org/member/?memberid=1737
web2 :
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key statements: On the Interpretation of Quantum Mechanics Galilean Electrodynamics, Volume 18, No. 2, What type of experimental arrangement is in fact viable to observe, for example, the value of momentum?
Kun Yan Origin : GSJ 2009
Category : Alternative theory
kind of theory : fractal universe kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://gsjournal.net/Science-Journals-Papers/Author/289/Kun,%20Yan
web2 : http://www.nature.ac.cn/papers/abs-info-cn.doc
web3 :
key statements: The Tendency Analytical Equations of Stable Nuclides and the Superluminal Velocity Motion Laws of Matter in Geospace Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed. Introductions on the medium shell and discrete orbits of celestial bodies motion: Fractal dimension structure of Cosmos and its mathematical foundations; superluminal velocity
Mu-Lin Yan Origin : MIT 2011
Category : Superluminal
kind of theory : kind of particle :
kind of critics : C of light as absolute kind of energy :
email :
email :
web2 : http://arxiv.org/abs/1111.4532
web3 : http://journals.aps.org/prd/abstract/10.1103/PhysRevD.62.094013
key statements: On determination of the geometric cosmological constant from the OPERA experiment of superluminal neutrinos Derives superluminal behaviour from special relativity with de Sitter space-time symmetry.
Pr. Hideaki Yanagisawa Origin : GSJ 2011
Category : Cosmology
kind of theory : kind of particle :
kind of critics : General Relativity Theory kind of energy :
email : [email protected]
email :
web1 : http://gsjournal.net/Science-Journals-Papers/Author/685/Hideaki,%20Yanagisawa
web2 :
web3 :
key statements: Energy ignored by Einstein: Dark Matter is not Required. The quantity of all stress is in direct proportion to the quantity of energy at time (t). Stress is the changed degree of energy per time. According to my stress equation (dE/dt=kE), energy ignored by Einstein was calculated. And it is added to his gravitational equation. Ignored energy E(t) with over time is ignored E(t)=E(0)(1-ekt)ekt Dark matter, dark energy and the big bang are not required. Limited galaxy sizes, a mandala structure and a pattern of constant dark energy can be explained by a new gravitational equation.
Pr. Ben-Luo Yang Origin : PHY DBN 2013
Category : Critics
kind of theory : kind of particle :
kind of critics : Maxwell equations kind of energy :
email : [email protected]
email :
web1 : http://physicsessays.org/browse-journal-2/category/152-issue-2-june-2014.html
web2 : http://db.naturalphilosophy.org/member/?memberid=669
web3 :
key statements: [ PE Volume 27: Pages 215-238,] Logical re-examination of the classical electromagnetism and rational reconstruction of the formal system to describe dynamic electromagnetic fields, Maxwell’s equations cannot directly construct a proper boundary value problem and have many logic improprieties and inconsistency implied in the old theorem.
Pr. Ben-Luo Yang Origin : BAC 1991
Category : Critics
kind of theory : kind of particle :
kind of critics : Special Relativity theory kind of energy :
email : [email protected]
email :
web1 : http://www.wbabin.net/physics/yuhua.pdf
web2 : http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4669406
web3 :
key statements: Logic Argumentation of the Absolute Pseudo of Minkowsky's Pseudo-space Professor Yang Benluo scientific network completely abandoned the theory of relativity the theology of the 20th century
Shi Jia Yang Origin : GSJ INE 2010
Category : Critics
kind of theory : fluid ether kind of particle : pair linked
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://gsjournal.net/Science-Journals-Papers/Author/199/Shijia,%20Yang
web2 :
web3 :
key statements: The Theory of Relativity Makes a Genius into a Fool Many Scholars Believe that "Ether" Exists I believe that ether exists firmly the Magnetic Field is a whirlpool of the ether. the ether of the pure electromagnetism field is an ocean that make of pair of positive electron and negative electron.
Shimin Yang Origin : MIT 2009
Category : Superluminal
kind of theory : kind of particle :
kind of critics : C of light as absolute kind of energy :
email : [email protected]
email :
web2 : http://arxiv.org/abs/0910.0897
web3 : http://apsjournals.apsnet.org/doi/abs/10.1094/PDIS-04-14-0398-RE
key statements: Lorentz violation in three-family neutrino oscillation
Dr. Xin-She Yang Origin : CLI 1998
Category : Cosmology
kind of theory : kind of particle :
kind of critics : General Relativity Theory kind of energy :
email :
email :
web1 : http://www.eclipse2006.boun.edu.tr/sss/paper02.pdf
web2 :
web3 :
key statements: two unexplained gravity anomaly valleys observed from the Mohe solar eclipse on 9 March 1997. There has not been such kind of anomalies. May be related to the fundamental properties of gravitation
Pr. Xintie Yang Origin : THE 2002
Category : Alternative theory
kind of theory : innovative kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://arxiv.org/abs/1503.02006
web2 : http://www.journaloftheoretics.com/Articles/aArchive.htm
web3 : http://www.journaloftheoretics.com/Articles/4-3/yang1-final.pdf
key statements: Journal of Theoretics Vol.4-3 The Application of Aerodynamic Method in the Development of Relativity In Continuous Medium Mechanics there exists an equivalent equation system to that of electromagnetic theory. This system is nonlinear and it serves as a reference for the advancement of a rue Maxwell equation system [11] such that the further nonlinearization of Maxwell’s equation by the aerodynamic method will yield two directions. One being viscosity and the other being compressibility.
Yanbin Yang Origin : CLI 2017
Category : Critics
kind of theory : modified Newton law kind of particle :
kind of critics : General Relativity Theory kind of energy :
email : [email protected]
email :
web1 : https://arxiv.org/abs/1702.06143
web2 :
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key statements: In two recent arXiv postings, Maji et al. Argue against the existence of a spatially thin, kinematically coherent Disk of Satellites (DoS) around the Milky Way (MW), and suggest that the DoS is "maybe a misinterpretation of the data". These claims are in stark contrast to previous works, and indeed we show that the conclusions of Maji et al. Do not hold up to scrutiny. We find no evidence for a significant kinematic coherence among the simulated satellite galaxies, in contrast to the observed MW system.
Dr. Yongfeng Yang Origin : DBN GSJ 2011
Category : Editor
kind of theory : kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://gsjournal.net/Science-Journals-Papers/Author/958/Yongfeng,%20Yang
web2 : http://db.naturalphilosophy.org/member/?memberid=2059
web3 :
key statements: Astronomy, Cosmology General Science Journal editor Motions of Observable Structures Ruled by Hierarchical Two-body Gravitation in the Universe. All objects in the universe are organized in an orderly series of hierarchical two-body systems with gravitation Under the effect of gravitation, a successive hierarchical orbital shrinkage results in high redshifts of distant galaxies and planar (disc) rotational profile of large-scale structures
Jonathan Yankovich Origin : RAP 2014
Category : Critics
kind of theory : kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://erg.ucd.ie/arupa/ratbag_antiphysics_rag97.html
web2 :
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key statements:
H. Yano Origin : CLI 2004
Category : Expanding Earth
kind of theory : kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://www.hist-geo-space-sci.net/5/135/2014/hgss-5-135-2014.pdf
web2 :
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key statements: The global accretion rate of extraterrestrial materials in the last glacial period estimated from the abundance of micrometeorites in Antarctic glacier ice
Pr. Dr. Aiping Yao Origin : FRI 2003
Category : Experiment
kind of theory : kind of particle :
kind of critics : Sagnac relativist interpretation kind of energy :
email : [email protected]
email :
web1 : http://en.wikipedia.org/wiki/Sagnac_effect
web2 : http://www.ekkehard-friebe.de/kap4.pdf
web3 :
key statements: Modified Sagnac experiment for measuring travel-time difference between counter-propagating light in a uniformly moving fiber 2003 see Prof. Ruyong Wang,
D. T. Yarbrough Origin : CLI 2013
Category : Critics
kind of theory : kind of particle :
kind of critics : General Relativity Theory kind of energy :
email :
email :
web2 :
web3 :
key statements: problems with the schwarzschild radius There are holes in this theory, but they're not black.
Pr. Natalya Yaremko Origin : GSJ 2013
Category : Critics
kind of theory : kind of particle :
kind of critics : Quantum Mechanics kind of energy :
email :
email :
web1 :
key statements: see O. Yaremko
Pr. Oleg Emmanuilovich Yaremko Origin : GSJ 2013
Category : Critics
kind of theory : kind of particle :
kind of critics : Quantum Mechanics kind of energy :
email : [email protected]
email :
web1 : http://gsjournal.net/Science-Journals-Papers/Author/1403/Oleg,%20Yaremko
key statements: Fractional degrees of heat conductivity, the string vibration
Yurij Yaremko Origin : CLI 2015
Category : Editor
kind of theory : kind of particle :
kind of critics : kind of energy :
email : [email protected]
email : [email protected]
web1 : http://www.ejtp.com/editorial.html
web2 :
web3 :
key statements: Electronic Journal of Theoretical Physics editor
Pr. Dr. Tolga Yarman Origin : DBN PHY 1997
Category : Superluminal
kind of theory : beyond relativity kind of particle :
kind of critics : C of light as absolute kind of energy :
email : [email protected]
email : [email protected]
web1 : http://www.tolgayarman.org/
web2 : http://db.naturalphilosophy.org/member/?memberid=1122
web3 : http://physicsessays.org/browse-journal-2/category/148-issue-4-december-2013.html
key statements: Just Like the Gravitational Field, the Electric Field Too, Slows Downs a Clock, Interacting With It: A Whole New Appraoch to the Bound Muon Decay :Coulomb Force is a Fundamental Law of Nature Insuring a Unique Matter Architecture the steady state electronic motion around a given nucleus in a non-circular orbit, depicts a rest mass variation, though the overall relativistic energy remains constant. This is, in no way, conflicting with the usual quantum mechanical approach.The approach leads to the de Broglie relationship, and superluminal speeds, yet excluding any exchange of energy, making the basis of quantum mechanics. Scaling properties of quantum mechanical equations working as the framework of relativity: Applications drawn by a unique architecture matter is made of The special relativity principle and superluminal velocities. Scaling properties of quantum mechanical equations working as the framework of relativity: Principal articulations about the Lorentz invariant structure of matter
M. N. Yaseen Origin : ARX 0
Category : Critics
kind of theory : kind of particle :
kind of critics : Philosophical kind of energy :
email :
email :
web1 : https://www.mail-archive.com/[email protected]/msg30836.html
web2 :
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key statements: In The Search Of Reality
Mark Yasin Origin : ARX 2000
Category : Alternative theory
kind of theory : innovative kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://pub9.bravenet.com/forum/static/show.php?usernum=696339869&frmid=3918&msgid=118247&cmd=show
web2 : https://www.mail-archive.com/[email protected]/msg30836.html
web3 :
key statements: Space and the Universal Laws of Physics: (book) The space fabric is the space in the universe composed of space bubbles and black matter. expanding media or space fabric eventually encounters the vortices. The space fabric spreads turbulently through these vortices, causing numerous space bubbles to engulf small black matter particles space fabric is a composition of pure matter black matter and anti-matter absolute vacuum both at equilibrium. In other words, space is composed of matter and anti-matter at rest. Dirac's theory. Dirac referred to two types of matter: ordinary particles and extraordinary particles, which are the space fabric this hole as an anti-particle Basic matter particles are black matter particles that cannot be part of the space fabric.pace fabric distortion is the compression and subsequent decompression that occurs when a particle moves from one space bubble (space point) to the next. gravitational field is a form of static distortion induced into the space fabric by the presence of matter.
G. Yassoon Origin : CLI 1997
Category : Cosmology
kind of theory : kind of particle :
kind of critics : kind of energy :
email :
email :
web1 :
web2 : http://www.driftline.org/cgi-bin/archive/archive_msg.cgi?file=spoon-archives/feyerabend.archive/feyerabend_1997/feyerabend.9706&msgnum=36&start=1661
web3 :
key statements: the continents are essentially extraterrestrial, that is, they were formed by an impact with an already formed earth and a satellite or cometary body approximately half the size of the moon
M. Yasuda Origin : CLI 1990
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Cold fusion
email :
email :
web1 : http://web.pdx.edu/~pdx00210/Lists/ListofPapers1.htm
web2 :
web3 :
key statements: Experimental Investigation of the Electrochemically Induced Nuclear Fusion
Iwamura Yasuhiro Origin : INE 2016
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Cold fusion
email :
email :
web1 : http://www.infinite-energy.com/iemagazine/issue126/index.html
web2 :
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key statements: Introduction of Condensed Matter Nuclear Science at Tohoku University
Joseph C. Yater Origin : REX 1979
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Over unity
email :
email :
web1 : http://rexresearch.com/yater/yater.htm
web2 :
web3 :
key statements: classical and quantum-effect diodes. Using selected experimental values for the diode nonlinearity factors in these circuits, open circuit voltages are computed that are not predicted by the second law of thermodynamics.
Bijan Yavari Origin : BOR 2000
Category : Alternative theory
kind of theory : innovative kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web3 :
key statements: Foundation Physics: P-Particle Theory: a neutrino-based TOE, postulated to be the fundamental constituent of all matter in the universe, and subsequently shown to be identifiable with the neutrino P includes not only quantum of matter but also E, M and G. P are compound or not; density of the universe. Matter being made up of fields; The fields have opposite poles; Opposite poles have a tendency to approach each other and collapse.
Xin Ye Origin : PHY 2013
Category : Critics
kind of theory : kind of particle :
kind of critics : Quantum Mechanics kind of energy :
email :
email :
web1 : http://physicsessays.org/browse-journal-2/category/152-issue-2-june-2014.html
web2 :
web3 :
key statements: [ PE ] An interesting method to calculate loop diagram in quantum electrodynamics
A. Yefremov Origin : PRP 2007
Category : Experiment
kind of theory : kind of particle :
kind of critics : General Relativity Theory kind of energy :
email : [email protected]
email :
web1 : http://www.ptep-online.com/index_files/issues.html
web2 :
web3 :
key statements: Notes on Pioneer Anomaly Explanation by Sattellite-Shift Formula of Quaternion Relativity: Remarks on "Less Mundane Explanation of Pioneer Anomaly from Q-Relativity" reliminary quantitative assessments made on the base of Pioneer 10/11 data demonstrate closure of the assumed relativistic deceleration and observed Doppler deceleration values.
I. A. Yeganova Origin : NAC 1990
Category : Cosmology
kind of theory : kind of particle :
kind of critics : kind of energy : Torsion field
email :
email :
web1 : http://www.chronos.msu.ru/old/EREPORTS/levich_substan_inter/levich_substan_inter.htm
web2 :
web3 :
key statements: On the remote influence of stars on the resistor. I.A.Yeganova exposes N.A.Kozyrev’s views by introducing a meta-interaction, embracing the whole material world and mediating the existence of all the manifestations of matter by self-regulation in a unified universal process (Yeganova 1984, p.2)
Anton I. Yegorov Origin : RNE 1995
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Conventional
email :
email :
web1 : http://www.nuenergy.org/new-energy-technologies-12/
web2 :
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key statements: Uranium Photoaccumulator
John Yemma Origin : INE 2001
Category : Critics
kind of theory : kind of particle :
kind of critics : Philosophical kind of energy :
email : [email protected]
email :
web1 : http://www.jmanimas.com/wtalight.htm
web3 :
key statements: Seeing Einstein in a New Light illustrated the current authoritarian grip the beliefs of scientists impose on our society. Mr. Yemma tells us that a professor of mathematics (who is sufficiently rebellious to be a mathematician in a female body), Domina Eberle Spencer, has developed a mathematical theory which, if correct, proves Einstein was wrong about the velocity of light and time.
Ka-In Yen Origin : CLI 2003
Category : Alternative theory
kind of theory : innovative kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://web.archive.org/web/20091018231729/http://geocities.com/redlorikee/index.html
web2 : http://www.iaswww.com/apr/Science/Physics/Relativity/Alternative/
web3 :
key statements: Ether-string Two components of magnetic force are derived from this ether-string model: one is drag force, the other Bernoulli force To derive them, negative potential mass, and vector of mass are introduced Charged particles are linked by ether-strings. the two components of magnetic force, drag force and Bernoulli force, are successfully derived from ether dynamics. But there are a lot of questions waiting for answer in ether dynamics; for example, the relative mass, and slower atomic clock on airplane etc, are well explained in the special theory of relativity.
Vladimir N. Yershov Origin : THE PRP 2003
Category : Alternative theory
kind of theory : beyong quantum mechanics kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web2 : http://arxiv.org/abs/physics/0301034
web3 : http://www.ptep-online.com/index_files/issues.html
key statements: Neutrino Masses and the Structure of the Weak Gauge Boson: by presents a composite model of fermions the massless neutrino is not consistent with the high values of the experimental masses of $W^\pm$ and $Z^0$. Consistency can be achieved on the assumption that the electron-neutrino has a mass of about 4.5 meV.
Mehmet Yesilgöz Origin : BOR 2012
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Free energy
email :
email :
web2 : http://www.naturscheck.de/artikel/artikel-interviews/artikel/der_traum_von_der_freien_energie
web3 :
key statements: The dream of free energy - When does it become reality?
José Yglesias Origin : QUA 0
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Free energy
email :
email :
web1 : http://www.quanthomme.info/catalogue/c10inventeurs.htm
web2 :
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key statements: Receiver for extracting Electricity from Air
Yong-Gwan Yi Origin : SAP PHY FRI 1997
Category : Critics
kind of theory : kind of particle :
kind of critics : Special Relativity theory kind of energy :
email : [email protected]
email :
web1 : http://physicsessays.org/browse-journal-2/category/110-issue-2-june-1997.html
web2 : http://home.btconnect.com/sapere.aude/
web3 : http://www.ekkehard-friebe.de/kap4.pdf
key statements: [ PE vol. 10 p. 186] In Time and Velocity, Which Component Would Appear Dilated to the Observer? the Galilean concept of time, in contrast to the currently accepted view, is even more natural for describing the physics of relativistic.
Zheng Yi Origin : FRI 2003
Category : Experiment
kind of theory : kind of particle :
kind of critics : Sagnac relativist interpretation kind of energy :
email :
email :
web1 : http://www.worldsci.org/php/index.php?tab0=Abstracts&tab1=Display&id=2747
web2 : http://www.ekkehard-friebe.de/kap4.pdf
web3 :
key statements: Modified Sagnac experiment for measuring travel-time difference between counter-propagating light in a uniformly moving fiber see Wang, Ruyong
Shan-Noon Yie Origin : PHY 2005
Category : Alternative theory
kind of theory : innovative kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://physicsessays.org/browse-journal-2/category/83-issue-1-march-2005.html
web2 : http://physicsessays.org/browse-journal-2/product/434-3-shan-noon-yie-physics-under-space-invariance.html
web3 :
key statements: [ PE vol. 18 p. 31] Physics under space invariance A Possible Answer to the Right-Left Asymmetry of beta Decay. A new concept Space Invariance and builds the particle field functions to approach each result of quantum field theory through many ways while escaping from its problems. The efforts are done in three aspects. (A) Identify actions of space invariance on the fundamental laws of quantum field theory (QFT), such as Dirac’s equation, the scattering formula of quantum mechanics, transition rule
Muslim Yildiz Origin : BOR 0
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Anti-gravity
email :
email :
web1 : http://www.borderlands.de/infos.contacts.browse.php3?pos=210&total=222
web2 :
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key statements: Antigravitation
Hüseyin Yilmaz (deceased) Origin : SAP DBN PHY 1965
Category : Alternative theory
kind of theory : innovative kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://en.wikipedia.org/wiki/Yilmaz_theory_of_gravitation
web2 : http://db.naturalphilosophy.org/site//member/?memberid=1413
web3 : http://www.amazon.com/Introduction-relativity-principles-Blaisdell-sciences/dp/B0006BM13M
key statements: Introduction to the Theory of Relativity and the Principles of Modern Physics new theory of gravity theory of gravitation which closely mimics general relativity in weak-field conditions, but in which event horizons cannot appear . PE Lorentz transformations and wave-particle unity
Pr. Dr. Ming Yin Origin : CLI 2005
Category : Alternative theory
kind of theory : gravity is electromagnetic kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://lanl.arxiv.org/ftp/physics/papers/0509/0509068.pdf
web2 :
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key statements: Experimental Indications of Electro-Gravity (see Timir Datta)
Dr. Nelson Ying Origin : INE 1993
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Cold fusion
email : [email protected]
email :
web1 : http://www.newphysics.se/archives/keelynet/energy/hightech.txt
web2 :
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key statements: Cold Fusion in a Ying Cell and Probability Enhancement by Boson Stimulation, Dr. Nelson Ying, a nuclear physicist, announced Friday that he is getting up to 100,000 TIMES more energy from a tabletop apparatus than he applies to it, and that he can repeat the procedure at will. "A workable cold fusion process --
Pr. Nicola Yordanov Origin : CLI 2015
Category : Editor
kind of theory : kind of particle :
kind of critics : kind of energy :
email : [email protected]
email : [email protected]
web1 : http://www.ejtp.com/editorial.html
web2 :
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key statements: Electronic Journal of Theoretical Physics editor
Dan York Origin : PEA 1995
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Free energy
email :
email :
web1 : http://www.keelynet.com/energy/clemreborn.html
web2 :
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key statements: Light force keelynet
Warren E. York Origin : YOR DBN GSJ THE 2003
Category : Alternative theory
kind of theory : fluid ether kind of particle :
kind of critics : kind of energy : Ether energy
email : [email protected]
email :
web1 : http://www.rexresearch.com/merkl/merkl.htm
web2 : http://gsjournal.net/Science-Journals-Papers/Author/305/Warren%20E.,%20York
web3 : http://zpower.com/ch/documents/ZPEPaper_ZeroPointEnergyDocumentCompilation.doc
key statements: The Aether exists. It is Time and Space itself. 2. The Aether is reciprocating omnidirectional grid of energy by nature. 3. The Aether and EMF are gyroscopic in nature.4. The Aether has properties of duality. The Aether is a fluidatic energy and follows some of the fluid dynamic laws of other known fluids but unique with additional properties being that of a fluidatic energy :Aether flow is inverse to magnetic flow. Electrons and Aether flow interact with each other (EMF [magnetic flux field like void flow opposite to particle flow) Quantum Gravity & Time as Derived From Pi/Time: by presents a theory of quantum gravity and a time derivation in the context of "4D Unified Math".
Harry Yosh Origin : CLI 2004
Category : Alternative theory
kind of theory : innovative kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://space-time-energy.org/Spacetime&Substance/SR2.pdf
web2 :
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key statements: Wave Equation A solution of Dirichlet problem using second partial derivatives of boundary function inertial mass and gravitational mass in Lagrangian follow the same gauge transformation
K. Yoshimoto Origin : CLI 2008
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Cold fusion
email :
email :
web1 : http://web.pdx.edu/~pdx00210/Lists/ListofPapers1.htm
web2 :
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key statements: NT in Micro-Craters and Excess Heat Data in W/H/Na(K) Systems by T. Ohmori et al Analyzed on TNCF Model
Dr. Charles A. Yost (deceased) Origin : SAP DBN RAP CHI 1983
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Tesla
email :
email :
web1 : http://home.btconnect.com/sapere.aude/
web2 : http://db.naturalphilosophy.org/member/?memberid=323
web3 :
key statements: Aether Propulsion Competition, ESJ Network, 73 Sunlight Drive, Leicester NC 28748, usa The Tesla Experiment: Lightning and Earth Electrical Resonance
Susan Yost Origin : BOR 2005
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Tesla
email :
email :
web3 :
key statements: Magnetic Propulsion, New Energy daughter of Charles Yost Electric Spacecraft Journal, USA
C.-F. You Origin : CLI 1994
Category : Expanding Earth
kind of theory : kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://www.sciencedirect.com/science/article/pii/0016703794902194
web2 :
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key statements: Mobilization of beryllium in the sedimentary column at convergent margins The Be mobilization provides an explanation of Be-10 enrichment in arc volcanic rocks and supports the argument of the importance of the fluid processes in subduction zones at convergent margins.
Jiangyang You Origin : CLI 2012
Category : Superluminal
kind of theory : kind of particle :
kind of critics : C of light as absolute kind of energy :
email : [email protected]
email :
web1 : https://archive.org/stream/arxiv-1111.4951/1111.4951#page/n0/mode/2up
web2 :
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key statements: Photon-neutrino interaction in theta-exact covariant noncommutative model. See R. Horvat.
Arthur M. Young (deceased) Origin : ARX DBN 1976
Category : Philosophical
kind of theory : kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://www.arthuryoung.com/
web2 : http://db.naturalphilosophy.org/member/?memberid=1685
web3 :
key statements: Theory of Process This is good news, for it is no longer appropriate to think of the universe as a gradually subsiding agitation of billiard balls. The universe, far from being a desert of inert particles, is a theatre of increasingly complex organization, a stage for development in which man has a definite place, without any upper limit to his evolution.
David Young Origin : DFI 1998
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Tesla
email :
email :
web2 : http://quanthomme.free.fr/energielibre/systemes/PageChercheurAEC3.htm
web3 :
key statements: Tesla Turbine
Dr. Iain S. Young Origin : CLI 2015
Category : Alternative theory
kind of theory : innovative kind of particle :
kind of critics : Maxwell equations kind of energy :
email : [email protected]
email :
web1 : http://www.jpier.org/PIER/pier151/08.15021106.pdf
web2 : https://www.liverpool.ac.uk/integrative-biology/staff/iain-young/
web3 :
key statements: Progress In Electromagnetics Research, Vol. 151, 83–93, 2015 Evaluation of Electron Beam Deflections across a Solenoid Using Weber-Ritz and Maxwell-Lorentz Electrodynamics
L. Steve Young Origin : BOR 2001
Category : Superluminal
kind of theory : kind of particle :
kind of critics : Quantum Mechanics kind of energy :
email :
email :
web1 : http://kaekae.oas.psu.ac.th/free-ebook/GD-Theory.pdf
web3 :
key statements: G-Dimensional Theory The Smarandache Quantum paradox Comparative Logic and Modern Quantum Theory ( a formal set of (anti-logic) statements inclusive in modern quantum theory.1. Invisible Paradox (Sorites Paradox): macroscopic visible particles are formed of invisible atomic and subatomic particles. . Uncertainty Paradox: macroscopic matter, which is under the 'determinist principle', is formed of subatomic particles, which are under Heisenberg's uncertainty principle. 3. Stability Paradox: Stable matter is formed of particles that are unstable in distinct form. 4. Lifetime Paradox: Long-lived matter particles are formed of short-lived elementary particles. 5. FTL Hypothesis: Quantum behavior implies instantaneous or faster-than-light connection between physically separate loci.
R. Rufus Young Origin : ARX 1996
Category : Cosmology
kind of theory : kind of particle :
kind of critics : Big Bang kind of energy :
email :
email :
web2 :
web3 :
key statements: Steady State Galaxy Theory At the center of each galaxy is a neutroid which acts to constantly recycle all the matter and energy in the galaxy. This neutroid is similar to a neutron star but is very much larger
Curt Youngs Origin : GSJ 2008
Category : Critics
kind of theory : kind of particle :
kind of critics : C of light as absolute kind of energy :
email :
email :
web1 : http://gsjournal.net/Science-Journals-Papers/Author/332/Curt,%20Youngs
web2 :
web3 :
key statements: The Propagation of Light Any one observer/detector will only detect a tiny ray out of the ever enlarging wave front sphere from any emission of EMR at any distance beyond the "near field," which is another related subject, not well understood by many
Mahmoud E. Yousif Origin : THE 2003
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Cold fusion
email : [email protected]
email :
web2 :
web3 :
key statements: The Universal Energies: by investigates some crucial main relations and sequence of the three mechanisms based on the magnetic interaction hypothesis The Magnetic Interaction (The Spinning Magnetic Force, & Elements of the Magnetic Lines of Force : hypotheses about this interaction mechanism
Pr. Saul Youssef Origin : CAL 2001
Category : Critics
kind of theory : kind of particle :
kind of critics : Quantum Mechanics kind of energy :
email : [email protected]
email :
web1 : http://physics.bu.edu/~youssef/
web2 : http://arxiv.org/abs/hep-th/0110253
web3 :
key statements: Questions beyond basic quantum theory where new insights are needed.
Ping Yu Origin : CLI 2013
Category : Critics
kind of theory : kind of particle :
kind of critics : General Relativity Theory kind of energy :
email : [email protected]
email :
web1 : http://dx.doi.org/10.4236/ijaa.2013.33036
web2 :
web3 :
key statements: Cosmology Should Directly Use the Doppler’s Formula to Calculate the Red Shift of Ia Supernova : It is proved that based on the Doppler’s formula and by the method of numerical calculation, the relation of red shift and distance of Ia supernova can be explained well. The hypotheses of dark energy and the accelerating expansion of the universe are completely unnecessary in cosmology
Dr. Xiang Yu Origin : INE 2011
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://www.infinite-energy.com/iemagazine/issue96/
web2 :
web3 :
key statements: See Liu, Fu A Carbon-Free Fuel from Electrolysis and Catalysis of Water
Sha Yin Yue Origin : GSJ 2009
Category : Critics
kind of theory : kind of particle :
kind of critics : Quantum Mechanics kind of energy :
email : [email protected]
email :
web1 : http://gsjournal.net/Science-Journals-Papers/Author/304/Sha%20Yin,%20Yue
web2 :
web3 :
key statements: n the Radius of the Neutron Proton Electron and the Atomic Nucleus The neutron can spontaneously produce disintegration and turn into a proton and at the same time eject an electron and some matterer time.
Zhou Yue Origin : GAL 2014
Category : Alternative theory
kind of theory : innovative kind of particle :
kind of critics : Special Relativity theory kind of energy :
email :
email :
web1 : http://www.eternalchaos.com/auth2.html
web3 :
key statements: see Xi, Zhou Re-Developing Emission Theory Kanarev, Photon Model. Galilean Electrodynamics Vol. 11, no. 6, and Comparison Between the Theory of Relativity and the Quantum Emission Theory Vol. 24, Special Issues 1, p. 17.
Pr. Dr. Hideki Yukawa (deceased) Origin : SAP 1946
Category : Relativist
kind of theory : kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://nobelprize.org/nobel_prizes/physics/laureates/1949/yukawa-bio.html
web2 : http://home.btconnect.com/sapere.aude/
web3 : http://www.ekkehard-friebe.de/kap4.pdf
key statements: The theories of Einstein and Planck are unable to reproduce certain phenomena in the atomic nucleus , and one should therefore give up these theories. This particular also because in the atomic nucleus are greater than the speed of light c = 300000 km / sec.
Robert Yukes Origin : INE 2000
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Free energy
email :
email :
web1 : http://www.infinite-energy.com/iemagazine/issue33/
web2 : http://www.infinite-energy.com/iemagazine/issue33/breakingthroughwater.html
web3 :
key statements: Water and Health electrochemical activation of water (IE, No. 18, p. 35 and IE, No. 21, p. 7). Robert Yukes provides an update and extension to this very, very heretical topic of health properties of specially treated waters
Oliver Yunick Origin : QUA 1970
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Conventional
email :
email :
web1 : http://www.quanthomme.info/catalogue/c10inventeurs.htm
web2 : http://peswiki.com/index.php/Directory:Inventors
web3 :
key statements: Vapor engine
Alexander V. Yurkin
Puschino, Russia. E-mail: Origin : PRP 2016
Category : Alternative theory
kind of theory : innovative kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://www.ptep-online.com/
web2 :
web3 :
key statements: PRP 2016 (vol. 12), issue 3 On the Descriptive Geometric Interpretation of Pauli Principle,Elements of the Mendeleev Table of Chemical Elements, and the Newtonian Laminar Current of a Liquid
David G. Yurth Origin : DBN 1998
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : ZPE
email : [email protected]
email :
web1 : http://db.naturalphilosophy.org/member/?memberid=312
web2 :
web3 :
key statements: Self-organizing Systems, New Energy
Dr. Hamit Yurtseven Origin : PHY 2010
Category : Critics
kind of theory : kind of particle :
kind of critics : Quantum Mechanics kind of energy :
email : [email protected]
email :
web1 : http://physicsessays.org/browse-journal-2/category/34-issue-4-december-2010.html
web2 :
web3 :
key statements: Physics Essays: , Vol. 23, No. 4 Calculation of the Raman frequencies of lattice modes in the disordered phase II of NH4Br at high pressures
Dr. Yasun Yurttas Origin : DBN 2010
Category : Critics
kind of theory : kind of particle :
kind of critics : Maxwell equations kind of energy :
email : [email protected]
email : [email protected]
web1 : http://db.naturalphilosophy.org/member/?memberid=1869
web2 :
web3 :
key statements:
Pr. Dr. Miroslaw Zabierowski Origin : SAP DBN 1976
Category : Cosmology
kind of theory : kind of particle :
kind of critics : Redshift relativist interpretation kind of energy :
email : [email protected]
email :
web1 : http://home.btconnect.com/sapere.aude/
web2 : http://db.naturalphilosophy.org/member/?memberid=1386
web3 :
key statements: Configurations and Redshifts of Galaxies Fornax - The Companion of the Milky Way and the Question of its Standard Motion Newtonian-Kantian mode of growth of star clumps
W. W. Zachary Origin : FRI 1996
Category : Critics
kind of theory : kind of particle :
kind of critics : Quantum Mechanics kind of energy :
email :
email :
web1 : http://www.physics.howard.edu/papers.html
web2 : www.ekkehard-friebe.de/kap4.pdf
web3 : http://arxiv.org/abs/math-ph/0405059
key statements: Classical and quantum relativistic many-particle theory. Canonical Proper-Time Formulation of Relativistic Particle Dynamics
Allan Zade Origin : GSJ 2016
Category : Philosophical
kind of theory : kind of particle :
kind of critics : Morley Michelson relativist interpretation kind of energy :
email :
email :
web2 :
web3 :
key statements: many scientists and enthusiasts try to override that point of view later. They used various optical devices in the attempt to detect observer to-light relative motion. Known experiments had not any success, but those experiments decline possibility to conduct an acoustic Michelson Morley experiment. The situation changed dramatically in 2010 when Norbert Feist from Gersthofen, Germany conducted his Acoustic Michelson-Morley Experiment and subsequently made publication of an article titled ‘Acoustic Michelson-Morley Experiment with an Ultrasonic Range Finder’ (shown in supplementary files of the same article). His findings were astonishing because he observed the same so -called null result in another environment (or in another signal medium combination). Nobody can explain such unusual observation.However, it shows clearly that Einstein’s postulate about a unique reference frame of the light is not correct any longer. In Einstein logics, Feist experiments means this. The speed of sound is the highest speed of signal propagation in the Universe and sound has its unique reference frame that exists regardless of observer’s state of motion. Moreover, an observer cannot detect his motion relative to sound because the speed of sound in every reference frame bound to a given observer has the same constant value. That principle should be named Acoustic Relativity. Obviously, it leads to many nonsenses in physics and falsification of Relativity because light loses its unique reference frame. However, nobody paid attention to Feist’s great achievement.
Nikolay E. Zaev Origin : RNE 2000
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Free energy
email :
email :
web1 : http://www.nuenergy.org/new-energy-technologies-8/
web2 : http://www.free-energy-info.co.uk/MagIndex.html
web3 :
key statements: Inductive conversion of heat energy to electrical energy, experiments with magnetic materials to get freeelectric energy from magnetic materials Ferrites and Ferromagnetics Free Energy Generation Research on the capacitance converter of environmental heat
Elie Zahar Origin : FRI 1980
Category : Critics
kind of theory : kind of particle :
kind of critics : Philosophical kind of energy :
email :
email :
web1 : http://www.jstor.org/discover/10.2307/687250?uid=3738016&uid=2129&uid=2&uid=70&uid=4&sid=56263888463
web2 :
web3 :
key statements: Einstein, Meyerson, and the role of mathematics in physical discovery.
Pr. M. Hussain Zahir Origin : CLI 2009
Category : Critics
kind of theory : kind of particle :
kind of critics : Quantum Mechanics kind of energy :
email : [email protected]
email :
web1 : http://journals.aps.org/pre/abstract/10.1103/PhysRevE.89.042907
web2 : http://www.teamliquid.net/forum/general/369503-free-will-in-living-organisms?page=9
web3 :
key statements: Prof. Dr. Zahir is one of Iraqi brilliant scientists who prove experimentally that Heisenberg uncertainty principle is wrong. That's why I think qm is irrelevant here. Substituting probablistic determinism for traditional determinism does not magically expose some gap or unexamined element within neuroscience suggestive of free will.
Dr. Corvin Zahn Origin : BOR 2012
Category : Critics
kind of theory : kind of particle :
kind of critics : Special Relativity theory kind of energy :
email : [email protected]
email :
web1 : http://www.spacetimetravel.org/
web3 : https://www.uni-hildesheim.de/no_cache/lsf/einrichtungen/organisation/?typo3state=persons&lsfid=2171
key statements: Time Travel? Relativity relatively clear, The theory of relativity holds a certain fascination for many people. At the same time it is often regarded as very abstract and difficult to understand.
Alexander K. Zaichenko Origin : REC 1995
Category : Superluminal
kind of theory : kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://arxiv.org/pdf/0709.2191.pdf
web2 : http://arxiv.org/pdf/nucl-th/0407108.pdf
web3 :
key statements: More about tunneling times,the dwell time and the Hartman effect. About the influence of space-time separations between sources of α-particle emission in the reaction p+11B3α on interference phenomena in their spectra
Oleg Zaimidoroga Origin : CLI 2017
Category : Alternative theory
kind of theory : innovative kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : https://arxiv.org/pdf/1203.2490.pdf
web3 :
key statements: Non relativistic theory of the electroscalar field being an expansion of the classical Maxwell's electrodynamics is discussed with the results of the solar eclipse august 2008
Arthur G. Zajonc Origin : CLI 1977
Category : Experiment
kind of theory : kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://www.iop.org/EJ/abstract/0022-3700/10/2/002
web2 : http://deepblue.lib.umich.edu/bitstream/handle/2027.42/48848/jbv10i2pL43.pdf?sequence=2&isAllowed=y
web3 :
key statements: Differential cross section for electron impact excitation of metastable helium measured by the atomic time-of-flight method
Michail Zak Origin : PHY 2009
Category : History
kind of theory : kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://physicsessays.org/browse-journal-2/category/66-issue-2-june-2009.html
web2 : http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/40811/1/04-1730.pdf?origin=publication_detail
web3 :
key statements: [ PE vol 22 p 173 ] Hidden statistics of Schrödinger equation
A. I. Zakazchikov Origin : CLI 2001
Category : Alternative theory
kind of theory : fluid ether kind of particle :
kind of critics : Special Relativity theory kind of energy :
email :
email :
web1 : www.antidogma.ru/english/node69.html
web2 :
web3 :
key statements: Returning to Ether critical study of the theory of relativity ; theoretical need for the ether to explain the set of specific facts of physics. ;rejection of the concept of relativity of time. Artificiality of this concept is proved with many examples. A new vision of the facts set out in terms of air concept, which has the ether never been seen before features.
Dr. Nazar M. Zaki Origin : DBN 2003
Category : Critics
kind of theory : kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : hhtp://www.faculty.uaeu.ac.ae/nzaki/
web2 : http://db.naturalphilosophy.org/member/?memberid=815
web3 :
key statements:
A. Zaldívar-Sandoval Origin : GSJ 2010
Category : Critics
kind of theory : kind of particle :
kind of critics : Special Relativity theory kind of energy :
email : [email protected]
email :
web2 : http://prespacetime.com/index.php/pst/article/view/746/754
web3 :
key statements: Algebraic Classification of Faraday Spinor 2nd Order Linear Differential Operator in its Exact Form see lopez bonilla
Andrey V. Zaloilo Origin : DBN 0
Category : Critics
kind of theory : kind of particle :
kind of critics : Special Relativity theory kind of energy :
email :
email :
web1 : http://db.naturalphilosophy.org/member/?memberid=1365
web2 :
web3 :
key statements: no details
V. V. Zamashchikov Origin : GAL 2002
Category : Critics
kind of theory : kind of particle :
kind of critics : Maxwell equations kind of energy :
email :
email :
web1 : http://www.eternalchaos.com/CUMDEX2.doc
web3 :
key statements: About the Invariance of Maxwell’s Equations. Galilean Electrodynamics, 13, (22, 32, 36),
Pr. Michel Zamboni-Rached Origin : REC 2002
Category : Superluminal
kind of theory : kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://arxiv.org/pdf/0709.2191.pdf
web2 : http://www0.fee.unicamp.br/cpg/Faculty.html
web3 :
key statements: A rigorous analysis of localized wave propagation in optical New localized Superluminal solutions to the wave equations with infinite total energies and arbitrary frequencies Superluminal localized solutions to Maxwell equations propagating along a normal-sized waveguide"
Dr. Adolfo Zamora Origin : CLI 2006
Category : Alternative theory
kind of theory : modified Newton law kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : https://tel.archives-ouvertes.fr/tel-00315725/document
web2 : https://arxiv.org/abs/astro-ph/0601247
web3 :
key statements: Adolfo Zamora. Alternative proposal to modified Newton dynamics
Edward J. Zampino Origin : CLI 1998
Category : Critics
kind of theory : kind of particle :
kind of critics : C of light as absolute kind of energy :
email :
email :
web1 : http://ralph.open-aerospace.org/deep/repository/zampino1.php
web2 :
web3 :
key statements: Can a Hyperspace really exist? faster than light travel in a higher-dimensional hyperspace in general, and the properties of a four dimensional Euclidian space in particular. The addition of a fourth spatial dimension is shown to produce some interesting effects
Vitaliy Zamsha Origin : REX 2011
Category : New Energy
kind of theory : kind of particle :
kind of critics : kind of energy : Torsion field
email :
email :
web1 : http://rexresearch.com/zamshatorsion/shkatovzamsha.html
web2 :
web3 :
key statements: Torsion Fields and Interstellar Communication
Pr. Dr. Giovanni Zanella Origin : CLI 2010
Category : Critics
kind of theory : kind of particle :
kind of critics : Special Relativity theory kind of energy :
email : [email protected]
email :
web1 : http://arxiv.org/ftp/arxiv/papers/1003/1003.4833.pdf
web2 :
web3 :
key statements: The wave nature of the light, applied to the kinematics of the moving bodies, permits to investigate and find a coherent solution, on some questions raised by the theory of special relativity about the Lorentz contraction.
Pr. Dr. Nino Zanghi Origin : CLI 2013
Category : Critics
kind of theory : kind of particle :
kind of critics : Quantum Mechanics kind of energy :
email :
email :
web1 : http://www.springer.com/us/book/9783642306891
web2 :
web3 :
key statements: Quantum Physics Without Quantum Philosophy
Pr. Dr. Lorenzo Zaninetti Origin : PHY 2010
Category : Cosmology
kind of theory : kind of particle :
kind of critics : General Relativity Theory kind of energy :
email : [email protected]
email :
web1 : http://physicsessays.org/browse-journal-2/category/36-issue-2-june-2010.html
web2 : http://www.df.unito.it/do/docenti.pl/Show?_id=lzaninet;sort=DEFAULT;search=;hits=238
web3 :
key statements: [Physics essays vol. 23, 298] New formulas for the Hubble constant in a Euclidean static universe
Felipe Sofia Zanuzzo Origin : DUF 2004
Category : Critics
kind of theory : kind of particle :
kind of critics : kind of energy :
email :
email :
web1 : http://homepages.xnet.co.nz/~hardy/cosmologystatement.html
web2 :
web3 :
key statements: Critics of Big Bang
Dr. Eng Achille Zanzucchi Origin : BAR GSJ 2013
Category : Alternative theory
kind of theory : solid ether LORENTZ kind of particle : vortices
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://gsjournal.net/Science-Journals-Papers/Author/1149/Achille,%20Zanzucchi
web3 :
key statements: The cosmic ether is the one substance in the universe, is a continuous, solid, perfectly elastic medium of high density and stiffness, is in state of oscillation and follows, as only law, the wave equation.The material bodies are all reducible to anticyclonic (electrons) and cyclonic (positrons) vortices of ether mechanical vibrations Relativity, Quantum Theory, Heisenberg’s Principle of Uncertainty and Standard Model are not considered. The material mass is a quantity of ether. The material mass is a quantity of ether.The material mass is a quantity of ether. The electron and the positron in motion in space exert on the surrounding ether, as a consequence of their internal structures according to the wave equation, trailing actions. These determine on the external ether a stressstate (of tension/deformation) in the several aspects of which the nuclear, electromagnetic and gravitational fields In this theory the velocity c exists, as characteristic quantity, because it results from the integration of the wave equation as velocity of propagation in space of the perturbations of the elastic medium ether. In the same way the positron, the photon and any other material body behave. The photon is 2 masses at points A and B, the second B of electronic type the A is positronic type. The universe a diapason tuner in vibration
Dr. Carl Andrew Zapffe (deceased) Origin : SAP DBN GAL FRI GSJ 1977
Category : Critics
kind of theory : kind of particle :
kind of critics : Philosophical kind of energy :
email :
email :
web1 : http://www.ekkehard-friebe.de/kap4.pdf
web2 : http://db.naturalphilosophy.org/member/?memberid=442
web3 : http://home.btconnect.com/sapere.aude/
key statements: Seven short essays on an epistemological analysis of the Lorentz transformation and the chronometric branch of relativistic physics Propagation of Light Through Outer Space - A New Model Laser Fiber-Ring Interferometric Gyroscopes and Einstein's Second Postulate Einstein's postulate that the velocity of light is c with respect to any observer is modified.
Dr. David Zareski Origin : PHY 2012
Category : Alternative theory
kind of theory : fluid ether kind of particle :
kind of critics : kind of energy :
email : [email protected]
email :
web1 : http://physicsessays.org/browse-journal-2/category/27-issue-2-june-2012.html
web2 :
web3 :
key statements: The ether is shown to be an elastic medium of point relative displacements Xi governed by the Navier-Stokes-Durand equation, the continuity one, and the divergence one. When div(Xi)=0 , the ether density Ro is constant, and these equations yield the fields, the particles constitutions, the electron spin, the "strong nuclear interaction", the quantum effects and show that electromagnetism is an approximation of general relativity. When div('XI)is not 0 , then Ro can increase causing the Dark Matter effect where the velocity of particles even of given energy increases as it appears for external stars of some galaxies.[PE 25 268] On the elasto-undulatory interpretation of fields and particles The elasto-gravitational interpretation of the strong interaction Fields and wave-particle reciprocity as changes in an elastic medium: The ether. [ PE ] On the elasto-undulatory interpretation of fields and particles . "Is dark-matter a particular state of the ether?" , International Journal of Pure and Applied Physics, Vol. 3, No. 3, December 2015 . Unification of physics theories by the ether elasticity theory. ISBN: 978-3-659-67720-5 published by LAP LAMBERT Academic Publishing, (2015), 102 pages.
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https://www.andreashandel.com/presentations/2022-09-ecmtb/
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# The impact of seasonal Influenza vaccine dose on homologous and heterologous immunity
A presentation given at the 12th European Conference on Mathematical and Theoretical Biology.
Research
Influenza
Author
Andreas Handel
Published
September 22, 2022
These are the slides for a presentation I gave at the 2022 ECMTB conference.
Note: I had to cancel the trip at the last minute and thus was not able to deliver the presentation. I decide to leave the slides here anyway.
## Citation
BibTeX citation:
``````@online{handel2022,
author = {Andreas Handel},
editor = {},
title = {The Impact of Seasonal {Influenza} Vaccine Dose on Homologous
and Heterologous Immunity},
date = {2022-09-22},
url = {https://www.andreashandel.com/presentations/2022-09-ECMTB},
langid = {en}
}
``````
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|
https://conference.ippp.dur.ac.uk/event/470/contributions/2553/
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The 34th International Symposium on Lattice Field Theory (Lattice 2016)
24-30 July 2016
Highfield Campus, University of Southampton
Europe/London timezone
Pseudo-scalar decay constants on three-flavour CLS ensembles with open boundaries
26 Jul 2016, 19:00
1h
Highfield Campus, University of Southampton
Highfield Campus, University of Southampton
Highfield Campus, Southampton SO17 1BJ, UK
Speaker
Mr Stefan Hofmann (Unversity of Regensburg) (German)
Description
We determine the masses and the pseudo-scalar decay constants of charmed mesons using non-perturbatively O($a$) improved Wilson quarks. Our analysis is based on the $N_{\rm f}=2+1$ ensembles using open boundary conditions, generated within the CLS effort. The status of results for 2 lattice spacings, $a\approx 0.086$ fm and $a\approx 0.064$ fm, will be presented. The pion mass is varied from 420 to 220 MeV. This is part of a continuing analysis by the RQCD and ALPHA Collaborations, aiming at a stable continuum extrapolation using several lattice spacings. To extrapolate to the physical masses, we follow both, the $(2m_l+m_s)=\mathrm{const.}$ and $m_s=\mathrm{const.}$ line.
Co-authors
Mr Kevin Eckert (Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster) Dr Sara Collins (University of Regensburg) Wolfgang Soeldner (Regensburg University)
Presentation Materials
There are no materials yet.
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http://softschools.com/math/algebra/topics/completing_the_square_when_a_notequal_1/
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# Completing the Square when a ≠ 1
A quadratic equation is an equation that contains a squared variable as its highest power on any variable. The general form of a quadratic equation is:
ax2 + bx + c = 0
Where a, b, and c are constants and a ≠ 0. In other words there must be a x2 term.
Some examples are:
x2 + 3x - 3 = 0
4x2 + 9 = 0 (Where b = 0)
x2 + 5x = 0 (where c = 0)
One way to solve a quadratic equation is by completing the square.
ax2 + bx + c = 0 → (x- r)2 = S
Where r and s are constants.
PART I of this topic focused on completing the square when a, the x2-coefficient, is 1. This part, PART II, will focus on completing the square when a, the x2-coefficient, is not 1.
Let's solve the following equation by completing the square:
2x2 + 8x - 5 = 0
Step 1: Write the equation in the general form ax2 + bx + c = 0. This equation is already in the proper form where a = 2 and c = -5. 2x2 + 8x - 5 = 0 Step 2: Move c, the constant term, to the right-hand side of the equation. c = -5 2x2 + 8x = 5 Step 3: Factor out a from the left-hand side. This changes the value of the x-coefficient. a = 2 2(x2 + 4x) = 5 Step 4: Complete the square of the expression in parentheses on the left-hand side of the equation. The expression is x2 + 4x. Divide the x-coefficient by two and square the result. x2 + 4x x-coefficient = 4 $\frac{4}{2}={2}\to {r}$ (2)2 = 4 Step 5: Add the result from Step 4 to the parenthetical expression on the left-hand side. Then add a x result to the right-hand side. To keep the equation true what is done to one side must also be done to the other. When adding the result to the parenthetical expression on the left-hand side the total value added is a x result. So this value must also be added to the right-hand side. 2(x2 + 4x + 4) = 5 + 2(4) Step 6: Rewrite the left-hand side as a perfect square and simplify the right-hand side. When rewriting in perfect square format the value in the parentheses is the x-coefficient of the parenthetical expression divided by 2 as found in Step 4. 2(x + 2)2 = 13 Now that the square has been completed, solve for x. Step 7: Divide both sides by a. ${\left(x+2\right)}^{2}=\frac{13}{{2}}$ Step 8: Take the square root of both sides of the equation. Remember that when taking the square root on the right-hand side the answer can be positive or negative. $x+2=±\sqrt{\frac{13}{2}}$ Step 9: Solve for x. $x=-2±\sqrt{\frac{13}{2}}$
Example 1: 3x2 = 6x + 7
Step 1: Write the equation in the general form ax2 + bx + c = 0. Where a = 3 and c = -7. 3x2 - 6x - 7 = 0 Step 2: Move c, the constant term, to the right-hand side of the equation. c = -7 3x2 - 6x = 7 Step 3: Factor out a from the left-hand side. This changes the value of the x -coefficient. a = 3 3(x2 - 2x) = 7 Step 4: Complete the square of the expression in parentheses on the left-hand side of the equation. The expression is x2 - 2x. Divide the x-coefficient by two and square the result. x2 - 2x x -coefficient = -2 $\frac{-2}{2}={-}{1}\to {r}$ (-1)2 = 1 Step 5: Add the result from Step 4 to the parenthetical expression on the left-hand side. Then add a x result to the right-hand side. To keep the equation true what is done to one side must also be done to the other. When adding the result to the parenthetical expression on the left-hand side the total value added is a x result. So this value must also be added to the right-hand side. 3(x2 - 2x + 1) = 7 + 3(1) Step 6: Rewrite the left-hand side as a perfect square and simplify the right-hand side. When rewriting in perfect square format the value in the parentheses is the x-coefficient of the parenthetical expression divided by 2, as found in Step 4. 3(x - 1)2 = 10 Now that the square has been completed, solve for x. Step 7: Divide both sides by a. ${\left(x-1\right)}^{2}=\frac{10}{{3}}$ Step 8: Take the square root of both sides of the equation. Remember that when taking the square root on the right-hand side the answer can be positive or negative. $x-1=±\sqrt{\frac{10}{3}}$ Step 9: Solve for x. $x=1±\sqrt{\frac{10}{3}}$
Example 2: 5x2 - 0.6 = 4x
Step 1: Write the equation in the general form ax2 + bx + c = 0. Where a = 5 and c = 0.6. 5x2 - 4x - 0.6 = 0 Step 2: Move c, the constant term, to the right-hand side of the equation. c = -0.6 5x2 - 4x = 0.6 Step 3: Factor out a from the left-hand side. This changes the value of the x-coefficient. a = 5 5(x2 - 0.8x) = 0.6 Step 4: Complete the square of the expression in parentheses on the left-hand side of the equation. The expression is x2 - 0.8x. Divide the x-coefficient by two and square the result. x2 - 0.8x x-coefficient = -0.8 $\frac{-0.8}{2}={-}{0.4}\to {r}$ (-0.4)2 = 0.16 Step 5: Add the result from Step 4 to the parenthetical expression on the left-hand side. Then add a x result to the right-hand side. To keep the equation true what is done to one side must also be done to the other. When adding the result to the parenthetical expression on the left-hand side the total value added is a x result. So this value must also be added to the right-hand side. 5(x2 - 0.8x + 0.16) = 0.6 + 5(0.16) Step 6: Rewrite the left-hand side as a perfect square and simplify the right-hand side. When rewriting in perfect square format the value in the parentheses is the x-coefficient of the parenthetical expression divided by 2 as found in Step 4. 5(x - 0.4)2 = 1.4 Now that the square has been completed, solve for x. Step 7: Divide both sides by a. ${\left(x-0.4\right)}^{2}=\frac{1.4}{{5}}=0.28$ Step 8: Take the square root of both sides of the equation. Remember that when taking the square root on the right-hand side the answer can be positive or negative. $x-0.4=±\sqrt{0.28}$ Step 9: Solve for x. $x=0.4±\sqrt{0.28}$
Related Links: Math algebra Factoring Quadratic Equations when a equals 1 Factoring Quadratic Equations when a ≠ 1 Algebra Topics
To link to this Completing the Square when a ≠ 1 page, copy the following code to your site:
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http://mathcenter.oxford.emory.edu/site/math111/probSetImplicitDiff/
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## Exercises - Implicit Differentiation
1. Suppose $y=f(x)$ to find $\displaystyle{\frac{d}{dx} 4y^3}$.
$\displaystyle{12y^2 \cdot \frac{dy}{dx}}$
2. Suppose $y=f(x)$ to find $\displaystyle{\frac{d}{dx} x^5 y^3}$.
$\displaystyle{3x^5 y^2 \cdot \frac{dy}{dx} + 5x^4 y^3}$
3. Suppose $x=g(t)$ to find $\displaystyle{\frac{d}{dt} (t + \cos x^3)}$.
$\displaystyle{1 - 3x^2 \sin(x^3) \cdot \frac{dy}{dx}}$
4. Find $\displaystyle{\frac{dy}{dx}}$ and $\displaystyle{\frac{d^2y}{dx^2}}$ if $x^2 + y^2 = r^2$ for some constant $r$.
First we find $\displaystyle{\frac{dy}{dx} = \frac{-x}{y}}$. Then, upon differentiating a second time and substituting in for the first derivative, we obtain $\displaystyle{\frac{d^2 y}{dx^2} = -\frac{x^2+y^2}{y^3}}$.
5. Find the equation of the tangent line at $(1,1)$ to the graph of $x^2y + 3y^4 = x^3 y^3 + 3$.
$\displaystyle{y-1 = \frac{1}{10}\left(x-1\right)}$
6. Find $\displaystyle{\frac{d^2y}{dx^2}}$ if $x^2 + 3y^2 = xy + 3$.
First, we find $\displaystyle{\frac{dy}{dx} = \frac{y-2x}{6y-x}}$. Then, upon differentiating again, simplifying, and substituting the first derivative, we obtain $\displaystyle{\frac{d^2 y}{dx^2} = -\frac{11(x^2 - xy + 6y)}{(x - 6y)^2}}$.
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https://brilliant.org/problems/far-far-away/
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Far, far away
A non-conducting thin rod of lenth 1 m has 1 coulomb of charge placed on it uniformly. Very far away from the rod, the electric field will drop off as some power $1/r^n$. What is $n?$
×
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http://mathoverflow.net/questions/88045/quasi-dense-subsets-of-boolean-algebras/88459
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## Quasi-dense subsets of boolean algebras
Definition: Let $B$ be a boolean algebra. Say $X \subseteq B$ is quasi-dense in $B$ if for all $b \in B$, there is $x \in X \setminus$ { $0,1$ } such that either $x \leq b$ or $b \leq x$.
Question: Suppose $A \subseteq B \subseteq C$ are atomless boolean algebras, $A$ is quasi-dense in $B$, and $B$ is dense in $C$. Does it follow that $A$ is quasi-dense in $C$?
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Here is a way to construct an atomless version of Joel´s counterexample:
Let $A_0 \subseteq A_1 \subseteq A_2$ be the algebras in Joel´s example (in his notation $A \subseteq B \subseteq C$) and let $X_0$,$X_1$ and $X_2$ be the corresponding Stone spaces. So $X_0$ and $X_1$ are both just a converging sequence and $X_2$ consists of two converging sequences (with different limit points). These spaces have isolated points, reflecting the fact that the algebras have atoms. So the idea now is to consider the (Stone) spaces $Z_i=X_i \times 2^\omega$ and their corresponding algebras of clopen subsets $B_i=Cl(Z_i)$ for $i \in 3$. These algebras are now atomless (since their Stone spaces have no isolated points).
The inclusion maps $A_0 \subseteq A_1$ and $A_1 \subseteq A_2$ induce surjective continuous functions $\pi_1:X_1 \to X_0$ and $\pi_2:X_2 \to X_1$ respectively, which we can use to produce the (also continuous and surjective) functions: $\pi_1 \times id_{2^\omega}: Z_1 \to Z_0$ and $\pi_2 \times id_{2^\omega}:Z_2 \to Z_1$. These in turn induce "inclusions" $B_0 \subseteq B_1 \subseteq B_2$. Arguments analogous to those in Joel´s answer can be used to show that:
1) $B_0$ is quasi-dense in $B_1$ (here you use that any clopen set in $Z_1$ is a finite union of boxes).
2) $B_1$ is dense in $B_2$ (using that any clopen set in $Z_2$ contains a box), and
3) $B_0$ is not quasi-dense in $B_2$ (here a problematic clopen subset of $Z_2$ would be $K \times 2^\omega$ where $K$ is one of the two converging sequences).
-
Well, this still doesn't answer the atomless question, but I've got a violation of the desired implication among atomic Boolean algebras.
Let $A$ consist of the finite or cofinite subsets of $\mathbb{N}$ that take $2k$ and $2k+1$ together, if at all. That is, $a\in A$ if $a\subset\mathbb{N}$ is finite or cofinite and for every $k$ we have $2k\in a\leftrightarrow 2k+1\in a$. Let $B$ be the Boolean algebra consisting of all finite or cofinite subsets of $\mathbb{N}$.
Note that $A$ is quasi-dense in $B$, since if $b$ is finite, then $b$ is contained in an interval $[0,2k+1]$ for some large $k$, and this is in $A$, and if $b$ is cofinite, then $b$ contains some final segment interval $[2k,\infty)$, which is in $A$.
Let $C$ be the algebra generated by the elements of $B$ together with the set $E$ of even numbers. Thus, every element of $C$ is the union of a finite or cofinite subset of $E$ with a finite or cofinite subset of $\mathbb{N}-E$. The algebra $B$ is dense in $C$, since the singletons are dense, and they are finite.
Finally, $A$ is not quasi-dense in $C$, because the set $E$ contains no nonzero element of $A$, as it contains no odd numbers, and is contained in no non-unital element of $A$, as the only element of $A$ containing all the even numbers is the whole of $\mathbb{N}$.
This is my original answer, which shows merely that quasi-density is not transitive.
The answer is no. For a counterexample, let $A$ have at least two atoms; let $B$ split one of those atoms, and let $C$ split both of them.
More explicitly, let $A$ be the 4-element Boolean algebra with atoms $\{0,1\}$ and $\{2,3\}$. Let $B$ be the $8$-element algebra with atoms $\{0\}$, $\{1\}$, $\{2,3\}$, and let $C$ be the full power set, with atoms $\{0\}$, $\{1\}$, $\{2\}$, $\{4\}$.
You may observe that $A$ is quasi-dense in $B$ and $B$ is quasi-dense in $C$ by inspection. But $A$ is not quasi-dense in $C$, since $\{0,2\}$ is neither above nor below any nontrivial element of $A$.
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The question was about "$B$ dense in $C$", not just quasi-dense. – Goldstern Feb 9 2012 at 23:33
But I said $B$ was dense in $C$, not just quasi-dense. This was not a typo. Also, I am only really interested in the case of atomless algebras. I will put that in the original question. – mbsq Feb 9 2012 at 23:36
Oh, sorry, I misread the question. – Joel David Hamkins Feb 9 2012 at 23:57
I have now posted a counterexample to the implication among atomic Boolean algebras. Perhaps it could be used to construct an atomless counterexample, but I don't see it yet. – Joel David Hamkins Feb 10 2012 at 4:46
It's a surprisingly difficult question! – Joel David Hamkins Feb 11 2012 at 0:16
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https://www.hackerearth.com/problem/algorithm/strong-contender-5b885a78/
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Billy's Game
/
Game Theory, Mathematics, Sprague–Grundy Theorem
Problem
Editorial
Analytics
Billy and Bob are best friends but when it comes to playing a game they do not let it go easily. They fight neck and neck, be it Chess, Go, etc. They are bored with playing old, classical games that involves standard opening theories. They have got their hands on some new game which is described as follows.
There are $N +\ 1$ buckets in a row. First $N$ buckets contain $1$ or more balls and the last bucket is empty. In a turn, a player can draw $1$ or more balls from a bucket such that a maximum of $floor(\sqrt{X})$ balls are left in that bucket where $X$ is the number of balls present in that bucket at that point of time. A player will lose if there is nothing left to draw.
Bob is going to start the game but we want Billy to win. So, what is the minimum number of balls that need to be added to the $(N\ +\ 1)^{th}$ bucket, so that our favorite Billy wins. Needless to say, both players will be playing optimally.
Input format
• First line: An integer $T$ denoting the number of test cases
• In each test case:
• First line: Integer $N$ as described in the problem statement
• Second line: $N$ integers denoting the number of balls in each bucket
Output format
Print the minimum number of balls that have to be put in the $(N\ +\ 1)^{th}$ bucket.
Constraints
$1 \le T \le 10$
$1 \le N \le 10^{5}$
The number of balls in the input buckets do not exceed $10^{9}$
SAMPLE INPUT
2
3
1 1 1
4
1 1 1 1
SAMPLE OUTPUT
1
0
Explanation
First test case:
In each turn, one of the buckets will be getting empty. We just need to have a nonempty bucket so that the last bucket is emptied by Billy.
Second test case:
In each turn, one of the buckets will be getting empty. The last bucket will be emptied by Billy then all the buckets will have 0 balls in them.
Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
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https://export.arxiv.org/list/nucl-th/2004?skip=0&show=50
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Nuclear Theory
Authors and titles for Apr 2020
[ total of 243 entries: 1-50 | 51-100 | 101-150 | 151-200 | 201-243 ]
[ showing 50 entries per page: fewer | more | all ]
[1]
Title: Extracting the jet transport coefficient of cold nuclear matter from world data
Comments: 4 pages, 2 figures, talk presented by Hongxi Xing at Quark Matter 2019 conference
Subjects: Nuclear Theory (nucl-th); Nuclear Experiment (nucl-ex)
[2]
Title: Comment on "Observation of annual modulation by $γ$ rays from ($α$,$γ$) reactions at the Soudan Underground Laboratory"
Authors: Peter Mohr
Comments: 3 pages, 1 figure; Phys. Rev. C, accepted for publication
Subjects: Nuclear Theory (nucl-th)
[3]
Title: A Consistency Test of EFT Power Countings from Residual Cutoff Dependence
Authors: Harald W. Griesshammer (George Washington U.)
Comments: 15 pages LaTeX2e (pdflatex) including 5 figures as .pdf files using includegraphics. Final version to appear in Europ. J. Phys. A topical issue "The Tower of Effective (Field) Theories and the Emergence of Nuclear Phenomena". arXiv admin note: substantial text overlap with arXiv:1511.00490 Author's note: substantial corrections in key argument and expansions. Version appearing in Eur Phys J A
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph); Atomic and Molecular Clusters (physics.atm-clus)
[4]
Title: On nonlinearity in hydrodynamic response to the initial geometry in relativistic heavy-ion collisions
Subjects: Nuclear Theory (nucl-th)
[5]
Title: Chirality and Magnetic Field
Comments: 8 pages, 6 figures, based on plenary talk at Quark Matter 2019; final version to be included in the QM19 conference proceedings
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph); Nuclear Experiment (nucl-ex)
[6]
Title: Transverse momentum fluctuations and their correlation with elliptic flow in nuclear collision
Journal-ref: Phys. Rev. C 102, 034905 (2020)
Subjects: Nuclear Theory (nucl-th)
[7]
Title: $α$ Decay Half-life Estimation and Uncertainty Analysis
Comments: To be published in Physical Review C
Subjects: Nuclear Theory (nucl-th)
[8]
Title: Masses and Decay widths of Charmonium states in presence of strong magnetic fields
Comments: 31 pages, 5 figures,to be published in Phys. Rev. C
Journal-ref: Phys. Rev. C 102, 045204 (2020)
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph)
[9]
Title: Landscape of pear-shaped even-even nuclei
Journal-ref: Phys. Rev. C 102, 024311 (2020)
Subjects: Nuclear Theory (nucl-th)
[10]
Title: Existence of higher nodal band states with $α$+$^{48}$Ca cluster structure in $^{52}$Ti
Authors: S. Ohkubo
Journal-ref: Physical Review C April issue 101,041301(R) (2020)
Subjects: Nuclear Theory (nucl-th); Nuclear Experiment (nucl-ex)
[11]
Title: Comment on the paper Eur. Phys. J. A (2019) 55:150
Subjects: Nuclear Theory (nucl-th)
[12]
Title: Threshold $π^-$ Photoproduction on the Neutron
Authors: W.J. Briscoe (GWU), A.E. Kudryavtsev (ITEP), I.I. Strakovsky (GWU), V.E. Tarasov (ITEP), R.L. Workman (GWU)
Comments: 7 pages, 4 figures, 2 tables
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Experiment (hep-ex); High Energy Physics - Phenomenology (hep-ph); Nuclear Experiment (nucl-ex)
[13]
Title: Many-body Dyson equation approach to the seniority model of pairing
Authors: Peter Schuck
Subjects: Nuclear Theory (nucl-th); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Superconductivity (cond-mat.supr-con)
[14]
Title: Correlation between mean transverse momentum and anisotropic flow in heavy-ion collisions
Comments: 7 pages; 4 figures; v2: published version
Journal-ref: Phys. Rev. C 103, 024909 (2021)
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph); Nuclear Experiment (nucl-ex)
[15]
Title: Secondary $γ$-ray decays from the partial-wave $T$ matrix with an $R$-matrix application to ${}^{15}{\rm N}(p,α_1γ){}^{12}{\rm C}$
Journal-ref: Phys. Rev. C 102, 024628 (2020)
Subjects: Nuclear Theory (nucl-th); Nuclear Experiment (nucl-ex)
[16]
Title: Elastic $α$-$^{12}$C scattering at low energies with the sharp resonant $0_3^+$ state of $^{16}$O
Authors: Shung-Ichi Ando (Sunmoon U.)
Comments: 14 pages, 4 eps figures, version accepted for publication in Phys. Rev. C
Journal-ref: Phys. Rev. C 102, 034611 (2020)
Subjects: Nuclear Theory (nucl-th)
[17]
Title: Solitons in nuclear time-dependent density functional theory
Authors: Yoritaka Iwata
Comments: [Invited] submitted to "Frontiers in Physics"
Journal-ref: Front. Phys. 8:154, 2020
Subjects: Nuclear Theory (nucl-th); Nuclear Experiment (nucl-ex)
[18]
Title: Prediction of the analyzing power for $\vec{p}$+$^{6}$He elastic scattering at 200 MeV from $\vec{p}$+$^{4}$He elastic scattering at 200 MeV
Journal-ref: Phys. Rev. C 103, 044605 (2021)
Subjects: Nuclear Theory (nucl-th); Nuclear Experiment (nucl-ex)
[19]
Title: Recent Progress in Basis Light-front Quantization
Comments: 8 pages, 6 figues, proceeding for the 18th International Conference on Hadron Spectroscopy and Structure (HADRON2019)
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph)
[20]
Title: Relativistic hydrodynamics for spin-polarized media
Comments: Presented by Radoslaw Ryblewski at XXVI Cracow Epiphany Conference, LHC Physics: Standard Model and Beyond, January 7-10, 2020, Krakow, Poland.; 11 pages, 5 figures
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph)
[21]
Title: Fluctuation dynamics near the QCD critical point
Comments: 29 pages, 18 figures. Some discussions are added; Fig. 1 is separated into two figures; in some figures, axis labels and line color styles are updated. Published as Phys. Rev. C 102, 054911 (2020)
Journal-ref: Phys. Rev. C 102, 054911 (2020)
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Nuclear Experiment (nucl-ex)
[22]
Title: Gamow Shell Model description of Li isotopes and their mirror partners
Journal-ref: Phys. Rev. C 102, 024309 (2020)
Subjects: Nuclear Theory (nucl-th)
[23]
Title: High-Energy Phase Diagrams with Charge and Isospin Axes under Heavy-Ion Collision and Stellar Conditions
Journal-ref: Phys. Rev. D 102, 076016 (2020)
Subjects: Nuclear Theory (nucl-th); High Energy Astrophysical Phenomena (astro-ph.HE); Solar and Stellar Astrophysics (astro-ph.SR); High Energy Physics - Phenomenology (hep-ph)
[24]
Title: Nuclear modification factor in Pb-Pb and p-Pb collisions using Boltzmann transport equation
Comments: 14 pages, 6 figures. Accepted by J. Phys. G
Journal-ref: J. Phys. G: Nucl. Part. Phys. 47 075101, 2020
Subjects: Nuclear Theory (nucl-th)
[25]
Title: Temperature fluctuations and Tsallis statistics in Relativistic Heavy Ion collisions
Comments: 19 pages 7 figures Revised version with improved figures and details of temperature calculation. Accepted for publication in MPLA
Journal-ref: Modern Physics Letters A Vol. 36, No. 22, 2150152 (2021)
Subjects: Nuclear Theory (nucl-th)
[26]
Title: The Non-perturbative Interaction of the Pseudovector Coupling for the Pion-nucleon Scattering
Authors: Susumu Kinpara
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph)
[27]
Title: Tensor and pairing interactions within the QMC energy density functional
Journal-ref: Phys. Rev. C 102, 034304 (2020)
Subjects: Nuclear Theory (nucl-th)
[28]
Title: Seebeck effect in a thermal QCD medium in the presence of strong magnetic field
Journal-ref: Phys. Rev. D 102, 096011 (2020)
Subjects: Nuclear Theory (nucl-th); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); High Energy Physics - Phenomenology (hep-ph)
[29]
Title: Transverse momentum dependent decorrelation in Pb-Pb collisions at LHC
Authors: De-Xian Wei
Comments: 6 pages, 3 figures; This version accepted by IJMPE
Journal-ref: Int. J. Mod. Phys. E Vol.29, No. 4 (2020) 2050057;
Subjects: Nuclear Theory (nucl-th)
[30]
Title: Elastic and inelastic scattering of neutrinos and weakly interacting massive particles on nuclei
Comments: 34 pages, 13 figures, 3 tables. V2: matches published version in PRC
Journal-ref: Phys. Rev. C 102, 035501 (2020)
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph)
[31]
Title: Dispersion relations applied to double-folding potentials from chiral EFT
Journal-ref: Phys. Rev. C 102, 014622 (2020)
Subjects: Nuclear Theory (nucl-th)
[32]
Title: Microscopic description of fission in superheavy nuclei with the parametrization D1M$^{*}$ of the Gogny energy density functional
Subjects: Nuclear Theory (nucl-th)
[33]
Title: Feeddown contributions from unstable nuclei in relativistic heavy-ion collisions
Comments: 8 pages, 5 figures, accepted version to appear in Physics Letters B
Journal-ref: Phys. Lett. B 809, 135746 (2020)
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph); Nuclear Experiment (nucl-ex)
[34]
Title: Chiral Magnetic Effect in Isobar Collisions from Stochastic Hydrodynamics
Subjects: Nuclear Theory (nucl-th); Nuclear Experiment (nucl-ex)
[35]
Title: Constraints on the neutron drip-line with the newly observed 39Na
Comments: 6 pages, 4 figures, submitted
Journal-ref: Phys. Rev. C 102, 014312 (2020)
Subjects: Nuclear Theory (nucl-th)
[36]
Title: Neutron dominance in excited states of $^{26}$Mg and $^{10}$Be probed by proton and alpha inelastic scattering
Journal-ref: Phys. Rev. C 102, 014607 (2020)
Subjects: Nuclear Theory (nucl-th)
[37]
Title: Structure functions generated by zero sound excitations
Authors: V. A. Sadovnikova (St. Petersburg, INP)
Comments: 14 pages, 3 figures, corrected misprint
Subjects: Nuclear Theory (nucl-th)
[38]
Title: Correlation between global polarization, angular momentum and flow in heavy-ion collisions
Comments: 8 pages, 9 figures. Title changed, two figures and their discussion added, version published in Phys. Rev. C
Journal-ref: Phys. Rev. C 102, 024916 (2020)
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph)
[39]
Title: Proto-Strange Quark Star Structure
Comments: 7 pages, 10 figures, Ind J. Phys. (2020) accepted for publication
Subjects: Nuclear Theory (nucl-th); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph)
[40]
Title: Chiral Effective Field Theory Calculations of Weak Transitions in Light Nuclei
Comments: 14 pages, 9 figures; Corrected experimental values for $^8$Li beta decay in Table V to be consistent with Table VI and the text; Corrected an error in row 2 column 4 of Figure 6, conclusions unchanged; Corrected errors in column 3 rows 3 and 4 of Figure 7, results unchanged; Corrected a typo in Equation 19, results in tables unchanged; Corrected $^8$He ground state isospin from $T=1$ to $T=2$
Journal-ref: Phys. Rev. C 102, 025501 (2020)
Subjects: Nuclear Theory (nucl-th)
[41]
Title: Momentum-dependent potential and collective flows within the relativistic quantum molecular dynamics approach based on relativistic mean-field theory
Comments: 11 pages, 7 figures, published in PRC
Journal-ref: Phys. Rev. C 102, 024913 (2020)
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph); Nuclear Experiment (nucl-ex)
[42]
Title: Investigation of Nuclear Structures of Self-conjugate Zn, Ge, Se, Kr, Sr Nuclei
Subjects: Nuclear Theory (nucl-th)
[43]
Title: Investigation of Nuclear Structures of Ne Isotopes by Nuclear Shell Model
Comments: 7 pages, in Turkish language, 7 figures, 1 table
Subjects: Nuclear Theory (nucl-th)
[44]
Title: The QCD critical point from the Nambu-Jona-Lasino model with a scalar-vector interaction
Journal-ref: Phys. Rev. D 103, 014006 (2021)
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph)
[45]
Title: Yrast band in the heavy $N = Z$ nucleus $^{88}$Ru: $α$-cluster approach
Authors: Peter Mohr
Comments: 6 pages, 1 figure, Europ. Phys. J. A, accepted for publication
Subjects: Nuclear Theory (nucl-th)
[46]
Title: Calculation of the ${}^6$Li ground state within the hyperspherical harmonic basis
Journal-ref: Phys. Rev. C 102, 014001 (2020)
Subjects: Nuclear Theory (nucl-th)
[47]
Title: EMC effect, few-nucleon systems and Poincaré covariance
Authors: Emanuele Pace (Università di Roma "Tor Vergata'' and INFN, Sezione di Roma Tor Vergata, Italy), Matteo Rinaldi (Università di Perugia and INFN, Sezione di Perugia, Italy), Giovanni Salmè (INFN, Sezione di Roma, Italy), Sergio Scopetta (Università di Perugia and INFN, Sezione di Perugia, Italy)
Comments: 14 pages, 1 figure. Proceedings of 8th International Conference on New Frontiers in Physics (ICNFP 2019) 21-29 August 2019, Kolymbari, Crete (Greece)
Subjects: Nuclear Theory (nucl-th)
[48]
Title: Hadron resonance gas with van der Waals interactions
Comments: 21 pages, 9 figures. Invited review for IJMPE
Journal-ref: Int. J. Mod. Phys. E 29, 2040002 (2020)
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Phenomenology (hep-ph)
[49]
Title: Baryon number fluctuations induced by hadronic interactions at low temperature and large chemical potential
Comments: 14 pages, 6 figures, to be published in Phys. Rev. D
Journal-ref: Phys. Rev. D 101, 074029 (2020)
Subjects: Nuclear Theory (nucl-th)
[50]
Title: Neutrino Long-Baseline Experiments and Nuclear Physics
Authors: Ulrich Mosel
Journal-ref: Nuclear Physics News, Volume 29, 2019 - Issue 4
Subjects: Nuclear Theory (nucl-th); High Energy Physics - Experiment (hep-ex); High Energy Physics - Phenomenology (hep-ph); Nuclear Experiment (nucl-ex)
[ total of 243 entries: 1-50 | 51-100 | 101-150 | 151-200 | 201-243 ]
[ showing 50 entries per page: fewer | more | all ]
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Links to: arXiv, form interface, find, nucl-th, 2206, contact, help (Access key information)
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https://www.debugpointer.com/check-if-file-exists-bash-script
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Published on
How to check if a file exist in a Bash Script?
Checking if a file exist or not can be easily done with the script below
if [ -f "$FILE_PATH" ]; then # If the$FILE_PATH exist, code inside the block will get executed, for example:
echo "File $FILE_PATH exist"; fi Or to check if a file doesn't exist: if [ ! -d "$FILE_PATH" ]; then
# If the $FILE_PATH does not exist, code inside the block will get executed, for example: echo "File$FILE_PATH does not exist";
fi
Are you looking for the scenario if a directory exist or not in bash scripts?
There is also a shorthand notation to check if a file exist or not:
Shorthand to check if a file exist
[ -f "$FILE_PATH" ] && echo "File$FILE_PATH exist";
Shorthand to check if a file does not exist
[ ! -f "$FILE_PATH" ] && echo "File$FILE_PATH does not exist";
You can have any statement after the && symbol.
The above code is an ideal way to check if a path is a file or not.
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https://www.apexprojects.in/golden-section-application-architecture-design/
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# Golden Section and its application in Architecture and Design
The GOLDEN SECTION is nothing but division & further sub-division of a whole – 1, ½ ….. & so on; which induces a sense of proportion especially visually.
Golden ratio is as such a concept derived from the nature where proportions make it symmetrical even in its natural form.
The real beauty is when the same proportion is noticed even in the finer details as the portion reduces.
First studied as a part of geometry & mathematics where scholars found a symmetry in polygons, this science has evolved manifolds & has been implied in various fields.
This is the case when THE GOLDEN RATIO isn’t followed.
There are a few standards conceptualised around this concept about the “human body”.
This is the sketch of “The Vitruvian Man” first conceptualised by Da Vinci followed by renovation of the idea by Vitruvius himself.
The famous architect Le Corbusier, developed a system named “MODULAR” on similar lines for studying & understanding human proportions for better architecture.
In architecture, which we perceive as a scientifically conceptualised & executed art, we expect to follow the same reducing proportionate detailing to please the human eye!! It is more about the aspect ratio as we speak about than anything else.
Since time immemorial, greatest of the builders have employed this technique knowingly or unknowingly in the most iconic structures which we see today.
Here are a few structures that will actually make you think ?!
1. Eiffel Tower, Paris
Despite its enormous height, Eiffel Tower doesn’t look out of proportion, all thanks to the golden ratio.
The base is broader while it narrows down to the top, perfectly following the golden section & as needed for stability.
2. Taj Mahal, India
Taj Mahal doesn’t look a misfit either despite its humungous size. The effect of the enormous dome has been subsided by complementing it with minarets.
Also, if you notice the order & proportion of the arches on the main structure keep reducing &reduce proportionately.
Horizontal proportionality is observed here.
3. Parthenon, Greece
Ancient Greek architecture considered the concept of the Golden Ratio very much while the planning of its structures & hence it can be seen in many of the ancient Greek structures.
The enormous pediment [roof] is complimented by the huge fluted columns placed at regular intervals.
In case of interiors as well, there is a certain proportion-pattern that can observed…
People have even tried to literally adapt the Golden Section idea in their design……let’s have a look
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https://www.thepoorcoder.com/hackerrank-modified-kaprekar-numbers-solution/
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## Hackerrank - Modified Kaprekar Numbers Solution
Beeze Aal
A modified Kaprekar number is a positive whole number with a special property. If you square it, then split the number into two integers and sum those integers, you have the same value you started with.
Consider a positive whole number with digits. We square to arrive at a number that is either digits long or digits long. Split the string representation of the square into two parts, and . The right hand part, must be digits long. The left is the remaining substring. Convert those two substrings back to integers, add them and see if you get .
For example, if , then . We split that into two strings and convert them back to integers and . We test , so this is not a modified Kaprekar number. If , still , and . This gives us , the original .
Note: r may have leading zeros.
Here's an explanation from Wikipedia about the ORIGINAL Kaprekar Number (spot the difference!):
In mathematics, a Kaprekar number for a given base is a non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again. For instance, 45 is a Kaprekar number, because 45² = 2025 and 20+25 = 45.
Given two positive integers and where is lower than , write a program to print the modified Kaprekar numbers in the range between and , inclusive.
Function Description
Complete the kaprekarNumbers function in the editor below. It should print the list of modified Kaprekar numbers in ascending order.
kaprekarNumbers has the following parameter(s):
• p: an integer
• q: an integer
Input Format
The first line contains the lower integer limit .
The second line contains the upper integer limit .
Note: Your range should be inclusive of the limits.
Constraints
Output Format
Output each modified Kaprekar number in the given range, space-separated on a single line. If no modified Kaprekar numbers exist in the given range, print INVALID RANGE.
Sample Input
1
100
Sample Output
1 9 45 55 99
Explanation
, , , , and are the Kaprekar Numbers in the given range.
### Solution in Python
def check(i):
sq = str(i**2)
le = len(str(i))
r = sq[-le:]
l = sq[:-le] or '0'
return sum(map(int,(l,r)))==i
def kaprekarNumbers(p, q):
return [i for i in range(p,q+1) if check(i)]
p = int(input())
q = int(input())
print(*kaprekarNumbers(p, q) or ["INVALID RANGE"])
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https://rdrr.io/cran/emplik/man/emplikH.disc.html
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# emplikH.disc: Empirical likelihood ratio for discrete hazard with right...
Description Usage Arguments Details Value Author(s) References Examples
### Description
Use empirical likelihood ratio and Wilks theorem to test the null hypothesis that
∑_i[f(x_i, θ) \log(1- dH(x_i))] = K
where H(t) is the (unknown) discrete cumulative hazard function; f(t,θ) can be any predictable function of t. θ is the parameter of the function and K is a given constant. The data can be right censored and left truncated.
When the given constants θ and/or K are too far away from the NPMLE, there will be no hazard function satisfy this constraint and the minus 2Log empirical likelihood ratio will be infinite. In this case the computation will stop.
### Usage
1 emplikH.disc(x, d, y= -Inf, K, fun, tola=.Machine\$double.eps^.25, theta)
### Arguments
x a vector, the observed survival times. d a vector, the censoring indicators, 1-uncensor; 0-censor. y optional vector, the left truncation times. K a real number used in the constraint, sum to this value. fun a left continuous (weight) function used to calculate the weighted discrete hazard in H_0. fun(x, theta) must be able to take a vector input x, and a parameter theta. tola an optional positive real number specifying the tolerance of iteration error in solve the non-linear equation needed in constrained maximization. theta a given real number used as the parameter of the function f.
### Details
The log likelihood been maximized is the ‘binomial’ empirical likelihood:
∑ D_i \log w_i + (R_i-D_i) \log [1-w_i]
where w_i = Δ H(t_i) is the jump of the cumulative hazard function, D_i is the number of failures observed at t_i, R_i is the number of subjects at risk at time t_i.
For discrete distributions, the jump size of the cumulative hazard at the last jump is always 1. We have to exclude this jump from the summation since \log( 1- dH(\cdot)) do not make sense.
The constants theta and K must be inside the so called feasible region for the computation to continue. This is similar to the requirement that in testing the value of the mean, the value must be inside the convex hull of the observations. It is always true that the NPMLE values are feasible. So when the computation stops, try move the theta and K closer to the NPMLE. When the computation stops, the -2LLR should have value infinite.
In case you do not need the theta in the definition of the function f, you still need to formally define your fun function with a theta input, just to match the arguments.
### Value
A list with the following components:
times the location of the hazard jumps. wts the jump size of hazard function at those locations. lambda the final value of the Lagrange multiplier. "-2LLR" The discrete -2Log Likelihood ratio. Pval P-value niters number of iterations used
Mai Zhou
### References
Fang, H. (2000). Binomial Empirical Likelihood Ratio Method in Survival Analysis. Ph.D. Thesis, Univ. of Kentucky, Dept of Statistics.
Zhou and Fang (2001). “Empirical likelihood ratio for 2 sample problem for censored data”. Tech Report, Univ. of Kentucky, Dept of Statistics
Zhou, M. and Fang, H. (2006). A comparison of Poisson and binomial empirical likelihood. Tech Report, Univ. of Kentucky, Dept of Statistics
### Examples
1 2 3 4 5 6 7 8 fun4 <- function(x, theta) { as.numeric(x <= theta) } x <- c(1, 2, 3, 4, 5, 6, 5, 4, 3, 4, 1, 2.4, 4.5) d <- c(1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1) # test if -H(4) = -0.7 emplikH.disc(x=x,d=d,K=-0.7,fun=fun4,theta=4) # we should get "-2LLR" 0.1446316 etc.... y <- c(-2,-2, -2, 1.5, -1) emplikH.disc(x=x,d=d,y=y,K=-0.7,fun=fun4,theta=4)
Search within the emplik package
Search all R packages, documentation and source code
Questions? Problems? Suggestions? or email at [email protected].
Please suggest features or report bugs with the GitHub issue tracker.
All documentation is copyright its authors; we didn't write any of that.
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https://research.utwente.nl/en/publications/on-ising-models
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# On Ising models
Research output: Book/ReportReportProfessional
## Abstract
For various Ising models two approaches are discussed, one is that of simulating lattices, also called gauging on exact equations, the other is that of calculating analytical expressions for the boundary free energy of Ising lattices. The first approach allows to conjecture a solution for some Ising models, that have sofar not been solved, once some exact partial result for the problem is known. The second approach aims at furnishing such a partial result in the form of a condition for the critical temperature. An example of such a result was recently given for the 2D Ising square lattice with nearest and next-nearest-neighbor interactions. The critical line that separates the ordered (ferromagnetic) phase from the disordered (paramagnetic) phase showed good agreement in the moderate and strong nearest neighbor coupling limit with several results obtained by Monte Carlo, transfer matrix and series expansion results. We extend the discussion of the critical line, finding an excellent fit, now also in other points, like the Padé point, as well as cusp behavior at the Onsager point where the lattice decouples into two 2D square lattices with only nearest-neighbor interaction. Combination of this result with a geometrical argument in the simulation approach leads to a critical exponent $2-\sqrt{2} \approx 0.5858,$ comparable to the exponent $4/7 \approx 0.5714$ found from renormalization arguments.
Original language Undefined Enschede Universiteit Twente, Faculteit Toegepaste Wiskunde 24 Published - Jun 2006
### Publication series
Name Applied Mathematics Memoranda Department of Applied Mathematics, University of Twente 1804 0169-2690
• EWI-8055
• MSC-82B20
• METIS-237577
• IR-66581
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https://brilliant.org/problems/greatest-integer-function/
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# Greatest Integer Function
Algebra Level 5
$$x$$ is a real number and satisfies the equation:
$$\frac{1}{[x]}+\frac{1}{[2x]}=x-[x]+\frac{1}{3}$$.
The sum of all such numbers can be expressed as $$\frac{m}{n}$$, where $$m$$ and $$n$$ are relatively prime positive integers. Find $$m+n$$
Details and Assumptions
$$[x]$$ denotes the Greatest Integer Function: $$[x]=n$$, where $$n$$ is the greatest integer less than $$x$$.
×
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https://metatalk.metafilter.com/10026/Its-hard-to-tell-in-text-if-a-threat-is-serious-so-dont-do-it
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# It's hard to tell in text if a threat is serious, so don't do it. August 23, 2005 6:17 PM Subscribe
I flagged it.
posted by loquax at 6:18 PM on August 23, 2005 [1 favorite]
you troll; you get threats. For all the insults and trash Paris throws around continually, he shouldn't expect anything better. In fact, i'm sure he desires responses like that.
posted by amberglow at 6:22 PM on August 23, 2005
There is such a thing as the high road. It probably doesn't involve contract beatings.
posted by loquax at 6:24 PM on August 23, 2005
Yeah and for $500 bucks? What a cheap skate. Just say'n. C'mon. You were all thinking it. posted by tkchrist at 6:24 PM on August 23, 2005 Wait - to whom do I have to pay the$500 to whack Paris, again?
posted by yhbc at 6:29 PM on August 23, 2005
There are many people here who I wish would simply disappear. I'm sure we all have a list; some short, others a little longer. But for the sake of civility, I would think that keeping (idle) threats to ourselves would be appropriate.
But, but...like the threat made against George W just a few days ago, I think this comment should be allowed to stay, if only to have ample evidence that the original poster is, in fact, a rude lunatic.
posted by SeizeTheDay at 6:30 PM on August 23, 2005
Could i just take the money and say i beat the crap out of him?
(and yes, the post is way out of line, IMO). I'm suprised it hasn't been deleted.
posted by delmoi at 6:30 PM on August 23, 2005
I think this comment should be allowed to stay,
I agreed with you about the Bush comment, but this is something targeted at another user. Needless to say, people should be free to express their views without fearing for their lives. Not that I believe fff was actually serious (I think), but it crosses the line to target other users.
posted by loquax at 6:35 PM on August 23, 2005
I think the point was that it crosses the line to target other people.
posted by cytherea at 6:36 PM on August 23, 2005
No need to punish anybody. I think the entire post created like an irony sigularity which collapsed and sucked both Paris and FFF down into a sub-reality with it.
posted by tkchrist at 6:37 PM on August 23, 2005
people should be free to express their views without fearing for their lives
If I had a dime for every time some guy on USENET threatened to kill me I'd
posted by tkchrist at 6:38 PM on August 23, 2005
I agree, he's a cheapskate -- 500 bucks? wtf?
posted by matteo at 6:39 PM on August 23, 2005
Where are the ban-lovers now? Holy cow; if ever it was called for...
posted by found missing at 6:40 PM on August 23, 2005
and I also wonder, is PayPal OK?
posted by matteo at 6:43 PM on August 23, 2005
The ironic part is that just a little while ago fff was yelling at anybody who responded to Paris for being big bait-taking dummies.
posted by PinkStainlessTail at 6:45 PM on August 23, 2005
See what I did. I made a joke about being killed and... aw... nobody cares... nevermind.
What the hell am I on today? Forgive me.
Ok. Seriously. I think FFF was way over the top. But it's kind of pussy thing to actually announce you'd pay somebody ELSE to beat up a guy. Generally that pretty much excludes it from ever happening. Never the less. It was really fucked up.
But to ban the guy? Can't we just make him apologize and kiss and make up or something?
posted by tkchrist at 6:47 PM on August 23, 2005
I think a comment like that merits banning.
posted by eustacescrubb at 6:47 PM on August 23, 2005
Not a banning, no way, but um, heated comments like that have warranted a cooling off period in the past.
posted by PinkStainlessTail at 6:48 PM on August 23, 2005
Banning, not! Time out? That is Matt's call (ignore my rash comment in the blue). This sort of thing is a little out of character for FFF. It still isn't right and an apology is probably due.
posted by caddis at 6:51 PM on August 23, 2005
Ok. Ban it is. That seems just and fair.
Question. Does this "banning" hurt and can somebody video tape it for me.
What?
posted by tkchrist at 6:52 PM on August 23, 2005
It is also ever so much a shame that one can not be sure of getting away with offering $500 to see a specific user banned. posted by matteo at 6:56 PM on August 23, 2005 Ok. Give me$500 and you'll never hear from me again. I promise.
posted by tkchrist at 6:58 PM on August 23, 2005
Hmmm. I thought this was a liberal place. Is this a small version of a WMD hunt?
posted by buzzman at 6:58 PM on August 23, 2005
FFF is making an ironic statement about the idea that it's okay for Pat Robertson to call for the assassination of Hugo Chavez. It doesn't deserve banning, and I'm sure that he doesn't mean it.
He's just making a statement--hamfisted as it is--about the nature of people calling for the harm of other people.
posted by interrobang at 7:00 PM on August 23, 2005 [1 favorite]
"FFF is making an ironic statement about the idea that it's okay for Pat Robertson to call for the assassination of Hugo Chavez. It doesn't deserve banning, and I'm sure that he doesn't mean it."
No, in his petty little paranoid world, he was referring to ME.
posted by ParisParamus at 7:03 PM on August 23, 2005
There is also the political fall out of banning the Prime Minister of Canada. Which I'm pretty sure is FFF. He does speak for Canada.
posted by tkchrist at 7:03 PM on August 23, 2005
The first statement - probably just what you describe.
The second statement - oh so wrong.
posted by caddis at 7:04 PM on August 23, 2005
FFF is the Sirhan Sirhan of Metafilter....
posted by ParisParamus at 7:06 PM on August 23, 2005
Is there a way of reading which of one's comments have been flagged? I've never figured that out.
posted by ParisParamus at 7:07 PM on August 23, 2005
He's just making a statement--hamfisted as it is--about the nature of people calling for the harm of other people.
If so, it was poorly-crafted, and an apology to PP is in order.
posted by eustacescrubb at 7:08 PM on August 23, 2005
No, in his petty little paranoid world, he was referring to ME.
We're always referring to you. Don't let them know I told you.
posted by cytherea at 7:09 PM on August 23, 2005
FFF is the Sirhan Sirhan of Metafilter..
so it's Sirhan vs Yigal Amir then?
posted by matteo at 7:12 PM on August 23, 2005
Is there a way of reading which of one's comments have been flagged? I've never figured that out.
All of 'em, PP. Trust me. I follow you around flagging every single comment you make. FFF paid me $500 to do it. I do find it amusing that people who thought it was ok to implore someone to murder the pre$ident a few days ago consider the offense graver when someone posts an obviously rhetorical "threat" against a . . . fellow MeFite. Consistency is for small minds.
And it was Shaw and not Churchill, whatever thread that was in.
posted by realcountrymusic at 7:13 PM on August 23, 2005
I agree, he should just put the $500 in his pocket, and kick Paris's ass himself. This ain't no union! posted by Balisong at 7:14 PM on August 23, 2005 Starring in The Bell Tolls for Whom is Referred. posted by cytherea at 7:15 PM on August 23, 2005 Robertson calls for a political assassination. Paris says that he'd be okay with it: Not the best of ideas, but I wouldn't lose any sleep if it happened. posted by ParisParamus at 11:00 PM CST on August 22 [!] Five fresh fish was parodying Paris's approbation of political killings. Distasteful and crude, but I'm still sure that he didn't mean it. posted by interrobang at 7:16 PM on August 23, 2005 Is there a way of reading which of one's comments have been flagged? I've never figured that out. No, there isn't. The flag queue is internal and unless we check, even we don't know whose comments have been flagged until we click through and read them. posted by jessamyn at 7:18 PM on August 23, 2005 Matteo, saying I wouldn't shed a tear of certain people were off'd doesn't make me an assasin. posted by ParisParamus at 7:18 PM on August 23, 2005 Your inability to spell "assassin" makes me shed a little tear, Paris. posted by interrobang at 7:20 PM on August 23, 2005 No, but condoning assassination (or torture, or other bad stuff), makes others less willing to give a shit if it happens to you. posted by Balisong at 7:20 PM on August 23, 2005 interrobang : "FFF is making an ironic statement about the idea that it's okay for Pat Robertson to call for the assassination of Hugo Chavez." ParisParamus : "No, in his petty little paranoid world, he was referring to ME." I'm unaware of whether FFF's world view is petty or paranoid, but your use of the word "no" is incorrect. FFF is making an ironic statement about the idea that it's okay for Pat Robertson to call for the assassination of Hugo Chavez. You are one of the people with that idea. Hence, the ironic statement is directed at you. So both you and interrobang are in agreement. ParisParamus : "Matteo, saying I wouldn't shed a tear of certain people were off'd doesn't make me an assasin." Saying you wish you could pay people to beat up other people, but you can't, so you won't, doesn't make one an assassin either. I think we can safely conclude that neither PP or FFF is an assassin. Still, I think it was way out of line. There had to have been a better way of making the point than that. posted by Bugbread at 7:24 PM on August 23, 2005 violence begets violence - threats beget threats.... lets paris and robertson rot in their cesspools of hate. posted by specialk420 at 7:28 PM on August 23, 2005 I seem to recall someone (angry modem?) calling for people to punch members at a meetup (specifically Wendell) in the face. No banning took place or cooling off. In fact, I don't think Matt even bothered to weigh in on that one. posted by dobbs at 7:30 PM on August 23, 2005 Probation at the least. Even I mange not to threaten people when I post, and I act like a total jackass half the time. Though, if threatening people is determined to be kosher, I might as well let it all hang out. posted by Snyder at 7:32 PM on August 23, 2005 this is just lame get over it, FFF posted by scarabic at 7:33 PM on August 23, 2005 of course, what dobbs said. and at least we have a tagline: MetaFilter: There had to have been a better way of making the point than that. posted by matteo at 7:34 PM on August 23, 2005 dobbs...I seem to recall it too, vaugely...hmm, maybe probation is a little too harsh then. I mean, if it's no big deal, then it's no big deal, neh? It depends on how that whole thing was resovled, don't it? posted by Snyder at 7:35 PM on August 23, 2005 I seem to recall someone (angry modem?) calling for people to punch members at a meetup (specifically Wendell) in the face. Wendell? Are you kidding me? Whatever for? Wendell is just sort of mellow and witty. Why would anyone get mad at Wendell? posted by caddis at 7:37 PM on August 23, 2005 FFF is very angry. It's hard to imagine being that angry in Canada; it's so nice up there... posted by ParisParamus at 7:38 PM on August 23, 2005 Probably the name, the accent, and the public school uniform. posted by cytherea at 7:39 PM on August 23, 2005 Not the best of ideas, but I wouldn't lose any sleep if it happened. posted by ParisParamus at 11:00 PM CST on August 22 [!] Five fresh fish was parodying Paris's approbation of political killings. Distasteful and crude, but I'm still sure that he didn't mean it. posted by interrobang at 7:16 PM PST on August 23 [!] Really, how over-blown can this be? Obvious parody mixed with mild intimidation and sarcasm doesn't a true threat make. This is just a misunderstanding. Move along kids, the fight is over. posted by snsranch at 7:40 PM on August 23, 2005 OK, If Paris wears the LGF shirt to the fight, I'll do it for free. posted by Balisong at 7:42 PM on August 23, 2005 Are you kidding me? No. posted by dobbs at 7:42 PM on August 23, 2005 christ almighty. posted by adampsyche at 7:56 PM on August 23, 2005 OK, If Paris wears the LGF shirt to the fight, I'll do it for free. posted by Balisong at 7:42 PM PST on August 23 [!] And use your butterfly knife thing too!!! Whoo hoo! (pulling leg or something) posted by snsranch at 8:03 PM on August 23, 2005 ...FFF. He does speak for Canada. The hell he does. posted by timeistight at 8:05 PM on August 23, 2005 FFF is obsessed. posted by dhoyt at 8:14 PM on August 23, 2005 You said that irony was the shackles of youth, uh-huh. See, that was an ironic REM reference. And that was sarcasm in the guise of an earnest description of the lyrical reference. And that was a further ironic statement parodying the notion that earnestness can ever possibly be achieved in contemporary society. Since everyone is claiming irony, is it possible that Pat Robertson was being ironic, too? In fact, I'm going to go ahead and suggest that The 700 Club is really a grand performance art / media installation project of the MIT Media Lab. Ubiquitous misuse of "irony" makes the baby Sophocles cry. posted by gramschmidt at 8:17 PM on August 23, 2005 Metafilter: A further ironic statement parodying the notion that earnestness can ever possibly be achieved in contemporary society. Do not ban him. A warning, possibly a timeout, is all that is called for. posted by voltairemodern at 8:28 PM on August 23, 2005 you troll; you get threats. For all the insults and trash Paris throws around continually, he shouldn't expect anything better. How did I know amberglow would sidestep condemning any threat directed at Paris, no matter how abhorrent? Amber, you'd be whinnying about Hate Crimes if the situation were reversed. Or blaming the soldiers for tossing candy to children. You also perceived you and JGreyNemo were on "the same Side" recently and nobly defended that threat ("he's not advocating assassination") in the weaseliest fashion as well. I guess Paris being on the Wrong Side earns him threats of violence without reprisal. posted by dhoyt at 8:43 PM on August 23, 2005 I guess Paris being on the Wrong Side earns him threats of violence without reprisal. Paris is not being threatened, his worldview is being parodied. Amberglow has nothing to do with this. posted by interrobang at 8:48 PM on August 23, 2005 Matteo, if I had$500 to pay someone to keep other mefites from making the tagline jokes that I want to make. You post would be smoked. Because if I could, I would -- and I am dead bloody serious about this -- offer that much to be the only guy who makes metafilter tagline jokes.
Wow, this was meta of me.
OMG, I just made it even more meta.
(Oh, and I don't think it's ban-able; we need some extremists on both sides for this stuff to have even a chance of being entertaining.)
posted by oddman at 8:49 PM on August 23, 2005
Now, now, people. Don't whack your PeePee and make a mess all over Mefi.
posted by weretable and the undead chairs at 9:24 PM on August 23, 2005
Heh. I love watching MeFites make physical threats. As if there's a single can of genuine whoop-ass in this House of Geek. We're such a bunch of sissies we have to fantasize about being able to pay someone to beat each other up.
posted by scarabic at 9:31 PM on August 23, 2005
There are a lot of people here, myself included, who have at various points deserved a solid fist (and in a few cases brick) to the face for things they've posted.
And admit it - we've all fantasized about tracking down that one special fucker, garroting him while watching his smug fucking face turn purple as he tries to gasp out one last troll and then dumping his body in a tub of lye. Admit it - you've thought about, maybe you were even unable to surpress a little grin at the thought, and then you felt ashamed. Or not.
posted by Ryvar at 9:32 PM on August 23, 2005
First of all: I disagree with five_fresh_fish as often and dislike him as much as I do ParisParamus. However, I don't think fishy's blurt merits banning either: he did not actually offer any bucks to bash PP, he did not threaten to do him any harm himself, and anyway I thought wishing harm to Paris was required for membership in the Metaheathers. So I've defended Mr. Paramus' right to Free (albeit senseless) Speech in the past, and now I must extend that defense to his enemy.
Furthermore I doubt Paris feels threatened by it -- at least I hope he's not that wussy.
(Oh poor Metafilter. It'd be awful quiet around here if people only said wise things.)
And on Preview, scarabic finally made me laugh. I didn't know he had it in him.
And Ryvar, speak for yourself while you're fucking yourself. With a chainsaw, as roughly as you please.
posted by davy at 9:36 PM on August 23, 2005
This witch-hunt banning thing on every other metatalk thread, did I need to read Lord of the Flies to understand it?
posted by hackly_fracture at 9:40 PM on August 23, 2005
How can I tell if that was intentionally ironic?
posted by Ryvar at 9:41 PM on August 23, 2005
He's got a timeout. In the shame corner.
PUT ON YOUR SHAME HAT AND STEW MR. FISH!
posted by mathowie (staff) at 9:41 PM on August 23, 2005
m-m-m-m fish stew
posted by Cranberry at 9:49 PM on August 23, 2005
Why are you people so fucking literal? ParisParamus WAS OKAY WITH THE IDEA THAT OUR COUNTRY SHOULD ENGAGE IN POLITICAL KILLINGS. FFF made fun of him. Why is FFF being given a time out?
posted by interrobang at 9:51 PM on August 23, 2005
Ban interrobang! Ban him!
posted by hackly_fracture at 9:55 PM on August 23, 2005
I'm in for $20. posted by Optimus Chyme at 9:56 PM on August 23, 2005 If five fresh fish is going to be given a time out over this, then fucking give me one, too. This is ridiculous. posted by interrobang at 9:59 PM on August 23, 2005 PS interrobang, whom I love like a sibling, it can't be literal: FFF NEVER MENTIONED WHICH USER! Everyone used their amazing powers of deduction, and meanwhile postroad just took the$500 and kneecapped dejah420!
posted by hackly_fracture at 10:03 PM on August 23, 2005
Why is FFF being given a time out?
It's a pretty bullshit move. You can post anything you want here as long as you're "conservative" for some reason. Hell, dios makes fun of retarded kids, but that's okay, I guess. That furiousxgeorge guy advocated nuking Mecca and killing millions of innocent people, but that's okay, too.
But no satire! NO FUCKING SATIRE ON THIS WEBSITE YOU GOT IT MISTER!? I WILL NOT HAVE YOU TALKING ABOUT EATING IRISH BABIES!
posted by Optimus Chyme at 10:03 PM on August 23, 2005
PP flapped his gums about politics. FFF levelled as much as a threat. I'm about the last person to defend PunyPenis but come on now.
posted by scarabic at 10:03 PM on August 23, 2005
(goes back and reads again, sheepishly retracts all-caps text)
posted by hackly_fracture at 10:11 PM on August 23, 2005
I wish we could just all agree on ignoring PP and its cohort for a while -- they would just go away. Can we agree on this please?
posted by NewBornHippy at 10:13 PM on August 23, 2005
It's a pretty bullshit move. You can post anything you want here as long as you're "conservative" for some reason
It's a pretty bullshit move. You can post anything you want here as long as you're "ironic" for some reason.
Stupid joke or not, I can't get behind people threatening other users on the site.
posted by mathowie (staff) at 10:15 PM on August 23, 2005
He probably meant to say stand behind or get behind. And now it is time for all to go outside and have a nice walk in the cool evening air.
We are Matt's guests, he makes the rules.
posted by Cranberry at 10:19 PM on August 23, 2005
ooh he fixed it
posted by Cranberry at 10:20 PM on August 23, 2005
God damn it, matt, he wasn't threatening Paris! He was saying something that obliquely sounded like a threat, and was about Paris's tone about the "okayness" of killing people! The statement was a metaphor, not a threat.
posted by interrobang at 10:20 PM on August 23, 2005
I hereby offer Pat Robertson 500 fresh fish to give ParisParasmus a good rogering.
posted by louigi at 10:21 PM on August 23, 2005
I do find it amusing that people who thought it was ok to implore someone to murder the pre$ident a few days ago consider the offense graver when someone posts an obviously rhetorical "threat" against a . . . fellow MeFite. Consistency is for small minds. posted by realcountrymusic I find it amusing that you wrote a book in the president thread but basically have nothing to say here. Consistency, huh? You can look at the thread in question and know from the start the nuts are going to come out. There's been violence threatened before and defended because they were making a brilliant observation on the world around us, or they simply didn't mean it. Whatever, as long as that view extends to everyone on metafilter. If five fresh fish is going to be given a time out over this, then fucking give me one, too. This is ridiculous. posted by interrobang Just turn off your computer. Time out granted. posted by justgary at 10:25 PM on August 23, 2005 *Timed out for a week. Fuck this place.* posted by interrobang at 10:30 PM on August 23, 2005 I don't want Paris and crew (dios, Steve@, other newcomers) to leave. There's nothing wrong with having a conservative viewpoint on the site to counter the liberal bias here. What I do want is for Paris and crew to get a clue, because overwhelmingly their arguments rely on misinformation that does not withstand inspection, or is disingenuous from the outset. All of this is assuming that they're making solid, declarative fact-based statements, which is a rather rare occurrence. It has been my experience that the significantly right-wing members of Metafilter spend the bulk of their time casting out blanket assertions based largely on preconceptions. And who can blame them? Given the lynch mob attitude we display - and that goes double for you, Mr. Man-in-the-mirror - what possible motivation could they have for sitting down and having a frank discussion? They're outnumbered a hundred to one and since not many people can make posting to MeFi a fulltime job, there's little point in starting such an exchange only to have to stop and appear 'weak.' As usual for online social problems, penis-size issues on both sides (and in both sexes) are the root cause here. posted by Ryvar at 10:32 PM on August 23, 2005 List of people who it's not okay to advocate assassinating: • George W. Bush • Metafilter Members List of people who it is okay to advocate assassinating: Am I missing anyone or do I have anyone misclassified? Just want to be clear on the Rules. posted by louigi at 10:37 PM on August 23, 2005 Ya know, it's wierd. As soon as I log onto LGF, all I can think of is the most inflamitory leftist drivel. Maybe they have some sort of political allergy. They want to contribute, and they think they are, but it all comes out with so many layers of sarcasm and bias, in a desperate attempt to reach just one viewer, that it turns into a brown stain on the wall. Don't worry, Paris, I've been there, too! posted by Balisong at 10:38 PM on August 23, 2005 I'm having a hard time understanding why any comment with "and I am dead bloody serious about this" should be given the benefit of the doubt as satire. mathowie: I can't get behind people threatening other users on the site. Sounds about right. Drawing a clear line at *any* threats from one user to another, named or not, seems to me a perfectly valid thing to do, even if I'm more used to the "just let the jerks embarrass themselves" approach. But if fff's comment is a punishable offense, I'm now wondering more than ever if amberglow shouldn't have gotten a timeout for his now-infamous comment that ParisParamus would "seriously regret it" if amberglow ever saw him at a meetup. I know this has been brought up repeatedly, but despite suggestions in those later threads, I don't recall amberglow ever quite clarifying what he meant by that comment. Did he actually plan on hitting a fellow member, or just getting up in his face at a meetup and screaming personal insults at him? If the latter, would that be an acceptable, non-timeout-able threat? I mean, as long as we're policing threatening outbursts, amberglow's furious (tho not specifically physical) threat was just as horridly shocking a precedent for the site as fff's furious (tho not specifically targetted) version. I'd be curious to hear from an admin what they thought the difference might be, if any. Seems an important guideline to be clear on. posted by mediareport at 10:55 PM on August 23, 2005 Oh, please. You can try to diffuse death threats against members, but there's nothing that says one member might go off and punch another. No matter how many time outs, or banination. There used to even be a time when it wasn't forbidden to be rude to somebody. I could run a vaccum cleaner salesman, or a Jehovah's Witness off my property with a shotgun. Alas, those days are behind us. posted by Balisong at 11:05 PM on August 23, 2005 mediareport: Obviously, I speak only for myself, but I think amberglow's comment, was, unfortunatly, just on this side of vaugeness to have plausible deniability. Even FFF tried the same tack with his comment, it was just a little more obvious. I think it's a bit hard to have a bright-line measure of such things, I mean, is "Amberglow, I hope you die horribly," a threat or just being super-boorish? Around here, it can be hard to tell. But I see your point, I just think there is already a large degree of jackassery (he said looking at himself,) that makes amberglow's quasi-threat kind of blend in. posted by Snyder at 11:06 PM on August 23, 2005 If I thought it would would work I'd pay 500 quatloos to somebody to help me kill myself so I can come back as a big scary puffball ghost and liberate the entire planet Earth. But with my luck those Bill Murray movies will turn out to be NON-fiction. I still don't think fishy was threatening anybody, nor have I seen PP say he's afraid or that he felt it was a threat. (And I wasn't threatening to kill myself or hire a kevorkian either; for one thing there's no such currency as a "quatloo".) By the way, there are few real liberals here unless Senator McCarthy was one. posted by davy at 11:06 PM on August 23, 2005 did you know that 500 bucks is over a million bolivars? posted by pyramid termite at 11:07 PM on August 23, 2005 You can try to diffuse death threats against members, but there's nothing that says one member might go off and punch another. Er, that's true, but it's not what we're talking about, Balisong. Mefi guidelines apply to Mefi, not real life. The tone of the site is a reasonable thing for the site guidelines to attempt to define. posted by mediareport at 11:09 PM on August 23, 2005 I think the next MeFi meetup is going to get interesting! posted by blue_beetle at 11:12 PM on August 23, 2005 Really, Please.. Five Fresh Fish is a Canadian of the Lefty persuasion. I have agreed with him on many points. I am probably more inclined to go on a shooting / slashing up my neighbors spree than he is. I knew he wasn't serious. Usually you back up claims like that with viceral, spitefull, heated, negative language. And lots of it! I wouldn't take FFF up on his scam any more than I would buy into a Nigerian scammer. posted by Balisong at 11:14 PM on August 23, 2005 I knew he wasn't serious. Bully for you. And I knew the comment crossed a line as soon as I saw it. Now, let's get back to the point, which is the effect on the long-term health of the site if intra-member threats become an acceptable part of the culture. I say it'd be bad. *Really* bad. And you say? posted by mediareport at 11:18 PM on August 23, 2005 Forget the long-term effects, the precedent, whatever. It's a stain and it should be wiped. When someone shits on your doorstep you don't worry about the precedent it's going to set for the neighborhood kids. You hose the fucking shit off your steps. Anybody who doesn't understand that threats of violence mark the point where it's no longer worth even having a website wherein to discuss and discourse... whoever that is has a big ass-kicking coming right up from me. posted by scarabic at 11:26 PM on August 23, 2005 Did he actually plan on hitting a fellow member, or just getting up in his face at a meetup and screaming personal insults at him? I'm pretty sure he was going to "discuss" him to death. Just a hunch. posted by justgary at 11:33 PM on August 23, 2005 I just wanted to point out, it's a bit silly to respond so negatively towards ParisParamus. I'm pretty sure he enjoys it, greatly: Diagnostic Criteria (DSM-IV-TR). posted by gsb at 11:36 PM on August 23, 2005 Any hitman you hire for$500 is gunna roll on you if he catches heat. I suggest paying full-fare, or doing it yourself.
posted by mosch at 12:21 AM on August 24, 2005
I don't want Paris and crew (dios, Steve@, other newcomers) to leave. There's nothing wrong with having a conservative viewpoint on the site to counter the liberal bias here.
The problem is not his conservative viewpoint.
ParisParamus's issue is that his political posts are generally designed to spark ire, not discussion. They routinely contain putdowns directed both at individuals and at large groups that he disagrees with politically.
Steve's issue is that he does not even make an attempt to participate in a political discussion. He just shits on the thread's topic and moves on. He's an extremely obvious troll, and nothing more.
Dios just likes to argue. His posts annoy a lot of people because of this, but they don't seem to be written in a malicious spirit, just an argumentative one. I don't think it's fair to lump him in with Steve or PP.
posted by mosch at 12:33 AM on August 24, 2005
I kick ass.
posted by uncanny hengeman at 12:52 AM on August 24, 2005
I don't want Paris and crew (dios, Steve@, other newcomers) to leave. There's nothing wrong with having a conservative viewpoint on the site to counter the liberal bias here.
So if a conservative asserts an opinion, it's a viewpoint. If a liberal asserts an opinion, it's bias. Good to know.
And it wasn't just an opinion, PP was obliquely calling for the assassination of a democratically elected official. That's fucked up, no matter which way you want to slice it.
On preview: Fucked is not in the dictionary.
posted by Talanvor at 12:53 AM on August 24, 2005
mosch, Dios relishes jumping into the second or third comment in a thread and shitting on it profusely, usually couching it with something "Oh, once again, the LeFites" etc. You give him too much credit.
As for PP, he considers all of the citizens of Venezuela to be "peasants." That's reprehensible. It's obvious he doesn't leave the house much.
I agree with FFF on a number of issues politically, but rank him up their with the former two in terms of his penchant for asshattery.
posted by bardic at 12:58 AM on August 24, 2005
Banning fff and then discussing him seems unfair and counterproductive -- if pp can sit in on this thread (calling fff "the Sirhan Sirhan of Metafilter" and so on), fff should be able to answer the charges for everyone to read.
Can't someone be banned from blue and green but allowed in brown, and perhaps only in this brown thread? Or is this application too inflexible for that?
posted by pracowity at 1:01 AM on August 24, 2005
I bet if you mapped the MeFette contribution rate to the grey -vs- the blue and compared it to the boys it would show....something to think about.
posted by peacay at 1:08 AM on August 24, 2005
(Is this grey? I thought it was a sort of muddy sewer-water brown. Maybe it's the pee-stain yellow buttons and links that fooled me.)
posted by pracowity at 1:15 AM on August 24, 2005
Balisong : "You can try to diffuse death threats against members, but there's nothing that says one member might go off and punch another. No matter how many time outs, or banination."
True. But that's not what bannination is for. Bannination is not an attempt to prevent real-world violence, it is an attempt to prevent folks from threatening other folks on Mefi. Much like when someone says "shut the fuck up, man!" when their roomate shouts "Wake up or I'm gonna pour a bucket of water on your head!", they aren't trying to prevent the bucket of water from being poured on themselves, they're trying to shut up their obnoxious roomate.
Balisong : "There used to even be a time when it wasn't forbidden to be rude to somebody. I could run a vaccum cleaner salesman, or a Jehovah's Witness off my property with a shotgun.
"Alas, those days are behind us."
Nah, you can still be rude to people. There's plenty of evidence of that all around.
Ryvar: "I don't want Paris and crew (dios, Steve@, other newcomers) to leave. There's nothing wrong with having a conservative viewpoint on the site to counter the liberal bias here."
Talanvor : "So if a conservative asserts an opinion, it's a viewpoint. If a liberal asserts an opinion, it's bias. Good to know."
Er, no. That's not what "bias" means. If a conservative asserts an opinion, it's a viewpoint (or an opinion, more likely). If a liberal asserts an opinion, it's a viewpoint (or an opinion, more likely). If a site has more liberal views or commentators than conservative, it has a liberal bias. If it has more conservative views or commentators than liberal, it has a conservative bias. MeFi is more liberal than conservative, so it has a liberal bias. Doesn't mean it's wrong, just means it tilts towards liberal.
pracowity : "(Is this grey? I thought it was a sort of muddy sewer-water brown. Maybe it's the pee-stain yellow buttons and links that fooled me.)"
Apparently it shows up as brown on some computers/monitors (perhaps browsers?). For me it's a very neutral flat smooth grey.
posted by Bugbread at 1:59 AM on August 24, 2005
I find it amusing that you wrote a book in the president thread but basically have nothing to say here. Consistency, huh?
No, fool. Boredom. I have nothing to add to this debate. I support Matt's decision here. I think threatening people with violence is always wrong except in self defense. On the other hand, I think threatening the president publicly is a specific crime. A vague threat against an unspecified person, as FFF did, is not a crime. It's gross, but not illegal. So the two issues are distinct.
If you really want to read my complete views on freedom of speech and the incitement of violence again, be my guest. . There is nothing inconsistent in my views.
posted by realcountrymusic at 4:18 AM on August 24, 2005
Besides, I love PP. I don't want to see it harmed. I would defend to the death its right to say the stupidest things I've ever read on the internets, d00d.
posted by realcountrymusic at 4:23 AM on August 24, 2005
If a conservative asserts an opinion, it's a viewpoint (or an opinion, more likely). If a liberal asserts an opinion, it's a viewpoint (or an opinion, more likely). If a site has more liberal views or commentators than conservative, it has a liberal bias. If it has more conservative views or commentators than liberal, it has a conservative bias. MeFi is more liberal than conservative, so it has a liberal bias. Doesn't mean it's wrong, just means it tilts towards liberal.
Thank you.
posted by Ryvar at 4:42 AM on August 24, 2005
Threatening someone: words.
Kicking someone's ass: not words.
Metafilter: words.
That's all I got.
posted by stavrosthewonderchicken at 5:30 AM on August 24, 2005
Offering money to have someone hurt: a crime (albeit fff did not name his target).
Urging others to commit violence against a US president: a crime (in some cases).
Some words: incitement, slander, obscenity = crimes.
It just isn't as simple as you make it sound, stavros. In no society in the world is speech absolutely free from all social constraints or sanctions.
posted by realcountrymusic at 5:40 AM on August 24, 2005
Heh. I love watching MeFites make physical threats. As if there's a single can of genuine whoop-ass in this House of Geek. We're such a bunch of sissies we have to fantasize about being able to pay someone to beat each other up.
posted by scarabic at 9:31 PM PST on August 23
Anybody who doesn't understand that threats of violence mark the point where it's no longer worth even having a website wherein to discuss and discourse... whoever that is has a big ass-kicking coming right up from me.
posted by scarabic at 11:26 PM PST on August 23 [!][!]
scarabic, are you just so much more meta that you're trying to freak us the fuck out? or do you think that this continual meetup photo p.r. that your agent insists upon is actually working? bizarrely, it seems that the only reason that all the broads (and amber and Paris, er, dios) think you're so hot is that you're not a total neo maxi zoom dweebie.
anyway, by all means, you should continue your "peace through violence and derision" campaign. it's bound to get you somewhere.
posted by Hat Maui at 5:45 AM on August 24, 2005
Paris is not being threatened, his worldview is being parodied.
That's how I read. Obviously the use of a <parody metamember="paris"> tag would have been useful.*
*Assuming of course I read it properly. Could be wrong. The ambiguity (or amberglowity for some) of the situation makes it a difficult call.
posted by juiceCake at 5:45 AM on August 24, 2005
this is a ridiculous timeout. there is no "there" there.
*awaits timeout from Recumbent Brother*
posted by Hat Maui at 5:50 AM on August 24, 2005
But if fff's comment is a punishable offense, I'm now wondering more than ever if amberglow shouldn't have gotten a timeout for his now-infamous comment that ParisParamus would "seriously regret it" if amberglow ever saw him at a meetup. I know this has been brought up repeatedly, but despite suggestions in those later threads, I don't recall amberglow ever quite clarifying what he meant by that comment. Did he actually plan on hitting a fellow member, or just getting up in his face at a meetup and screaming personal insults at him? If the latter, would that be an acceptable, non-timeout-able threat?
I mean, as long as we're policing threatening outbursts, amberglow's furious (tho not specifically physical) threat was just as horridly shocking a precedent for the site as fff's furious (tho not specifically targetted) version. I'd be curious to hear from an admin what they thought the difference might be, if any. Seems an important guideline to be clear on.
Is it really a threat when it's crystal clear that the person spoken of never dares show his face at the frequent meetups? It was a statement of intent--but one that i knew would never come to pass, unfortunately. Call it a proposal, if you like, or call it a threat. I don't care. Some people (thankfully just a few here) deserve no better. Their actions invite that kind of response.
I said it before and i'll say it again--Paris continually insults and derides everyone on this site daily. He is incapable of making a comment unless it also includes a disparagement of either everyone here or specific members. He is a troll. It's not those people who are fed up with his continual shitting--on this site and other members--that should be given a timeout.
posted by amberglow at 6:26 AM on August 24, 2005
Can I offer five bucks for someone to rub a lot of gum in Paris's hair?
That's pretty much consistent with the level of annoyance I feel when reading him.
posted by klangklangston at 6:32 AM on August 24, 2005
louigi - by my recollection the rules also make it acceptable to advocate assassinating:
• Yasser Arafat
• Jacques Chirac
• But talk shit about a Mefite and wind up dead timed-out.
posted by McGuillicuddy at 6:33 AM on August 24, 2005
I think it's absolutely disgusting that this Ma Thowie lady can just switch us on or off like we are some kind of disembodied shock-jock on radio station W.A.N.K. If someone here can't post for, say, a week, just think of the incredible damage they'll do "on the outside".
Basically, the problem is that mefi provokes the most terrible cacoethes within the tiny, withered minds of its inhabitants - scurrying as they do within its dank and cavernous catacombs, bathing in rivers of malice, and only emerging bile-heavy to the world of thin sunlight in order to belch vast gobs of acidic hate onto the unblemished countenances of the innocent.
Apart from that, though, its quite a delightful community - or "blogopolis", as the modern lexicon mandates.
posted by the quidnunc kid at 6:42 AM on August 24, 2005
If you hadn't just spent so long trying to think up zany things to write, you might have been able to make it to the bathroom in time.
Oh well.
posted by NinjaPirate at 6:48 AM on August 24, 2005
Artist's rendition.
posted by selfnoise at 6:50 AM on August 24, 2005
It just isn't as simple as you make it sound, stavros.
Of course. Nothing is simple if you think about it too much. The trick is not thinking so hard, unless absolutely necessary.
posted by stavrosthewonderchicken at 6:56 AM on August 24, 2005
Can't resist:
Metafilter: As if there's a single can of genuine whoop-ass in this House of Geek
posted by found missing at 7:00 AM on August 24, 2005
This witch-hunt banning thing on every other metatalk thread, did I need to read Lord of the Flies to understand it?
heh heh.
posted by OmieWise at 7:03 AM on August 24, 2005
Metafilter: The trick is not thinking so hard
Heh.
posted by realcountrymusic at 7:30 AM on August 24, 2005
Gezz. I remember when it was okay to threaten to beat up other members. I once got another member's phone number and address. I called him up and said I was coming over to beat him up. Most people here at that time seemed to think that was okay, although there were several dissenters.
I never did drive over to his apartment. My goal was only to get him to stop posting, and that worked - He never came back. My point is that as ugly as it is, sometimes threatening to beat someone up can be very productive. In PP's case I don't think it's justified though. His schtick is just too pointless and inane. If we beat up members just for being trolling, pointless windbags we'd have to go after 25% of the membership. Not worth the bother in my humble opinion.
posted by y6y6y6 at 7:36 AM on August 24, 2005
How did I know amberglow would sidestep condemning any threat directed at Paris, no matter how abhorrent?
Yeah, amberglow is a fine fellow as long as you agree with him politically. Otherwise, you're not human and he's happy to threaten you or cheer any bad things that happen to you. Not that that's unusual around here.
The timeout is silly. The callout is silly. All of this is just words; talking about "crime" is silly. I personally find that kind of thread valuable because it refreshes my memory as to who's worth listening to and who's a babbling asshole; I really don't see how people can get so bent out of shape about childish threats and "ironic" comments. Some of you seem never to have experienced an actual fight and think that impolite words on your computer screen are the moral equivalent of war.
Oh, and just to get past the "we don't really know who he was talking about" stuff, here's an earlier comment that seems to have been ignored:
I'm kicking in C$50 to the "assasinate ParisParamus" fund. Let's get rid of the fucker. posted by five fresh fish at 2:02 PM EST on August 23 posted by languagehat at 7:40 AM on August 24, 2005 On nonpreview: if y6y6y6 is being ironic, I'm missing the point. If what he's saying is true, he's an incredible asshole. posted by languagehat at 7:42 AM on August 24, 2005 I said it before and i'll say it again--Paris continually insults and derides everyone on this site daily. He is incapable of making a comment unless it also includes a disparagement of either everyone here or specific members. He is a troll. It's not those people who are fed up with his continual shitting--on this site and other members--that should be given a timeout. I agree with this. ParisParamus is a troll. Unfortunately, trolling the site is acceptable, so long as you toss in a few right-wing sentiments in between insults. posted by mosch at 7:48 AM on August 24, 2005 Is it really a threat when it's crystal clear that the person spoken of never dares show his face at the frequent meetups? It was a statement of intent--but one that i knew would never come to pass, unfortunately. Ha... I would kick you in your coddled shit-covered nuts if I ever saw you at a meetup. Just a statement of intent... not an actual threat of course. posted by Witty at 8:01 AM on August 24, 2005 "If what he's saying is true, he's an incredible asshole." /shrug Judge for yourself. At ther time you failed to weigh in on the issue as far as I can tell. Also - I find it interesting that even back in that thread we were talking about what an ass PP was. Good times. posted by y6y6y6 at 8:03 AM on August 24, 2005 FFF get s the timeout and PP, yet again, doesn't ? It's not those people who are fed up with his continual shitting--on this site and other members--that should be given a timeout. Agreed. Given this new policy, "Stupid joke or not, I can't get behind people threatening other users on the site", I trust Witty will be indulged in his unambiguous request for a timeout? posted by Zetetics at 8:16 AM on August 24, 2005 FREE FFF posted by mr.marx at 8:18 AM on August 24, 2005 I don't think many of you realize how hollow your comments sound. It is often said that people want diversity of viewpoints here. But they often complain that people who have a differing view aren't straightforward, honest, sincere or whatever as if the opposing viewpoints have to held to a higher standard, even though they have to deal with more grief. It is a shame that I only see a few people who consistently understand and are fair about noting the extreme bad faith with which an opposing viewpoint is recieved. Any vocal poster with an opposing viewpoint is assume to be the worst, have untoward motives for posting, disingenuous, stupid, trolling, etc or just a plain jerk. Treated like that, who could behave differently? If you want opposing viewpoints, don't be so openly threatening to them and insulting to them. A person with opposing views can't possibly be vocal without heaps of scorn. I submit no one with an opposing viewpoint can be respectful and vocal here. Because eventually the sheer amount of bad faith, scorn, insults and the like that the person has to deal with would eventually cause anyone to break down to more base rhetoric. I know this has been pointed out by many people before me and the mob mentality isn't likely to change. But I am just flabbergasted by people who hate PP because he isn't congenial, but then threaten him and joke about him to the point he is turned into a monster. As if he could be anything else by the way he is treated. posted by dios at 8:25 AM on August 24, 2005 I submit no one with an opposing viewpoint can be respectful and vocal here. I submit justgary as example of a poster with an often opposing viewpoint who is both respected and respectful. And respectfully await Witty's timeout. posted by If I Had An Anus at 8:33 AM on August 24, 2005 y6y6y6, you yourself said that you refrained from threatening the guy in that thread (the page with the emails is down, so I can't read the actual correspondence), and then someone else in the thread was criticized for only suggesting to send the guy a virus. And that was concerning a user who was bypassing banning attempts and who openly declared that he wanted to ruin the site. How does that apply here? posted by loquax at 8:33 AM on August 24, 2005 y6y6y6: My apologies; that was before my time, which is why I didn't weigh in and why I had no memory of what you were talking about. The fact that Matt said "Mob. Go. Now. Find him" certainly gives you whatever cover you might need. But it would have been sensible to link to the thread in your first comment; as it stands, you have to agree you sound over-the-top. I was amused to see this comment by fooljay in that thread: What I think would be really really really cool is to have his posts only show up to him and non-authenticated visitors. IOW, when he looks at the site, he sees his posts. When anyone else looks at the site (while logged in), his posts don't appear. Mute-button banning I'll call it. Kills many birds with one bush if you think about it for a second. These ideas just keep cropping up, don't they? posted by languagehat at 8:35 AM on August 24, 2005 "How does that apply here?" It doesn't. Not really. I mean maybe it sort of does. Or not. You know? posted by y6y6y6 at 8:36 AM on August 24, 2005 y6y6y6 - not to pick on you for comments made years ago (seriously), but I couldn't resist delicious irony! Matt should press charges. Seriously. How will people ever learn that you can't just threaten to beat people up if we just stand by while PParts breaks the law? (PParts not referring to ParisParamus, but to the troll in question at the time) posted by loquax at 8:42 AM on August 24, 2005 As if there's a single can of genuine whoop-ass in this House of Geek. Hah! Very true. Any actual physical altercation between two of us would definitely be a slap fight. posted by LarryC at 8:44 AM on August 24, 2005 Hat Maui - I'm gathering that you desperately need more attention in your life, and that you disagree with something I said. But that second part is still vague. Can you take the gimp mask off and repeat? posted by scarabic at 8:54 AM on August 24, 2005 "you have to agree you sound over-the-top" Score another point for me!!!! The Internet is one of my favorite things. My point is that these things have a context. I did indeed threaten to beat the guy up, I just left that completely out of the MeTa thread. I didn't think it would ever come to blows, but I wanted to completely disconnect that from MetaFilter just in case. In truth, we had exchanged so many emails that I felt I knew him pretty well, and I knew him to be a complete coward. So the best response was to confront his threat to beat up me and Matt by making him confront his cowardice. The context in my case was confronting a racist bully. He threatened to beat me up, I said okay I'll be right over, he slunk away forever. In FFF's case the context was a joke born of complete exasperation and exhaustion. So PP is allowed to troll the site for years, constantly goading people into anger without offering much in the way of thought provoking counterpoint. But when fff gets fed up and responds with some provocative irony, he gets banned. Or whatever. It just seems like we've grown into some tight-asses. posted by y6y6y6 at 9:00 AM on August 24, 2005 Ad hominem arguments offered in refutation of empirically substantiable claims are not "respectful" of an opposing viewpoint, from either (or all) side(s) of a debate. They invite, and sometimes deserve, ad hominem responses, but at the cost of lowering the tone. This well describes contemporary US politics. And it well describes the effects of the political polorization in this country on even our most intimate spheres, let alone our public engagements such as the ones we have on MeFi. Of all the terrible effects of the far right's inexorable ascendancy in the US since the 1980s, the worst is the casting of legitimate opposition as stupid, traitorous, venal, or immoral. It happens from all sides these days (as it has in the past - I'm not claiming the present moment is unique) and it is deeply exacerbated in a time of war. (The more cynical among us think that we are at war largely because of this effect, which is to the advantage of the party in power and with control of the media.) I love to debate with conservatives, even ideologues, who can engage in serious and fact-based argument. There are a few on MeFi. I honestly would be happy to see more, and converse with them. I plead guilty to plenty of ad hominem snark myself. It's very hard to rise above where things are. But this goes beyond right/left polarization. It goes to a cheapening of discourse, and a declining sense of community if it is tolerated. MeFi is (even with all its troubles) an island of civil and passionate debate in a sea of ideological and physical brutality. [/anticipates obligatory "Metafilter: tagline reply] It stays that way by having standards, and a strong hand or two on the rudder. Obviously, enduring the usual snarky banter is part of the deal, and part of the fun. Insults, polemics, and sarcasm can be valuable seasoning for reasoned debate. Threats of physical harm cannot, even if they are registered in insulting, polemical, or sarcastic tones. That way lies trouble and oppression. There's a very bright line, sections of which are enshrined in law, and others in longstanding conventions for civil discourse here and in general, that is simply not hard to see. The point of the "book" I wrote in the presidential thread was that observing this line makes us more rather than less free. We don't need to parse rules like "no physical threats" too finely. They are self-evident. posted by realcountrymusic at 9:07 AM on August 24, 2005 sp: polArization posted by realcountrymusic at 9:08 AM on August 24, 2005 Murdering PP, Dios and Steve@? Not the best of ideas, but I am not going to lose any sleep if it happens. posted by weretable and the undead chairs at 9:12 AM on August 24, 2005 If I had a nickle for every political thread (although not limited to) that someone from the left hasn't jumped in early with a zippy snark-filled trolling comment, well... I just love that this is always everyone's major complaint about the conservative contributers... that and being insensitive, aggressive, insulting, etc. All I know is, it goes both ways and there's plenty more coming from the left than there is from the right (on this site), due primarily to the fact that there are simply more of the former. posted by Witty at 9:22 AM on August 24, 2005 Care to share some examples, Witty? posted by If I Had An Anus at 9:24 AM on August 24, 2005 I am not a troll. I attempt to make points using humor given that I'm outnumbered in outlook, what, 100-2? It remains pathetic that this is not understood by more people (it's the same blindness that go you John Kerry and Howard Dean, but...whatever). posted by ParisParamus at 9:40 AM on August 24, 2005 I think we could all use a good beating from time to time. Maybe we should have a service that at some point, when we least expect it, kicks our ass. I actually agree with the "opposition" on this one. There are certainly trolls on the left and certainly rude snarkiness from the left and there are sure a heck of a lot more of them. For every one PP there are a dozen lefties. I can see how that has got to be frustrating. It's no excuse, but it's got to be frustrating. I don't participate in freep, but I've got to imagine that it is a little maddening to hear 75 times for each post that you are a liberal weenie. I think the only thing I can say to guys like Paris is that the less you give in to just spouting a position and the more time you spend giving more concrete reasoning for your opinions, at least you will come off as presenting an argument and less as a troll and the more the detractors on the left side will look like jackasses. One liners don't seem to be winning over any hearts and minds. posted by Pollomacho at 9:55 AM on August 24, 2005 "It remains pathetic that this is not understood by more people" It remains your responsiblity to actually be funny and get your point across. posted by OmieWise at 9:59 AM on August 24, 2005 Here's a recent example "If I Had An Anus". I won't suggest that it's the best example or is the kind of example that covers all cases. But you take any FPP that targets Bush or the administration, for example, and you can be GUARANTEED to read AT LEAST 50% snark, trolls, insults against conservative MeFi members that aren't even present, etc. within the first 10-20 comments. Every time? Maybe not. Most of the time? Absolutely. posted by Witty at 10:04 AM on August 24, 2005 "It remains your responsiblity to actually be funny and get your point across." I try. Maybe you get my point(s), maybe you laugh, but if you don't, that doesn't make me a troll. Hey, next March will mark my FIFTH year of Metafilter! posted by ParisParamus at 10:10 AM on August 24, 2005 Good comment, Dios. Enforcement of standards here is erratic and ad hoc but, I strongly believe, well-intentioned and, on average, fair. It's probably not a good idea to say something that can be construed as a specific threat to another commenter. posted by Ethereal Bligh at 10:14 AM on August 24, 2005 I agree with dios. Hmmm, again. That's strange. Anyway, I took a critical view of Cindy Sheehan in one of the recent posts, and was pretty roundly attacked for it, despite not being one of the conservative "usual suspects." posted by monju_bosatsu at 10:23 AM on August 24, 2005 I try. Maybe you get my point(s), maybe you laugh, but if you don't, that doesn't make me a troll. Hey, next March will mark my FIFTH year of Metafilter! Bad breath has been around since the dawn of time, but that doesn't make it a good thing. I will not go into the definition of "troll" or whether you are one, but you are clearly, at the very least, an attention whore. You are nearly, if not entirely, universally despised by the other members of the site, yet you keep showing up and asking for abuse. The only possible conclusions are that you enjoy stirring up trouble for its own sake or that you enjoy abuse. If you were not around, there would still be plenty of people who would espouse a conservative point of view and who would do so more cogently and in a less hostile manner than you do. People who continue to show up where they're not wanted or appreciated may not be trolls, but they are sad. posted by anapestic at 10:26 AM on August 24, 2005 Ryvar writes "They're outnumbered a hundred to one" Right wing people have trouble being taken seriously? Cry me a river. I have experienced plenty of ignorance and verbal violence in response to my comments here. I have responded with links to support my position and exposition. That is what I have learned to do following years of contributing to this site. As usual for online social problems, penis-size issues on both sides (and in both sexes) are the root cause here So, lets forget about the political orientation and focus on the real issue, people need not feel persecuted. Thicker skin may help with this. posted by asok at 10:29 AM on August 24, 2005 "If you were not around, there would still be plenty of people who would espouse a conservative point of view and who would do so more cogently and in a less hostile manner than you do. People who continue to show up where they're not wanted or appreciated may not be trolls, but they are sad." Yeah, plenty of conservative/neoconservative posters here. Sure. I guess you consider the number "6" to be plenty. If I'm so awful, feel free to ignore me. posted by ParisParamus at 10:45 AM on August 24, 2005 The truth is that the same narrowmindedness and arrogance that dominates the Left causes people to feel obliged to call me a troll, or critique the number of links or annotations in my posts. Sorry, I ain't goin nowhere. posted by ParisParamus at 10:48 AM on August 24, 2005 Hey, next March will mark my FIFTH year of Metafilter! And you should be proud of raising the tone here so much during that time. You're such a witty, sparkling conversationalist--so full of bon mots and links to factual information. You never spout talking points and lies and fail to back them up with links or proof--no sir, not you. No insults have ever dripped from your honeyed tongue. You truly are a ray of sanity shining upon hopelessly delusional people. posted by amberglow at 10:50 AM on August 24, 2005 Make that 7, ParisParamus. I don't think you're a troll. I do think you enjoy being one of the magnificent sane voices in this leftist pit of sin. posted by gsb at 10:59 AM on August 24, 2005 Um, scarabic, you see that quote from five_fresh_fish up there at the head of the thread? The one that started all this? I wish you, and those with you, would please explain why you think that's a threat. I think your wussery interefered with your reading comprehesion. Again: that JGN guy did NOT thtreaten Gee Dubya, Pat Robertson did NOT threaten Chavez, and five_fresh_fish did NOT threaten ParisParamus. And if I say "I think somebody should threaten to threaten to punch you in the nose so you'll know a real threat from an excuse to demonstrate wussiness" I will NOT be threatening you. (Note: I just used something called the second Conditional Mood, which a lot of you people should read before you get your panties bunched up; furthermore I did not speak of harming anyone, but said 'sometimes I think that someone should threaten to threaten'.) I have no doubt that scarabic will again start babbling about what a homicidal psycho I am. posted by davy at 11:14 AM on August 24, 2005 Thicker skin may help with this. Or thicker somethings. Cry me a river is right. This is a voluntary community. It leans left. Just because you are outnumbered doesn't give you a right to be abusive. Convert others or attract new members who come for the brilliant conservative repartee. On the other hand, just because liberals are a numerical majority doesn't make it right to abuse conservatives with ad hominem attacks either. I don't agree that most liberals on MeFi are "abusive" toward conservatives, though it happens and it's wrong. And monju, on the Sheehan thread, I don't think you were really attacked. I thought that was a good and substantive debate, and that your contributions were cogent and were responded to, for the most part, seriously. Maybe I am remembering it wrong. But let's not let the grey-area thinking (pun intended) overwhelm what's black and white here. It's never ok to threaten or call for physical violence in civil debate. Right? Isn't that the point? Snarky, ad hominem, bilious, vituperative polemic ain't pretty, but it's not the same as "I'm gonna kick your ass." (or kill you, etc.) posted by realcountrymusic at 11:25 AM on August 24, 2005 I just used something called the second Conditional Mood, which a lot of you people should read before you get your panties bunched up Rendering a statement deniable while letting its supposedly deniable implication stand is a common rheotrical tactic, as is insinuation of a threat, or incitement ("Won't somebody please shoot . . ." or "if it were legal I would pay$500 for someone to kick the ass of . . ."). If such an implication is made, it behooves a thoughtful debater to add "just kidding" or something of the sort, at least. Mistakes were made. The only question is by whom? Something doesn't have to rise to illegality to be wrong. I fully agree that fff's statement was technically not a threat, nor do I think it was meant to be taken as one, nor did I (or anyone else, I think) actually imagine fff writing a check and PP getting a bloody nose the next day. Doesn't make it right.
posted by realcountrymusic at 11:31 AM on August 24, 2005
And monju, on the Sheehan thread, I don't think you were really attacked. I thought that was a good and substantive debate, and that your contributions were cogent and were responded to, for the most part, seriously. Maybe I am remembering it wrong.
You're correct that there were several civil participants on both sides in that thread, and the debate between those participants was productive, or at least not abusive. However, the background noise in that thread was pretty loud, though. Like mooncrow calling those critical of Sheehan "cynical ... sick shits" whose voices "will die away in the coming whirlwind." A few others dismissed any criticism of Sheehan as an "ad hominem" attack. And that thread was mild, frankly.
I disagree that "snarky, ad hominem, bilious, vituperative polemic" is any different from faux threats of physical violence here. With rare exceptions, there is no opportunity or expectation that any such threat would be carried out. I view threats as little more than rhetorical puffery, and would frankly be shocked if they were actually intended as anything more.
posted by monju_bosatsu at 11:45 AM on August 24, 2005
On the other hand, just because liberals are a numerical majority doesn't make it right to abuse conservatives with ad hominem attacks either. I don't agree that most liberals on MeFi are "abusive" toward conservatives, though it happens and it's wrong.
It does happen, that's true. But part of the problem is, it happens (damn near) every time though. I agree that most liberals on Mefi are not "abusive" towards conservatives. But you can count on any politically-driven thread, where a conservative dares to show his/her face, that they will be "abused" by someone (and I'm only using that term for continuity's sake). Very rarely, if ever, especially in hot topics, can a conservative escape attack-free. When I read threads like those, I get the feeling that opposing views and opinions aren't welcome, despite everyone's supposed best intentions. It's more of a "get out troll, with your obviously-wrong conservative views... this thread belongs to the left, where we will spend all day trying to one-up each other with ridiculous jokes, sarcastic one-liners and direct insults to you and your kind".
That being said, it's obvious that conservatives shouldn't be looking for comfort and like-minded individuals around here. It just ain't happnin'. Nor should it, necessarily. But damn if it isn't fucking old listening to the masses moan and groan, whine and complain about the same handful of conservative contributers when there's 10 or more left-leaning dickheads for every one on the right. Get the fuck over it already.
posted by Witty at 11:56 AM on August 24, 2005
gsb, Je vous remercie de votre attitude sain.
posted by ParisParamus at 12:00 PM on August 24, 2005
y6y6y6y you're a hardass. Seriously that was pretty cool thing. I would have never gone that far fearing someone might actually call me out on it and be a bigger hardass than I. Good work.
posted by geoff. at 12:09 PM on August 24, 2005
davy, you're right but I'm afraid you're still a homicidal psycho.
As for the so-called value of "diverse opinions" it's bullshit. PP rarely offers an opinion. Take a moment to look up some of his comments. This is a person who has literally gone into threads, shouted, in all caps, an idiotic remark only tangentially related to the topic, and then disappeared. That's not a diverse opinion, it's just trolling. And when PP is such a complete asshole--really he must either enjoy it or just be severely damaged--he shouldn't expect anything but such assholery in return.
Also, dios and bugbread deliberately misuse the word "bias," as it applies to blogs, to somehow provide for some sort of conservative exception. Also bullshit. Sadly, there was a once upon time when interesting, nuanced discussions did frequently occur. There was one poster in particular I actually looked forward to--was it Midas something? Anyways, it's laughable that dios, somebody who starts most every post with the obligatory "Lefites," would even have the audacity to complain about invective, but I digress.
fff's comment was in poor taste and the callout was fine, but the timeout leaves a bad taste in my mouth. It's quite clear fff was not seriously threatning PP and it may have even been an ironic comment on PP's above comment.
posted by nixerman at 12:15 PM on August 24, 2005
"PP rarely offers an opinion"
False. I just spice my opinion up with some entertainment value. Because minority viewpoints need that to get heard. It's just that you have little or no tolerance for people who disagree with you.
posted by ParisParamus at 12:22 PM on August 24, 2005
Just to get things strait here, I was under the impression that trolls lived under bridges and trawls were drift nets, no?
posted by Pollomacho at 12:23 PM on August 24, 2005
But rcn, again you're muddying the waters by dragging in something extraneous: we're not arguing here about whether it's right (or polite, or conducive to scholarly discourse) to speak to anybody in any particular way; we're discussing whether what fishy posted (apparently) at Paris was a threat to PP's well-being, or if it was meant to be taken as one, or if it sounds like any harm to PP might result from it. Whether it's "right" or not is beside the point, orthogonal and extraneous. On Metafilter people say things that are not "right" all the time without getting "timed out" for it and without provoking long threads like this.
What matters here is that sanctions were brought to bear because of a misreading of what was said. As far as "rhetorical deniability" goes, that's just silly: my posting "If I were Stalin I'd have half of you shot!", e.g., does not give any reasonable person any reasonable cause for any reasonable fear. That is because a) I am not Stalin, b) nor am I likely to ever be the head of any tyrannical party-state (in fact even my hair won't obey me), so c) all I've really done is vented hot air concerning a dislike of mine which d) I would clearly not in any position to carry out if I had meant it as a threat (see A and B above).
Getting freaked out by the tone someone uses to say something that's pretty innocuous is silly: if I in a loud snarling tone say "Alright you liberal pantywaists, come get your free factory-sealed cans of beer!" have I threatened anybody?
To quote myself, 'What matters here is that sanctions were brought to bear because of a misreading of what was said.' As you've no doubt figured out (I doubt even scarabic could miss it since flat out I've said so several times) what gets me going is when these threads point out things that people do offline as well which bear deleterious implications for civil liberties. If I say, for example, that "I don't think Muslim communal prayer should be outlawed" I have NOT committed a terrorist act nor have I even indicated my approval of any terrorism: I have merely expressed a not-completely-anti-Muslim opinion, which won't stop a lot of "patriots" from hollering about my alleged "hatred of Freedom". That way lies the worst kind of tyranny, the totally stupid kind.
My point here is that if we can teach people to read what is written as well as to hallucinate between the lines we will advance the cause of liberty, and if we can't train highly-educated folks like your average Mefite to do that or to even understand what we're talking about we might as well practice heiling hitler and work on our death-camp skills.
As far as having something nice to say, a lot of us spend a lot of time on the bench beside Ms. Parker. Whether we have any idea what we're yammering about or not. As others here have pointed out, that's just the way political threads go on Metafilter, or anywhere else, on the Net or off, for that matter. This is not the Ladies Sewing Circle: if that's what you want I suggest you get out your needles and thread and go find yourself some ladies. (You could also simply avoid political threads: I haven't seen anything but these go on for this long in ages.)
posted by davy at 12:28 PM on August 24, 2005
PP, lying to yourself isn't tolerated after age 3. I won't even bother addressing your point because it's quite clear to anybody who glances over your posting history that your modus operandi is to show up, shit in the thread, and disappear.
But, just to entertain the remote possibility that you do have an opinion, consider that the majority of users here see your actions as nothing but trolling. In light of this truth, perhaps--if you actually want to participate in the discussion--you should drop the "spice" and focus on making a cogent argument.
posted by nixerman at 12:35 PM on August 24, 2005
It's pretty rad that anyone can say all they want about FFF in this thread and he can't defend himself. What a cool, fun idea.
So here's a message from him:
The ironic part is that just a little while ago fff was yelling at anybody who responded to Paris for being big bait-taking dummies.
posted by PinkStainlessTail at 6:45 PM PST on August 23
ParisParamus has been voicing his sincere support and desire to see someone murdered. Several times over, in fact.
I suppose my mistake was to offer payment.
No biggie. Back whenever, or not. Ciao."
posted by Optimus Chyme at 1:00 PM on August 24, 2005
"I am not a troll."
(why is that like Nixon saying I’m not a crook?)
Va te faire foutre.
You’re a self-avowed troll (Oh, but let’s AGAIN carefully forget you stated explicitly you are here to distrupt this board) and a myopic unprincipled pogue
You see, like many here I believe in free speech. Don’t confuse your disruption with speech. However I don’t believe one has the right to silence another’s voice. I don’t believe in doing violence for money or over empty words. If I did I’d be in Park Slope standing behind you right now.
Mea mihi conscientia pluris est quam omnium sermo
That said, I understand FFF’s frustration. I myself wrote in another thread I would smash someone’s testicles flat out of frustration, but I did make it very explicit I meant no real threat. Perhaps FFF forgot that bit. Perhaps he was serious. I don’t know.
Ira furor brevis est
But I do believe you can’t throw down an challenge and not have it answered. PP does that and tries to play the victim. Dios, others, don’t. Fighting words are not always words.
For example: I take exception to gsb’s comment lumping me in “this leftist pit of sin.”
Well,
All Americans suck their mothers asses.
All military people are scumbags.
All ‘X’ists perform ‘x’ unnatural acts.
If someone looked at me and said something like that, I’d be pissed and I might lose my temper. Not just because I identify with them, but I’m there whether I like it or not.
If someone like gsb writes that, I figure they’re talking about THOSE Americans, or THOSE MeFi’ers.
That’s not what PP does.
Making someone angry can be as simple an act as picking your teeth or clicking a pen. If it goes on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on and on - as PP said for five years, well, someone might lose it.
And if you walk into the middle of that seeing only someone click a pen a few times after being told to stop scores of thousands of times, you might not see where that frustration is coming from and think the one lashing out is the one who is wrong.
Manipulating someone into that position is worse than someone who gives in to that anger and lashes out.
Gutta cavat lapidem, non vi sed saepe cadendo
Unlike any other “conservative” voice here - perhaps neocon is appropriate - PP does this. It’s his stated purpose for being here. You can’t challenge someone then run and hide behind mama’s skirt like this.
baisez votre mère
Pardon my French.
PP
349 MetaFilter users near this user:
Not one of them offered to take FFF up.
"By their works shall ye know them"
“I personally find that kind of thread valuable because it refreshes my memory as to who's worth listening to and who's a babbling asshole”
/Although I had babbling asshole after eating 4 bran muffins and a 4 shot espresso.
posted by Smedleyman at 1:26 PM on August 24, 2005
I am not a troll. I attempt to make points using humor given that I'm outnumbered in outlook, what, 100-2?
It's funny to insult people's intelligence, and to tell them to fuck off?
It remains pathetic that this is not understood by more people (it's the same blindness that go you John Kerry and Howard Dean, but...whatever).
Ah yes, and then there's the mandatory derisive comment, not just disagreeing with a viewpoint, but insulting the intelligence of the people who hold it.
You're a troll, and nothing more.
posted by mosch at 1:28 PM on August 24, 2005
The truth is that the same narrowmindedness and arrogance that dominates the Left causes people to feel obliged to call me a troll, or critique the number of links or annotations in my posts.
Yes, and now the entire Left is narrowminded and arrogant.
When will the administrators wake up and realize that ParisParamus is not a purveyor of an alternate opinion, he's a fucking troll.
posted by mosch at 1:30 PM on August 24, 2005
fff - there's a difference between wishing for another's death and specifically wishing for the death of another user.
You might have been making an ironical point, but it was still a threat.
posted by bshort at 1:45 PM on August 24, 2005
mosch, wow, you're great.
posted by ParisParamus at 1:51 PM on August 24, 2005
mosch, wow, you're great.
And you're a troll.
You got me to try out the mefi-killfile greasemonkey script, but it's sadly ineffective because all the angry replies are still visibile, often containing quoted material where you insult the whole of MeFi.
posted by mosch at 2:00 PM on August 24, 2005
If PP's goal is to convince people to listen to him, he's doing the worst possible job. So bad, in fact, that I've sometimes wondered if he's a Marxist with an extremely black sense of humor.
Witty: Yeah, yeah, conservatives are often abused. Conservatives (including you, my friend) often jump right in with the abuse as well. Or is that justified by virtue of being the underdog?
Dios: I've had conversations on this site where we disagree fundamentally but have been cordial. However, when you say something uninformed and biased, I have no problem calling bullshit.
I flag the bullshit trolling crap from leftists. But the sheer number means that I have no real desire to call them out publicly every time they say something stupid (though I will argue vociferously with them from time to time).
posted by klangklangston at 2:04 PM on August 24, 2005
I don't get what the big fuss is all about. All Paris ever seems to post is [killed comment]. What's the big deal?
posted by mullingitover at 2:05 PM on August 24, 2005
Matt, apparently in recognition that conservatives are in the distinct majority, has been consistantly bending over backwards to give them MORE leeway with offensive/trolling/personal/content-free opinions than the "lefties". That is having the unfortunate effect of bringing out MORE abuse from the liberal members, while doing nothing to encourage more reasonable conservatives to join the discussion.
FYI, the domain freefish.org is available (and can be reused the next time fishfucker or troutfishing gets in trouble here).
posted by wendell at 2:58 PM on August 24, 2005
If it were a democracy, I'd vote "parody." I don't think it warranted a ban or suspension, but it's not my site.
PP is a troll. I learned to ignore him years ago, but when there's an easy correction to make (as happens time after time after time after time), it's hard to resist.
However, he's not enough of a troll to warrant a ban or suspension (from what I've seen). He hides his trollness behind moderately relevant comments, which is actually the worst kind of troll, because there's no defense except ignoring him.
posted by mrgrimm at 3:11 PM on August 24, 2005
"He hides his trollness behind moderately relevant comments, which is actually the worst kind of troll, because there's no defense except ignoring him."
= wow. that's really clever. "Moderate relevant." I always thought I was post-Moderate.
posted by ParisParamus at 3:17 PM on August 24, 2005
20 GOTO 10
posted by Optimus Chyme at 3:46 PM on August 24, 2005
My point here is that if we can teach people to read what is written as well as to hallucinate between the lines we will advance the cause of liberty, and if we can't train highly-educated folks like your average Mefite to do that or to even understand what we're talking about we might as well practice heiling hitler and work on our death-camp skills.
This is, of course, completely hyperbolic. But you know that. I guess after all these words I am still struggling to make my own position clear. Never for a moment did I think that fff's post was serious. (I'll leave the JGN threat aside, since there's no way to really know its meaning.) I have no problem distinguishing between violent utterances as expressions of a sociopathically violent person and the merely rhetorical use of such expressions. I'm not auditioning for a job at a death camp, and I'm a paid up member of the ACLU. I fancy myself somewhat expert on the subject of the first amendment, in fact. It is deeply meaningful to me as a writer. To defend it, I'd enlist tomorrow.
But you wouldn't threaten violence, even in jest, in a board meeting, a parent/teacher conference, or a political debate, to name a few discourse events that are governed by standards of civility that do constrain "free speech" by convention and a mutual commitment to respectful dialogue. It might not be illegal. But it's still incivil and rude, and I would argue a lot ruder than what passes for "abuse" and "snark" around MeFi most of the time. Defending standards of discourse that are situationally appropriate and conventional community standards does not make you a Nazi. It lowers the tone of discourse to let it pass or overlook it. If a colleague expressed, even in jest, an interest in having another colleague beat up at a faculty meeting, for example, that might well be censurable conduct. At the least, it would damage the reputation of the speaker. Such remarks are destructive of community. It's that basic. On reflection, I think fff's time out is a little severe -- the post should certainly have been deleted, I think. But it's Matt's website, and his call, and sends a message that vitriol and ad hominem attacks can in fact go to far here. I think that's important. All of us with any experience online can cite many communities that have been ruined by anything-goes policies (or lack of policies). MeFi is a remarkable community. It has standards. Enforcing them is both Matt's perogative, and crucial to the maintenance of MeFi's quality, for all of us. The analogy to Nazis, as such analogies usually are, is reductio ad absurdum. I hear your point, but I think it's overstated, just as taking fff's post as a serious threat to do PP bodily harm would be an absurd reaction -- you're correct about that. It's still inappropriate and objectionable, at least to many of us. And that doesn't make those of us who are offended wimps to call it out.
posted by realcountrymusic at 4:27 PM on August 24, 2005
(french note) When trying to insult someone, you usually don't use the formal "vous", but would use "tu" as it implies familiarity. (/french note)
posted by blue_beetle at 4:28 PM on August 24, 2005
Is it really a threat when it's crystal clear that the person spoken of never dares show his face at the frequent meetups?
Yes. It's still "really" a threat. And I'm obviously not the only one still wondering what you meant by it.
It was a statement of intent
To do what, exactly? That's one of the issues, amberglow, that makes some of us hesitate to just let it go as another of the site's many heated outbursts (which often result in apologies). You've repeatedly neglected to clarify the nature of the threat, and left it unclear whether it still stands. Does it? And this, really, is just a fudge:
--but one that i knew would never come to pass, unfortunately.
You don't really know that. Regardless of your perception of Paris' future behavior, the violence inherent in your statement couldn't have been more clear, even if the vagueness comes across as a bit cowardly. We don't know if you mean to punch Paris, toss a glass of water in his face or just yell at him a lot if you ever see him IRL, but either way, the threat of some kind of violence shines through. It's very different from the kind of horrid bullshit Paris regularly pulls here, and surprising coming from someone who, er, regularly allies himself with the forces of peace and thoughtfulness.
posted by mediareport at 4:48 PM on August 24, 2005
It just occurs to me to wonder if any women MeFites are here. God. we men are predictable.
I think the invocation of violence, in jest or not, is specifically objectionable because in the male of the species, myself included, it sparks a reaction that exceeds words. If such a thing were said in face-to-face conversation, say in a bar, there's a good chance even words meant in jest could spill over into actual violence. I've wanted to kick the ass of more than one internet adversary over the years, and only anonymity and inconvenience have intervened in my instinctive reaction.
On the flip side, because we are disembodied here, it's so much easier to let such remarks slip, to act toward others in a way we would not act in face-to-face encounters even with someone truly awful unless very seriously provoked. And it's also easier to dismiss such remarks as "just words." Because in a sense, that's true, and truer than it would be offline for certain. So maybe we are just applying different contextual filters here. I try to apply the same ethics to online as I'd apply in offline encounters, as much as I love the specificities of the net as a context. Do some things "go" online that wouldn't be so cool offline? Empirical evidence suggests they do.
But MeFi is a different kind of online community, one in which many participants are not anonymous, members routinely meet up, many of us work in a few industries and probably know people in common. Some of us are close to each other in real life. We put our selves into this conversation in ways that expose our trust in the high level of self-policing and self-analysis that obtains here, the explicit "meta-" commitment to making the community itself, and its culture, objects of care, attention, and maintenance. At least that's my impression, as a member for only a few months, though a longer-time follower and admirer of the site.
What is that worth? This is hardly near the bigger challenges this community has endured, to judge from the archives, though I do think the Iraq war is a cancer on society that is setting people against each other in newly fierce ways as it becomes more intractable and ugly and obviously based on lies, and that we are enduring a long slow challenge to civil discourse in the US (at least, I know MeFi is international) of a very grave sort from our political culture. Two long conversations about threats, violence, assassination, and the limits of appropriate speech on MeFi and under the law in a row, following two threads in which political assassination was discussed like the latest cool Flash animation (I exaggerate) . . . this conversation matters.
I guess I am just saying, via the Clinton White House website, via the National Archives, and via Rodney King can't we all just get along? (irony alert on link)
I'm sure in real life each one of us could really kick some ass. We ought to have the next meetup in Sturges and prove it.
Here's a better idea.
posted by realcountrymusic at 5:07 PM on August 24, 2005
I really do think the world would be a better place if people were nicer to each other. Maybe after we line Those People up and shoot them we can try it sometime. But for now I'm afraid we'll have to stick to "Sing 'Kumbaya' with all us liberal nonconformists or get sent to Gitmo, you impolite scumbag!"
posted by davy at 7:22 PM on August 24, 2005
P.S. That was irony, parody (and self-parody), sarcasm and hyperbole. So to paraphrase Benny Goodman: take my life, please!
posted by davy at 7:26 PM on August 24, 2005
Benny Goodman? I think you mean Henny Youngman.
posted by Snyder at 7:32 PM on August 24, 2005
But RCN, the beach people get disappeared from is Aruba. But wait, that might only work for pretty blond girls; maybe you'd have better luck "losing" me from the 22nd Street Landing.
And by the way, Robertson says his remarks about Chavez were misinterpreted.
posted by davy at 7:32 PM on August 24, 2005
Jesus H. Christ, if I paid $500 to have everyone beaten up whom I think is a complete prick, I'd be in much debt. Have all other options of retribution been exhausted, like name-calling, trolling accusations, and insults involving the target's mother? and those are just the three obvious ones... posted by clevershark at 7:36 PM on August 24, 2005 That "take my wife" guy was Henny Youngman? [Google search] I'll be a durned flapdoodle, it was. I stand corrected. At least I knew it wasn't Charles Nelson Reilly. posted by davy at 7:39 PM on August 24, 2005 the beach people get disappeared from is Aruba. But wait, that might only work for pretty blond girls Actually, according to a real journalist who's a blogger, Aruba's safer than Jamaica, Puerto Rico, the Virgin Islands, etc. etc. (I regret not doing a FPP on this... but not much) FreeFish! posted by wendell at 8:55 PM on August 24, 2005 nixerman : "Also, dios and bugbread deliberately misuse the word 'bias,' as it applies to blogs, to somehow provide for some sort of conservative exception. Also bullshit." I neither deliberately used nor misused the word "bias". I explained what the term meant in the context of Ryvar's statement. My comment was neither an endorsement nor a rebuttal of Ryvar's statement. (Like if someone said "It's a goddamn shame that thing A happened" and someone else responded "You're saying that God has damned the fact that it happened!". I'm just saying "No, that's not what he meant. He used the word 'goddamn' as an expletive indicating emphasis, not a statement of holy damnation". That is neither in agreement or disagreement with whether it's actually a good or bad thing that thing A happened) davy : "we're not arguing here about whether it's right (or polite, or conducive to scholarly discourse) to speak to anybody in any particular way; we're discussing whether what fishy posted (apparently) at Paris was a threat to PP's well-being, or if it was meant to be taken as one, or if it sounds like any harm to PP might result from it." We're discussing both. Or, rather, some are discussing one, others are discussing the other, and yet others are discussing both. Personally, I don't think FFF was making a real, viable, worryable threat against PP. However, I support his timeout, on the grounds of politeness, etiquette, social mores, or whatever you would call it. FFF : "I suppose my mistake was to offer payment." I suspect FFF's annoyance is clouding his perception: the issue being brought up here is not the offering of payment, it's the direction of the threat at another member. Whether it's a real threat, parody, satire, irony, synechdochy, or soliloquy is another issue, but the problem is certainly not the offer of payment. And I think realcountrymusic is my new favorite MeFite posted by Bugbread at 9:15 PM on August 24, 2005 "It just occurs to me to wonder if any women MeFites are here. God. we men are predictable." posted by realcountrymusic at 5:07 PM PST on August 24 [!] Yes, rcm, there was one at 9:49 and 10:19 August 23rd. Twenty four hours later, it is easy to see that my suggestion to take a nice walk in the cool evening air was not accepted. Where were the other female mefites? Filing their nails? Ironing a blouse for work? Popping corn for the performance? Rolling their eyes thinking "Here they go again"? Yawning? posted by Cranberry at 9:21 PM on August 24, 2005 i've always thought expert trolling had one valuable and wonderful benefit ... it causes people to reveal things about themselves that they would never otherwise reveal ... like they'd joke about paying someone 500 bucks to beat another poster up ... or they'd stamp their feet in impotent and childish rage every time that poster dared to make a comment i don't agree with pp's politics ... not at all ... but i understand what he's doing and why he's doing it ... he's revealing that some of you don't really think as much as you emote ... and that a few of you can't even emote all that well he's doing us a service by showing us that there are those on the left who are potentially as much a danger to freedom and truth as the usual suspects on the right ... because of their willingness to be led into demonizing and imitation demogoguery he could be just this guy making snarky remarks that no one pays attention to ... if you'd only let him i find this whole tempest and the last one about him showing up at air america in an lgf t-shirt to be funny as hell posted by pyramid termite at 9:27 PM on August 24, 2005 Give it a break, all. It's a timeout. BFD. I guess I'm going to just sit back and enjoy the fact that I agree with Matt. Not sure what else to say. PP is neither troll nor truthspeaker. He's a caricature. And davy, I hate to break it to you but I have no opinion of you whatsoever. posted by scarabic at 10:23 PM on August 24, 2005 *rolls eyes* this is so Jr. high. *sigh* posted by edgeways at 11:10 PM on August 24, 2005 realcountrymusic is the new EB as far as comment length is concerned. I will pay$500 towards getting him an editor.
posted by longbaugh at 5:03 AM on August 25, 2005
I'm in for $20. Just kiddin', rcm; that was a great comment. posted by Optimus Chyme at 6:13 AM on August 25, 2005 Where were the other female mefites? Filing their nails? Ironing a blouse for work? Popping corn for the performance? Rolling their eyes thinking "Here they go again"? Yawning? They're probably too busy contributing worthwhile material to worthwhile threads. posted by Pollomacho at 7:12 AM on August 25, 2005 However, I support his timeout, on the grounds of politeness, etiquette, social mores, or whatever you would call it. So would you support the same for amberglow's threat? posted by languagehat at 8:16 AM on August 25, 2005 Pollomacho, you just earned yourself 1000 points for skilful use of flattering. Very slick. posted by funambulist at 8:41 AM on August 25, 2005 realcountrymusic is the new EB as far as comment length is concerned. I will pay$500 towards getting him an editor
Point taken. I considered the username "prolix" when I signed up for MeFi. And this topic compels me. I'm taking a time out myself for a few days to give y'all a break.
posted by realcountrymusic at 9:31 AM on August 25, 2005
ParisParamus: "I am not a troll. I attempt to make points using humor given that I'moutnumbered in outlook, what, 100-2?"
So if I'm the only white guy on the bus I need to yell racials slurs as loud as I can to balance things out?
posted by 31d1 at 9:43 AM on August 25, 2005
First Rule of Comedy: If nobody else thinks you're funny, you're not.
posted by quantumetric at 10:10 AM on August 25, 2005
Yes, rcm, there was one at 9:49 and 10:19 August 23rd. Twenty four hours later, it is easy to see that my suggestion to take a nice walk in the cool evening air was not accepted.
I rest my case. Often on MeFi it can be hard to guess the sex of the poster, and this can be interesting for the way it deforms the usual gender dynamics of informal conversation, but sometimes it is dead easy. On behalf of my male interlocutors, right, left, and otherwise, let me simply say that, predictably, you were right about that walk thing. Now I'm doing it, albeit on an airplane, so adieu.
posted by realcountrymusic at 10:39 AM on August 25, 2005
So if I'm the only white guy on the bus I need to yell racials slurs as loud as I can to balance things out?
Yes, actually. Do that. It would be a really good learning experience for you and would only cost you bus fare and insurance deductible.
The satisfied grin on the other riders faces as they bounce your face off the pavement - priceless.
posted by Pollomacho at 10:52 AM on August 25, 2005
Often on MeFi it can be hard to guess the sex of the poster, and this can be interesting for the way it deforms the usual gender dynamics of informal conversation, but sometimes it is dead easy.
No kidding. I am often mistakenly identified on MeFi, and I'm not exactly sure why..
posted by monju_bosatsu at 11:06 AM on August 25, 2005
You mean you're not a transsexual?
posted by Pollomacho at 11:45 AM on August 25, 2005
See what I mean?
posted by monju_bosatsu at 12:09 PM on August 25, 2005
Pollomacho: "Yes, actually. Do that. It would be a really good learning experience for you and would only cost you bus fare and insurance deductible.
The satisfied grin on the other riders faces as they bounce your face off the pavement - priceless.
"
Umm, ok. All i was trying to say is that what matters in a debate is ultimately ones ideas, not the level of representation. If you're the only one to make the case, then make the damn case, and if it's good enough then you might change peoples minds.
No ones shutting PP out of arguments here, and as far as power goes his boys are basically running things in this country, so i don't need to hear him say that because his views are underrepresented on a message board he has an obligation to troll harder.
(Believe it or not I was not advocating yelling racial slurs on a crowded bus!, but now that I'm here I will wonder aloud about why Mefi is so incredibly diverse in all things, except, for some reason, politics.)
posted by 31d1 at 12:20 PM on August 25, 2005
I know what you were saying, and I agreed with it, I still think it would be pretty hi-larious if you got on a bus and went buck wild.
posted by Pollomacho at 1:41 PM on August 25, 2005
languagehat : "So would you support the same for amberglow's threat?"
No, but only because it's far less clear whether the threat was physical or to talk someone to death. If amberglow's threat was more explicitly physical, hell yeah.
(And that's not meant to imply that the same should or shouldn't happen in response to amberglow's threat, it's just my personal opinion. It's a close enough call that if matt and the majority of folks decided the same should be done, I wouldn't find the conclusion particularly problematic)
posted by Bugbread at 9:31 PM on August 25, 2005
posted by If I Had An Anus at 9:09 PM on August 31, 2005
posted by gramschmidt at 10:15 AM on September 1, 2005
[not very animated gif]
posted by goodnewsfortheinsane at 4:17 PM on September 1, 2005
BTW guys, "/g/if" as in "get" or "/j/if" as in "jet"? Discuss.
posted by goodnewsfortheinsane at 4:19 PM on September 1, 2005
The important thing to remember is never, never run GIS for 'jif' with SafeSearch turned off.
Unless, of course, you have just been trolled by dios/god/stay-puft.
.|.
posted by If I Had An Anus at 7:15 PM on September 1, 2005
posted by If I Had An Anus at 7:57 PM on September 1, 2005
Oh, how nice! A little fire. Thanks IIHAA.
posted by Cranberry at 11:06 PM on September 1, 2005
posted by goodnewsfortheinsane at 4:09 AM on September 2, 2005
and (uni)corny
posted by If I Had An Anus at 5:06 AM on September 2, 2005
G as in "Get" or "jet"? Huh. I've been pronouncing it "Throat-Warbler Mangrove".
posted by gramschmidt at 9:36 AM on September 2, 2005
Sorry to take so long goodnews, while this ahem burning issue dominated you thinking. Although a PC user, I never ever thought "jiff" - as demonstrated above, jif is peanut butter.
GIF
(Graphics Interchange Format) A popular bitmapped graphics file format developed by CompuServe. Pronounced "giff" by Macintosh users and "jiff" by PC users, GIF supports 8-bit color (256 colors) and is widely used on the Web, because the files compress well. GIFs include a color table that includes the most representative 256 colors used. For example, a picture of the forest would include mostly greens. This method provides excellent realism in an 8-bit image.
posted by Cranberry at 1:11 AM on September 3, 2005
An all-inclusive Happy Birthday to longboat survivors with special application to raedyn and grapefruit moon.
posted by Cranberry at 12:55 PM on September 4, 2005
Happy Birthday veterans!
posted by goodnewsfortheinsane at 5:57 PM on September 4, 2005
The pronunciation of the image format mirrors the pronunciation of the peanut butter brand. More here: The GIF Pronunciation Page
posted by ryanrs at 3:48 AM on September 5, 2005
And congrats on the engagement Cranberry and gnfti! And on the initiation, ryan!
posted by If I Had An Anus at 5:12 AM on September 5, 2005
Disclaimer: no users were betrothed (or hazed) in the making of the preceding comment. I was just *makes quotey fingers* engaging in playful banter.
posted by If I Had An Anus at 5:19 AM on September 5, 2005
Hi folks.
posted by kenko at 8:33 AM on September 5, 2005
I am engaged? Why, that is wonderful news, er, make that good news. Gnfti, you are in the Netherlands, right? Near Amsterdam where all the excellent diamond cutters are, right? What a happy circumstance. Nothing too flashy please, no larger than four blue white carats, in a tasteful emerald cut.
Hi, kenko.
posted by Cranberry at 12:28 PM on September 5, 2005
Now,4 hours later when MetaFilter has resumed at least a temporary semblance of life, thanks for the shoutout IIHAA.
posted by Cranberry at 4:24 PM on September 5, 2005
*sniff*
I will forever shed a single ridiculous, animated gif tear for Harry Morgan. This particular, extremely touching and generous outwardly-directed shout is much appreciated, danO.
posted by gramschmidt at 9:37 PM on September 5, 2005
Did anyone show up claiming to not be orthogonality?
posted by gramschmidt at 9:42 PM on September 5, 2005
Those were superb shoutouts, danO. I got a real and true birthday shoutout. I'm so touched.
Meanwhile, I've been away for a week the mycomments page tells me. Actually it tells me "You have not commented on any items in the past 7 days... you need more MeFi in your life." And it's true, it's true. MeFi knows me so well.
Instead of sitting at my desk, writing to you all, I've been on strike for a week (and counting). grrr. But I'm trying to remember the positive parts. Like I'm losing my fishbelly whiteness - looks like I might get a tan. And between not being able to afford proper food and all that damn walking I might loose some weight. Not that either of these things is important to me, but shh, don't remind me of that, I need stuff to feel good about!
posted by raedyn at 2:28 PM on September 6, 2005
Should we send raedyn a cake CARE package?
posted by Cranberry at 3:11 PM on September 6, 2005
Meantime, raedyn, congratulate yourself for sacrificing in support of your principles while getting exercise and losing weight. Silver lining? Are you picketing and getting all that good walking? Hope you are wearing a hat and sunblock.
posted by Cranberry at 3:16 PM on September 6, 2005
I too appreciate the shoutout.
posted by kenko at 8:24 PM on September 6, 2005
Wow, I must have passed out on the lawn again. I can't remember anything about the party. What outrageous promises did I make to Cranberry this time? I was just trying to get some, you know. Yeah I know, spare me your men-are-pigs criticism, I'm just being honest.
(There *was* some heavy s-t-r-k-i-n-g going on, though.)
Thanks for the shout-out, Bereft of Orifice.
posted by goodnewsfortheinsane at 1:45 PM on September 7, 2005
Does this mean that I am Bereft of Four Carat Blue White from Amsterdam? Oink!
posted by Cranberry at 3:18 PM on September 7, 2005
*music swells*
*tear wells*
I'm sorry, berrybelly! Come here shrub, let's snuggle.
*snuggles with cran*
*plots bank robbery to finance four carat blue white*
posted by goodnewsfortheinsane at 4:33 PM on September 7, 2005
posted by If I Had An Anus at 7:35 PM on September 7, 2005
Hi, kenko. Did you meet any sharks out west? You went west didn't you? I have never been west.
I considered doing it myself, schmidtmeister G. But then orthogonality returned truimphant and we saw his 'O' face. And quonsar was there. And you, Uncle Miguel,... you were there too.
posted by If I Had An Anus at 8:13 PM on September 7, 2005
Dear John gnfti, I think IIHAA should rob the bank or do whatever is necessary to purchase a blue-white four carat for each of us. After all, the whole thing was his idea.
But we can always be friends.
posted by Cranberry at 12:47 AM on September 8, 2005
Uh oh.
posted by If I Had An Anus at 9:10 AM on September 8, 2005
I see what you mean IIHAA. We will be homeless on September 23 because 10127 is closed.
We have 15 days for top level conferences to decide how to negotiate an alternate site/date, or to find supermarket shopping carts for our possessions.
posted by Cranberry at 12:10 PM on September 8, 2005
Not only that: uh oh. However, these two seem like the kind of thread we could thrive in.
posted by goodnewsfortheinsane at 2:35 PM on September 8, 2005
Thriving in 10126 sounds 9622v2-ish since it is about being unable to post to closed threads. Somehow I got the impression that after hours posting is possible, if not exactly welcome.
There may be even better candidates before the 9-23 deadline. No need to panic yet.
posted by Cranberry at 4:00 PM on September 8, 2005
posted by If I Had An Anus at 7:39 PM on September 8, 2005
Are we supposed to move to Area 51 and get picked up by space ships? Isn't that a bit extreme? Longboat to space ship with in a few weeks of time? Are we sufficiently evolved?
posted by Cranberry at 8:06 PM on September 8, 2005
Are we sufficiently evolved?
Not me, certainly.
posted by If I Had An Anus at 6:52 PM on September 9, 2005
Hey! Wait a gosh-tootin' minute...I'm supposed to hold up a bank becuase you two can't express your feelings for each other without exchanging rocks?
Well, OK, but only because I love you guys.
posted by If I Had An Anus at 7:02 PM on September 9, 2005
ill-timed joke about hating you all.
posted by Jamie Farr at 8:28 PM on September 9, 2005
Btw, there is but One GIS result for gosh-tootin. He is really Gosh? What's making him toot? Why does he taunt America?
posted by If I Had An Anus at 8:39 PM on September 9, 2005
we all love your dress, klinger
posted by Cranberry at 10:55 PM on September 9, 2005
I feel I've become hopelessly out of the loop. Stupid strike.
Feel free to ignore the bitter woman in the corner (me).
On the plus side I'm walking 10 miles per day. My feel are taking a beating, but othr than that it's probably good for me.
posted by raedyn at 9:51 AM on September 10, 2005
Also on the plus side, today I don't have to picket. I've decided not to wear pants today in honour of the occasion.
posted by raedyn at 9:53 AM on September 10, 2005
raedyn! On your day off from picketing, you deserve to be comfortable.Are you with the same company as before eggbert was born?
posted by Cranberry at 11:15 AM on September 10, 2005
Whoah!
Also whoah. 9000thrds ago
posted by If I Had An Anus at 8:06 PM on September 10, 2005
Congrats on the nakedness.
posted by If I Had An Anus at 8:07 PM on September 10, 2005
Are you with the same company as before eggbert was born? - Cranberry
No. I took my year of maternity leave (thank you Canada) then went back there for 8 months. Now I've been working in the civil service for a year.
Thanks for reminding me of that blog, BTW. I haven't looked at it for at least a year, maybe more. It's interesting to go back and read it now. Particularly since I spent this afternoon at a baby shower for a girlfriend that is expecting her first child, so I was already thinking a lot about pregnancy and birth and that whole experience.
posted by raedyn at 5:38 PM on September 11, 2005
posted by Cranberry at 8:33 PM on September 11, 2005
posted by Cranberry at 8:33 PM on September 11, 2005
Hi again. I just scheduled me some cable internet! Hoo boy! Come the 17th I will be rocking the online world again, and not from a library neither!
posted by kenko at 12:33 PM on September 12, 2005
Look out world, here comes kenko.
posted by Cranberry at 11:55 PM on September 12, 2005
If this kenko is rockin', don't come knockin'.
posted by If I Had An Anus at 6:19 AM on September 13, 2005
Congratumalations, kenko.
kenko's getting high-speed, raedyn's on strike, Cranberry and gnfti are enjoying their post-honeymoon annulment, IIHAA shivved the CFO of Wild Oats, Inc. on live TV, and Jamie Farr can be accused and found wholly guilty only of keeping it real.
I, on the other hand, have just moved, and now nothing is true.
However,
posted by gramschmidt at 10:48 AM on September 13, 2005
"Bilgi" means "information" or "knowledge", and I suspect "Matematik Oyunlari" means "Maths for Kids".
Other books in the series include "Anam Orospu Olma" and "Ibneler: Cok Guzel".
I sure hope no Turks are reading this.
posted by goodnewsfortheinsane at 2:22 PM on September 13, 2005
That was a brain fart. It means "Math Games". I stand by the rest of my statement, however.
posted by goodnewsfortheinsane at 2:27 PM on September 13, 2005
Is it time for a house warming yet, gram? *prepares party hats*
posted by raedyn at 3:41 PM on September 14, 2005
posted by If I Had An Anus at 8:38 PM on September 14, 2005
posted by If I Had An Anus at 8:48 PM on September 14, 2005
Does Eğlenceli Bİlgi mean Ethereal Bligh in Turkish?
posted by If I Had An Anus at 8:52 PM on September 14, 2005
If that meteor hit gram's new abode, the party will be at kenko's - unless the meteor hit the bay area.
I just hope getting there is overland this time.
posted by Cranberry at 9:07 PM on September 14, 2005
Damn, it did hit gram's house!
posted by If I Had An Anus at 1:35 PM on September 15, 2005
Gram lives lived in the big tag?
posted by Cranberry at 4:54 PM on September 15, 2005
posted by goodnewsfortheinsane at 11:10 AM on September 16, 2005
Please tell me we still have at least unidirectional text sizing.
posted by gramschmidt at 12:52 PM on September 16, 2005
Hey everyone, DuffStone is throwing a piccie party. Bring your surviving tags and a side dish.
posted by If I Had An Anus at 1:07 PM on September 16, 2005
My, what long fingers you have, gnfti.
posted by If I Had An Anus at 1:08 PM on September 16, 2005
Matt is thus enforcing modesty over ostentation. Some of us, however, refuse.
posted by gramschmidt at 1:11 PM on September 16, 2005
Geez, how many trips to the dentist has that guy had to endure? I count at least two cavities and some bridge work.
posted by If I Had An Anus at 8:44 PM on September 16, 2005
posted by If I Had An Anus at 9:21 PM on September 16, 2005
posted by gramschmidt at 12:18 PM on September 17, 2005
Finally! Internet! In my vaginahome!
I hate the way comcast refuses to tell you unless you REALLY PRESS that you don't actually need to run their rinky-dink CD in order to register your modem. Why, oh why, can't they also send instructions for setting proxy servers and doing it over teh webs for those so inclined? Where "inclined" might mean "forced to do so owing to running Linux". This wouldn't even mean officially supporting Linux, since, one, that's really a modem thing anyway, and two, it would just be a way of saying "here, you can do it this way if you've got the courage to do so. By the way, don't ask for tech support if you do it this way."
Christ!
posted by kenko at 1:54 PM on September 17, 2005
Some important questions:
-If he spent so much time among the Smurfs, how come Gargamel never found out the location of the Smurf village?
-If he hated the Smurfs so much, why did he want to eat them?
posted by goodnewsfortheinsane at 5:51 AM on September 18, 2005
Don't you want to eat the people you hate?
posted by kenko at 4:25 PM on September 18, 2005
Yes. But I don't know where they live.
posted by goodnewsfortheinsane at 7:55 AM on September 19, 2005
Neither did Gargamel. What's the problem?
posted by kenko at 10:11 AM on September 19, 2005
I believe our ears are burning. Or at least smoking, or they've been doused with lighter fluid, and someone's working the bellows, but they're not quite ready for Joan of Arc yet.
posted by gramschmidt at 11:13 AM on September 19, 2005
Oh, caddis, not to worry! This is a moveable feast!
Is it possible that caddis thinks "progressive party" is only a political term?
Longboat survivors know that the term also applies to a party with serial hosts: cocktails at one home, salads at another, main dish at yet another, etc.
If dessert is to be fruit and nuts, perhaps kenko would host that portion since he seems to have moved to the land of.
posted by Cranberry at 12:33 PM on September 19, 2005
« Backwards stroke | longboat Forwards??? »
posted by If I Had An Anus at 12:47 PM on September 19, 2005
OMG this party has been going on all summer.
Lots of good stuff, but I still like the roasting marshmallows.
posted by caddis at 3:23 PM on September 19, 2005
From online Dictionary:
n. A coarse woolen fabric, yarn, or ribbon binding.
It's a fishing thing.
caddis, please explain how a coarse woolen fabric is a fishing thing. Unless it involves blood or explosives. As you can see, this page has plenty of those. And marshmallows.
posted by Cranberry at 3:49 PM on September 19, 2005
posted by caddis at 4:18 PM on September 19, 2005
Bookburing is so wrong.
posted by caddis at 4:19 PM on September 19, 2005
I'm not so sure about IHAA's suggested new hangout. Kids over there are strange.
posted by goodnewsfortheinsane at 5:38 PM on September 19, 2005
Quick! Which Roman emperor feasted in the manner Cranberry described?
posted by kenko at 5:55 PM on September 19, 2005
Although I am, of course, extremely excited about the prospect of life in Smurfdom, I instead humbly propose a temporary 9622v2 Extension Anomaly.
Let 9622v2 be defined as
http://metatalk.metafilter.com/mefi/{9622 + 101n}
where n ∈ Ζ* .
We should, as discussed, obviously next move to 10127, which is closed. As is 10128. And 10126 is a step backward chronologically, if not morally.
Compounding our struggle is the fact that 10228 doesn't yet exist.
Thus, in order to form a more perfect longboat, and to ensure the blessings of 9622v2 to ourselves and our posterity (latent Americocentrism notwithstanding), I propose we temporarily discard our theoretical framework and inhabit 10129. It seems hospitable and accommodating, despite the big tag having been wrested from our arsenal.
In the event that we do, in fact, get 29 more MeTa threads in the next four days, my proposal will be rendered superfluous, and we shall proceed to 10228.
Also, the regular procession to 10228 (once it exists) shall be contingent upon the accessibility of the thread and its own procession off the front page and into our hearts.
posted by gramschmidt at 6:41 PM on September 19, 2005
I vote in favor of gramschidt's proposal. Henceforth, let $\textrm{9622v2} \equiv \left\{ \begin{array}{ll} \textrm{http://metatalk.metafilter.com/mefi/9622}+101n & n \elem \boldmath{Z}* - \{5\} \\ \textrm{http://metalk.metafilter.com/mefi/10129} & n = 5\end{array}$. I think we can all agree to that!
posted by kenko at 9:06 PM on September 19, 2005
caddis-fly n : small moth-like insect having two pairs of hairy membranous wings and aquatic larvae
Why, thank you caddis for promptly enlightening me on this burning book issue. Are you one of the authors?
Never mind! I do not want to start another thread about "outing" mefites rl identity!
Love that little campfire. Can we have s'mores on the journey to 10129? I'll bring graham crackers.
posted by Cranberry at 9:43 PM on September 19, 2005
here we go
posted by kenko at 10:08 PM on September 19, 2005
golly! kenko posted an invalid parameter. Now I am worried. Kenko, are you not a valid integer?
posted by Cranberry at 10:37 PM on September 19, 2005
btw kenko
Quick! Which Roman emperor feasted in the manner Cranberry described?
I give up. Which? and the answer better not be bloody or explosive.
posted by Cranberry at 10:54 PM on September 19, 2005
I can't remember!
posted by kenko at 11:36 PM on September 19, 2005
He's mentioned in the Larousse Gastronomique, though, so if anyone wants to just read it straight through and find it, go ahead.
posted by kenko at 11:36 PM on September 19, 2005
posted by gramschmidt at 8:43 AM on September 20, 2005
No it wasn't.
(You thought I wouldn't check?)
posted by kenko at 10:56 AM on September 20, 2005
Bookburing is so wrong.
Indeed it is.
posted by If I Had An Anus at 8:40 PM on September 20, 2005
Or vice versa?
posted by If I Had An Anus at 8:40 PM on September 20, 2005
gnifty, that is a wonderful, wonderful thread concerning the status of the blue in the age of gargamel, but--well you know--they're doing that math thing again, and its portents are skewing rapidly towards Bookburing 10129.
Maybe we can ask Matt to implement UBB-code here. It'll be almost the same.
posted by If I Had An Anus at 8:48 PM on September 20, 2005
posted by If I Had An Anus at 9:09 PM on September 20, 2005
I do hope raedyn gets off strike before we load up the hippy bus for the legendary bay area. Maybe we can leave her a sandwich with an arrow pointing the way.
posted by If I Had An Anus at 9:20 PM on September 20, 2005
That picnic certainly isn't a MeFi meet! Where is the preponderance of males?
And no campfire, so no s'mores.
Raedyn can do the Hansel and Gretel thing with marshmallows instead of bread crumbs. They will guide her and sustain her on the extra long trek past 10127.
posted by Cranberry at 10:43 PM on September 20, 2005
It's the birthday of the man who first put high quality literature into paperbacks, Sir Allen Lane, born in Bristol, England (1902), the founder of Penguin Books.
Yoo hoo! Over here Sir Allen. Just look at all the high quality writing on this page.
posted by Cranberry at 12:03 AM on September 21, 2005
Hi grapefruitmoon.
posted by If I Had An Anus at 7:47 AM on September 22, 2005
stroke |Forwards??? Forwards »
posted by If I Had An Anus at 7:52 AM on September 22, 2005
Heavens, the front page has been on fire lately.
Additionally, moift was responsible for my untimely demise, in a coffee shop no less. I suppose I'll have to find another place to study where I'm not known as the snickering lunatic on the floor.
posted by gramschmidt at 10:38 AM on September 22, 2005
posted by kenko at 10:52 AM on September 22, 2005
Sir Allen's dead? Rats. I baked him a cake and was just lighting the 103rd candle.
posted by Cranberry at 12:06 PM on September 22, 2005
I killed him.
posted by kenko at 8:26 PM on September 22, 2005
He was delicious.
posted by kenko at 8:26 PM on September 22, 2005
Did he taste like chicken penguin?
posted by Cranberry at 11:55 PM on September 22, 2005
posted by Cranberry at 12:01 AM on September 23, 2005
I call potatoes
posted by If I Had An Anus at 6:01 AM on September 23, 2005
posted by Cranberry at 1:16 PM on September 23, 2005
I'll see you there. Thanks for the sandwich. Walking makes me hungry.
posted by raedyn at 3:59 PM on September 23, 2005
We've got about 90 minutes left, I think.
posted by kenko at 4:42 PM on September 23, 2005
posted by If I Had An Anus at 5:34 PM on September 23, 2005
Interesting.
posted by goodnewsfortheinsane at 6:13 PM on September 23, 2005
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https://www.gamedev.net/forums/topic/122169-trouble-with-classes-includes-/
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#### Archived
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# Trouble with classes includes !
This topic is 5594 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
Hello, I'm quite experienced with game programming, but my problem is a newbie one... I have troubles with includes. I have various classes for like : - CCast - CMember - CScene - CSprite - CScript CCast : Library of medias Does not have inheritance, but have CMember** (list of childs) type inside it. CMember : Any media Does not have inheritance, but have CCast* (parent) type inside it. CScene : Scene with objects Does not have inheritance, but have CSprite** (list of childs) type inside it CSprite : Instance of bitmap member Inherits from CScript (because it is also a script) and have CMember* (media reference) type inside it. CScript : Linked nodes of execution Does not have inheritance, but have CScript** (list of childs) and CScript* (parent) type inside it. To declare safely, I define my classes before use in a file named "Classes.h" like this : class CCast; class CMember; class CScene; class CSprite; class CScript; Then it is followed by includes of their header containing all the complete class declaration like this : #include "CCast.h" #include "CMember.h" #include "CScene.h" #include "CSprite.h" #include "CScript.h" In each header I have the complete class declaration. The problem is with "CSprite" when I do inheritance like this class CSprite : public CScript { public: CScript(); ~CScript(); Render(); public: CMember *m_pMember; POINT m_ptPosition; FLOAT m_fRotation; POINT m_ptSize; INT m_intZ; DWORD m_dwColoration; }; The compiler gives me an error in the declaration of the class "class CSprite : public CScript" telling me that it has not been declared ! but it is, no ? Also, the compiler does not give me an error for my "CMember *m_pMember" class member ! it is I, or there is a lack of logic here... thanks in advance
/* Bullmax */ ------------- Reality has many forms : good and evil, black and white, ying and yang. [edited by - Bullmax on November 1, 2002 9:38:30 PM]
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which did you make first: CSprite or Cscript?
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To inherit from a class, the complete declaration of that class has to be "visible" (or whatever the technical term should be).
Thus, the following code will fail:
class MyParentClass;class MyChildClass : public MyParentClass{private: int someData;public: void someFunction();};
The reason this code fails is because MyChildClass is inheriting from the incomplete type MyParentClass. The following code corrects this:
class MyParentClass{public: void someParentFunction();};class MyChildClass : public MyParentClass{private: int someData;public: void someFunction();};
This works because MyParentClass is now complete.
As com alluded to, in your example the declaration of CScript (the parent class) is included after the declaration of CSprite (the child class). These includes must be reversed, so that:
#include "CCast.h"#include "CMember.h"#include "CScene.h"#include "CSprite.h"#include "CScript.h"
becomes:
#include "CCast.h"#include "CMember.h"#include "CScene.h"#include "CScript.h"#include "CSprite.h"
The reason that "CMember *m_pMember;" does not give an error is that the compiler knows that no matter what exactly a CMember is, a pointer to a CMember will always be a four byte entity. So when declaring pointers to classes, an incomplete forward declaration such as "class CMember;" is enough. If the variable you were declaring was not a pointer, however, the compiler would have complained about it. Thus, the following code would give an error:
class MyClass;class MyClassUser{private: MyClass* m_pMyClass; // this line is OK -- pointer so no error MyClass m_MyClass; // this line gives an error};
Sorry that was so long...hopefully it makes sense. If you have any other questions, just ask.
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https://slideplayer.com/slide/1507253/
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# A graph of the instantaneous velocity of an object over a specified period of time Time is independent (x-axis) Velocity is dependent (y-axis) Remember,
## Presentation on theme: "A graph of the instantaneous velocity of an object over a specified period of time Time is independent (x-axis) Velocity is dependent (y-axis) Remember,"— Presentation transcript:
A graph of the instantaneous velocity of an object over a specified period of time Time is independent (x-axis) Velocity is dependent (y-axis) Remember, velocity details magnitude (how fast) and direction (which way)
Units for the slope of time vs. velocity graph (m/s)/s m/s 2 Slope of t vs. v graph tells instantaneous acceleration Straight lines on t vs. v graph = uniform (constant) acceleration
Slope of t vs. v graph = acceleration
Area Under t vs. v graph = displacement 16 m/s 4 s A = 32 m
Instantaneous Velocity Velocity of an object at a specific moment Average Velocity Avg velocity of an object over time Instantaneous Acceleration How much objects velocity is changing at a specific moment Displacement Change in position of an object over time
Download ppt "A graph of the instantaneous velocity of an object over a specified period of time Time is independent (x-axis) Velocity is dependent (y-axis) Remember,"
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https://www.atlantis-press.com/proceedings/ifsa-eusflat-15/23637
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# A distributed learning algorithm for Self-Organizing Maps intended for outlier analysis in the GAIA – ESA mission
Authors
Daniel Garabato, Carlos Dafonte, Minia Manteiga, Diego Fustes, Marco A. Álvarez, Bernardino Arcay
Corresponding Author
Daniel Garabato
Available Online June 2015.
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.126How to use a DOI?
Keywords
Gaia mission, self-organizing maps, distributed computing, Hadoop.
Abstract
Since its launch in December 2013, the Gaia space mission has collected and continues to collect tremendous amounts of information concerning the objects that populate our Galaxy and beyond. The international Gaia Data and Analysis Consortium (DPAC) is in charge of developing computer algorithms that extract and process astrophysical information from these objects. It organizes its work by means of work packages; one of these packages, Outlier Analysis, is ded0icated to the exploration of vast amounts of outlier objects detected during the main classification of the observations. We present a method that is based on Self-Organizing Maps (SOM) and parallelized by means of the Hadoop framework so as to improve its performance. We also compare the execution times of both the sequential and the distributed versions of the algorithm.
Open Access
TY - CONF
AU - Daniel Garabato
AU - Carlos Dafonte
AU - Minia Manteiga
AU - Diego Fustes
AU - Marco A. Álvarez
AU - Bernardino Arcay
PY - 2015/06
DA - 2015/06
TI - A distributed learning algorithm for Self-Organizing Maps intended for outlier analysis in the GAIA – ESA mission
BT - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
PB - Atlantis Press
SP - 895
EP - 901
SN - 1951-6851
UR - https://doi.org/10.2991/ifsa-eusflat-15.2015.126
DO - https://doi.org/10.2991/ifsa-eusflat-15.2015.126
ID - Garabato2015/06
ER -
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http://math.stackexchange.com/users/9843/manuel
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# Manuel
less info
reputation
29
bio website location age member for 3 years, 8 months seen Nov 1 at 1:32 profile views 135
# 29 Questions
8 embedding of $\mathbb{RP}^2$ in $\mathbb{R}^4$ 7 normal bundle of level set 6 Obstruction cocycle of Stiefel manifold 6 1-form with positive integral over a path 6 Stokes for integration along the fiber
# 582 Reputation
+10 exact differential n-forms +5 Shape operator and principal curvature +5 Fiber bundle M x M - diagonal +5 Stokes for integration along the fiber
2 Undergraduate Research Problems 1 Elementary symmetric polynomials and matrices of 1-forms 0 Introduction to topological manifolds? 0 $k[x]$-module and cyclic module over a finite dimensional vector space
# 28 Tags
2 general-topology × 3 0 algebraic-topology × 12 2 open-problem 0 differential-geometry × 11 1 differential-forms × 6 0 differential-topology × 8 1 linear-algebra × 4 0 fiber-bundles × 6 1 multilinear-algebra × 2 0 multivariable-calculus × 3
# 2 Accounts
Mathematics 582 rep 29 MathOverflow 505 rep 214
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http://tex.stackexchange.com/users/17670/user-17670?tab=activity&sort=all&page=4
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User 17670
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1,376
Next privilege 2,000 Rep.
Apr 22 comment How to switch to upright greek in math mode? @Aydin They're both the same Apr 21 comment How to make the math font slightly thicker? Nice question! I'd like to know if there is a way to locally make certain math characters slightly thinner. For example, the letter $\Psi$ looks almost bold by default and so stands out on a page; it's kinda ugly. Apr 21 accepted How may I insert white vertical space between subequations? Apr 21 asked How may I insert white vertical space between subequations? Apr 21 accepted How can I box multiple aligned equations? Apr 21 comment How can I box multiple aligned equations? Thanks, how would I go about adjusting the vertical margins? Apr 21 comment How can I box multiple aligned equations? @cmhughes Yes, I checked previous related questions and didn't find what I am looking to achieve. Apr 21 asked How can I box multiple aligned equations? Apr 21 comment Attractive Boxed Equations DavidHammen Wrong; a load of physics and mathematics textbooks use boxes (regardless of the level). @TH- Who says it's for publication? Apr 20 comment Why does spell check not work if the figure has a label? @MarcoDaniel Any reason that should happen (is it bad LaTeX syntax?) or is this a bug? Apr 19 comment Move-around box in PDF display @AlexG To clarify: The command \tooltip{formula} produces the word "formula" in the PDF, in red, and as a clickable object. But, say I'm referring to an equation that was introduced 3 section ago, whose \label is "GoodEq" and whose number in the PDF is "(3.12)" I'd like to write, "using \eqref{GoodEq} we see that..." to give a PDF output of "using (3.12) we see that...", where the "(3.12)" part is clickable. This would be very useful and very cool. Apr 19 comment Move-around box in PDF display @AlexG Mother of God! img.mu.cdn.li/Ao/xqefEH.jpg Excellent work! Questions: Could it be made so that (in your MWE) "formula" could be replaced by \eqref{}, if you know what I mean? Also, does the end-user require anything other than a PDF viewer? Apr 19 comment Why does spell check not work if the figure has a label? @MarcoDaniel That actually fixes the problem, for whatever reason. Apr 19 asked Why does spell check not work if the figure has a label? Apr 18 comment LyX participates in the Google Summer of Code - which project ideas could be suggested? @Bugbusters In the case of a pspicture, sure, it would (I presume) need the whole environment recompiling. Like Daniel said though, the chance of that taking 'too long' is small. Apr 18 comment LyX participates in the Google Summer of Code - which project ideas could be suggested? @Bugbusters It's already been used in physics.SE and maths.SE with mathjax and it works really well. Compiling a total ball-ache. Also, would you really need to recompile everything? Apr 18 comment How can I nicely align a single split equation? +1 Nice. Visually, it's exactly what I was after (see my answer). Apr 18 answered How can I nicely align a single split equation? Apr 18 comment How can I nicely align a single split equation? +1 Thanks for the suggestions! The idea of a subexpression never occurred to me, I got too focused on the LaTeX. It's a bit awkward to introduce at this point in the document however, so I've opted for a modified version of Gonzalo's answer. I'll add it in a minute. Apr 18 accepted How can I nicely align a single split equation?
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https://philpapers.org/s/Guy%20Hindley
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## Results for 'Guy Hindley'
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1. Summary Background Self-binding directives instruct clinicians to overrule treatment refusal during future severe episodes of illness. These directives are promoted as having potential to increase autonomy for individuals with severe episodic mental illness. Although lived experience is central to their creation, service users’ views on self-binding directives have not been investigated substantially. This study aimed to explore whether reasons for endorsement, ambivalence, or rejection given by service users with bipolar disorder can address concerns regarding self-binding directives, decision-making capacity, and human (...)
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2. Homenaje a Alain Guy.Romero Baró, José Ma & Alain Guy (eds.) - 2005 - Publicacions I Edicions de la Universitat de Barcelona.
El filósofo francés Alain Guy (La Rochelle, 1918 - Narbonne, 1998) dedicó por entero su vida al estudio de la filosofía española e hispanoamericana, dándola a conocer no sólo en el extranjero sino también en nuestro país.
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3. Guy Axtell.Guy Axtell - 1994 - Social Epistemology 8:69.
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4. Nature and Necessity: Guy Robinson.Guy Robinson - 1975 - Royal Institute of Philosophy Supplement 9:200-215.
Determinism is a spectre that has haunted our scientifically-oriented culture from the beginning. I happen to think that it is literally a ‘spectre’, a trick of the vision, an appearance with an internal cause only, and that it is no more than the ghost of our own conceptual determinations projected outward into a world in which it has no place and no proper being. From one point of view it is no more than an alienated fantasy involving a number of (...)
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5. Negation: Bradley and Wittgenstein: Guy Stock.Guy Stock - 1985 - Philosophy 60 (234):465-476.
There are two main claims that Bradley makes concerning negative judgment in the Principles of Logic : Negative judgment ‘stands at a different level of reflection’ from affirmative judgment. Negative judgment ‘presupposes a positive ground’. I will consider what Bradley means by these claims, and draw comparisons with Wittgenstein's views on negation as they developed between the Tractatus and the Philosophical Remarks.
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6. The Routledge Handbook of Philosophy of Well-Being.Guy Fletcher (ed.) - 2015 - Routledge.
The concept of well-being is one of the oldest and most important topics in philosophy and ethics, going back to ancient Greek philosophy and Aristotle. Following the boom in happiness studies in the last few years it has moved to centre stage, grabbing media headlines and the attention of scientists, psychologists and economists. Yet little is actually known about well-being and it is an idea often poorly articulated. The Routledge Handbook of Philosophy of Well-Being provides a comprehensive, outstanding guide and (...)
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7. The Society of the Spectacle.Guy Debord - 1994 - Zone Books.
Analyzes the relationship of power, bureaucracy, and change in modern society.
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8. Philosophers and social scientists will welcome this highly original discussion of Max Weber's analysis of the objectivity of social science. Guy Oakes traces the vital connection between Weber's methodology and the work of philosopher Heinrich Rickert, reconstructing Rickert's notoriously difficult concepts in order to isolate the important, and until now poorly understood, roots of problems in Weber's own work.Guy Oakes teaches social philosophy at Monmouth College and sociology at the New School for Social Research.
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9. BCK and BCI Logics, Condensed Detachment and the $2$-Property. [REVIEW]J. Roger Hindley - 1993 - Notre Dame Journal of Formal Logic 34 (2):231-250.
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10. Wittgenstein on Russell's Theory of Judgment: Guy Stock.Guy Stock - 1973 - Royal Institute of Philosophy Supplement 7:62-75.
In the early years of this century the debate as to the nature of judgment was a central issue dividing British philosophers. What a philosopher said about judgment was not independent of what he said about perception, the distinction between the a priori and empirical, the distinction between external and internal relations, the nature of inference, truth, universals, language, the reality of the self and so on.
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11. The Philosophy of Well-Being: An Introduction.Guy Fletcher - 2016 - Routledge.
Well-being occupies a central role in ethics and political philosophy, including in major theories such as utilitarianism. It also extends far beyond philosophy: recent studies into the science and psychology of well-being have propelled the topic to centre stage, and governments spend millions on promoting it. We are encouraged to adopt modes of thinking and behaviour that support individual well-being or 'wellness'. What is well-being? Which theories of well-being are most plausible? In this rigorous and comprehensive introduction to the topic, (...)
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12. Having It Both Ways: Hybrid Theories and Modern Metaethics.Guy Fletcher & Michael R. Ridge (eds.) - 2014 - Oxford University Press.
In twelve new essays, contributors explore hybrid theories in metaethics and other normative domains.
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13. Intentional Communication in the Chimpanzee: The Development of Deception.Guy Woodruff & David Premack - 1979 - Cognition 7 (4):333-362.
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14. Problems of Religious Luck: Assessing the Limits of Reasonable Religious Disagreement.Guy Axtell - 2019 - Lanham, MD, USA & London, UK: Lexington Books/Rowman & Littlefield.
To speak of being religious lucky certainly sounds odd. But then, so does “My faith holds value in God’s plan, while yours does not.” This book argues that these two concerns — with the concept of religious luck and with asymmetric or sharply differential ascriptions of religious value — are inextricably connected. It argues that religious luck attributions can profitably be studied from a number of directions, not just theological, but also social scientific and philosophical. There is a strong tendency (...)
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15. History And Persons.Guy Kahane - 2019 - Philosophy and Phenomenological Research 99 (1):162-187.
The non-identity problem is usually considered in the forward-looking direction but a version of it also applies to the past, due to the fact that even minor historical changes would have affected the whole subsequent sequence of births, dramatically changing who comes to exist next. This simple point is routinely overlooked by familiar attitudes and evaluative judgments about the past, even those of sophisticated historians. I shall argue, however, that it means that when we feel sadness about some historical tragedy, (...)
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16. Dear Prudence: The Nature and Normativity of Prudential Discourse.Guy Fletcher - 2021 - Oxford, UK: Oxford University Press.
Philosophers have long theorized about what makes people's lives go well, and why, and the extent to which morality and self-interest can be reconciled. However, we have spent little time on meta-prudential questions, questions about prudential discourse—thought and talk about what is good and bad for us; what contributes to well-being; and what we have prudential reason, or prudentially ought, to do. This situation is surprising given that prudence is, prima facie, a normative form of discourse and cries out for (...)
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17. A Fresh Start for the Objective-List Theory of Well-Being.Guy Fletcher - 2013 - Utilitas 25 (2):206-220.
So-called theories of well-being (prudential value, welfare) are under-represented in discussions of well-being. I do four things in this article to redress this. First, I develop a new taxonomy of theories of well-being, one that divides theories in a more subtle and illuminating way. Second, I use this taxonomy to undermine some misconceptions that have made people reluctant to hold objective-list theories. Third, I provide a new objective-list theory and show that it captures a powerful motivation for the main competitor (...)
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18. Knowledge, Belief, and Character: Readings in Virtue Epistemology.Guy Axtell (ed.) - 2000 - Rowman & Littlefield Publishers.
This is a unique collection of new and recently-published articles which debate the merits of virtue-theoretic approaches to the core epistemological issues of knowledge and justified belief. The readings all contribute to our understanding of the relative importance, for a theory of justified belief, of the reliability of our cognitive faculties and of the individuals responsibility in gathering and weighing evidence. Highlights of the readings include direct exchanges between leading exponents of this approach and their critics.
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20. Evolutionary Debunking Arguments.Guy Kahane - 2011 - Noûs 45 (1):103-125.
Evolutionary debunking arguments are arguments that appeal to the evolutionary origins of evaluative beliefs to undermine their justification. This paper aims to clarify the premises and presuppositions of EDAs—a form of argument that is increasingly put to use in normative ethics. I argue that such arguments face serious obstacles. It is often overlooked, for example, that they presuppose the truth of metaethical objectivism. More importantly, even if objectivism is assumed, the use of EDAs in normative ethics is incompatible with a (...)
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21. Philosophical Remarks.Guy Stock - 1976 - Philosophical Quarterly 26 (103):178-180.
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22. Introduction to Combinators and (Lambda) Calculus.J. Roger Hindley - 1986 - Cambridge University Press.
Combinatory logic and lambda-conversion were originally devised in the 1920s for investigating the foundations of mathematics using the basic concept of 'operation' instead of 'set'. They have now developed into linguistic tools, useful in several branches of logic and computer science, especially in the study of programming languages. These notes form a simple introduction to the two topics, suitable for a reader who has no previous knowledge of combinatory logic, but has taken an undergraduate course in predicate calculus and recursive (...)
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23. Objective List Theories.Guy Fletcher - 2016 - In The Routledge Handbook of Philosophy of Well-Being. Routledge. pp. 148-160.
This chapter is divided into three parts. First I outline what makes something an objective list theory of well-being. I then go on to look at the motivations for holding such a view before turning to objections to these theories of well-being.
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25. William James on Pragmatism and Religion.Guy Axtell - 2018 - In Jacob Goodson (ed.), William James, Moral Philosophy, and the Ethical Life: The Cries of the Wounded. London: Lexington Books. pp. 317-336.
Critics and defenders of William James both acknowledge serious tensions in his thought, tensions perhaps nowhere more vexing to readers than in regard to his claim about an individual’s intellectual right to their “faith ventures.” Focusing especially on “Pragmatism and Religion,” the final lecture in Pragmatism, this chapter will explore certain problems James’ pragmatic pluralism. Some of these problems are theoretical, but others concern the real-world upshot of adopting James permissive ethics of belief. Although Jamesian permissivism is qualified in certain (...)
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26. Beyond Sacrificial Harm: A Two-Dimensional Model of Utilitarian Psychology.Guy Kahane, Jim A. C. Everett, Brian D. Earp, Lucius Caviola, Nadira S. Faber, Molly J. Crockett & Julian Savulescu - 2018 - Psychological Review 125 (2):131-164.
Recent research has relied on trolley-type sacrificial moral dilemmas to study utilitarian versus nonutili- tarian modes of moral decision-making. This research has generated important insights into people’s attitudes toward instrumental harm—that is, the sacrifice of an individual to save a greater number. But this approach also has serious limitations. Most notably, it ignores the positive, altruistic core of utilitarianism, which is characterized by impartial concern for the well-being of everyone, whether near or far. Here, we develop, refine, and validate a (...)
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27. Moral Testimony: Once More with Feeling.Guy Fletcher - 2016 - Oxford Studies in Metaethics 11:45-73..
It is commonly claimed that reliance upon moral testimony is problematic in a way not common to reliance upon non-moral testimony. This chapter provides a new explanation of what the problem consists in—one that enjoys advantages over the most widely accepted explanation in the extant literature. The main theses of the chapter are as follows: that many forms of normative deference beyond the moral are problematic, that there is a common explanation of the problem with all of these forms of (...)
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28. Is the Universe Indifferent? Should We Care.Guy Kahane - 2022 - Philosophy and Phenomenological Research 104 (3):676-695.
Philosophy and Phenomenological Research, Volume 104, Issue 3, Page 676-695, May 2022.
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29. Introduction to Combinatory Logic.J. Roger Hindley - 1972 - Cambridge University Press.
Introduction Combinatory logic deals with a class of formal systems designed for studying certain primitive ways in which functions can be combined to form ...
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31. If Nothing Matters.Guy Kahane - 2017 - Noûs 51 (2):327-353.
The possibility that nothing really matters can cause much anxiety, but what would it mean for that to be true? Since it couldn’t be bad that nothing matters, fearing nihilism makes little sense. However, the consequences of belief in nihilism will be far more dramatic than often thought. Many metaethicists assume that even if nothing matters, we should, and would, go on more or less as before. But if nihilism is true in an unqualified way, it can’t be the case (...)
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33. Process Pragmatism: Essays on a Quiet Philosophical Revolution.Guy Debrock (ed.) - 2003 - Rodopi.
This book discusses Process Pragmatism, the view that whatever is, derives from interactions. The contributors examine and defend its merits by focusing on major topics, including truth, the existence of unobservables, the origin of knowledge, scientific activity, mathematical functions, laws of nature, and moral agency.
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34. The Neural Basis of Intuitive and Counterintuitive Moral Judgement.Guy Kahane, Katja Wiech, Nicholas Shackel, Miguel Farias, Julian Savulescu & Irene Tracey - 2011 - Social Cognitive and Affective Neuroscience 7 (4):393-402.
Neuroimaging studies on moral decision-making have thus far largely focused on differences between moral judgments with opposing utilitarian (well-being maximizing) and deontological (duty-based) content. However, these studies have investigated moral dilemmas involving extreme situations, and did not control for two distinct dimensions of moral judgment: whether or not it is intuitive (immediately compelling to most people) and whether it is utilitarian or deontological in content. By contrasting dilemmas where utilitarian judgments are counterintuitive with dilemmas in which they are intuitive, we (...)
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35. A Chronometric Analysis of Simple Addition.Guy J. Groen & John M. Parkman - 1972 - Psychological Review 79 (4):329-343.
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36. Taking Prudence Seriously.Guy Fletcher - 2019 - Oxford Studies in Metaethics 14:70-94.
Philosophers have long theorized about which things make people’s lives go well, and why, and the extent to which morality and self-interest can be reconciled. Yet little time has been spent on meta-prudential questions, questions about prudential discourse. This is surprising given that prudence is, prima facie, a normative form of discourse and, as such, cries out for further investigation. Chapter 4 takes up two major meta-prudential questions. It first examines whether there is a set of prudential reasons, generated by (...)
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37. Lambda-Calculus and Combinators in the 20th Century.Felice Cardone & J. Roger Hindley - 2009 - In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier. pp. 5--723.
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39. Methodological Issues in the Neuroscience of Moral Judgement.Guy Kahane & Nicholas Shackel - 2010 - Mind and Language 25 (5):561-582.
Neuroscience and psychology have recently turned their attention to the study of the subpersonal underpinnings of moral judgment. In this article we critically examine an influential strand of research originating in Greene's neuroimaging studies of ‘utilitarian’ and ‘non-utilitarian’ moral judgement. We argue that given that the explananda of this research are specific personal-level states—moral judgments with certain propositional contents—its methodology has to be sensitive to criteria for ascribing states with such contents to subjects. We argue that current research has often (...)
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40. Should We Want God to Exist?Guy Kahane - 2011 - Philosophy and Phenomenological Research 82 (3):674-696.
Whether God exists is a metaphysical question. But there is also a neglected evaluative question about God’s existence: Should we want God to exist? Very many, including many atheists and agnostics, appear to think we should. Theists claim that if God didn’t exist things would be far worse, and many atheists agree; they regret God’s inexistence. Some remarks by Thomas Nagel suggest an opposing view: that we should want God not to exist. I call this view anti-theism. I explain how (...)
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41. Causal Responsibility and Robust Causation.Guy Grinfeld, David Lagnado, Tobias Gerstenberg, James F. Woodward & Marius Usher - 2020 - Frontiers in Psychology 11:1069.
How do people judge the degree of causal responsibility that an agent has for the outcomes of her actions? We show that a relatively unexplored factor -- the robustness of the causal chain linking the agent’s action and the outcome -- influences judgments of causal responsibility of the agent. In three experiments, we vary robustness by manipulating the number of background circumstances under which the action causes the effect, and find that causal responsibility judgments increase with robustness. In the first (...)
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42. The Locative Analysis of Good For Formulated and Defended.Guy Fletcher - 2012 - Journal of Ethics and Social Philosophy (JESP) 6 (1):1-27.
THE STRUCTURE OF THIS PAPER IS AS FOLLOWS. I begin §1 by dealing with preliminary issues such as the different relations expressed by the “good for” locution. I then (§2) outline the Locative Analysis of good for and explain its main elements before moving on to (§3) outlining and discussing the positive features of the view. In the subsequent sections I show how the Locative Analysis can respond to objections from, or inspired by, Sumner (§4-5), Regan (§6), and Schroeder and (...)
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43. Our Cosmic Insignificance.Guy Kahane - 2013 - Noûs 47 (2):745-772.
The universe that surrounds us is vast, and we are so very small. When we reflect on the vastness of the universe, our humdrum cosmic location, and the inevitable future demise of humanity, our lives can seem utterly insignificant. Many philosophers assume that such worries about our significance reflect a banal metaethical confusion. They dismiss the very idea of cosmic significance. This, I argue, is a mistake. Worries about cosmic insignificance do not express metaethical worries about objectivity or nihilism, and (...)
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44. Combinatory Logic.Haskell B. Curry, J. Roger Hindley & Jonathan P. Seldin - 1977 - Journal of Symbolic Logic 42 (1):109-110.
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45. Self-Control, Injunctive Norms, and Descriptive Norms Predict Engagement in Plagiarism in a Theory of Planned Behavior Model.Guy J. Curtis, Emily Cowcher, Brady R. Greene, Kiata Rundle, Megan Paull & Melissa C. Davis - 2018 - Journal of Academic Ethics 16 (3):225-239.
The Theory of Planned Behavior predicts that a combination of attitudes, perceived norms, and perceived behavioral control predict intentions, and that intentions ultimately predict behavior. Previous studies have found that the TPB can predict students’ engagement in plagiarism. Furthermore, the General Theory of Crime suggests that self-control is particularly important in predicting engagement in unethical behavior such as plagiarism. In Study 1, we incorporated self-control in a TPB model and tested whether norms, attitudes, and self-control predicted intention to plagiarize and (...)
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46. Ineffability and Religious Experience.Guy Bennett-Hunter - 2014 - Routledge.
Ineffability—that which cannot be explained in words—lies at the heart of the Christian mystical tradition. It has also been part of every discussion of religious experience since the early twentieth century. Despite this centrality, ineffability is a concept that has largely been ignored by philosophers of religion. In this book, Bennett-Hunter builds on the recent work of David E. Cooper, who argues that the meaning of life can only be understood in terms of an ineffable source on which life depends, (...)
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47. On the Wrong Track: Process and Content in Moral Psychology.Guy Kahane - 2012 - Mind and Language 27 (5):519-545.
According to Joshua Greene’s influential dual process model of moral judgment, different modes of processing are associated with distinct moral outputs: automatic processing with deontological judgment, and controlled processing with utilitarian judgment. This paper aims to clarify and assess Greene’s model. I argue that the proposed tie between process and content is based on a misinterpretation of the evidence, and that the supposed evidence for controlled processing in utilitarian judgment is actually likely to reflect generic deliberation which, ironically, is incompatible (...)
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48. Pain for the Moral Error Theory? A New Companions-in-Guilt Argument.Guy Fletcher - 2018 - Australasian Journal of Philosophy 96 (3):474-482.
The moral error theorist claims that moral discourse is irredeemably in error because it is committed to the existence of properties that do not exist. A common response has been to postulate ‘companions in guilt’—forms of discourse that seem safe from error despite sharing the putatively problematic features of moral discourse. The most developed instance of this pairs moral discourse with epistemic discourse. In this paper, I present a new, prudential, companions-in-guilt argument and argue for its superiority over the epistemic (...)
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49. Palliative Opioid Use, Palliative Sedation and Euthanasia: Reaffirming the Distinction.Guy Schofield, Idris Baker, Rachel Bullock, Hannah Clare, Paul Clark, Derek Willis, Craig Gannon & Rob George - 2020 - Journal of Medical Ethics 46 (1):48-50.
We read with interest the extended essay published from Riisfeldt and are encouraged by an empirical ethics article which attempts to ground theory and its claims in the real world. However, such attempts also have real-world consequences. We are concerned to read the paper’s conclusion that clinical evidence weakens the distinction between euthanasia and normal palliative care prescribing. This is important. Globally, the most significant barrier to adequate symptom control in people with life-limiting illness is poor access to opioid analgesia. (...)
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https://adventures.michaelfbryan.com/posts/lastpass/
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# How I Reverse Engineered the LastPass CLI Tool
A couple days ago I was writing an install script for my dotfiles and reached a point where I wanted to grab some secrets (my SSH keys) from my LastPass vault and copy them to the file system.
This is easy enough to do using the browser plugin, or even when working with their command line tool (lpass) in an interactive way, but I found there was no way to ask lpass which files are attached to a secret, and get the output in a machine readable format.
Like most self-respecting members of the open-source community, I filed an issue on their GitHub page and in the meantime I started digging into the source code to find where changes might need to be made. That way I can make the change myself if it’s easy enough, or I’ll be able to provide someone else with a bit more information.
However, reading through the source code got me thinking. There currently aren’t any libraries for working with LastPass, and although the lpass tool is GPL’d and the source code is freely accessible on GitHub, by reading the source code you can quickly tell it was only ever intended as a command-line tool.
Soo….. Why not rewrite it in Rust?
## A Quick Note On Goals
In the long run, I’d like for this to be a fully-featured library for working with a LastPass vault. Although, in the short term I’m going to make a beeline for downloading and decrypting attachments, seeing as that was the original inspiration for this endeavour.
Someone may want to create a nice command-line tool on top of the library, but I don’t have any intention of being that someone (for now, anyways).
I’ve also got a lot of experience writing FFI code, so I’d like to write bindings so the library is usable from Python (my dotfiles install script is written in Python) and C. I might wait a bit to flesh out the crate’s API though, that way I’ll have a better idea of how the bindings should be consumed and it’ll reduce unnecessary code churn.
The lpass tool has roughly three responsibilities,
1. Communicate with the LastPass HTTP API
2. Perform the appropriate crypto so we can encrypt/decrypt the LastPass vault
3. Use the file system and a daemon to allow caching of the vault and persist login sessions across multiple invocations of the lpass command (e.g. so you don’t need to keep entering your master password every time)
As a library, the third point is usually left up to the frontend application so we’ve already made our job 33% easier.
I’d also consider the HTTP bit a solved problem. The reqwest crate provides a robust and fully-featured asynchronous HTTP client, and we can leverage serde’s serialization superpowers to make sending or receiving structured data a breeze.
I’m a little worried about the crypto side of things. On one hand, we don’t need to implement any cryptography routines ourselves (the aes and pbkdf2 crates already exist and are well-respected), but it’s easy to mess things up an accidentally introduce a security vulnerability.
I figure the best course of action here is to just copy what lpass do.
## Baby Steps
After creating the repository, the first thing to do is get a copy of the lastpass/lastpas-cli project so we can refer to the source code when needed.
$git submodule init$ git submodule add [email protected]:lastpass/lastpass-cli.git vendor/lastpass-cli
Cloning into '/home/michael/Documents/lastpass/vendor/lastpass-cli'...
remote: Enumerating objects: 2388, done.
remote: Total 2388 (delta 0), reused 0 (delta 0), pack-reused 2388
Receiving objects: 100% (2388/2388), 821.19 KiB | 463.00 KiB/s, done.
Resolving deltas: 100% (1565/1565), done.
There are a couple strategies you can use when trying to reverse engineer an existing application. The Bottom-Up strategy involves finding the snippet of code you care about (e.g. sending a HTTP request to the login endpoint) and tracing backwards to see how you construct the right inputs. On the other hand, the Top-Down approach starts at main() and steps through the program until you hit the juicy parts, similar to how a debugger works.
My first aim will be to log in and get any necessary session tokens. I know the LastPass API endpoint for logging in will almost certainly be a string starting with login, so we can start from there.
$rg '"login' vendor/lastpass-cli vendor/lastpass-cli/endpoints.c 236: reply = http_post_lastpass("login_check.php", session, NULL, "method", "cli", NULL); vendor/lastpass-cli/endpoints-login.c 170: *reply = http_post_lastpass_v(login_server, "login.php", NULL, NULL, args); 228: *reply = http_post_lastpass_v(login_server, "login.php", NULL, NULL, args); 296: *reply = http_post_lastpass_v(login_server, "login.php", NULL, NULL, args); vendor/lastpass-cli/contrib/lpass_zsh_completion 116: "login:Authenticate with the LastPass server and initialize a local cache" vendor/lastpass-cli/cmd.h 75:#define cmd_login_usage "login [--trust] [--plaintext-key [--force, -f]] " color_usage " USERNAME" I’m guessing the file we’re looking for is the aptly-named endpoints-login.c. Opening the file up and jumping to the appropriate lines show there are three login functions. // vendor/lastpass-cli/endpoints-login.c static bool ordinary_login(const char *login_server, const unsigned char key[KDF_HASH_LEN], char **args, char **cause, char **message, char **reply, struct session **session, char **ret_login_server) { char *server; free(*reply); *reply = http_post_lastpass_v(login_server, "login.php", NULL, NULL, args); if (!*reply) return error_post(message, session); *session = xml_ok_session(*reply, key); if (*session) { (*session)->server = xstrdup(login_server); return true; } *cause = xml_error_cause(*reply, "cause"); if (!*cause) return error_other(message, session, "Unable to determine login failure cause."); *ret_login_server = xstrdup(login_server); return false; } static bool oob_login(const char *login_server, const unsigned char key[KDF_HASH_LEN], char **args, char **message, char **reply, char **oob_name, struct session **session) { ... terminal_fprintf(stderr, TERMINAL_FG_YELLOW TERMINAL_BOLD "Waiting for approval of out-of-band %s login%s" TERMINAL_NO_BOLD "...", *oob_name, can_do_passcode ? ", or press Ctrl+C to enter a passcode" : ""); append_post(args, "outofbandrequest", "1"); for (;;) { free(*reply); *reply = http_post_lastpass_v(login_server, "login.php", NULL, NULL, args); if (!*reply) { if (can_do_passcode) { append_post(args, "outofbandrequest", "0"); append_post(args, "outofbandretry", "0"); append_post(args, "outofbandretryid", ""); xstrappend(oob_name, " OTP"); goto failure; } else { error_post(message, session); goto success; } } ... } ... } static bool otp_login(const char *login_server, const unsigned char key[KDF_HASH_LEN], char **args, char **message, char **reply, const char *otp_name, const char *cause, const char *username, struct session **session) { ... for (;;) { multifactor = password_prompt("Code", multifactor_error, "Please enter your %s for <%s>.", otp_name ? otp_name : replied_multifactor->name, username); if (!multifactor) return error_other(message, session, "Aborted multifactor authentication."); append_post(args, replied_multifactor->post_var, multifactor); free(*reply); *reply = http_post_lastpass_v(login_server, "login.php", NULL, NULL, args); ... } } So it looks like there are 3 methods for doing login… I’m guessing the ordinary_login() is for a standard username/password login and oob_login() and otp_login() are for multi-factor authentication where you’ve got an out-of-band authentication device (e.g. a USB dongle) or are using an app that uses one-time-pads (e.g. the Google Authenticator app). I don’t care about multi-factor authentication for now, so let’s have a skim through ordinary_login() and try to identify the important bits. I’m not 100% sure what the _v suffix in http_post_lastpass_v() means, but it seems to be a function that sends a HTTP POST request to lastpass.com. The two NULL parameters are a pointer to a session (presumably for auth, but we haven’t logged in yet so we don’t have one) and a place to put the reply string’s length (which we don’t care about because it’s a null-terminated string). From there, it looks like the response body is parsed as XML into a session using xml_ok_session(). Interestingly, we need to pass in a key, so presumably parts of the response will be encrypted with our master password. If parsing was successful, the parsed session is “returned” to the caller via the session pointer and we leave the function. The rest of the function seems to be around identifying the cause for a login failure, so we can ignore it for the time being. Looking up the stack to the function that calls ordinary_login(), we reach lastpass_login(). // vendor/lastpass-cli/endpoints-login.c struct session *lastpass_login(const char *username, const char hash[KDF_HEX_LEN], const unsigned char key[KDF_HASH_LEN], int iterations, char **error_message, bool trust) { char *args[33]; ... memset(args, 0, sizeof(args)); append_post(args, "xml", "2"); append_post(args, "username", user_lower); append_post(args, "hash", hash); append_post(args, "iterations", iters); append_post(args, "includeprivatekeyenc", "1"); append_post(args, "method", "cli"); append_post(args, "outofbandsupported", "1"); if (trusted_id) append_post(args, "uuid", trusted_id); if (ordinary_login(LASTPASS_SERVER, key, args, &cause, error_message, &reply, &session, &login_server)) return session; ... } It looks like this is responsible for constructing the POST data and sending a request to ordinary_login(). I’ve elided the bits afterwards because they just fall back to the out-of-band and one-time-pad logins. If you squint at append_post() calls in the previous snippet, you’ll see that we’re constructing the key-value pairs to submit a HTML form. At this point we actually know enough to start sending login requests to the LastPass API! I’m going to use the HTTP client from the reqwest crate for this. As well as having nice things like connection pooling, async, TLS, and automatic cookie storage, there’s this awesome feature where you can use anything implementing serde::Serialize as the form data. First, we’ll create a struct with all the data to be submitted in the form. // src/endpoints/login.rs use serde_derive::Serialize; #[derive(Debug, Serialize)] struct Data<'a> { xml: usize, username: &'a str, hash: &'a str, iterations: usize, includeprivatekeyenc: usize, method: &'a str, outofbandsupported: usize, uuid: Option<&'a str>, } Then we can write a function to send this data to the login.php endpoint. // src/endpoints/login.rs pub async fn login( client: &Client, hostname: &str, username: &str, login_key: &str, iterations: usize, ) -> Result<Session, LoginError> { let data = Data { xml: 2, username, hash: login_key, iterations, includeprivatekeyenc: 1, method: "cli", outofbandsupported: 1, trusted_id, }; let url = format!("https://{}/login.php", hostname); let response = client .post(&url) .form(&data) .send() .await? .error_for_status()?; let body = response.text().await?; unimplemented!("How do we parse the body into a session? {}", body); } Throughout this I’ll be assuming you’re either moderately familiar with Rust, or have played with enough programming languages that you’ll understand common concepts like method chaining and async-await. I’ve also taken the liberty of stubbing out a Session type based on the session struct in session.h. // src/session.rs #[derive(Debug, Clone, PartialEq)] pub struct Session { pub uid: String, pub token: String, pub private_key: Vec<u8>, pub session_id: String, } // vendor/lastpass-cli/session.h struct session { char *uid; char *sessionid; char *token; char *server; struct private_key private_key; }; I also hacked together a quick program to send requests to LastPass and dump the login response. // src/bin/main.rs use anyhow::Error; use reqwest::Client; use lastpass::endpoints; #[tokio::main] async fn main() -> Result<(), Error> { env_logger::init(); let client = Client::builder() .user_agent(lastpass::DEFAULT_USER_AGENT) .cookie_store(true) .build()?; let session = endpoints::login( &client, "lastpass.com", "[email protected]", "SUPER_SECRET_LOGIN_KEY_I_GOT_FROM_LPASS", 100100, ) .await?; println!("Logged in as [email protected] {:#?}", session); Ok(()) } Assuming we used the correct login_key, the login.php endpoint sends us back a big blob of XML. A big blob of XML <?xml version="1.0" encoding="UTF-8"?> <response> <ok sitesver="" formfillver="" bigicon="5617" bigiconenabled="1" uid="999999999" language="en-US" sessionid="SESSIONID1234" disableoffline="0" pushserver="https://lp-push-server-455.lastpass.com/ws/1111111111111111111111111111111111111 main" new_save_site="1" first_time_login="0" infield_enabled="1" mobile_active="1" ziggy="1" better_generate_password_enabled="1" omar_ia="1" retire_3_0="1" family_shared_folders_enabled="1" family_legacy_shared_folders_enabled="1" try_families_enabled="1" premium_sharing_restricted="1" emergency_access_restricted="1" is_families_trial_started="" predates_families="0" seen_vault_post_families="1" privatekeyenc="DEADBEEF" migrated="0" autofill_https_test="1" nopassword_integration_enabled="1" save_a_site_otp="1" site_feedback="1" omar_vault_migration="0" account_version_tracking="" blob_version_set="1" yubikeyenabled="0" googleauthenabled="1" microsoftauthenabled="0" outofbandenabled="0" serverts="1586587085100000" iconsversion="85" isadmin="0" lpusername="[email protected]" email="[email protected]" loglogins="1" client_enc="1" accts_version="198" pwdeckey="PASSWORDDECODEKEY" hih="0" genh="0" addh="0" seclvl="0" updated_enc="1" login_site_prompt="0" edit_site_prompt="0" edit_sn_prompt="0" view_pw_prompt="0" view_ff_prompt="0" improve="1" switch_identity_prompt="1" switch_f_prompt="0" multifactor_reprompt="" multifactor_singlefactor="" singlefactortype="" country="AU" model="3" banner="0" ratings_prompt="1" reqdversion="1.39" pollinterval="-1" logoff_other_ses="0" generatedpw="0" pageloadthres="800000" attachversion="3" pwresetreqd="0" accountlinkrequired="0" trialduration="30" token="BASE64ENCODEDTOKEN=" companyadmin="0" iterations="123456" showcredmon="0" adlogin="0" note_title="" note_text="" note_button="" note_url="" lastchallengets="0" extended_shared_folder_log="0" multifactorscore="9" disablepwalerts="0" emailverified="1" prefdata="" pbt="1" logloginsvr="loglogin.lastpass.com" pollserver="pollserver.lastpass.com" do_totp="1" newsettings_enabled = '0' show_extension_popup = '0' is_legacy_premium="0" /> </response> Considering the Session struct only has a handful of fields, it’s safe to assume most of this is unnecessary information that’s probably used by other LastPass products (e.g. their browser extension). To see how the relevant information is extracted, I’m going to look at the xml_ok_session() function (which tries to parse the happy case out of the XML) and see if anything jumps out. // vendor/lastpass-cli/xml.c #include "xml.h" #include "util.h" #include "blob.h" #include <string.h> #include <libxml/parser.h> #include <libxml/tree.h> #include <errno.h> struct session *xml_ok_session(const char *buf, unsigned const char key[KDF_HASH_LEN]) { struct session *session = NULL; xmlDoc *doc = NULL; xmlNode *root; doc = xmlReadMemory(buf, strlen(buf), NULL, NULL, 0); if (!doc) goto out; root = xmlDocGetRootElement(doc); if (root && !xmlStrcmp(root->name, BAD_CAST "response")) { for (root = root->children; root; root = root->next) { if (!xmlStrcmp(root->name, BAD_CAST "ok")) break; } } if (root && !xmlStrcmp(root->name, BAD_CAST "ok")) { session = session_new(); for (xmlAttrPtr attr = root->properties; attr; attr = attr->next) { if (!xmlStrcmp(attr->name, BAD_CAST "uid")) session->uid = (char *)xmlNodeListGetString(doc, attr->children, 1); if (!xmlStrcmp(attr->name, BAD_CAST "sessionid")) session->sessionid = (char *)xmlNodeListGetString(doc, attr->children, 1); if (!xmlStrcmp(attr->name, BAD_CAST "token")) session->token = (char *)xmlNodeListGetString(doc, attr->children, 1); if (!xmlStrcmp(attr->name, BAD_CAST "privatekeyenc")) { _cleanup_free_ char *private_key = (char *)xmlNodeListGetString(doc, attr->children, 1); session_set_private_key(session, key, private_key); } } } out: if (doc) xmlFreeDoc(doc); if (!session_is_valid(session)) { session_free(session); return NULL; } return session; } Looking at just the string literals and function names, it seems like we’re expecting a root <ok> node. From there we skim through the <ok> node’s attributes and copy "uid", "sessionid", "token", and "privatekeyenc" to the relevant fields on session. That seems easy enough. I’ll be using the serde_xml_rs crate to parse the response document. This lets us declaratively define how an “ok” document should look, then lean on serde and serde_xml_rs to do the heavy lifting. // src/endpoints/login.rs #[derive(Debug, Deserialize)] struct Document { #[serde(rename = "$value")]
root: Root,
}
#[derive(Debug, Deserialize)]
enum Root {
#[serde(rename = "ok")]
Ok {
uid: String,
/// A base64-encoded token.
token: String,
#[serde(rename = "privatekeyenc")]
private_key: String,
/// The PHP session ID.
#[serde(rename = "sessionid")]
session_id: String,
/// The user's primary email address
email: String,
},
...
}
Now we’ve got something that represents the document schema, we actually have everything we need to parse it into a Session.
// src/endpoints/login.rs
client: &Client,
hostname: &str,
iterations: usize,
...
let body = response.text().await?;
let doc: Document = serde_xml_rs::from_str(&body)?;
interpret_response(doc.root)
}
fn interpret_response(root: Root) -> Result<Session, LoginError> {
match root {
Root::Ok {
uid,
token,
private_key,
session_id,
..
} => Ok(Session { uid, token, private_key, session_id }
...
}
}
Running the test program shows we’ve got an actual session.
$cargo run Logged in as [email protected] Session { uid: "123456789", token: "X3BYcEFjRDFZYlRoVG42r1kTj/UvbBGar2zRpDXgzQyIbQpCMkocUHSFS3AMt3duyU4=", private_key: "DEADBEEFCAFEBABE", session_id: "3d,UxdQVzFSznYkCXfYXabP2Bw8", } Success! While it may seem like we’ve written a lot of code our quick’n’dirty login function, complete with error handling code (which I’ve skipped for simplicity), and a test program, only took about 100 lines of Rust. The vast majority of time was actually spent reading through the lastpass-cli project’s source code and figuring out how all the components interact. This was made a lot harder because C promotes a culture of Primitive Obsession, so everything is a char * (the login key is a char *, the response is a char *, errors are a char *, the key-value pairs for our POST form is a char ** array where even items are keys and odd items are values, etc.). The lack of generics and RAII also makes it hard to create nice layers of abstraction in a C program because you are constantly interspersing business logic with memory management, or you need to implement your own doubly-linked list. ## Creating an Abstraction for Key Management Now that we’re able to log in, let’s start getting rid of those hard-coded values. ### Login Keys The first thing I’d like to do is create a LoginKey. After a little digging, it looks like we use kdf_login_key() to derive the login key based on the user’s username and master password. // vendor/lastpass-cli/kdf.c void kdf_login_key(const char *username, const char *password, int iterations, char hex[KDF_HEX_LEN]) { unsigned char hash[KDF_HASH_LEN]; size_t password_len; _cleanup_free_ char *user_lower = xstrlower(username); password_len = strlen(password); if (iterations < 1) iterations = 1; if (iterations == 1) { sha256_hash(user_lower, strlen(user_lower), password, password_len, hash); bytes_to_hex(hash, &hex, KDF_HASH_LEN); sha256_hash(hex, KDF_HEX_LEN - 1, password, password_len, hash); } else { pbkdf2_hash(user_lower, strlen(user_lower), password, password_len, iterations, hash); pbkdf2_hash(password, password_len, (char *)hash, KDF_HASH_LEN, 1, hash); } bytes_to_hex(hash, &hex, KDF_HASH_LEN); mlock(hex, KDF_HEX_LEN); } Now we can see that the iterations parameter is used by PBKDF2 to increase the number of times the hash is applied, allowing the algorithm to scale as hardware gets faster. As a special case, when iterations <= 1 we do two passes through SHA-256. This looks like a backwards compatibility thing, where the LoginKey used by older servers or accounts was computed using SHA-256 and they later transitioned to PBKDF2 for increased security. Looking through the source code we can see that a login key is KDF_HASH_LEN bytes long, or about 64 bytes + 1 for a null terminator. // /usr/include/openssl/sha.h # define SHA256_DIGEST_LENGTH 32 // vendor/lastpass-cli/kdf.h #include <openssl/sha.h> #define KDF_HASH_LEN SHA256_DIGEST_LENGTH #define KDF_HEX_LEN (KDF_HASH_LEN * 2 + 1) This tells us enough to define a LoginKey. For now it’s just a newtype around a [u8; 64] array, we don’t need the null terminator because arrays in Rust always know how long they are. // src/keys/login_key.rs /// A hex-encoded hash of the username and password. pub struct LoginKey([u8; LoginKey::LEN]); const KDF_HASH_LEN: usize = 32; impl LoginKey { pub const LEN: usize = KDF_HASH_LEN * 2; } You can create a LoginKey using the LoginKey::calculate() constructor. This just defers to LoginKey::sha256() and LoginKey::pbkdf2() based on the number of iterations. // src/keys/login_key.rs impl LoginKey { ... /// Calculate a new [LoginKey]. pub fn calculate( username: &str, password: &str, iterations: usize, ) -> Self { let username = username.to_lowercase(); if iterations <= 1 { LoginKey::sha256(&username, password) } else { LoginKey::pbkdf2(&username, password, iterations) } } fn sha256(username: &str, password: &str) -> Self { unimplemented!() } fn pbkdf2(username: &str, password: &str, iterations: usize) -> Self { unimplemented!() } } I’ll start with the LoginKey::sha256() constructor because that seems easiest, so let’s have a look at the sha256_hash() function used by lastpass-cli. // vendor/lastpass-cli/kdf.c static void sha256_hash(const char *username, size_t username_len, const char *password, size_t password_len, unsigned char hash[KDF_HASH_LEN]) { SHA256_CTX sha256; if (!SHA256_Init(&sha256)) goto die; if (!SHA256_Update(&sha256, username, username_len)) goto die; if (!SHA256_Update(&sha256, password, password_len)) goto die; if (!SHA256_Final(hash, &sha256)) goto die; return; die: die("Failed to compute SHA256 for %s", username); } Seems fair enough, it’ll generate a hash of the username + password, then hash that with the password. I don’t particularly want to implement any of this myself myself, so let’s pull in a couple crates: And then we can implement LoginKey::sha256(). // src/keys/login_key.rs use digest::Digest; use sha2::Sha256; impl LoginKey { ... fn sha256(username: &str, password: &str) -> Self { let first_pass = Sha256::new() .chain(username) .chain(password) .result(); let first_pass_hex = hex::encode(&first_pass); let second_pass = Sha256::new() .chain(&first_pass_hex) .chain(password) .result(); LoginKey::from_bytes(&second_pass) } fn from_bytes(bytes: &[u8]) -> Self { assert_eq!(bytes.len() * 2, LoginKey::LEN); let mut key = [0; LoginKey::LEN]; hex::encode_to_slice(bytes, &mut key) .expect("the assert guarantees we've got the right length"); LoginKey(key) } } To make sure I’ve implemented this correctly, I gave the lpass program a dummy set of credentials and using the debugger was able to see what they should hash to. This lets me write a simple sanity test. // src/keys/login_key.rs #[cfg(test)] mod tests { use super::*; #[test] fn login_key_with_sha256() { let username = "[email protected]"; let password = "My Super Secret Password!"; let should_be = LoginKey(*b"b8a31d9784fa9a263d0e7a0d866b70612687f7067733126d74ccde02d3bab494"); let got = LoginKey::sha256(username, password); assert_eq!(got, should_be); } } I can implement the LoginKey::pbkdf2() constructor in much the same way, again letting the proper crate (in this case, pbkdf2) do the heavy lifting. // src/keys/login_key.rs use sha2::Sha256; use hmac::Hmac; impl LoginKey { ... fn pbkdf2(username: &str, password: &str, iterations: usize) -> Self { // the first rearranges the password (maintaining length), salting it // with the username let mut first_pass = [0; KDF_HASH_LEN]; pbkdf2::pbkdf2::<Hmac<Sha256>>( password.as_bytes(), username.as_bytes(), iterations, &mut first_pass, ); // we then hash the previous key, salting with the password // previous key let mut key = [0; KDF_HASH_LEN]; pbkdf2::pbkdf2::<Hmac<Sha256>>( &first_pass, password.as_bytes(), 1, &mut key, ); LoginKey::from_bytes(&key) } } In much the same way, we can use the debugger to find a set of inputs and outputs to test that our LoginKey::pbkdf2() function was implemented correctly. // src/keys/login_key.rs #[cfg(test)] mod tests { use super::*; ... #[test] fn login_key_with_pbkdf2() { let username = "[email protected]"; let password = "My Super Secret Password!"; let iterations = 100; let should_be = LoginKey(*b"f93111b2fb6699de187ef8307aa84b1e9fdabf4a46cb821e83e507a95c3f7c97"); let got = LoginKey::pbkdf2(username, password, iterations); assert_eq!(got, should_be); } } Now we can construct a LoginKey, we can update the test executable to accept credentials instead of a hard-coded login key. // src/bin/main.rs use anyhow::Error; use lastpass::{endpoints, keys::LoginKey}; use reqwest::Client; use structopt::StructOpt; #[tokio::main] async fn main() -> Result<(), Error> { env_logger::init(); let args = Args::from_args(); log::debug!("Starting application with {:#?}", args); let client = Client::builder() .user_agent(lastpass::DEFAULT_USER_AGENT) .cookie_store(true) .build()?; let iterations = endpoints::iterations(&client, &args.host, &args.username).await?; let login_key = LoginKey::calculate(&args.username, &args.password, iterations); endpoints::login( &client, &args.host, &args.username, &login_key, iterations, ) .await?; log::info!("Logged in as {}", args.username); Ok(()) } #[derive(Debug, StructOpt)] struct Args { #[structopt( long = "host", default_value = "lastpass.com", help = "The LastPass server's hostname" )] host: String, #[structopt(short = "u", long = "username", help = "Your username")] username: String, #[structopt(short = "p", long = "password", help = "Your master password")] password: String, } While you reading through the earlier section, I took the liberty of creating a function that asks LastPass how many iterations to use when generating a login key. The iterations.php endpoint replies with a single integer, so it’s dead simple. // src/endpoints/iterations.rs pub async fn iterations( client: &Client, hostname: &str, username: &str, ) -> Result<usize, EndpointError> { let url = format!("https://{}/iterations.php", hostname); let data = Data { email: username }; let response = client .post(&url) .form(&data) .send() .await? .error_for_status()?; let body = response.text().await?; body.trim().parse().map_err(EndpointError::from) } #[derive(Debug, Serialize)] struct Data<'a> { email: &'a str, } ### Decryption Keys To accompany the LoginKey, which has been shared with the LastPass servers to prove who you are, there is also a DecryptionKey for decrypting your actual LastPass vault. This second key is derived from your master password and never leaves your computer, hence the claim that LastPass themselves can’t read your personal data. The DecryptionKey is also constructed using SHA-256 or PBKDF2, so I won’t go into detail on that. Instead, I’d like to add a method for decrypting ciphertext using a DecryptionKey. I guess the best place to start is by looking at how the lastpass-cli project decrypts things using the DecryptionKey. // vendor/lastpass-cli/cipher.c char *cipher_aes_decrypt(const unsigned char *ciphertext, size_t len, const unsigned char key[KDF_HASH_LEN]) { EVP_CIPHER_CTX *ctx; char *plaintext; int out_len; if (!len) return NULL; ctx = EVP_CIPHER_CTX_new(); if (!ctx) return NULL; plaintext = xcalloc(len + AES_BLOCK_SIZE + 1, 1); if (len >= 33 && len % 16 == 1 && ciphertext[0] == '!') { if (!EVP_DecryptInit_ex(ctx, EVP_aes_256_cbc(), NULL, key, (unsigned char *)(ciphertext + 1))) goto error; ciphertext += 17; len -= 17; } else { if (!EVP_DecryptInit_ex(ctx, EVP_aes_256_ecb(), NULL, key, NULL)) goto error; } if (!EVP_DecryptUpdate(ctx, (unsigned char *)plaintext, &out_len, (unsigned char *)ciphertext, len)) goto error; len = out_len; if (!EVP_DecryptFinal_ex(ctx, (unsigned char *)(plaintext + out_len), &out_len)) goto error; len += out_len; plaintext[len] = '\0'; EVP_CIPHER_CTX_free(ctx); return plaintext; error: EVP_CIPHER_CTX_free(ctx); secure_clear(plaintext, len + AES_BLOCK_SIZE + 1); free(plaintext); return NULL; } Although the code is a bit convoluted due to way error handling and argument validation are done, it looks like we switch between two input algorithms at the start based, then pass the ciphertext through the decryption function. Similar to the LoginKey::calculate() function I’m guessing this is because the encryption algorithm has changed over time. So it was initially just using AES-256 with the ECB block cipher mode, then later they transitioned to CBC with a 16-byte initialization vector (that’s why there’s the ciphertext[0] == '!' and all that pointer arithmetic). The aes and block-modes crates made this a lot easier than I was expecting. // src/keys/decryption_key.rs use aes::Aes256; use block_modes::{block_padding::Pkcs7, BlockMode, Cbc, Ecb}; impl DecryptionKey { pub fn decrypt( &self, ciphertext: &[u8], ) -> Result<Vec<u8>, DecryptionError> { if ciphertext.is_empty() { // If there's no input, there's nothing to decrypt return Ok(Vec::new()); } let decrypted = if uses_cbc(ciphertext) { let iv = &ciphertext[1..17]; let ciphertext = &ciphertext[17..]; Cbc::<Aes256, Pkcs7>::new_var(&self.0, &iv)? .decrypt_vec(ciphertext)? } else { Ecb::<Aes256, Pkcs7>::new_var(&self.0, &[])? .decrypt_vec(ciphertext)? }; Ok(decrypted) } } fn uses_cbc(ciphertext: &[u8]) -> bool { ciphertext.len() >= 33 && ciphertext.len() % 16 == 1 && ciphertext.starts_with(b"!") } The lastpass-cli project doesn’t have any tests with examples of decrypted data (or any tests at all for that matter), so I’ll need to resort to using debugger on lpass and seeing how real data is decrypted if I want to make sure my code works. // src/keys/decryption_key.rs #[cfg(test)] mod tests { use super::*; #[test] fn decrypt_some_text() { let key = DecryptionKey::from_raw(b"..."); let ciphertext = [ 33, 11, 151, 186, 165, 216, 165, 58, 154, 207, 238, 219, 138, 19, 26, 178, 141, 91, 241, 31, 28, 69, 189, 39, 5, 10, 161, 76, 57, 10, 240, 137, 11, 124, 42, 129, 213, 123, 192, 182, 178, 194, 84, 175, 73, 19, 104, 137, 123, ]; let got = key.decrypt(&ciphertext).unwrap(); assert_eq!( String::from_utf8(got).unwrap(), "Example password without folder" ); } } Well the test passes, so if everything goes to plan we should have everything we need to decode the vault. ## Reading the Vault Now we’ve implemented the fundamental things like crypto and calling a couple API endpoints, we’re getting into the more juicy stuff. The next step is to download a copy of the password vault and read it into memory. ### Retrieving the Vault Once you’ve logged in, retrieving a copy of the password vault from LastPass is really easy. We don’t need to supply any authentication information because LastPass already gave us a PHP session cookie and I’ll be reusing the same reqwest::Client for both calls. Just like login.php and iterations.php, we need to send a POST request to the getaccts.php endpoint and read the response body. // src/endpoints/vault.rs use crate::{ Vault, VaultParseError }; use reqwest::{Client, Error as ReqwestError}; use serde_derive::Serialize; const LASTPASS_CLI_VERSION: &str = "1.3.3.15.g8767b5e"; /// Fetch the latest vault snapshot from LastPass. pub async fn get_vault( client: &Client, hostname: &str, ) -> Result<Vault, VaultError> { let data = Data { mobile: 1, request_src: "cli", // I'm not sure why lastpass-cli used its version number instead of a // bool here, but \_(ツ)_/¯ has_plugin: LASTPASS_CLI_VERSION, }; let url = format!("https://{}/getaccts.php", hostname); let body = client .post(&url) .form(&data) .send() .await? .error_for_status()? .bytes() .await?; Vault::parse(&body).map_err(VaultError::Parse) } #[derive(Debug, Serialize)] struct Data<'a> { mobile: usize, #[serde(rename = "requestsrc")] request_src: &'a str, #[serde(rename = "hasplugin")] has_plugin: &'a str, } #[derive(Debug, thiserror::Error)] pub enum VaultError { /// The HTTP client encountered an error. #[error("Unable to send the request")] HttpClient(#[from] ReqwestError), #[error("Unable to parse the vault")] Parse(#[from] VaultParseError), } For now I’ve also stubbed out a Vault type and given it a Vault::parse() method that accepts a &[u8] and will return either a Vault or a VaultParseError. ### Decoding the Vault Running our test program again and inserting a line which will write the response body to disk shows a big hunk of binary. Let’s print this data out as hex and see if we can spot any patterns… # xxd src/vault_from_dummy_account.bin | head -n 30 00000000: 4c50 4156 0000 0002 3132 4154 5652 0000 LPAV....12ATVR.. 00000010: 0001 3145 4e43 5500 0000 2c35 4e5a 5969 ..1ENCU...,5NZYi 00000020: 7967 7236 6659 514d 3950 424f 3765 5243 ygr6fYQM9PBO7eRC 00000030: 6357 6f71 4336 454d 7a6c 3159 594b 705a cWoqC6EMzl1YYKpZ 00000040: 7357 7272 446b 3d43 4243 5500 0000 0131 sWrrDk=CBCU....1 00000050: 4242 5445 0000 000a 3135 3839 3236 3534 BBTE....15892654 00000060: 3836 4950 5445 0000 000a 3135 3839 3236 86IPTE....158926 00000070: 3534 3836 574d 5445 0000 000a 3135 3839 5486WMTE....1589 00000080: 3236 3534 3836 414e 5445 0000 000a 3135 265486ANTE....15 00000090: 3839 3236 3534 3836 444f 5445 0000 000a 89265486DOTE.... 000000a0: 3135 3839 3236 3534 3836 4645 5445 0000 1589265486FETE.. 000000b0: 000a 3135 3839 3236 3534 3836 4655 5445 ..1589265486FUTE 000000c0: 0000 000a 3135 3839 3236 3534 3836 5359 ....1589265486SY 000000d0: 5445 0000 000a 3135 3839 3236 3534 3836 TE....1589265486 000000e0: 574f 5445 0000 000a 3135 3839 3236 3534 WOTE....15892654 000000f0: 3836 5441 5445 0000 000a 3135 3839 3236 86TATE....158926 00000100: 3534 3836 5750 5445 0000 000a 3135 3839 5486WPTE....1589 00000110: 3236 3534 3836 5350 4d54 0000 0037 0000 265486SPMT...7.. 00000120: 0001 3000 0000 0130 0000 0001 3000 0000 ..0....0....0... 00000130: 0130 0000 0001 3000 0000 0131 0000 0001 .0....0....1.... 00000140: 3100 0000 0130 0000 0001 3000 0000 0130 1....0....0....0 00000150: 0000 0001 304e 4d41 4300 0000 0136 4143 ....0NMAC....6AC 00000160: 4354 0000 01c4 0000 0013 3534 3936 3233 CT........549623 00000170: 3039 3734 3133 3031 3830 3637 3300 0000 0974130180673... 00000180: 3121 0b97 baa5 d8a5 3a9a cfee db8a 131a 1!......:....... 00000190: b28d 5bf1 1f1c 45bd 2705 0aa1 4c39 0af0 ..[...E.'...L9.. 000001a0: 890b 7c2a 81d5 7bc0 b6b2 c254 af49 1368 ..|*..{....T.I.h 000001b0: 897b 0000 0031 215d ae99 4843 6321 5162 .{...1!]..HCc!Qb 000001c0: 80f5 6587 f669 4628 588e 8ba5 51b5 e6a3 ..e..iF(X...Q... 000001d0: 83ed ba28 65e4 786d 2b2a 7ef8 c7d2 ccf9 ...(e.xm+*~..... After staring at the wall of hex for a couple seconds I noticed an interesting pattern. This blob contains a repeating pattern… • a 4-byte ASCII mnemonic • a 4-byte big-endian integer, n • n bytes worth of data, sometimes cleartext (e.g. base64-encoded text or a long number that looks like a unix timestamp) and other times it’ll look like garbage (encrypted data) Now we have a rough idea of how a vault is structured, let’s dive into some source code and see how it’s turned into something more usable. Internally, it looks like LastPass refer to this thing as a blob, and there happens to be blob_parse() function in blob.h. Let’s start there. // vendor/lastpass-cli/blob.c struct blob *blob_parse(const unsigned char *blob, size_t len, const unsigned char key[KDF_HASH_LEN], const struct private_key *private_key) { ... while (read_chunk(&blob_pos, &chunk)) { if (!strcmp(chunk.name, "LPAV")) { versionstr = xstrndup((char *) chunk.data, chunk.len); parsed->version = strtoull(versionstr, NULL, 10); } else if (!strcmp(chunk.name, "ACCT")) { account = account_parse(&chunk, last_share ? last_share->key : key); if (!account) goto error; ... } else if (!strcmp(chunk.name, "ACFL") || !strcmp(chunk.name, "ACOF")) { ... } else if (!strcmp(chunk.name, "LOCL")) { parsed->local_version = true; } else if (!strcmp(chunk.name, "SHAR")) { ... } else if (!strcmp(chunk.name, "AACT")) { ... } else if (!strcmp(chunk.name, "AACF")) { ... } else if (!strcmp(chunk.name, "ATTA")) { ... } if (!versionstr) goto error; return parsed; error: blob_free(parsed); return NULL; } This seems simple enough. Those patterns we saw earlier are called chunks, and parsing a blob is just a case of reading each chunk in the blob, invoking different routines depending on a 4-character mnemonic. Let’s have a look at how each chunk is parsed. // vendor/lastpass-cli/blob.h struct chunk { char name[4 + 1]; const unsigned char *data; size_t len; }; // vendor/lastpass-cli/blob.c static bool read_chunk(struct blob_pos *blob, struct chunk *chunk) { if (blob->len < 4) return false; chunk->name[0] = blob->data[0]; chunk->name[1] = blob->data[1]; chunk->name[2] = blob->data[2]; chunk->name[3] = blob->data[3]; chunk->name[4] = '\0'; blob->len -= 4; blob->data += 4; if (blob->len < sizeof(uint32_t)) return false; chunk->len = be32toh(*((uint32_t *)blob->data)); blob->len -= sizeof(uint32_t); blob->data += sizeof(uint32_t); if (chunk->len > blob->len) return false; chunk->data = blob->data; blob->data += chunk->len; blob->len -= chunk->len; return true; } This can be converted fairly mechanically into Rust. The only noticeable difference is that instead of mutating the slice every time we read some data off the front, I’ll return a new slice. This means when the caller removes some data from a buffer they’ll be able to shadow the old variable, making sure it’s not possible to accidentally confuse what has been already parsed and what hasn’t. I’ve found this pattern works quite well when parsing. // src/parser.rs use byteorder::{BigEndian, ByteOrder}; struct Chunk<'a> { name: &'a [u8], data: &'a [u8], } impl<'a> Chunk<'a> { fn parse(buffer: &'a [u8]) -> Option<(Chunk<'a>, &'a [u8])> { if buffer.len() < 4 { return None; } let (name, buffer) = buffer.split_at(4); if buffer.len() < std::mem::size_of::<u32>() { return None; } let (num_bytes, buffer) = buffer.split_at(std::mem::size_of::<u32>()); let num_bytes: usize = BigEndian::read_u32(num_bytes).try_into().unwrap(); if num_bytes > buffer.len() { return None; } let (data, rest) = buffer.split_at(num_bytes); let chunk = Chunk { name, data }; Some((chunk, rest)) } } Now we can read a Chunk from the front of a byte buffer, we can start working on the Parser. Instead of leaving all the state and code inline like they did in blob_parse(), I’ve decided to pull intermediate values into their own Parser struct and give each chunk type its own handle_XXX() method. That just helps to keep functions at a manageable size and improve readability. // src/parser.rs use crate::{Account, Share, App, DecryptionKey, VaultParseError}; #[derive(Debug, Default)] struct Parser { vault_version: Option<u64>, accounts: Vec<Account>, shares: Vec<Share>, app: Option<App>, local: bool, } impl Parser { fn new() -> Self { Parser::default() } fn parse( &mut self, mut buffer: &[u8], decryption_key: &DecryptionKey, ) -> Result<(), VaultParseError> { while let Some((chunk, rest)) = Chunk::parse(buffer) { buffer = rest; self.handle_chunk(chunk, decryption_key)?; } Ok(()) } } You can see the Parser::parse() method just reads chunks and passes them to the Parser::handle_chunk() method. Likewise, Parser::handle_chunk() just does a match on the chunk’s name and passes the chunk body to the appropriate method. // src/parser.rs impl Parser { ... fn handle_chunk( &mut self, chunk: Chunk<'_>, decryption_key: &DecryptionKey, ) -> Result<(), VaultParseError> { match chunk.name { b"LPAV" => { self.vault_version = chunk.data_as_str()?.parse().ok(); }, b"ACCT" => self.handle_account(chunk.data, decryption_key)?, b"ATTA" => self.handle_attachment(chunk.data)?, b"LOCL" => self.local = true, b"SHAR" => self.handle_share(chunk.data)?, b"AACT" => self.handle_app(chunk.data, decryption_key)?, _ => {}, } Ok(()) } fn handle_account(&mut self, buffer: &[u8], decryption_key: &DecryptionKey) -> Result<(), VaultParseError> { self.accounts.push(parse_account(buffer, decryption_key)?); Ok(()) } fn handle_attachment(&mut self, buffer: &[u8]) -> Result<(), VaultParseError> { let attachment = parse_attachment(buffer)?; match self.accounts.iter_mut().find(|account| account.id == attachment.parent) { Some(parent) => { parent.attachments.push(attachment); }, None => return Err(VaultParseError::AttachmentWithoutAccount { attachment_id: attachment.id, account_id: attachment.parent, }), } Ok(()) } fn handle_share(&mut self, buffer: &[u8]) -> Result<(), VaultParseError> { self.shares.push(parse_share(buffer)?); Ok(()) } fn handle_app(&mut self, buffer: &[u8], decryption_key: &DecryptionKey) -> Result<(), VaultParseError> { self.app = Some(parse_app(buffer, decryption_key)?); Ok(()) } } Let’s have a think about what we’ll need to write the parse_account() function. In LastPass parlance, an Account is the fundamental unit in the vault. These are used to represent things like account credentials (e.g. username and password), it lets you attach a URL so you can quickly jump to the website, you can have notes (a free-form string), attached files, and much more. As I’ve coded it, an Account looks something like this: // src/account.rs use crate::{Attachment, DecryptionError, DecryptionKey, Id}; use url::Url; /// A single entry, typically a password or address. pub struct Account { pub id: Id, /// The account's name. pub name: String, /// Which group the account is in (think of it like a directory). pub group: String, /// The URL associated with this account. pub url: Url, /// Any notes that may be attached. pub note: String, pub note_type: String, /// Did the user mark this [Account] as a favourite? pub favourite: bool, /// The associated username. pub username: String, /// The associated password. pub password: String, /// Should we prompt for the master password before showing details to the /// user? pub password_protected: bool, /// An encrypted copy of the key used to decode this [Account]'s /// attachments. pub encrypted_attachment_key: String, /// Does this account have any [Attachment]s? pub attachment_present: bool, pub last_touch: String, pub last_modified: String, /// Files which may be attached to this [Account]. pub attachments: Vec<Attachment>, } // src/attachment.rs /// Metadata about an attached file. pub struct Attachment { pub id: Id, /// The ID of the parent [Account]. pub parent: Id, /// The file's mimetype. pub mime_type: String, /// An opaque string which is used by the backend to find the correct /// version of an attached file. pub storage_key: String, /// The size of the attachment, in bytes. pub size: u64, /// The attachment's filename, encrypted using the account's /// attachment_key. pub encrypted_filename: String, } Like a lot of core business objects tend to do, you can see the Account has grown a large number of fields over the years. To help handle the monotony of parsing dozens of fields, lastpass-cli has introduced a couple helper macros and functions. // vendor/lastpass-cli/blob.c static bool read_item(struct chunk *chunk, struct item *item) { ... } static char *read_hex_string(struct chunk *chunk) { ... } static char *read_plain_string(struct chunk *chunk) { ... } static char *read_crypt_string(struct chunk *chunk, const unsigned char key[KDF_HASH_LEN], char **stored_base64) { ... } static int read_boolean(struct chunk *chunk) { ... } #define entry_plain_at(base, var) do { \ char *__entry_val__ = read_plain_string(chunk); \ if (!__entry_val__) \ goto error; \ base->var = __entry_val__; \ } while (0) #define entry_plain(var) entry_plain_at(parsed, var) #define entry_hex_at(base, var) do { \ char *__entry_val__ = read_hex_string(chunk); \ if (!__entry_val__) \ goto error; \ base->var = __entry_val__; \ } while (0) #define entry_hex(var) entry_hex_at(parsed, var) #define entry_boolean(var) do { \ int __entry_val__ = read_boolean(chunk); \ if (__entry_val__ < 0) \ goto error; \ parsed->var = __entry_val__; \ } while (0) #define entry_crypt_at(base, var) do { \ char *__entry_val__ = read_crypt_string(chunk, key, &base->var##_encrypted); \ if (!__entry_val__) \ goto error; \ base->var = __entry_val__; \ } while (0) #define entry_crypt(var) entry_crypt_at(parsed, var) #define skip(placeholder) do { \ struct item skip_item; \ if (!read_item(chunk, &skip_item)) \ goto error; \ } while (0) The only non-trivial helper is read_crypt_string(), the equivalent of our DecodeKey::decode(). The rest just pop the next item from a Chunk and parse it into the desired format. From here, we can see how the account_parse() function is implemented. It’s not complicated per-se, just long. // vendor/lastpass-cli/blob.c static struct account *account_parse(struct chunk *chunk, const unsigned char key[KDF_HASH_LEN]) { struct account *parsed = new_account(); entry_plain(id); entry_crypt(name); entry_crypt(group); entry_hex(url); entry_crypt(note); entry_boolean(fav); skip(sharedfromaid); entry_crypt(username); entry_crypt(password); entry_boolean(pwprotect); skip(genpw); skip(sn); entry_plain(last_touch); skip(autologin); skip(never_autofill); skip(realm_data); skip(fiid); skip(custom_js); skip(submit_id); skip(captcha_id); skip(urid); skip(basic_auth); skip(method); skip(action); skip(groupid); skip(deleted); entry_plain(attachkey_encrypted); entry_boolean(attachpresent); skip(individualshare); skip(notetype); skip(noalert); entry_plain(last_modified_gmt); skip(hasbeenshared); skip(last_pwchange_gmt); skip(created_gmt); skip(vulnerable); if (parsed->name[0] == 16) parsed->name[0] = '\0'; if (parsed->group[0] == 16) parsed->group[0] = '\0'; if (strlen(parsed->attachkey_encrypted)) { parsed->attachkey = cipher_aes_decrypt_base64( parsed->attachkey_encrypted, key); } if (!parsed->attachkey) parsed->attachkey = xstrdup(""); /* use name as 'fullname' only if there's no assigned group */ if (strlen(parsed->group) && (strlen(parsed->name) || account_is_group(parsed))) xasprintf(&parsed->fullname, "%s/%s", parsed->group, parsed->name); else parsed->fullname = xstrdup(parsed->name); return parsed; error: account_free(parsed); return NULL; } Our parse_account() function looks quite similar, although deciding to just use helper functions and not macros means it’s more visually cluttered. pub(crate) fn parse_account( buffer: &[u8], decryption_key: &DecryptionKey, ) -> Result<Account, VaultParseError> { let (id, buffer) = read_parsed(buffer, "account.id")?; let (name, buffer) = read_encrypted(buffer, "account.name", decryption_key)?; let (group, buffer) = read_encrypted(buffer, "account.group", decryption_key)?; let (url, buffer) = read_hex_string(buffer, "account.url")?; let (note, buffer) = read_encrypted(buffer, "account.note", &decryption_key)?; let (fav, buffer) = read_bool(buffer, "account.fav")?; let buffer = skip(buffer, "account.sharedfromaid")?; let (username, buffer) = read_encrypted(buffer, "account.username", decryption_key)?; let (password, buffer) = read_encrypted(buffer, "account.password", decryption_key)?; let (password_protected, buffer) = read_bool(buffer, "account.pwprotect")?; let buffer = skip(buffer, "account.genpw")?; let buffer = skip(buffer, "account.sn")?; let (last_touch, buffer) = read_str_item(buffer, "account.last_touch")?; let buffer = skip(buffer, "account.autologin")?; let buffer = skip(buffer, "account.never_autofill")?; let buffer = skip(buffer, "account.realm_data")?; let buffer = skip(buffer, "account.fiid")?; let buffer = skip(buffer, "account.custom_js")?; let buffer = skip(buffer, "account.submit_id")?; let buffer = skip(buffer, "account.captcha_id")?; let buffer = skip(buffer, "account.urid")?; let buffer = skip(buffer, "account.basic_auth")?; let buffer = skip(buffer, "account.method")?; let buffer = skip(buffer, "account.action")?; let buffer = skip(buffer, "account.groupid")?; let buffer = skip(buffer, "account.deleted")?; let (attachkey_encrypted, buffer) = read_str_item(buffer, "account.attachkey_encrypted")?; let (attachment_present, buffer) = read_bool(buffer, "account.attachpresent")?; let buffer = skip(buffer, "account.individualshare")?; let (note_type, buffer) = read_str_item(buffer, "account.notetype")?; let buffer = skip(buffer, "account.noalert")?; let (last_modified_gmt, buffer) = read_str_item(buffer, "account.last_modified_gmt")?; let buffer = skip(buffer, "account.hasbeenshared")?; let buffer = skip(buffer, "account.last_pwchange_gmt")?; let buffer = skip(buffer, "account.created_gmt")?; let buffer = skip(buffer, "account.vulnerable")?; let _ = buffer; Ok(Account { id, name, username, password, password_protected, note: note.to_string(), note_type: note_type.to_string(), last_touch: last_touch.to_string(), encrypted_attachment_key: attachkey_encrypted.to_string(), attachment_present, favourite: fav, group, last_modified: last_modified_gmt.to_string(), url: Url::parse(&url).map_err(|e| VaultParseError::BadParse { field: "account.url", inner: Box::new(e), })?, attachments: Vec::new(), }) } I’m not going to go show too much more parsing code (because it’s all kinda the same and you can read it on github), but I’d like to show how simple it is to read an encrypted field is. Most of the code is actually dedicated to providing detailed parse errors to the caller. // src/parser.rs fn read_encrypted<'a>( buffer: &'a [u8], field: &'static str, decryption_key: &DecryptionKey, ) -> Result<(String, &'a [u8]), VaultParseError> { // read the next "item" (&[u8]) from the front of our buffer let (ciphertext, buffer) = read_item(buffer, field)?; // then decrypt it using our decryption key let decrypted = decryption_key .decrypt(ciphertext) .map_err(|e| VaultParseError::UnableToDecrypt { field, inner: e })?; // and interpret the decrypted text as a UTF-8 string let decrypted = String::from_utf8(decrypted) .map_err(|e| VaultParseError::BadParse { field, inner: Box::new(e) })?; Ok((decrypted, buffer)) } We’re actually able to read the Vault into memory and start looking at its contents now! Let’s update the example executable so it’ll log in and print out the first Account in my test vault. $ RUST_LOG=info cargo run --username $EMAIL --password=$PASSWORD
Sending a request to https://lastpass.com/getaccts.php
Account {
id: Id(
"533903346832032070",
),
group: "",
note: "This is a super secure note.",
note_type: "Generic",
favourite: false,
encrypted_attachment_key: "!MOEcIddt5GaMMH8eoMWyRA==|BWdjMSoIvClMRyWrDdIlz38tZiU3O1nmcbg95PRXCT4zKLTTG4s0OD9v/co2l2PwNaKL4oaVPSIB8oUFhk3kAl77qBbrkAH03lWY/wIModA=",
attachment_present: true,
last_touch: "0",
last_modified: "1586717786",
attachments: [
Attachment {
id: Id(
"533923346832032065-27281",
),
parent: Id(
"533923346832032065",
),
mime_type: "other:txt",
storage_key: "100000020283",
size: 70,
encrypted_filename: "!zdLMAcQ2okxs3MFWNjoCaw==|B7NqfcNPX0IbYFXNtykqEw==",
},
],
}
An interesting part about accounts is that each gets an encrypted_attachment_key field. This is a key that is base64-encoded and encrypted using your master key, and is what you use for all attachment-related decryption.
Let’s give the Account a helper method for extracting the account key.
// src/account.rs
impl Account {
/// Get the key used to work with this [Account]'s attachments.
pub fn attachment_key(
&self,
decryption_key: &DecryptionKey,
) -> Result<DecryptionKey, DecryptionError> {
let hex = decryption_key.decrypt_base64(&self.encrypted_attachment_key)?;
let key = DecryptionKey::from_hex(&hex)?;
Ok(key)
}
}
Now we’ve got the attachment key, we can decrypt an Attachment’s filename from the metadata stored in the vault.
// src/attachment.rs
use crate::{DecryptionError, DecryptionKey, Id};
#[derive(Debug, Clone, PartialEq)]
#[non_exhaustive]
pub struct Attachment {
pub id: Id,
/// The ID of the parent [crate::Account].
pub parent: Id,
/// The file's mimetype.
pub mime_type: String,
/// An opaque string which is used by the backend to find the correct
/// version of an attached file.
pub storage_key: String,
/// The size of the attachment, in bytes.
pub size: u64,
/// The attachment's filename, encrypted using the account's attachment_key.
pub encrypted_filename: String,
}
impl Attachment {
pub fn filename(
&self,
attachment_key: &DecryptionKey,
) -> Result<String, DecryptionError> {
attachment_key
.decrypt_base64(&self.encrypted_filename)
.map(|filename| String::from_utf8(filename).unwrap())
}
}
So now we’re able to read an attachment’s filename.
It may not sound like much, but by this point we’ve actually gone through three levels of encryption…
1. First we needed a login key to prove who we are
2. Then we needed to use the master decryption key so we can read things like an account’s name, associated username and password, and extract the attachment key
3. Then we used the attachment key to read the attachment’s filename
It looks like the Attachment’s storage_key field doesn’t actually have anything to do with encryption. When I first saw it, my thoughts were “oh great, yet another layer of encryption”, but after printing the value out you can see it’s obviously not a key or encrypted data.
Don’t just take my word on it though, here’s the Debug representation of an Attachment:
Attachment {
id: Id(
"533903346832032070-27282",
),
parent: Id(
"533903346832032070",
),
mime_type: "other:txt",
storage_key: "100000027282",
size: 70,
encrypted_filename: "!zdLMAcQ9okxR3MFWNjoCaw==|B7NqfcNPX0IayFXNtxkqEw==",
}
The value 100000027282 seems far too regular to be anything related to crypto, so I’m guessing the use of the word “key” is intended as “unique identifier”.
I’m guessing it’s an ID that LastPass use to refer to a particular resource stored on S3 or in a database somewhere. I doubt only 27282 attachments have been uploaded to LastPass, so that means they’re probably randomising storage keys instead of using an auto-incrementing number.
To figure out how attachments are downloaded, let’s have another look at the lastpass-cli source code.
At the very bottom of endpoints.h there’s a declaration for the lastpass_load_attachment() function… That seems promising 🙂
// vendor/lastpass-cli/endpoints.c
/*
* Get the attachment for a given attachment id. The crypttext is returned
* and should be decrypted with account->attachkey. The pointer returned
* in *result should be freed by the caller.
*/
const char *shareid,
struct attach *attach,
char **result)
{
char *p;
*result = NULL;
struct http_param_set params = {
.argv = NULL,
.n_alloced = 0
};
"token", session->token,
"getattach", attach->storagekey,
NULL);
if (shareid) {
"sharedfolderid", shareid,
NULL);
}
session, NULL,
¶ms);
free(params.argv);
return -ENOENT;
/* returned string is json-encoded base64 string; unescape it */
while (*p) {
if (*p == '\\') {
memmove(p, p + 1, strlen(p));
} else {
p++;
}
}
return 0;
}
This lastpass_load_attachment() function seems fairly straightforward.
1. Send a request to getattach.php with a token and getattach, our storage_key (I don’t care about shared folders for now, so we can ignore the sharedfolderid parameter)
2. Parse the string that’s returned as a JSON string (i.e. wrapped in quotes and with escape characters)
3. Base64-decode it to get the blob of bytes that makes up the encrypted attachment
4. Decrypt the attachment using the attachment key. This isn’t strictly part of lastpass_load_attachment(), but I’d prefer to do it all in the same function so callers aren’t second-guessing whether the Vec<u8> they’ve got is still encrypted
By now you’ve already seen me write several endpoint definitions and we’ve used the DecryptionKey once or twice, so nothing should be overly new here.
First we define a Data type to hold our form data.
// src/endpoints/load_attachment.rs
use serde_derive::Serialize;
#[derive(Debug, Serialize)]
struct Data<'a> {
token: &'a str,
#[serde(rename = "getattach")]
storage_key: &'a str,
}
I’m also creating a dedicated error type, because no other endpoints deal with these particular base64-decoding and decryption errors.
// src/endpoints/load_attachment.rs
#[derive(Debug, thiserror::Error)]
/// The HTTP client encountered an error.
#[error("Unable to send the request")]
HttpClient(#[from] reqwest::Error),
Decrypt(#[from] crate::DecryptionError),
#[error("Unable to decode the decrypted attachment")]
Decode(#[from] base64::DecodeError),
}
And finally, the endpoint function itself.
// src/endpoints/load_attachment.rs
client: &Client,
hostname: &str,
token: &str,
storage_key: &str,
decryption_key: &DecryptionKey,
let data = Data { token, storage_key };
let url = format!("https://{}/getattach.php", hostname);
let response = client
.post(&url)
.form(&data)
.send()
.await?
.error_for_status()?;
let ciphertext: String = response.text().await?;
let data = decryption_key.decrypt_base64(&ciphertext)?;
// not only was the ciphertext in base64, the attachment body was too
}
The thing I really like about this is once you have the underlying abstractions (key management, an ergonomic HTTP client, async-await, the base64 crate, serialization to/from arbitrary formats, etc.) everything sort of falls into place.
I mean, loading an attachment only took about 30 lines of easily readable code and about half of that is taken up by the definitions for Data and LoadAttachmentError.
And check it out…
*** My Secure Note - hello-world.txt (70 bytes) ***
Sending a request to https://lastpass.com/getattach.php
Hello, World
It was able to download our hello-world.txt attachment! 🎉
## Conclusions
Sorry if it took a while, but we got there in the end. It turns out reading through the source code for a 15,000-line C program and explaining how my 2,000-line Rust implementation works takes a while…
I’m no professional cartographer, but it seems like the LastPass system has been pretty well designed. They’ve deliberately separated the LoginKey from the key you use to decrypt your vault. Plus the defence-in-depth (e.g. attachment keys) should help protect users from attacking a vault that’s been cached locally.
You’ve probably noticed already but I’m also pleasantly surprised at how easy this was to implement. Rust has a really nice ecosystem, and thanks to the work of projects like serde, reqwest, and RustCrypto, I have all the necessary pieces at my fingertips. You’d hardly notice that async-await is only 4 months old.
The hardest bit was actually deciphering the blob parsing code, and that’s because it was written in C and the lack of existing unit tests meant I spent a fair amount of time running lpass under the debugger to see what certain values are meant to be. It’s not a deal breaker, but you’d think a C program for accessing your passwords and bank account details would have some sort of unit testing or input fuzzing…
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http://mathhelpforum.com/math-topics/26036-electric-field.html
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# Math Help - electric field.
1. ## electric field.
An electric field of 281,000 N/C points due west at a certain point. What are the magnitude and direction of the force that acts on a charge of -7.4 µC at this spot?
magnitude in Newtons
direction?
couldn't this be set up as: F = (-7.4uC) * (281,000 N/C)
is uC the same as C? just uC is a micro Coulomb?
also, do i need this expressed in scientific notation to make it correct.
2. Originally Posted by rcmango
An electric field of 281,000 N/C points due west at a certain point. What are the magnitude and direction of the force that acts on a charge of -7.4 µC at this spot?
magnitude in Newtons
direction?
couldn't this be set up as: F = (-7.4uC) * (281,000 N/C)
is uC the same as C? just uC is a micro Coulomb?
also, do i need this expressed in scientific notation to make it correct.
To get a force in units of newton you need to express -7.4uC as $-7.4 x 10^{-6}$ C, then do the multiplication. Giving the answer using scientific notation is probably the simplest way of giving it.
With the cancellation of powers of 10, it'll actually just be F = -7.4 x 0.281 N = ......
You should be able to the multiplication on paper - without a calculator
And you do realise that you 'lose' the minus once you give the direction ....?
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http://aas.org/archives/BAAS/v34n4/aas201/827.htm
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AAS 201st Meeting, January, 2003
Session 16. Stars in SDSS
Poster, Monday, January 6, 2003, 9:20am-6:30pm, Exhibit Hall AB
## [16.04] Magnetic Activity in Low Mass Stars: SDSS Results
S. L. Hawley, A. A. West, K. R. Covey, S. N. Raymond, L. M. Walkowicz (University of Washington)
We present a study of the magnetic activity properties of low-mass stars in the Sloan Digital Sky Survey. Using the H\alpha emission line as an activity indicator, we examine the fraction of active stars as a function of spectral type and find a peak near type M7, confirming previous results. We investigate the ratio of the luminosity emitted in H\alpha compared to the bolometric luminosity for each star, and find a roughly constant ratio (with large scatter) over the range M0-M9. There does not appear to be a decrease in the ratio for types M8-M9, in contrast to previous determinations. We also explore the effect of metallicity on activity, and examine whether activity is correlated with changes in the SDSS colors.
Bulletin of the American Astronomical Society, 34, #4
© 2002. The American Astronomical Soceity.
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https://brilliant.org/problems/atomic-spectra/
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# Atomic spectra
Chemistry Level 2
What would be the wavelength of the radiation emitted from an $$\text{Li}^{2+}$$ if the transition occurred from $$n=3$$ to $$n=2?$$
Hint: The transition from $$n=3$$ to $$n=2$$ in a neutral hydrogen atom has a wavelength of $$656.1$$ nm.
×
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http://math.stackexchange.com/questions/128341/proof-for-an-inequality?answertab=active
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# Proof for an Inequality
Let $e^{e^x}=\sum\limits_{n\geq0}a_nx^n$, prove that
$$a_n\geq e(\gamma\log n)^{-n}$$
for $n\geq2$, where $\gamma$ is some constant great than $e$.
-
Can I ask which topics have recently been covered in your course or book? – bgins Apr 5 '12 at 21:42
I present three different approaches below, which may or may not appeal to you in helping you to formulate your own answer.
I think you can get this from the Taylor series at $0$ just by differentiating. If $y=y^{(0)}$ is your function and $y^{(n)}=yf_n(e^x)$, then $f_0(t)=1$, $y'=ye^x\implies f_1(t)=t$ and $y^{(n+1)}=y'f_n(e^x)+y\,e^xf_n'(e^x)$ $\implies$ $f_{n+1}(t)=f_1f_n+t\,f_n'$. Now $a_n=\frac{e\,f_n(1)}{n!}$ and $f_n(1)=\href{http://en.wikipedia.org/wiki/Bell_number}{B_n}$ (as @Autolatry points out) and it shouldn't be hard to show that this sequence is increasing and has (more than) the desired growth.
Upon further reflection, we want to show that for $n\ge2$, $$a_n \ge e \left( \gamma \, \log n \right)^{-n}$$ $$\left( \gamma \, \log n \right)^{-n} \le \frac{a_n}{e} = \frac{B_n}{n!}$$ $$\gamma \, \log n \ge \left( \frac{a_n}{e} \right)^{-1/n} = \left( \frac{n!}{B_n} \right)^{1/n}$$ $$\gamma \ge \sup \gamma_n \qquad\text{for}\qquad \gamma_n = \frac1{\log n} \left( \frac{a_n}{e} \right)^{-1/n} = \frac1{\log n}\left( \frac{n!}{B_n} \right)^{1/n}$$
Experiment suggests that $\gamma_n$ has a global minimum at $\gamma_{37}=0.56352\,15372\,44847$, lies below its pseudonym, the Euler-Mascheroni constant, $0.57721\,56649\,01532\cdots$, for $17\le n\le 114$, and may have its global maximum at $\gamma_2=1.44269\,50408\,88963$, depending on its asymptotic value. Using a recent bound (Berend-Tassa 2010) for $B_n$ and Stirling's formula for the factorial, $$\gamma_n \ge \frac{\log(n+1)}{0.792\,n\,\log n}\Bigl( n! \Bigr)^{1/n} \approx \frac{\log(n+1)}{0.792\,\,n\log n}\cdot\frac{n}{e}\cdot\left(2\pi n\right)^{1/2n} \rightarrow\frac1{0.792\,e}\approx0.46449\,,$$ so that $\gamma=\gamma_2=\sup_{n\ge2}\gamma_n$ is in fact the best constant we can choose.
If we start from $y=e^{e^x}=\sum_{n=0}^{\infty}a_n\,x^n$ and differentiate to get $\sum_{n=0}^{\infty}(n+1)a_{n+1}\,x^n=y'=e^x\cdot e^{e^x}=\left(\sum_{n=0}^{\infty}\frac{x^n}{n!}\right)\left(\sum_{n=0}^{\infty}a_n\,x^n\right)=\sum_{n=0}^{\infty}\left(\sum_{k=0}^n\frac{a_k}{(n-k)!}\right)x^n$, then we need to show (perhaps inductively) that the recursion $(n+1)a_{n+1}=\sum_{k=0}^n\frac{a_k}{(n-k)!}$ implies the desired inequality. Now $a_0=a_1=e\cdot1$ and the first few values we care about are $a_2=e\cdot\frac22$, $a_3=e\cdot\frac56$, $a_4=e\cdot\frac{15}{24}$, which as we already know satisfy our inequality for $\gamma\ge\gamma_1$ for our inductive base ($n=2$). As inductive hypothesis (with cumulative induction), we assume the inequality for $k\le n$: $$a_k \ge e \left( \gamma \, \log k \right)^{-k}$$ from which it follows by induction (and from the recursion) that \eqalign{ \frac{a_{n+1}}{e}\,\left(\gamma\log(n+1)\right)^{n+1} &\ge \frac{\left(\gamma\log(n+1)\right)^{n+1}}{n+1} \sum_{k=0}^n \frac{(\gamma\log k)^{-k}}{(n-k)!} \\ & > \frac{\left(\gamma\log(n+1)\right)^{n+1}}{n+1} \sum_{k=0}^n \frac{(\gamma\log n)^{-k}}{(n-k)!} \\ & > \frac{\gamma\log(n+1)}{n+1} \sum_{k=0}^n \frac{(\gamma\log n)^{n-k}}{(n-k)!} \\ & > \frac{\gamma\log(n+1)}{n+1} \sum_{k=0}^n \frac{(\gamma\log n)^k}{k!} \\ & \color{red}{>} \frac{\gamma\log(n+1)}{n+1} \left(e^{\gamma\log n} - \frac{(\gamma\log n)^{n+1}}{(n+1)!} \right) \\ & = \frac{\gamma\log(n+1)}{n+1} \left(n^\gamma - \frac{(\gamma\log n)^{n+1}}{(n+1)!} \right) \\ & \color{blue}{\ge 1 \qquad\text{(what we want!)}} } where the last inequality (in red) follows from the error theorem for Taylor series. On the subsequent line, the two terms in parentheses exhibit opposite asymptotic behavior: the former grows toward $\infty$ for all $\gamma > 1$, while the latter decays toward $0$. We need only show that the last expression is $\color{blue}{\ge1}$ for some fixed $\gamma$ and all $n\ge2$. Clearly, this is true asymptotically for all $\gamma > 1$ by the relative asymptotic growth of $\log n$ versus $n^{\gamma-1}$ (e.g. using L'Hopital's rule). I suspect a slight modification of this argument would yield the result more elegantly.
-
Due to the expansion of the function $e^{e^x}$, we know that $a_n=\frac{eB_n}{n!}$. – Riemann Apr 5 '12 at 13:51
Yes, of course. Thanks! – bgins Apr 5 '12 at 14:41
Hint:
$$e^{e^{x}} = e \sum_{k=0}^{\infty} \frac{x^{k}B_{k}}{k!}$$
Where $B_{k}$ is the $k$-th Bell number which is the number of partitions of a set with k entries, or the number of equivalence relations on it. Starting with $B_{0} = B_{1} = 1$, the first few Bell numbers are: $$1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975 \ldots$$
-
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http://wikieducator.org/Thread:Bullet_and_Number_Lists_(2)
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# Bullet and Number Lists
Jump to: navigation, search
Hi
Can you specify which examples are confusing and which ones you would like to replace?
Thanks
19:31, 11 July 2009
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https://www.physicsforums.com/threads/please-check-my-working.306353/
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1. Apr 10, 2009
### kateman
There are 3 questions below with my working and answers, could someone please check that I am right, even if you can only give approval or correction on just one question and nothing else - anything would be appreciated. Please forgive my not following the template, as I didn't think it would work with checking correct answers. Thanks for any responces!
-----------------------------------------------------------------
Q1: A theoretical salt (X2Y3) (with Ksp= 6.26 x 10 -15 ) is in a saturated solution. What is its millimolar concentration (mM) of X?
A1: Ksp= [X]2 [Y]3 = 6.26 x 10 -15
therefore concentration of Y = 3/2 concentration of X (or is it 2/3, iam not sure?)
therefore rewrite Y as [3/2 X]3
therefore Ksp= [X]2x 27/8 X3
= 27/8 [X]5
therefore, with rearranging, [M] = 1.131514468x10-3 mol/L
= 1.131514468 mM/L
-------------------------------------------------------------------
Q2: A reaction at temperature of 287K gives a change in enthaply of -7KJ and a free energy change of -10kJ, what is the change in entropy for this reaction (in J/K)?
A2: $$\Delta$$G = $$\Delta$$H - T$$\Delta$$S
with rearranging: $$\Delta$$S = $$\Delta$$H - $$\Delta$$G / T
=(-7 - -10)/287 = 0.010452961 J/K
That doesn't seem right to me.
-----------------------------------------------------------------
Q3: If a 0.5 L solution at a temperature of 294.75 K contains 13.7g of an unknown solute (with a molecular mass of 60.094g), what is its osmotic pressure in atmospheres?
A3: since moles (n) = concentration (c)/ volume (v) = mass (m)/ molecular weight (M)
then C = m/Mv = 13.7 / (60.094x0.5) = 0.455952341 mol/L
Now use the values of C, T and the gas constant (8.314 J/mol K) into the osmotic pressure formula P=CRT
P= 0.455952341x8.314x294.75 = 1117.334694 Pa (am I right to say that its in pascals, or is it in killapascals [Kpa]?)
atmospheres = 101.325 Kpa = 101325 Pa
osmotic pressure (in atmospheres) = 1117.334694/101325 = 0.011027236 atms
This is something iam really not sure about, the answer seems almost wrong to me but iam not sure where I would have gone wrong in my working, can someone please help? It would be very much appreciated!
Thank you!
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
2. Apr 10, 2009
### Staff: Mentor
You use too many significant digits every time.
First looks OK.
Second and third - approach seems correct (even if in the second your formula misses parantheses), but second opinion won't hurt.
3. Apr 10, 2009
### kateman
Thank you Borek, and I agree, I'd still appreciate at least another person's opinion on my working.
Similar Discussions: Please Check my working
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https://www.physicsforums.com/threads/complexification-of-a-vector-space.182966/
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# Complexification of a vector space
1. Sep 4, 2007
### quasar_4
Hello all,
I've just learned a bit about the complexification of a real vector space V to include scalar multiplication by complex numbers. A bit of confusion has ensued, which I am hoping someone can help me with conceptually: 1) how does one generate a basis for the new space Vc? It seems that one obtains the basis by somehow extending the basis for V, but I am very confused about this. In fact, I'm not exactly sure how vectors in the new space should be defined at all. :yuck:
2) does anyone know how one would prove that the dim(Vc)=dim(V)? I'm not asking for homework; I've just heard that this is the case, but haven't seen anything proved.
3) Under what circumstances would one want to complexify V? anyone have some good examples?
Thanks.
2. Sep 4, 2007
### dextercioby
1. If the vectors in the real space are C-linear independent, then they provide a basis for the complexfication.
2. This part is valid in the case the condition in 1. is satisfied.
3. Complexification of Lie algebras is a tool useful for representation theory.
3. Sep 4, 2007
### matt grime
I don't like the previous answer.
1. the bases are the same.
2. you mean dim_C of one and dim_R of the other - since, by 1, the basis sets are the same this is a vacuous question.
3. extension of scalars is in general an important concept, far beyond dexter's note. Please google for it.
4. Sep 5, 2007
### mathwonk
complexification makes all characteristic polynomials split.
5. Sep 18, 2007
### quasar_4
the basis thing is still a bit odd. According to my class if the basis for V is given by {e1,e2,...,en} then the basis for Vc is given by {(e1,0),(e2,0),...,(en,0)}. But then, I guess that is basically the same except that we've sneakily made the vectors into ordered pairs. Somehow this is now representative of VxV?
6. Sep 18, 2007
### mathwonk
the complexification of the space with real basis (1,0), (0,1), is the complex space with absis (1,0),(0,1).
i.e. the complexification of the space of ordered pairs of reals, is the space of ordered pairs of complexes.
or try this one: if V is a real vector space, then since C is also a real vector space, you can consider all real linear maps from V to C. this is a complex vector space since you can multiply the values by complex numbers.
or you could let V* be the real dual of V and consider all real linear maps V*-->C.
then given an element v of V, you could define a map v**:V*-->C by sending the real linear map t in V*, to the complex number t(v) = v**(t). this shows how to embed V into the new space HomR(V*,C). so we could regard HomR(V*,C) as a complex vector space which contains V, namely as the subspace of maps with images in R, i.e,. then V is the subspace HomR(V*,R) = V** = V (in finite dimensions only of course.)
then any real basis v1,...vn of V corresponds to a real basis of HomR(V*,R) and also a complex basis v1**,...,vn** of HomR(V*,C).
how do you like them apples? i made that up just for you.
Last edited: Sep 18, 2007
7. Sep 18, 2007
### mathwonk
so i guess i want my complexification of V to be a complex vector space W containing V as a real subspace and such that W equals V + iV, which is a direct sum decomposition of the real space underlying W, as a sum of two real subspaces.
it should follow that a subset of V is real independent if and only if it is complex independent as a subset of W, and spans V over R iff it spans W over C.
In particular, any real basis of V is a complex basis of W.
8. Sep 18, 2007
### mathwonk
i am getting no feedback on my post 6, of which i am somewhat proud. i.e. i have given you a construction that does not mention tensor products, hence is elementary.
9. Sep 18, 2007
### mathwonk
as stated above, after complexifying, there should be more eigenvectors.
i.e. the main point is not just complexifying the spaces but also the maps.
i.e. every real linear map of V-->V should become a complex linear map from the complexification to itself. and presumably with the same characteristic polynomial?
so a 90 degree rotation, becomes multiplication by i or -i.
presumably then one can transform the proof of diagionalizability of the complex operator into a classification of the real operators. i.e. we should be able to use the complex spectral theorem to deduce a real classification for orthogonal matrices.
i.e. just as in ode, the diff eq f''+f = 0 has compklex basis of solutions either e^(ix) or e^(-ix), but realsolutiions cosc and sinx.
i guess the complexification of the real solution space should be the complex solutiion space. and just as letting d act on sin, cos, rotates them into each other, letting it act on thiose exponentials, gives eigenfunctiions.
you are beginnin to make this seem interesting, once you combine it with ode, as all linear algebra should be!!!! but seldom is.
Last edited: Sep 18, 2007
10. Sep 18, 2007
### mathwonk
here is alittle easier sounding version of that construction. take any n objects and call them e1,...,en.
then define a vector space V as the set of all functions from the set {e1,...,en}-->R.
Then define the complexification of V to be the set of all functiuions from
{e1,...,en}-->C. notice that in both cases a basis consist of the n functions ei*, each taking exactly one of the ei to 1, and the others to 0.
thus the same set of n things is an R basis for V and a C basis for its compl.....tion.
but i regress, as it gets late. i will retire before i become rude again.
11. Sep 20, 2007
### mathwonk
notice that the complexification of a real space has more structure than a general complex space, i.e. it also has a real conjugation operator on it, defined by composing the functioins above by complex conjugation.
or if you like by writing each vector as an element of V + iV, and using the identity on the first summand and the minus map on the second one.
12. Sep 20, 2007
### mathwonk
13. Sep 27, 2007
### quasar_4
wow - it's taken a few days for my brain to absorb all of this. It is making more sense now though. So, should one care to take a coordinate vector [x] on the basis B for V and rewrite [x] on the basis B' for the complexified space, why would the components of [x] change at all? wouldn't our change of basis matrix just be the identity?
14. Sep 27, 2007
### quasar_4
in fact, that seems like a trivial question. There isn't effectively a "change" of basis at all, the only thing happening is that you'd have to rewrite your vectors as an ordered pair (right?) so [x]={x1, x2,...,xn} rewritten for the basis for W becomes [x]={(x1,0),(x2,0),...,(xn,0)}. Is that correct?
15. Sep 27, 2007
### quasar_4
oh, and, I liked the ode stuff. To be honest, no one's even mentioned odes to me since about 3 years ago. I wish they did tie them more into linear algebra. It would make for a lovely depth of understanding on my diff eqs.
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https://www.physicsforums.com/threads/question-about-molecular-orbital-theory.595622/
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# Question about molecular orbital theory
1. Apr 11, 2012
### reyrey389
I know that the sigma 2p bonding orbital could be less/higher in energy than the pi 2p bonding (based on if it is C2,N2,B2 etc), but
Why is the sigma 2p antibonding orbital always higher in energy than the pi 2p antibonding one?
2. Apr 12, 2012
### DrDu
When you neglect in a first step the s orbitals, the sigma bonding p orbital would be below the pi bonding p orbitals. However, in the second step the sigma bonding p orbital mixes with the sigma bonding s orbitals which shifts them up in energy. Also the antibonding p orbital can be shifted up by that mechanism, although the effect is weaker due to their larger energetic separation and it would not change the ordering of the orbitals.
Similar Discussions: Question about molecular orbital theory
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http://ptsymmetry.net/?p=1804&utm_source=rss&utm_medium=rss&utm_campaign=pt-non-pt-symmetric-and-non-hermitian-hellmann-potential-approximate-bound-and-scattering-states-with-any-ell-values
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## PT-/non-PT-Symmetric and non-Hermitian Hellmann Potential: Approximate Bound and Scattering States with Any $$\ell$$-Values
Altug Arda, Ramazan Sever
We investigate the approximate bound state solutions of the Schrodinger equation for the PT-/non-PT-symmetric and non Hermitian Hellmann potential. Exact energy eigenvalues and corresponding normalized wave functions are obtained. Numerical values of energy eigenvalues for the bound states are compared with the ones obtained before. Scattering state solutions are also studied. Phase shifts of the potential are written in terms of the angular momentum quantum number $$\ell$$.
http://arxiv.org/abs/1409.0518
Quantum Physics (quant-ph)
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https://www.investopedia.com/terms/f/fixed-chargecoverageratio.asp
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• General
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# Fixed-Charge Coverage Ratio (FCCR): Examples, Formula, Meaning
## What Is the Fixed-Charge Coverage Ratio?
The fixed-charge coverage ratio (FCCR) measures a firm's ability to cover its fixed charges, such as debt payments, interest expense, and equipment lease expense. It shows how well a company's earnings can cover its fixed expenses. Banks will often look at this ratio when evaluating whether to lend money to a business.
### Key Takeaways
• The fixed-charge coverage ratio (FCCR) shows how well a company's earnings can be used to cover its fixed charges such as rent, utilities, and debt payments.
• Lenders often use the fixed-charge coverage ratio to assess a company's overall creditworthiness.
• A high FCCR ratio result indicates that a company can adequately cover fixed charges based on its current earnings alone.
1:46
## The Formula for the Fixed-Charge Coverage Ratio Is:
\begin{aligned} &FCCR = \frac{EBIT + FCBT}{FCBT + i} \\ &\textbf{where:}\\ &EBIT=\text{earnings before interest and taxes}\\ &FCBT=\text{fixed charges before tax}\\ &i=\text{interest}\\ \end{aligned}
## How to Calculate the Fixed-Charge Coverage Ratio
The calculation for determining a company's ability to cover its fixed charges starts with earnings before interest and taxes (EBIT) from the company's income statement and then adds back interest expense, lease expense, and other fixed charges.
Next, the adjusted EBIT is divided by the amount of fixed charges plus interest. A ratio result of 1.5, for example, shows that a company can pay its fixed charges and interest 1.5 times out of earnings.
## What Does the Fixed-Charge Coverage Ratio Tell You?
The fixed-charge ratio is used by lenders looking to analyze the amount of cash flow a company has available for debt repayment. A low ratio often reveals a lack of ability to make payments on fixed charges, a scenario lenders try to avoid since it increases the risk that they will not be paid back.
To avoid this risk, many lenders use coverage ratios, including the times-interest-earned ratio (TIE) and the fixed-charge coverage ratio, to determine a company's ability to take on and pay for additional debt. A company that can cover its fixed charges at a faster rate than its peers is not only more efficient but more profitable. This is a company that wants to borrow to finance growth rather than to get through a hardship.
A company's sales and the costs related to its sales and operations make up the information shown on its income statement. Some costs are variable costs and dependent on the volume of sales over a particular time period. As sales increase, so do the variable costs. Other costs are fixed and must be paid regardless of whether or not the business has activity. These fixed costs can include items such as equipment lease payments, insurance payments, installment payments on existing debt, and preferred dividend payments.
## Example of the Fixed-Charge Coverage Ratio in Use
The goal of computing the fixed-charge coverage ratio is to see how well earnings can cover fixed charges. This ratio is a lot like the TIE ratio, but it is a more conservative measure, taking additional fixed charges, including lease expenses, into consideration.
The fixed-charge coverage ratio is slightly different from the TIE, though the same interpretation can be applied. The fixed-charge coverage ratio adds lease payments to earnings before income and taxes (EBIT) and then divides by the total interest and lease expenses.
Let's say Company A records EBIT of $300,000, lease payments of$200,000, and $50,000 in interest expense. The calculation is$300,000 plus $200,000 divided by$50,000 plus $200,000, which is$500,000 divided by \$250,000, or a fixed-charge coverage ratio of 2x.
The company's earnings are two times greater than its fixed costs, which is considered low. That's because the company would only be able to pay the fixed charges twice with the earnings it has, increasing the risk that it cannot make future payments. The higher this ratio is, the better.
Like the TIE, the higher the FCCR ratio, the better.
## Limitations of the Fixed-Charge Coverage Ratio
The FCCR doesn't consider rapid changes in the amount of capital for new and growing companies. The formula also doesn't consider the effects of funds taken out of earnings to pay an owner's draw or pay dividends to investors. These events affect the ratio inputs and can give a misleading conclusion unless other metrics are also considered.
For this reason, when banks evaluate a company's creditworthiness for a loan, they typically look at several other benchmarks in addition to the fixed-charge coverage ratio in order to gain a more complete view of the company's financial condition.
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http://www.cds.caltech.edu/~murray/wiki/index.php?title=CDS_140b_Spring_2014_Homework_1&oldid=17018
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# CDS 140b Spring 2014 Homework 1
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
R. Murray, D. MacMartin Issued: 2 Apr 2014 (Wed) CDS 140b, Spring 2014 Due: 9 Apr 2014 (Wed)
__MATHJAX__
Note: In the upper left hand corner of the second page of your homework set, please put the number of hours that you spent on this homework set (including reading).
1. Perko, Section 2.14, problem 1
(a) Show that the system
<amsmath>\aligned
\dot x&=a_{11}x+a_{12}y+Ax^2-2Bxy+Cy^2\\ \dot y&=a_{21}x-a_{11}y+Dx^2-2Axy+By^2
\endaligned</amsmath>
is a Hamiltonian system with one degree of freedom; i.e., find the Hamiltonian function $H(x,y)$ for this system.
(b) Given $f\in C^2(E)$, where $E$ is an open, simply connected subset of $\mathbb R^2$, show that the system $\dot{x}=f(x)$ is a Hamiltonian system on $E$ iff $\nabla\cdot f(x)=0$ for all $x\in E$.
2. Perko, Section 2.14, problem 7. Show that if $x_0$ is a strict local minimum of $V(x)$ then the function $V(x)-V(x_0)$ is a strict Lyapunov function (i.e., $\dot{V}<0$ for $x\neq 0$) for the gradient system $\dot x=-\mathrm{grad}V(x)$.
3. Perko, Section 2.14, problem 12. Show that the flow defined by a Hamiltonian system with one degree of freedom is area preserving. Hint: Cf. Problem 6 in Section 2.3
4. A planar pendulum (in the $x$-$z$ plane) of mass $m$ and length $\ell$ hangs from a support point that moves according to $x=a\cos (\omega t)$. Find the Lagrangian, the Hamiltonian, and write the first-order equations of motion for the pendulum.
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http://mathhelpforum.com/calculus/41199-curvature.html
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# Math Help - curvature
1. ## curvature
find the curvature K of the curve....
r(t) = 4t i + 3 cos t j + 3 sin t k
i am confused after i find r'(t)...
2. Originally Posted by chris25
find the curvature K of the curve....
r(t) = 4t i + 3 cos t j + 3 sin t k
i am confused after i find r'(t)...
Here is the formula
$\kappa=\frac{|\frac{dr}{dt} \times (\frac{dr}{dt})^2|}{|\frac{dr}{dt}|^3}$
I have to go to work. I will finish later if no one else has.
Good luck.
3. Originally Posted by TheEmptySet
Here is the formula
$\kappa=\frac{|\frac{dr}{dt} \times \color{red}(\frac{dr}{dt})^2\color{black}|}{|\frac {dr}{dt}|^3}$
I have to go to work. I will finish later if no one else has.
Good luck.
As far as I know, it's $\kappa = \frac{\left | \frac{dr}{dt} \times \frac{d^2r}{dt^2}\right |}{\left | \frac{dr}{dt} \right |^3} = \frac{\left | \dot {r} \times \ddot {r} \right |}{\left | r \right |^3}$
See here if you wonder how to get the formula:
Curvature -- from Wolfram MathWorld
4. Originally Posted by wingless
As far as I know, it's $\kappa = \frac{\left | \frac{dr}{dt} \times \frac{d^2r}{dt^2}\right |}{\left | \frac{dr}{dt} \right |^3} = \frac{\left | \dot {r} \times \ddot {r} \right |}{\left | r \right |^3}$
See here if you wonder how to get the formula:
Curvature -- from Wolfram MathWorld
@ wingless You are correct Thanks that is what I get for trying to do it in a hurry.
$r(t)=<4t,3\cos(t),3\sin(t)$
$\frac{dr}{dt}=<4,-3\sin(t),3\cos(t)>$
$\frac{d^2r}{dt^2}=<0,-3\cos(t),-3\sin(t)>$
Now we take the cross product to get
$\begin{vmatrix}
i & j & k \\
4 & -3\sin(t) & 3\cos(t) \\
0 & -3\cos(t) & -3\sin(t) \\
\end{vmatrix}=(9\sin^2(t)+9\cos(t))\vec i-(-12\sin(t)-0)\vec j+(-12\cos(t)-0)\vec k$
Simplifying and taking the magnitude we get
$=|<9,12\sin(t),-12\cos(t)>|=\sqrt{(9)^2+(12\sin(t))^2+(-12\cos(t))^2}$
$=\sqrt{81+144(\sin^{2}(t)+\cos^{2}(t))}=\sqrt{225} =15$
Now we need the magnitude of
$\bigg| \frac{dr}{dt}\bigg|=\sqrt{4^2+(-3\sin(t))^2+(3\cos(t))^2}=\sqrt{16+9(\sin^2(t)+\co s^2(t))}=\sqrt{25}=5$
Finally we get
$\kappa=\frac{15}{5^3}=\frac{3}{25}$
Yeah.
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https://www.physicsforums.com/threads/probability-question-on-school-classes.404227/
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# Homework Help: Probability question on school classes
1. May 19, 2010
1. The problem statement, all variables and given/known data
In a high-school graduating class of 100 students, 54 studied math, 69 studied history, and 35 studied both math and history. If 1 of the students is selected at random, find the probability that
(a) the student took math or history;
(b) the student did not take either of these subjects;
(c) the student took history but not math.
2. Relevant equations
P = n/N
3. The attempt at a solution
Ok. I am thinking that I actually need to figure out how many students took math only and history only (pretty sure this is just algebra).
So I know that there are 54 math students; this must include those who studied both. Thus, the number of students who studied *math only* is 54 - 35 = 19.
Similarly, those who took History only 69 - 35 = 34.
So for (a) P(M U H) = (19 + 34) / 100 = 53/100 ... but this is wrong. Book says 22/25. So I am off to a bad start. What am I screwing up here?
2. May 19, 2010
### gabbagabbahey
"or" is an inclusive word, so you also need to include the 35 who took both math and history
3. May 19, 2010
I guess an alternative approach to this would be
$P(M\cup H) = P(M) + P(H) - P(M\cap H)$
where M is the math set, H is the History set, etc.
Just curious as to why my first attempt fails?
EDIT:
I see. I was wondering about that and had somehow convinced myself that it was exclusive. In general, is "or" inclusive in probability? How about math in general?
4. May 19, 2010
### gabbagabbahey
Or is inclusive in math, probability and computer science...The only instance where "or" is exclusive , that comes to mind, is in common everyday conversational usage.
5. May 19, 2010
Hence why my waitress never says, "that comes with soup or salad or both."
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https://brilliant.org/problems/5-real/
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# 5 real
Algebra Level 3
I have 5 real numbers whose product is non-zero. Now, I increase each of the 5 numbers by 1 and again multiply all of them. Is it possible that this new product is the same as the non-zero number obtained earlier?
×
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https://math.stackexchange.com/questions/585176/splitting-integrand/585185
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# Splitting integrand
Consider the integral:
$\int \frac{1}{(x+3)(5+2x)}$
My teacher splits this first into two unknown fractions with two unknown numerators, namely:
$\frac{A}{(x+3)}+\frac {B}{(5+2x)}$
He then goes on to perform some sort of magic to find that A = -1 and B = 2
Knowing that my teacher is indeed NOT a magician, I come to you for assistance.
What is my teacher doing and why does it work? Thank you.
• Partial fractions – user61527 Nov 29 '13 at 1:07
• He's a mathemagician.... – Eleven-Eleven Nov 29 '13 at 1:14
• @ChristopherErnst Apparently, my professor had that written on one of his teacher evaluation forms. :) – apnorton Nov 29 '13 at 15:45
• When my students know how to do a step relatively well and I want to skip the step I wave my hands magically and they all sigh at me.... :) – Eleven-Eleven Nov 29 '13 at 15:55
If you get a common denominator of $(x+3)(5+2x)$, then the numerators must be equal. Thus, $$1=A(5+2x)+B(x+3)$$ $$1=5A+2Ax+Bx+3B$$ $$0x+1=(2A+B)x+(5A+3B)$$ This means that $$2A+B=0$$ $$5A+3B=1$$ Solve for A and B using substitution or whatever method you prefer. Now you can solve the integral.
Because $\frac{A}{(x+3)}+\frac {B}{(5+2x)} = \frac{A(5+2x)+B(x+3)}{(5+2x)(x+3)} = \frac{(2A+B)x+(5A+3B)}{(5+2x)(x+3)}=\frac{1}{(5+2x)(x+3)}$, this would mean that $2A+B=0$ and $5A+3B=1$. Solving these equations gives $A=-1$ and $B=2$.
You would want to do the following $$A/(x+3)+B/(5+2x) =1/[(x+3)(5+2x)]$$ $$A(5+2x) + B(x+3) = 1$$ Essentially you've multiply both by linear factors of your initial integrand. Equate the coefficients of x and 1.
$$2A+B=0$$ $$5A+3B=1$$
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https://share.cocalc.com/share/5d54f9d642cd3ef1affd88397ab0db616c17e5e0/www/talks/padic_heights/pheight.tex?viewer=share
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CoCalc Public Fileswww / talks / padic_heights / pheight.tex
Author: William A. Stein
1\documentclass[11pt]{article}
2\hoffset=-0.06\textwidth
3\textwidth=1.12\textwidth
4\voffset=-0.06\textheight
5\textheight=1.12\textheight
6\bibliographystyle{amsalpha}
7\include{macros}
8\renewcommand{\set}{\leftarrow}
9\title{An Algorithm for Computing $p$-Adic Heights Using Monsky-Washnitzer Cohomology}
10\date{Notes for a Talk at MIT on 2004-10-15}
11\author{William Stein}
12\renewcommand{\E}{\mathbb{E}}
13\begin{document}
14\maketitle
15%\tableofcontents
16
17Let $E$ be an elliptic curve over~$\Q$ and suppose
18$$P=(x,y)=\left(\frac{a}{d^2},\frac{b}{d^3}\right)\in E(\Q),$$ with $a,b,d\in\Z$ and
19$\gcd(a,d)=\gcd(b,d)=1$. The
20\defn{naive height} of $P$ is
21$$\tilde{h}(P) = \log\max\{|a|,d^2\},$$
22and the \defn{canonical height} of $P$ is
23$$24 h(P) = \lim_{n\to\infty} \frac{h(2^n P)}{4^n}. 25$$
26This definition is not good for computation, because
27$2^n P$ gets huge very quickly, and computing
28$2^n P$ exactly, for~$n$ large, is not reasonable.
29%The canonical height is quadratic, in the sense that
30%$h(mP) = m^2 h(P)$ for all integer $m$.
31
32In \cite[\S3.4]{cremona:algs}, Cremona describes an efficient method
33(due mostly to Silverman) for computing $h(P)$. One defines
34\defn{local heights} $\hat{h}_p:E(\Q)\to\R$, for all primes $p$, and
35$\hat{h}_\infty:E(\Q)\to\R$ such that $$h(P) = \hat{h}_\infty(P) + 36\sum \hat{h}_p(P).$$
37The local heights $\hat{h}_p(P)$ are easy to
38compute explicitly. For example, when $p$ is a prime of good
39reduction, $\hat{h}_p(P) = \max\{0,-\ord_p(x)\}\cdot \log(p)$.
40
41{\em This paper is {\bf NOT} about local heights $\hat{h}_p$, and we will
42not mention them any further.} Instead, this paper is about a canonical global
43$p$-adic height function
44$$h_p : E(\Q)\to\Q_p.$$
45These height functions are genuine height functions; e.g., $h_p$
46is a quadratic function, i.e, $h_p(mP) = m^2 h(P)$ for all~$m$.
47They appear when defining the $p$-adic regulators that appear in the
48Mazur-Tate $p$-adic analogues of the Birch and Swinnerton-Dyer
49conjecture.
50
51\vspace{3ex}
52\noindent{\bf Acknowledgement:} Barry Mazur, John Tate, Mike Harrison,
53Christian Wuthrich, Nick Katz.
54
55\section{The $p$-Adic Height Pairing}
56Let $E$ be an elliptic curve over~$\Q$ and suppose $p\geq 5$ is a prime
57such that $E$ has good ordinary reduction at $p$. Suppose $P\in E(\Q)$
58is a point that reduces to $0\in E(\F_p)$ and to the connected
59component of $\mathcal{E}_{\F_\ell}$ at all bad primes $\ell$.
60We will define functions $\log_p$, $\sigma$, and $d$ below.
61In terms of these functions, the $p$-adic height of $P$ is
62\begin{equation}\label{eqn:heightdef}
63 h_p(P) = \frac{1}{p}\cdot \log_p\left(\frac{\sigma(P)}{d(P)}\right) \in \Q_p.
64\end{equation}
65The function $h_p$ satisfies $h_p(nP) = n^2 h_p(P)$ for all integers~$n$,
66so it naturally extends to a function on the full Mordell-Weil group $E(\Q)$.
67Setting $$\langle P, Q\rangle = \frac{1}{2}\cdot (h_p(P+Q)-h_p(P)-h_p(Q)),$$
68we obtain a {\em nondegenerate} pairing on
69$E(\Q)_{/\tor}$, and the $p$-adic regulator is the discriminant
70of this pairing (which is well defined up to sign).
71
72Investigations into $p$-adic Birch and Swinnerton-Dyer conjectures for
74pairings, which motivate our interest in computing it to
75high precision.
76
77We now define each of the undefined quantities in
78(\ref{eqn:heightdef}). The function $\log_p:\Q_p^* \to \Q_p$ is the
79unique homomorphism with $\log_p(p)=1$ that extends the homomorphism
80$\log_p:1+p\Z_p \to \Q_p$ defined by the usual power series of $\log(x)$ about $1$. Thus
81if $x\in\Q_p^*$, we can compute $\log_p(x)$ using the formula
82$$\log_p(x) = \frac{1}{p-1}\cdot \log_p(u^{p-1}),$$
83where $u = 84p^{-\ord_p(x)} \cdot x$.
85
86The denominator $d(P)$ is the square root of the denominator of the
87$x$-coordinate of $P$.
88
89The $\sigma$ function is the most mysterious quantity in
90(\ref{eqn:heightdef}), and it turns out the mystery is closely related
91to the difficulty of computing the $p$-adic number $\E_2(E,\omega)$,
92where $\E_2$ is the $p$-adic weight $2$ Eisenstein series. There are
93{\em many} ways to define or characterize $\sigma$, e.g.,
94\cite{mazur-tate:sigma} contains $11$ different characterizations!
95Let $$x(t) = \frac{1}{t^2} + \cdots \in \Z((t))$$
96be the formal power
97series that expresses $x$ in terms of $t=-x/y$ locally near $0\in E$.
98Then Mazur and Tate prove there is exactly one function $\sigma(t)\in 99t\Z_p[[t]]$ and constant $c\in \Q_p$ that satisfy the equation
101x(t)
102+ c = -\frac{d}{\omega}\left( \frac{1}{\sigma}
103 \frac{d\sigma}{\omega}\right).
104\end{equation}
105This defines $\sigma$, and,
106unwinding the meaning of the expression on the right, it leads to an
107algorithm to compute $\sigma(t)$ to any desired precision,
108which we now sketch.
109
110If we expand (\ref{eqn:sigmadef}), we can view $c$ as a formal
111variable and solve for $\sigma(t)$ as a power series with coefficients
112that are polynomials in $c$. Each coefficient of $\sigma(t)$ must be
113in $\Z_p$, so when there are denominators in the polynomials in $c$,
114we obtain conditions on $c$ modulo powers of $p$. Taking these
115together for many coefficients yields enough scraps of information to
116get $c\pmod{p^n}$, for some small $n$, hence $\sigma(t) \pmod{p^n}$.
117However, this algorithm is {\em extremely inefficient} and its
118complexity is unclear (how many coefficients are needed to compute $c$
119to precision $p^n$?).
120
121For the last 15 or 20 years, the above unsatisifactory algorithm has
122been the standard one for computing $p$-adic heights, e.g., when
123investigating $p$-adic analogues of the BSD conjecture.
124\begin{center}
125{\em The situation
126 changed a few weeks ago...}
127\end{center}
128\section{Using Cohomology to Compute $\sigma$}
129Suppose that $E$ is an elliptic curve over $\Q$ given by a Weierstrass equation
130$$131y^2 + a_1 xy + a_3 y = x^3 + a_2 x^2 + a_4 x + a_6. 132$$
133Let $x(t)$ be the formal series as before, and set
134$$\wp(t) = x(t) + (a_1^2 + 4a_2)/12\in\Q((t)).$$
135(The function $\wp$ satisfies $(\wp')^2 = 4\wp^3 - g_2 \wp - g_3$, etc.; it's
136the formal analogue of the usual complex $\wp$-function.)
137In \cite{mazur-tate:sigma}, Mazur and Tate prove that
138$$139 x(t) + c = \wp(t) + \frac{1}{12}\cdot \E_2(E,\omega), 140$$
141where $\E_2(E,\omega)$ is the value of the Katz $p$-adic
142weight~$2$ Eisenstein series at $(E,\omega)$, and the equality is of
143elements of $\Q_p((t))$. Thus computing $c$ is equivalent
144to computing $\E_2(E,\omega)$.
145
146This summer, Mazur, Tate, and I explored many ideas for computing
147$\E_2(E,\omega)$. Though each was interesting and promising, nothing
148led to a better algorithm that just computing $c$ as sketched above.
149Perhaps the difficult of computing $\E_2(E,\omega)$ is somehow at the
150heart of the theory?
151
152Barry wrote to Nick Katz, who fired off the following email:
153
154\subsection{Katz's Email}
155\begin{verbatim}
156Date: Thu, 8 Jul 2004 13:53:13 -0400
157From: Nick Katz <[email protected]>
158Subject: Re: convergence of the Eisenstein series of weight two
159To: [email protected], [email protected]
160Cc: [email protected], [email protected]
161
162It seems to me you want to use the interpretation of P as the
163"direction of the unit root subspace", that should make it fast to
164compute. Concretely, suppose we have a pair (E, \omega) over Z_p, and
165to fix ideas p is not 2 or 3. Then we write a Weierstrass eqn for E,
166y^2 = 4x^3 - g_2x - g_3, so that \omega is dx/y, and we denote by \eta
167the differential xdx/y. Then \omega and \eta form a Z_p basis of
168H^1_DR = H^1_cris, and the key step is to compute the matrix of
169absolute Frobenius (here Z_p linear, the advantage of working over
170Z_p: otherwise if over Witt vectors of an F_q, only \sigma-linear).
171[This calculation goes fast, because the matrix of Frobenius lives
172over the entire p-adic moduli space, and we are back in the glory days
173of Washnitzer-Monsky cohomology (of the open curve E - {origin}).]
174
175 Okay, now suppose we have computed the matrix of Frob in the
176basis \omega, \eta. The unit root subspace is a direct factor, call
177it U, of the H^1, and we know that a complimentary direct factor is
178Fil^1 := the Z_p span of \omega. We also know that Frob(\omega) lies
179in pH^1, and this tells us that, mod p^n, U is the span of
180Frob^n(\eta). What this means concretely is that if we write,
181for each n,
182
183 Frob^n(\eta) = a_n\omega + b_n\eta,
184
185then b_n is a unit (cong mod p to the n'th power of the Hasse
186invariant) and that P is something like the ratio a_n/b_n (up to a
187sign and a factor 12 which i don't recall offhand but which is in my
188Antwerp appendix and also in my "p-adic interp. of real
189anal. Eis. series" paper).
190
191 So in terms of speed of convergence, ONCE you have Frob, you
192have to iterate it n times to calculate P mod p^n. Best, Nick
193\end{verbatim}
194
195\subsection{The Algorithms}
196The following algorithms culminate in an algorithm for computing
197$h_p(P)$ that incorporates Katz's ideas with the discussion elsewhere
198in this paper. I have computed $\sigma$ and $h_p$ in numerous
199cases using the algorithm described below, and using my
200implementations of the integrality'' algorithm described above
201and also Wuthrich's algorithm, and the results match. The analysis
202of some of the necessary precision is not complete. I also have
203not analyzed the complexity.
204
205The first algorithm computes $\E_2(E,\omega)$.
206\begin{algorithm}{Evaluation of $\E_2(E,\omega)$}\label{alg:e2}
207 Given an elliptic curve over~$\Q$ and prime~$p$, this algorithm
208 computes $\E_2(E,\omega)\in \Q_p$ (to precision $O(p^n)$ say) . We
209 assume that Kedlaya's algorithm is available for computing a
210 presentation of the $p$-adic Monsky-Washnitzer cohomology of
211 $E-\{(0,0)\}$ with Frobenius action.
212\begin{steps}
213\item Let $c_4$ and $c_6$ be the $c$-invariants of a minimal model
214of~$E$. Set
215$$a_4\set -\frac{c_4}{2^4\cdot 3}\qquad\text{and}\qquad 216a_6 \set -\frac{c_6}{2^5\cdot 3^3}.$$
217\item Apply Kedlaya's algorithm to the hyperelliptic curve
218$y^2=x^3 + a_4x + a_6$ (which is isomorphic to $E$) to obtain the matrix
219$M$ of the action of absolute Frobenius
220on the basis
221$$\omega=\frac{dx}{y}, \qquad \eta=\frac{xdx}{y}$$
222to precision $O(p^n)$. (We view $M$ as acting
223from the left.)
224\item
225We know $M$ to precision $O(p^n)$.
226Compute the $n$th power of $M$ and let
227$\vtwo{a}{b}$ be the second column of $M^n$.
228Then $\Frob^n(\eta) = a\omega + b\eta$
229
230\item Output $M$ and $-12a/b$ (which is $\E_2(E,\omega)$), then terminate.
231\end{steps}
232\end{algorithm}
233
234The next algorithm uses the above algorithm to compute $\sigma(t)$.
235\begin{algorithm}{The Canonical $p$-adic Sigma Function}\label{alg:sigma}
236 Given an elliptic curve~$E$ and a good ordinary prime~$p$, this
237 algorithm computes $\sigma(t)\in\Z_p[[t]]$ modulo $(p^n, t^m)$ for
238 any given positive integers $n,m$. (I have {\em not} figured out
239 exactly what precision each object below must be computed to.)
240\begin{steps}
241\item Using Algorithm~\ref{alg:e2}, compute $e_2 = \E_2(E,\omega)\in 242 \Z_p$ to precision $O(p^n)$.
243\item Compute the formal power series $x = x(t) \in \Q[[t]]$
244 associated to the formal group of $E$ to precision $O(t^m)$.
245\item Compute the formal logarithm $z(t) \in \Q((t))$ to precision
246$O(t^m)$ using that $\ds z(t) = \int \frac{dx/dt}{(2y(t)+a_1x(t) + a_3)},$
247where $x(t)=t/w(t)$ and $y(t)=-1/w(t)$ are the formal $x$
248and $y$ functions, and $w(t)$ is given by the explicit inductive
249formula in \cite[Ch.~7]{silverman:aec}. (Here $t=-x/y$ and $w=-1/y$ and
250we can write $w$ as a series in $t$.)
251\item Using a power series reversion'' (functional inverse)
252 algorithm (see e.g., Mathworld), find the power series $F(z)\in\Q[[z]]$ such that
253 $t=F(z)$. Here $F$ is the reversion of $z$, which exists because
254 $z(t) = t + \cdots$.
255\item Set $\wp(t) \set x(t) + (a_1^2 + 4a_2)/12 \in \Q[[t]]$ (to precision
256$O(t^m)$), where the
257 $a_i$ are the coefficients of the Weierstrass equation of $E$.
258Then compute the series $\wp(z) = \wp(F(z))\in \Q((z))$.
259\item Set $\ds g(z)\set \frac{1}{z^2} - \wp(z) + \frac{e_2}{12}\in\Q_p((z))$.
260(Note:
261 The theory suggests the last term should be $-e_2/12$ but the calculations do not
262 work unless I use the above formula. Maybe there are two
263 normalizations of $E_2$ in the literature?)
264\item Set
265$\ds \sigma(z) \set z\cdot \exp\left(\int \int g(z) \dz \dz\right) 266\in \Q_p[[z]]$.
267\item Set $\sigma(t) \set \sigma(z(t))\in t\cdot \Z_p[[t]]$, where $z(t)$
268is the formal logarithm computed above. Output $\sigma(t)$
269and terminate.
270\end{steps}
271\end{algorithm}
272
273\begin{remark}
274 The trick of changing from $\wp(t)$ to $\wp(z)$ is essential so that
275 we can solve a certain differential equation using just operations
276 with power series.
277\end{remark}
278
279The final algorithm uses $\sigma(t)$ to compute the $p$-adic height.
280\begin{algorithm}{$p$-adic Height}
281Given an elliptic curve~$E$ over $\Q$, a good ordinary prime~$p$,
282and an element $P\in E(\Q)$, this algorithm computes the
283$p$-adic height $h_p(P) \in \Q_p$ to precision $O(p^n)$.
284(I will ignore the precision below, though this must be not
285be ignored for the final version of this paper.)
286\begin{steps}
287\item{}[Prepare Point] Compute an integer $m$ such that
288$mP$ reduces to $0\in E(\F_p)$ and to the connected
289component of $\mathcal{E}_{\F_\ell}$ at all bad primes $\ell$.
290For example,~$m$ could be the least common multiple of the Tamagawa numbers
291of $E$ and $\#E(\F_p)$. Set $Q\set mP$ and write $Q=(x,y)$.
292\item{}[Denominator] Let $d$ be the positive integer square root of the
293denominator of $x$.
294\item{}[Compute $\sigma$] Compute $\sigma(t)$ using
295 Algorithm~\ref{alg:sigma}, and set $s \set \sigma(-x/y) \in \Q_p$.
296\item{}[Logs] Compute
297$\ds h_p(Q) \set \frac{1}{p}\log_p\left(\frac{s}{d}\right)$, and
298$\ds h_p(P) \set \frac{1}{m^2} \cdot h_p(Q)$. Output $h_p(P)$ and terminate.
299\end{steps}
300\end{algorithm}
301
302\section{Future Directions}
303
304Suppose $E_t$ is an elliptic curves over $\Q(t)$. It might be
305extremely interesting to obtain formula for $\E_2(E_t)$ as something
306like (?) a power series in $\Q_p[[t]]$. This might shed light on the
307analytic behavior of the $p$-adic modular form $\E_2$, and on Tate's
308recent surprising experimental observations about the behavior of the
309$(1/j)$-expansion of~$\E_2 E_4/E_6$.
310
311It would also be interesting to do yet more computations in support of
312$p$-adic analogues of the BSD conjectures of \cite{mtt}, especially
313when $E/\Q$ has large rank. Substantial theoretical work has been
314done toward these $p$-adic conjectures, and this work may be useful to
315algorithms for computing information about Shafarevich-Tate and Selmer
316groups of elliptic curves. For example, in \cite{pr:exp}, Perrin-Riou
317uses her results about the $p$-adic BSD conjecture in the
318supersingular case to prove that $\Sha(E/\Q)[p]=0$ for certain~$p$ and
319elliptic curves~$E$ of rank $>1$, for which the work of Kolyvagin and
320Kato does not apply. Mazur and Rubin (with my computational input)
321are also obtaining results that could be viewed as fitting into this
322program.
323
324I would like to optimize the implementation of the algorithm.
325Probably the most time-consuming step is computation of
326$\E_2(E,\omega)$ using Kedlaya's algorithm. My current implementation
327uses Michael Harrison's implementation of Kedlaya's algorithm for
328$y^2=f(x)$, with $f(x)$ of arbitrary degree. Perhaps implementing
329just what is needed for $y^2=x^3+ax+b$ might be more efficient. Also,
330Harrison tells me his implementation isn't nearly as optimized as it
331might be.
332
333It might be possible to compute $p$-adic heights on Jacobians of
334hyperelliptic curves.
335
336Formulate everything above over number fields, and extend to the case
338
339Supersingular reduction?
340
341\section{Examples}
342The purpose of this section is to show you how to use the MAGMA package
343I wrote for computing with $p$-adic heights, and give you a sense
344for how fast it is.
345
346\begin{verbatim}
347> function EC(s) return EllipticCurve(CremonaDatabase(),s); end function;
348> E := EC("37A");
350> P := good_ordinary_primes(E,100); P;
351[ 5, 7, 11, 13, 23, 29, 31, 41, 43, 47, 53, 59, 61, 67, 71, 73,
35279, 83, 89, 97 ]
353> for p in P do time print p, regulator(E,p,10); end for;
3545 22229672 + O(5^11)
355Time: 0.040
3567 317628041 + O(7^11)
357...
35889 15480467821870438719 + O(89^10)
359Time: 1.190
36097 -11195795337175141289 + O(97^10)
361Time: 1.490
362
363> E := EC("389A");
364> P := good_ordinary_primes(E,100); P;
365[ 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
36667, 71, 73, 79, 83, 89, 97 ]
367> for p in P do time print p, regulator(E,p,10); end for;
3685 -3871266 + O(5^11)
369Time: 0.260
3707 483898350 + O(7^11)
371...
37289 9775723521676164462 + O(89^10)
373Time: 1.330
37497 -13688331881071698338 + O(97^10)
375Time: 1.820
376
377> E := EC("5077A");
378> P := good_ordinary_primes(E,100); P;
379[ 5, 7, 11, 13, 17, 19, 23, 29, 31, 43, 47, 53, 59, 61, 67, 71,
38073, 79, 83, 89, 97 ]
381> for p in P do time print p, regulator(E,p,10); end for;
3825 655268*5^-2 + O(5^7)
383Time: 0.800
3847 -933185758 + O(7^11)
385...
38689 -3325438607428779200 + O(89^10)
387Time: 1.910
38897 -5353586908063282167 + O(97^10)
389Time: 2.010
390
391--------
392
393> E := EC("37A");
394> time regulator(E,5,50);
395115299522541340178416234094637464047 + O(5^51)
396Time: 1.860
397> Valuation(115299522541340178416234094637464047 - 22229672,5);
3989
399
400> time regulator(E,97,50);
401-5019271523950156862996295340254565181870308222348277984940964806\
402 97957622583267105973403430183075091 + O(97^50)
403Time: 31.7
404\end{verbatim}
405
406
407\bibliography{biblio}
408\end{document}
409
410
411
412
413
414
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http://mathoverflow.net/users/35874/par
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# par
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bio website location age member for 8 months seen Nov 8 '13 at 12:52 profile views 7
# 1 Question
3 Monotonicity preserving parabolic operators
# 116 Reputation
+15 Monotonicity preserving parabolic operators
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# 2 Tags
0 linear-pde 0 parabolic-pde
# 5 Accounts
Mathematics 2,361 rep 111 TeX - LaTeX 258 rep 4 Stack Overflow 127 rep 5 MathOverflow 116 rep 3 Super User 101 rep 1
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http://www.cut-the-knot.org/arithmetic/combinatorics/PascalTriangleProperties.shtml
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# Patterns in Pascal's Triangle
Pascal's Triangle conceals a huge number of various patterns, many discovered by Pascal himself and even known before his time.
#### Pascal's Triangle is symmetric
In terms of the binomial coefficients, $C^{n}_{m} = C^{n}_{n-m}.$ This follows from the formula for the binomial coefficient
$\displaystyle C^{n}_{m}=\frac{n!}{m!(n-m)!}.$
It is also implied by the construction of the triangle, i.e., by the interpretation of the entries as the number of ways to get from the top to a given spot in the triangle.
Some authors even considered a symmetric notation (in analogy with trinomial coefficients)
$\displaystyle C^{n}_{m}={n \choose m\space\space s}$
where $s = n - m.$
#### The sum of entries in row $n$ equals $2^{n}$
This is Pascal's Corollary 8 and can be proved by induction. The main point in the argument is that each entry in row $n,$ say $C^{n}_{k}$ is added to two entries below: once to form $C^{n + 1}_{k}$ and once to form $C^{n + 1}_{k+1}$ which follows from Pascal's Identity:
$C^{n + 1}_{k} = C^{n}_{k - 1} + C^{n}_{k},$
$C^{n + 1}_{k+1} = C^{n}_{k} + C^{n}_{k+1}.$
For this reason, the sum of entries in row $n + 1$ is twice the sum of entries in row $n.$ (This is Pascal's Corollary 7.)
As a consequence, we have Pascal's Corollary 9: In every arithmetical triangle each base exceeds by unity the sum of all the preceding bases. In other words, $2^{n} - 1 = 2^{n-1} + 2^{n-2} + ... + 1.$
#### There are well known sequences of numbers
Some of those sequences are better observed when the numbers are arranged in Pascal's form where because of the symmetry, the rows and columns are interchangeable.
The first row contains only $1$s: $1, 1, 1, 1, \ldots$
The second row consists of all counting numbers: $1, 2, 3, 4, \ldots$
The third row consists of the triangular numbers: $1, 3, 6, 10, \ldots$
The fourth row consists of tetrahedral numbers: $1, 4, 10, 20, 35, \ldots$
The fifth row contains the pentatope numbers: $1, 5, 15, 35, 70, \ldots$
"Pentatope" is a recent term. Regarding the fifth row, Pascal wrote that ... since there are no fixed names for them, they might be called triangulo-triangular numbers. Pentatope numbers exists in the $4D$ space and describe the number of vertices in a configuration of $3D$ tetrahedrons joined at the faces.
In the standard configuration, the numbers $C^{2n}_{n}$ belong to the axis of symmetry. Numbers $\frac{1}{n+1}C^{2n}_{n}$ are known as Catalan numbers.
Every two successive triangular numbers add up to a square: $(n - 1)n/2 + n(n + 1)/2 = n^{2}.$
#### Hockey Stick Pattern
In Pascal's words (and with a reference to his arrangement), In every arithmetical triangle each cell is equal to the sum of all the cells of the preceding row from its column to the first, inclusive (Corollary 2). In modern terms,
(1)
$C^{n + 1}_{m} = C^{n}_{m} + C^{n - 1}_{m - 1} + \ldots + C^{n - m}_{0}.$
Note that on the right, the two indices in every binomial coefficient remain the same distance apart: $n - m = (n - 1) - (m - 1) = \ldots$ This allows rewriting (1) in a little different form:
(1')
$C^{m + r + 1}_{m} = C^{m + r}_{m} + C^{m + r - 1}_{m - 1} + \ldots + C^{r}_{0}.$
The latter form is amenable to easy induction in $m.$ For $m = 0,$ $C^{r + 1}_{0} = 1 = C^{r}_{0},$ the only term on the right. Assuming (1') holds for $m = k,$ let $m = k + 1:$
\begin{align} C^{k + r + 2}_{k + 1} &= C^{k + r + 1}_{k + 1} + C^{k + r + 1}_{k}\\ &= C^{k + r + 1}_{k + 1} + C^{k + r}_{k} + C^{k + r - 1}_{k - 1} + \ldots + C^{r}_{0}. \end{align}
Naturally, a similar identity holds after swapping the "rows" and "columns" in Pascal's arrangement: In every arithmetical triangle each cell is equal to the sum of all the cells of the preceding column from its row to the first, inclusive (Corollary 3).
(2)
$C^{n + 1}_{m + 1} = C^{n}_{m} + C^{n - 1}_{m} + \ldots + C^{0}_{m},$
where the second index is fixed.
#### Parallelogram Pattern
(3)
$C^{n + 1}_{m} - 1 = \sum C^{k}_{j},$
where $k \lt n,$ $j \lt m.$ In Pascal's words: In every arithmetic triangle, each cell diminished by unity is equal to the sum of all those which are included between its perpendicular rank and its parallel rank, exclusively (Corollary 4). This is shown by repeatedly unfolding the first term in (1).
#### Fibonacci Numbers
If we arrange the triangle differently, it becomes easier to detect the Fibonacci sequence:
The successive Fibonacci numbers are the sums of the entries on sw-ne diagonals:
\begin{align} 1 &= 1\\ 1 &= 1\\ 2 &= 1 + 1\\ 3 &= 1 + 2\\ 5 &= 1 + 3 + 1\\ 8 &= 1 + 4 + 3\\ 13 &= 1 + 5 + 6 + 1 \end{align}
#### The Star of David
The following two identities between binomial coefficients are known as "The Star of David Theorems":
$C^{n-1}_{k-1}\cdot C^{n}_{k+1}\cdot C^{n+1}_{k} = C^{n-1}_{k}\cdot C^{n}_{k-1}\cdot C^{n+1}_{k+1}$ and
$\mbox{gcd}(C^{n-1}_{k-1},\,C^{n}_{k+1},\,C^{n+1}_{k}) = \mbox{gcd}(C^{n-1}_{k},\,C^{n}_{k-1},\, C^{n+1}_{k+1}).$
The reason for the moniker becomes transparent on observing the configuration of the coefficients in the Pascal Triangle.
Tony Foster observed that with $k=1,$
$\displaystyle C^{n-2}_{k-1}\cdot C^{n-1}_{k+1}\cdot C^{n}_{k}=\frac{(n-2)(n-1)n}{2}=C^{n-2}_{k}\cdot C^{n-1}_{k-1}\cdot C^{n}_{k+1}$
so that
\displaystyle\begin{align} \prod_{m=1}^{N}\bigg[C^{3m-1}_{0}\cdot C^{3m}_{2}\cdot C^{3m+1}_{1} + C^{3m-1}_{1}\cdot C^{3m}_{0}\cdot C^{3m+1}_{2}\bigg] &= \prod_{m=1}^{N}(3m-2)(3m-1)(3m)\\ &= \prod_{m=1}^{3N}m = (3N)! \end{align}
#### Not without $e$
Harlan Brothers has recently discovered the fundamental constant $e$ hidden in the Pascal Triangle; this by taking products - instead of sums - of all elements in a row:
$S_{n}$ is the product of the terms in the $n$th row, then, as $n$ tends to infinity,
$\displaystyle\lim_{n\rightarrow\infty}\frac{s_{n-1}s_{n+1}}{s_{n}^{2}} = e.$
I placed the derivation into a separate file.
#### Catalan Numbers
Tony Foster's post at the CutTheKnotMath facebook page pointed the pattern that conceals the Catalan numbers:
I placed an elucidation into a separate file.
#### Sums of the Binomial Reciprocals
A post at the CutTheKnotMath facebook page by Daniel Hardisky brought to my attention to the following pattern:
I placed a derivation into a separate file.
#### Squares
As I mentioned earlier, the sum of two consecutive triangualr numbers is a square: $(n - 1)n/2 + n(n + 1)/2 = n^{2}.$ Tony Foster brought up sightings of a whole family of identities that lead up to a square.
For example,
$C^{n+2}_{3} - C^{n}_{3} = n^{2}.$
and also
$C^{n+3}_{4} - C^{n+2}_{4} - C^{n+1}_{4} + C^{n}_{4} = n^{2}.$
I placed a derivation into a separate file.
#### Squares of the Binomials
$\displaystyle\sum_{k=0}^{n}(C^{n}_{k})^{2}=C^{2n}_{n}.$
I placed a derivation into a separate file.
#### Cubes
Underfatigble Tony Foster found cubes in Pascal's triangle in a pattern that he rightfully refers to as the Star of David - another appearance of that simile in Pascal's triangle.:
$\displaystyle n^{3}=\bigg[C^{n+1}_{2}\cdot C^{n-1}_{1}\cdot C^{n}_{0}\bigg] + \bigg[C^{n+1}_{1}\cdot C^{n}_{2}\cdot C^{n-1}_{0}\bigg] + C^{n}_{1}.$
Here's his original graphics that explains the designation:
There is a second pattern - the "Wagon Wheel" - that reveals the square numbers.
I placed a derivation into a separate file.
### $pi$ in Pascal
This is due to Daniel Hardisky
$\displaystyle\pi = 3+\frac{2}{3}\bigg(\frac{1}{C^{4}_{3}}-\frac{1}{C^{6}_{3}}+\frac{1}{C^{8}_{3}}-\cdot\bigg).$
I placed a derivation into a separate file.
### Products of Binomial Coefficients
For integer $n\gt 1,\;$ let $\displaystyle P(n)=\prod_{k=0}^{n}{n\choose k}\;$ be the product of all the binomial coefficients in the $n\text{-th}\;$ row of the Pascal's triangle. Then
$\displaystyle\frac{\displaystyle (n+1)!P(n+1)}{P(n)}=(n+1)^{n+1}.$
To illustrate,
I placed a derivation into a separate file.
Eventually, Tony Foster found an extension to other integer powers:
I placed a derivation into a separate file.
### References
1. J. H. Conway and R. K. Guy, The Book of Numbers, Springer-Verlag, NY, 1996.
2. H. Eves, Great Moments in Mathematics After 1650, MAA, 1983
3. Great Books of the Western World, v 33, Encyclopaedia Britannica, Inc., 1952.
4. P. Hilton, D. Holton, J. Pederson, Mathematical Reflections, Springer Verlag, 1997
5. A. R. Kanga, Number Mosaics, World Scientific Co., 1995.
6. R. Graham, D. Knuth, O. Patashnik, Concrete Mathematics, 2nd edition, Addison-Wesley, 1994.
7. J. A. Paulos, Beyond Numeracy, Vintage Books, 1992
8. H.-O. Peitgen et al, Chaos and Fractals: New Frontiers of Science , Springer, 2nd edition, 2004
9. D. E. Smith, History of Mathematics, Dover, 1968
10. D. E. Smith, A Source Book in Mathematics, Dover, 1959
11. D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, 1987
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https://mathoverflow.net/questions/249300/what-is-the-motivation-behind-the-characteristic-variety-of-a-d-module-and-what
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What is the motivation behind the characteristic variety of a D-module and what does it's geometry tell me about the D-module?
Given a smooth algebraic variety $X$, and an $\mathcal{M}\in \text{Mod}(D_X)$, there is the characteristic variety of $\mathcal{M}$ defined as $$\text{Char}(\mathcal{M}):= V\left(\sqrt{Ann(\mathcal{M})}\right) \subset T^*X$$ These varieties have a number of nice properties
1. Their dimension is equal to the dimension of the underlying $D_X$-module
2. Their dimension is greater than or equal to the dimension of $X$
3. Behaves well with restriction to open subsets of $X$
4. They behave well with respect to exact sequences of coherent $D_X$-modules
5. They are coisotropic subvarieties of $T^*X$
6. They are lagrangian iff the underlying D-module is holonomic
Unfortunately, it's not clear why these varieties are useful and what their motivation for construction is.
• I don't recall the details (I am not an analyst), but the motivation comes primarily from distribution theory; the characteristic variety of a holonomic D-module (which as you know is cyclic, generated by a distribution) is related to the singular spectrum of the distribution. I would go have a look at the original work of Kashiwara and Saito, it might be enlightening. – Ketil Tveiten Sep 8 '16 at 8:15
• You may also think of it as an invariant of the PDE, for example the classical distinction between elliptic parabolic or hyperbolic PDE can be read from the characteristic variety. – Michael Bächtold Sep 8 '16 at 18:12
Here’s one way to think about them: they tell you how far a $$D$$-module is from being an integrable connection (i.e. finitely generated over $$\mathcal O$$). Here’s what I mean: let $$M$$ be a $$D$$-module on $$X$$. Then $$M$$ is an integrable connection in a neighborhood of a point $$x\in X$$ if and only if $$\operatorname{Char}(M)\cap T^*_x X$$ is zero (i.e. is contained in the zero section).
I also want to correct your point number 1. The dimension of a $$D$$-module is by definition the dimension of its characteristic variety.
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http://m.freestd.us/soft4/3190768.htm
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Home >> Standards Worldwide >> Environmental Protection Standards >> HJ 504-2009 ambient air-determination of ozone-indigo disulphonate spectrophotometry
## HJ 504-2009 ambient air-determination of ozone-indigo disulphonate spectrophotometry
Standard Number: HJ 504-2009
Title: ambient air-determination of ozone-indigo disulphonate spectrophotometry
Language: Simplified Chinese
Replacing Standard: GB/T 15437-1995
Publication Date: 2009/10/20
Execute Date: 2009/12/1
International Classification for Standards (ICS)ENVIRONMENT. HEALTH PROTECTION. SAFETY>>Air quality
Publisher: Environmental Protection Standards
Price:12.00
Number of Pages:10
Description:This standard stimulates the determination of ozone in the air of indigo disulfonic acid sodium spectrophotometric method.
This standard applies to the environment, the determination of ozone in the air. Relatively closed environment, such as interior, car, etc.) on the determination of ozone in the air can also be reference standard.
When the sampling volume of 30 l, this standard was developed for the determination of ozone in the air detection limit of 0.010 mg/m < 3 > superscript, determination of lower limit of 0.040 mg/m (superscript 3 >.
When the sampling volume of 30 L, absorbing liquid mass concentration of 2.5 mu g/ml or 5.0 mu g/ml, the determination of upper limit were 0.50 mg/m (superscript 3 > or < superscript 3 > 1.00 mg/m. When the concentration of ozone in the air quality more than the limit, can reduce the sampling volume appropriately.
Cross References:GB/T 15437-1995
File Format: PDF(Acrobat Reader) or Word version doc Document
File Size: 634KB
Tile in English: ambient air-determination of ozone-indigo disulphonate spectrophotometry
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http://cvgmt.sns.it/paper/859/
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# Thin-walled beams: a derivation of Vlassov theory via $\Gamma$-convergence
created by freddi on 27 Apr 2006
modified on 26 Feb 2007
[BibTeX]
Published Paper
Inserted: 27 apr 2006
Last Updated: 26 feb 2007
Journal: Journal of Elasticity
Volume: 86
Number: 3
Pages: 263-296
Year: 2007
Abstract:
This paper deals with the asymptotic analysis of the three-dimen\-sional problem for a linearly elastic cantilever having an open cross-section which is the union of rectangles with sides of order $\varepsilon$ and $\varepsilon^2$, as $\varepsilon$ goes to zero. Under suitable assumptions on the given loads and for homogeneous and isotropic material, we show that the three-dimensional problem $\Gamma$-converges to the classical one-dimensional Vlas\-sov model for thin-walled beams.
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