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Currently i include png/jpg files with graphicx package compiling with lualatex, no problem, in particular no error message because of bounding box not found. This question is about historic ways to compile because I don't want to break old code. First question: Is it true that when compiling into pdf with any of the modern compilers like lualatex with graphicx package command includegraphics, there is no special treatment necessary to get a bounding box? Second, I seem to have no problem with bounding box either when compiling into dvi. What makes me a bit nervous is, that I remember that message. I am sure i used package bmpsize and also command ebb to get the bounding box and this was necessary to avoid the error message cannot determine the size of the graphic But I cannot remember the details. My question is whether the issue with the bounding box is resolved by new compilers, even if compiling into dvi or xdv. I made a remark by hand, that bmpsize does not work with xelatex. Is it obsolete? May it be the case that behavior depends on the source of the jpg/png? Are there aspects related with the dvi to pdf converters? Are there other formats needing bmpsize or ebb? Please feel free to mention other aspects also. I am afraid about dropping ebb or bmpsize when there is still a use case. In the meantime I found out that my problem is specific for texlive distribution. Seemingly miktex neither provides bmpsize nor ebb. | 0 |
The following pop science video discusses the experimental difficulty of measuring "quanta" of gravity. It seems to me that a significant argument involves how it would be difficult to investigate fluctuations of gravity on the plank scale, requiring detection methods that have densities that would collapse as a black hole. In optics, one way of "seeing" a photon is by interfering it with using homodyne detection to interfere it with a strong signal. The strong signal essentially magnifies the signal, allowing it to be seen by detectors that are much less sensitive than single photon level. Could such a scheme be used to measure gravitons? For example, if strong gravitational waves can be detected by LIGO, shouldn't a sufficiently strong wave already be measuring the "amplitude" statistics of the graviton? Similar to how a local oscillator (in a balanced homodyne detector) measures the shot noise (amplitude statistics) of the vacuum. I suppose the issue is that this needs to be a particuarly strong wave signal so be above experimental noise? | 0 |
In the diagram, OA is perpendicular to PQ. O is the centre of the circle. AC and EP meet at B on the circle and QC and AE meet at D on the circle. The goal is to prove that AP=AQ. I had tried to prove this by drawing a line through E parallel to PQ and I had proved some of the triangles were similar. However, this is the part where I got stuck. I drew a line parallel to PQ through E. I named the meeting point between PE and QC "G", between the line produced at E and CQ "F" and between CA and the line produced at E "H". I then proved that triangle CBG is similar to DEG, CAD is similar to BAE, HBE is similar to ABP, FDE is similar to ADQ and FGE is similar to PGQ. It is at this point when I got stuck. | 0 |
Recently, I tried to understand the effect of Quantum levitation. I read that there is some well-known fact: Relative distance between superconductor and magnet must be preserved, because of flux pinning mostly occurred in type II superconductor. My rough understanding about this is, quantisation of (penetrated) magnetic flux inside the superconductor, and continuity of magnetic flux depending on the distance from the magnet, induces the fixation of relative distance (It couldn't move continuously after fixation because there is no no-jump-but-continuous motion). I could understand the second part of the video. I guess it's because of the circular symmetry of magnetic field. There is nothing hard to understand the story. However, what about the first part? If we rotate the magnet, then what makes the superconductor follow it? Obviously, it's due to the preservation of relative distance in layman's terms. However, could we more elaborate on it? For instance, in the context of classical electrodynamics, someone could try to explain this by the induced electric fields and currents from time-varying magnetic fields. However, it may not be an answer because of the quantum nature of a superconductor. The quantised flux varies by the time dependent magnetic field, but could we describe such a variation in terms of the motion of the magnet?, and so, could we derive and describe the equation of motion of a superconductor? | 0 |
I've noticed this quite often from Disney sound tracks. Lyrics are in a certain rhyming scheme - one line happens and the next line approaches the end of the line, but the last word subverts the rhyme. I have looked at this question and feel it's related, but not the same effect. Example: "In Summer" from Olaf in Frozen Da da, da doo, a bubba bubba boo The hot and the cold are both so intense Put them together ? it just makes sense! Rata ta ta dada dada da doo Winter's a good time to stay in and cuddle But put me in summer and I'll be a happy snowman! Obviously, the expectation is that the word is "puddle" It feels like a lyrical version of deceptive cadence, but I cannot find a succinct term for such an effect. The linked question accepts the answer "Broken Lyric" or "Enjambment", which may still be the answer here, but I am certain that these are two different effects. | 0 |
I am a first year student of applied mathematics. I currently find myself always trying to explain any phenomenon with mathematical models- the few ones (models) that I encountered till now. I always try to fit phenomenas to models like a data scientist does when he fits data to models. Recently I found this book: Robert B. Banks Growth and Diffusion Phenomena: Mathematical Frameworks and Applications This book is different from other applied mathematics books in the sense that it focuses on a particular model unlike others that try to model the whole world in a single book. It particularly focuses on growth and diffusion phenomena. Which is , to me , great because this book studies these two models in great detail rather than just stating many models on the surface level. I also found some book that is specific to some single phenomenon like this book on Hysteresis Mathematical Models of Hysteresis and their Applications Can someone please recommend to me some books like these that describes a certain phenomena or discusses a certain mathematical framework to study in detail and apply some phenomena? Any book that discusses and models in detail some phenomena: could be growth,could be decline, could be (what happens in the limiting case)- type of thing, could be something else, could be anything... | 0 |
The boundary of a simple closed curve has each point on it, touching two adjacent points one on each side. Can the entire boundary be represented as a series of circles of the same diameter "d" where each circle is touching the adjacent circle at exactly one point only without overlap in areas between the two circles. This will allow us to approximate the simple closed curve with a polygon where each side of the polygon is represented by a line joining the centers of adjacent circles and at a distance equal to the diameter "d" of the circle. Such approximation would imply that a inscribed square exists on the polygon (Toeplitz conjecture special cases) and therefore an "almost square" whose vertices are within the error range of the diameter of the circle must exist. Shrinking the size of the circles used will reduce the error of the "almost squares" to smaller and smaller values. | 0 |
I'm working on an algorithm to allow a vehicle to reverse and then line up and stop on a given spot facing a specific direction. The best approach I've been able to come up with involves two internally tangent circles with the larger extending from the point of tangency of the vehicle. Vehicle starts at point A and is parallel with tangent line T. Vehicle reverses to B, then moves forward to C, then to A so that it is parallel with the vector displayed instead. r represents the minimum turning radius of the vehicle Given that line AC is always arranged vertically and knowing point A, but that the tangent line T can vary, is it possible to be able to determine points B and C? If not what other info is needed? Medium tangent Steep tangent Shallow tangent For simplicity I've made it so that the radius of the larger circle is twice the radius of the smaller. If this restriction is not required to solve the problem how could this larger radius be determined as well? | 0 |
A few days ago, I came to an amazing intuition while using GeoGebra, and I could not prove whether it was previously discovered or is it new, please mention a source if it already exists... The sum of the lengths of the tangents of two circles touching a conic section, each of which touches it at two points, and starting from a point on the circumference of the conic section is equal to the distance between the centers of the two circles multiplied by the reciprocal of the coefficient of central difference, where the lengths of the two tangents are two vectors and the shortest of them will take a negative value if the point taken from the segment is not located between the two circles. These are illustrations that include different relative states: direct result: The length of a tangent to a circle tangent to a conic at two points that radiates from the point of tangency to another circle tangent to it at two points is equal to the distance between the centers of the two circles. | 0 |
I've read some description of certain house design as below: Living and dining rooms are towards the front with kitchens to the rear, with bedrooms either off the hallway or upstairs if it's a two-storey terrace. and here's the corresponding house plan: the definition of "off" in google: as I understand, and which can be seen from the floor design, "bedrooms are off the hallway" sort of indicates that bedrooms are separated by and adjacent to the hallway, and here "off" is preposition, but I'm not sure which one of the two preposition definitions fits it. The definition "situated or leading in a direction away from (a main route or intersection)." seems close but I think it's used to describe something not adjacent to the main route such as in "my house is off the main road", which is obviously not the case in above house plan example. Thanks in advance for your help! | 0 |
Suppose we have a closed circuit composed of a time constant voltage battery, a resistor and superconducting wires connecting them in series. In the equilibrium state, both the free charge the electric field in the interior of the superconducting wire should vanish, lest the free charge accelerates and there be no equilibrium/steady current. The electric field generated by the charges in the battery should be counteracted by nonzero surface charges on the superconducting wire in order to generate the zero electric field inside the wire. At the locations of the wire that are far from the battery and with small curvature which should approximate a straight wire, the surface charge density should be close to uniform. However, I have often read people claiming a superconducting wire with a constant equilibrium (direct) current should be free of surface charge. I would like to know what the bases is for their argument. Are there some references on this topic? | 0 |
why potential at any point in a uniform electric field is not same i.e. why potential difference between any two points in the uniform electric field is not zero? According to me if i bring a test charge from infinity to a point A in uniform electric field [assume the field is due to a positive charge] then i will have to apply external force on the test charge against the electrostatic force by the uniform field such that external force is equal to electrostatic force so that kinetic energy of test charge would remain constant thus some potential energy will be stored in the test charge at point A.....NOW if i will bring the test charge from infinity to some another point in the uniform electric field...let the point be B then according to me i will do the same amount of work done on the test charge to bring it to point B because i will apply the external force that will also be equal to electrostatic force by the uniform electric field.....and because the electric field is uniform the test charge will experience the same amount of electrostatic force at each point on the uniform electric field i.e. electrostatic force at both the points A and B due the field will be same. Hence according to me the potential energy at each point on the uniform electric field will be the same thus the potential also. Kindly explain.... why not? thanks! | 0 |
In the Hertz experiment, when light falls on the anode, electrons are emitted and they move towards the cathode and thus flow through the circuit. However, when reverse voltage is applied and the polarity of the electrodes is reversed, electrons being emitted from the anode (formerly, a cathode) only come out in the air/vacuum of the glass tube and do not flow in the circuit even though voltage is applied. How is it so? The emitted electrons should be repelled by the cathode and should enter the circuit through the wire attached to the anode as the increase in free electrons results in increase of current. The applied voltage should also direct the electrons to pass through the anode. In this way, a sort of capacitor might be created. Instead, the current is said to reach zero as stopping potential is reached. How can this be justified? | 0 |
In fluids, in the state of equilibrium, there can only appear internal normal forces and these forces always have a tendency to compress the bounded volume in the fluid. Cited - Physics Galaxy ( Ashish Arora ) Would it be apt to say that in context with fluids, if I drop a block, the pressure exerted by the fluid on the block will be the effect of a compressive internal normal force over an area ? In addition, why is pressure independent of the amount of fluid above it, since it is the weight of the fluid that is causing the compressive force to act? What i think: Maybe somehow Pascal's principal acts on this, equalizing the forces and leading to pressure equalizing at all heights irrespective of the shape of the tube, if I'm right, could you elaborate on how it actually happens? | 0 |
I want to recreate a plot where the area that is not visible from a certain point on earth (latitude and longitude) trough a full year. An example of this plots for example can be: Where in white is marked the zone a telescope is not seeing over all year. I searched in internet but i can not find anything related on how to do it, also Astropy don't seem to have any tool to do this calculus. My first idea for the approach can be first of all maybe represent in equatorial coordinates where this areas should be straight lines (but i don't know how to calculate the coordinates that this straight lines will have). And maybe after we can transform to galactic coordinates somehow. If someone have an idea on how to do this will be helpful. | 0 |
Some examples needing an explanation, thank you for the help. "I came up with (an) idea, we can do..." We should use "an", shouldn't we? But why, if we have a specific idea explained further? What about "He gave me a/the idea to admit to the university" then? "The conclusion is ..." Why should we use "the", when it's the first mention of the conclusion. Maybe because that conclusion is specific, only for that situation. Then should i use "the" in the next sentence "I came up with the conclusion. The conclusion is..."? "I have a/the feeling i don't love him". "The" because i tell what specific feeling i have further? "I am gonna watch a/the video". What if only i know that video, and i want to watch a specific video, but another person in a dialogue doesn't know that video. | 0 |
Consider for example the open sentence, x lives in India where 'x' is a variable, which can be substituted by various constants to make declarative sentences. For instance, Harshit lives in India Carol lives in India Zaid lives in India where 'x' has been replaced by constants 'Harshit', 'Carol' and 'Zaid', respectively. I don't understand how do we exactly come to know which constants can substitute the variables in an open sentence. I mean, if someone says, significant substitutes are names of people, in this example, I would say why not of pets? Why not just of people of a particular City or ethnicity? Since, this question is from logic, which is a prerequisite (AFAIK) of set theory, I would humbly expect no notions from set theory to be used. | 0 |
In the most known incarnations of string theory, we have to compactify the needed, additional dimensions that are then taken to be a.) periodic and b.) "small" in some sense (most of the time their size/radius is taken to be on the order of the Planck length). Some models do propose so-called large extra dimensions but even in these the extra dimensions are compact. Now my question is, are there any string theory models in which some or all of the extra dimensions are non-compact and if there are, can you recommend me any literature? I am thinking of brane world scenarios such as this, but with six or at least some non-compact dimensions (but I would be glad about any example, even if it is not a brane world scenario). | 0 |
Find the perspective sequence that maps collinear points A,B,C,D to D,C,B,A. Attempt: If we need to find a sequence of three perspectives that (A,B,C)->(A,C,B), where A, B, C are collinear, then first we mark p is a line through A, B, C, let S be some point that does not lie on p, let q be a line through A and S, let p' be a line through A different from p and q, let B' be an element of the line BS and C' an element of the line CS, and let S' be the intersection of the lines BC' and B'C. Then the first pespectivity maps us from the line p to the line p' and has its center in S: A->A, B->B', C->C', and the second one from p' to p and has its center in S': A ->A, B'->C, C'->B. | 0 |
I would (like many before me) like to take my lecture notes using LaTeX. As writing pure LaTeX-code is very time consuming and not nearly as fast as handwriting, I can only really consider switching to LaTeX if I can use snippets and anything else that makes notetaking faster. I have discovered this post on how to get faster using vim, but at this point I don't really want to learn vim anymore. I know it is very hyped, and probably worth learning, but I have so much else do learn already that I don't know if I will ever find the time. At the moment I am very happy with VS Code (or really VSCodium) for all developing, scripting and stuff that I do, and as I can perfectly do just about everything within this one editor, I would very much like to keep it. Saying this, has anyone an idea or a hint for me on how to set up something like the blog post describes using VS Code? That would be very appreciated. | 0 |
I am confused whether I should use "a" or "the" when I refer to an object given/identified by some other object. For example: The package is now in [a / the] deposit box with the number you received by SMS. For me this is the deposit box I previously stored the package in, but it seems to me, that for others (including the listener), it is still just some deposit box in the given vault: if I make a typo in the SMS message, my listener may hear from the front desk of the vault: A box with this number does not exist in our vault. Regardless of any such mistake, my assumption at the moment of speaking is that the listener will be able to find or identify the box unambiguously based on the number. Which is the correct article in such situations? | 0 |
Take a primordial black hole and measure the Hawking radiation over a large amount of time by gamma-ray detectors, as well as a Large neutrino detector. Using theoretical calculations about the composition of Hawking radiation combined with the detected neutrino flux you can determine the neutrino luminosity. Combine that with the luminosity in the form of gamma rays and whatever particles the Black hole is hot enough to produce, and then compare that with the loss in mass over time. If you detect a discrepancy, it's likely the missing flux is in the form of gravitons. Would this experiment work? I did also consider using a primordial black hole cold enough to not emit neutrinos but the Hawking radiation calculator I used gave a black hole lifetime greater than most estimates of the lifetime of a proton. | 0 |
Many problems in classical mechanics, classical and quantum field theory among others require the study of systems of partial differential equations where questions like existence and uniqueness cannot be answered with the typical counting-equations/variables arguments - questions which have physical relevance and that need to be addressed before going to numerics. For instance, problems in surface mechanics always involve the Gauss-Codazzi equations which is a non-linear overdetermined system of PDE. The most powerful technology to properly study general systems of PDEs are Exterior Differential Systems, and there are some canonical references in the mathematics literature like Bryant et. al. I found this challenging for a standard theoretical physics graduate because it requires a solid background in non-conventional math topics for physics like commutative algebra and number theory, so I wonder if there is any reference treating EDS for physicist. | 0 |
I'm looking at a few English sentences, and I've realized that many verbs can be used as nouns in their infinitive form. For example. I am going on a run and in the present tense I am running. There are many more verbs that this can be done to. Are you going to take the jump? Why did you do three pitches? You know he would have hit one of them. (baseball) Can you please do your exercise elsewhere? It is too loud right here. So 'pitches' in the example is not in the true infinitive, but is in the plural infinitive, so this may not be a true example. 'jump' and 'exercise' are however. Normally, I would say that these are gerunds, however, after looking online for a while,. it seems that gerunds always use the present tense, and never the infinitive. What is the name for these verbs that can be nouns when in the infinitive form? | 0 |
I'm writing longer mathematical texts (lecture notes) regularly, and I don't know where else to ask this question. I regularly find myself enunciating (in the typographical sense) every statement I make. This means that I will put any even vaguely mathematical statement, not only theorems, corollaries, definitions, etc., into an enumerated environment in Latex. As of now, I always use Remark for them, and I feel like I'm overusing it. Question: When do you write mathematical comments in some numbered environment, like Discussion, Observation, Remark, Idea, etc., and when do you write mathematical comments standalone in the running text? What other environments do you use to mark up mathematical comments? Edit: The reason why I enunciate this often is simple: Later on in the text or in the lecture, I might want to refer to this comment. E.g. in a mathematical comment, we combine all results in an informal discussion on how to compute fibres of maps between prime spectra. This result is somewhat important as it will come up every now and then, but its statement in the lecture was more or less like an argument, making it difficult to encase this as a corollary. | 0 |
I have written a long book in latex memoir. I now want to feed its content to a machine translator into another language (say, German). I will use the automated translation for a first pass for a better human translation. Translators do not understand latex. There are a couple of methods to go about feeding them. I could use some online latex parsers, write a quick parser myself, etc. It occurs to me that I could also ask latex to create a pdf that is better suited to pdftotext (poppler). It should make big spaces between paragraphs, not break paragraphs across pages, etc., probably take out tables and figures, page headings, footings, and sidemargins, footnotes. (Eventually, I will also need to write a parse-match to integrate the translation back into a latex document that uses the original structure, but just replaces the text. Thus, I am thinking of adding a number for each paragraph, so that I can take the translation input and output and reconstruct a latex file.) Has someone written a style file to improve the results of pdf text extraction? or found a better solution? | 0 |
I am trying to learn about neural networks. I was reading the paper An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem which uses graph neural networks such that given a graph we get a hamiltonian cycle which hopefully is nearly optimal. However, they use as ground truth the concorde algorithm, which when I ask google and chat-GPT seems seem to be an exact algorithm but in section E (solution visualization), there are some cases where the author say : The model predicts a shorter tour than Concorde for this instance by choosing a different contour around the nodes at the top-left of the graph But how can it be better? Doesn't concord compute the optimal solution already? Did I get something wrong about the traveling salesman problem? | 0 |
i have taken two course in complex analysis, one variable and the other in several variable and the begining of complex manifolds, my understanding in one variable go well but in several variable our prof use two books, one of krantz and the other of Hoermander, i think due to my lack in the theory of integration(multiple and differential forms integration) i don't understand some proofs,in particular some construction for Hartog's extension theorem and the other about separate Holomorphicity And this brings me to my questions: do you think a good understanding of Lebesgue integral and Mesure theory can replace Riemann integration theory. what to study in complex analysis to develop geometric intuition,in particular for abstract algebraic geometry and sheaf theory, and if possible is there an approach that don't depend on functional analysis and PDE. and thanks | 0 |
I use LaTeX for a lot of my classwork (worksheets, graphics, etc). One thing I have not transitioned is my exam writing. An example page of an exam might look like this. This is just a portion, doesn't have the header and such, I'm comfortable working with those. I've not moved to LaTeX because of my need to be placing the answer boxes and blanks in specific spots on the page, and it's frankly pretty easy to drag little rounded text boxes around MS Word to achieve my layout. But there could be a fair bit of programmatic benefit in being able to make some of those blanks more consistently, layout chemical equations more simply, etc. I also have a page of multiple choice for each exam that I'd love to shuttle off a lot of that layout work to LaTeX. Is achieving looks like this reasonable with enough flexibility to be able to shift around those blanks and such on a question-by-question basis? I've found this page about using a zero-sized box. Seems like it be applicable, but just want to check before I start down this path. Any resources or general code ideas for doing what I'd like would be appreciated. I'm sure in the future I'll come back with some MWE, but for now just gathering info on even executing this. Also if the answer is "Probably more work than it's worth and keep using MS Word", I can accept that too :) | 0 |
I am posting the specific problem I am dealing with for reference and then explain the part I am confused with. My Understanding and approach to the problem I identified that in the ground frame the disc will have some inertia and thus simply remain stationary as the plank below slides away.When viewing from the plank's reference frame it's acceleration will be added to the COM of the disc in the opposite direction.So initially the instantaneous center of rotation is at the exact center. The Confusion I am unable to visualise how the instantaneous center of rotation will change as the COM gains velocity due to the acceleration. The solution that I found said that the points that have tangential velocity along the acceleration will have some added velocity while those against will have some net velocity in the direction of the acceleration.According to me if that happened then the rotation would completely stop which does not make any intuitive sense. Here's the solution for reference Conceptual Confusion The main concept I am struggling with is the instantaneous centere of rotation of the disc.I tried reading up about it on wikipedia but that doesn't clarify it for me. | 0 |
This question is born out of the riddle where there are two characters, one that always lies and one that always tells the truth, and you want them to tell you which of two doors is the "good" or "bad" door. You can ask either character, "what would the other character say is the good door?" And the lier will answer with the bad door, and the truther will also answer with the bad door. My question is a variation, given two characters where each character might always tell the truth, or might always lie, but both characters think the other always tells the truth, are there any questions you can ask that allow you to determine more information about the composition? For example it could be that character A and B both always tell the truth (and each thinks the other always tells the truth) or it could be that character A and B both always lie (but again each thinks the other always tells the truth), or it could be that one character always tells the truth and the other always lies (but again they both think the other always tells the truth). Are there any questions that can be asked to determine the composition? | 0 |
Is there a possible slight difference between protons and electrons behaviour while they are accelerated at speeds that cause relativistic changes to their mass. Why am I asking that? Because for a proton we know that it is made of several components which of them are the three quarks. If they have some speed inside the proton it is logical that this is not the same as they have no any intrinsic speed and that this speed does not matter as a portion that is added to the overall speed of the proton that is accelerated to a relativistic speed. Should that small part of the overall speed make a difference between the theoretical calculation of the particle speed to relativistic mass ratio and the empyrical results as the theoretical calculation threats the proton as an elementary particle because the intrinsic speeds of proton components are neglected in the formula? | 0 |
An electromagnetic wave is usually illustrated with two sine wave shaped fields, one for the electric field and one for the magnetic field. As in the picture below: But as how I understand magnetism, it consists of two poles, north and south (alternatively described with field lines, with a direction, where north and south connects). So to focus only on the magnetic field (the red, B) in an electromagnetic wave; where are the poles located in such a sine wave (the red part)? Is only one of the poles illustrated, such that another sine wave could be added for the other pole? Update: In this video, Maxwell's second equation is described as the field lines in the magnetic field is always connected (north and south pole) - how these field lines are organized in a wave is what I don't understand. Later in the same video, the fields emitted from an antenna, are illustrated as "bubbles of fields" - quite different from how the "arrows/vectors" are illustrated in my picture above. Field lines from the video: | 0 |
Lill's method is a visual way to find the real roots of a polynomial equation. It involves drawing a straight line with lengths equal to the coefficients of the polynomial. The solution can be found by using a slope of a right triangle. Lill's method - Wikipedia The values of a polynomial function can be "defined" as a distance between the vertice of the last polynomial coefficient and the path that we draw using right angles. Polynomial function's value Cubic function with defined function's value What I want to do is to find the local maximum and minimum in Lill's path. So, I'm curious if I can "define" a line that represents the first derivative of a cubic function and let it equal to zero, or if it can't be done. What I have done is by using the derivative's definition, and I got that a point (P in the picture) is the derivative of a function which its value is zero. But I think that's not the correct way to do it. My way to do the derivative in cubic function I drew the function and its derivative with the same "first coefficient" Please correct me if I'm wrong, Thanks. | 0 |
I need to retrieve Roll and Pitch (but not Yaw) rotation values from rotation matrix (or euler angles, or quaternion, input can be different, fortunately, it can be converted from one form to another). [Info table] X points Left. Y points Up. Z points Forward. Rotation around local X axis is Pitch. Rotation around local Y axis is Yaw. Rotation around local Z axis is Roll. If I just use Euler Angles then, in some situations, I get wrong values. As I think, this due to rotation can be represented with multiple variations of Euler Angles, so it breaks when rotation around X axis (Pitch) and Z axis (Roll) is represented also using Y axis (Yaw). gif (How it works | How it should be, but I need rotation without Yaw axis) Also algorithm is running in time, so, solutions, computing some delta rotation, are also accepted. | 0 |
When fluids are subject to external perturbations or put in certain geometries, they always show arguably the most fascinating structures : Starting from the eddies and vortices in pipe flows at large Reynold numbers, vortices of flows past an obstacle, or the vortices in fluids confined between two rotation cylenders. Yet, a fluid at rest is often thought of just as a completely structureless phase : Apart from very small-scale features such as the arrangement of nearest neighbors or solvation structures in liquids, it is just a random phase and the trajectory of a tagged particle from the fluid simply obeys the Brownian law, without any other features. But what I somehow intuitively expect is that most of the above mentioned "non-equilibrium" structures appearing under well defined conditions are present in the resting "equilibrium" fluid. This means if were to look at the trajectory of some fluid particle I expect to see imprints of the coherent non-equilibrium structures in the equilibrium trajectory, and not just see a Brownian trajectory. Can you somehow relate to this ? | 0 |
Lets imagine you have a universe where the average matter density is extremely close the the boundary between one that will expand forever and one that will eventually re-collapse. Now lets imagine that there are very large scale fluctuations in density at the Gpc/Tpc scale and above. Could this result in differences in the rate of expansion between some parts and others, causing parts of the universe to collapse and parts to expand forver? If yes what would this look like near the boundary? What if the region was non simply connected. (E.G. a torus, or hollow ball.) How about a universe with bee marginally above the critics density with some very large under dense regions, perhaps ones large enough for the centre to become causally disconnected form the edges. | 0 |
There is a good discussion here (Referring to past times with "hence") that concludes that hence can't be used like "ago" to refer to a past event, not even to describe how much time has passed "since" that event. However, what if using the past perfect and then referring to time forward from that point, Could "hence" be used there? The specific construction I'm wondering about goes like this: They had left me there to die. Even now, one-and-a-half moons hence, it would be a simple matter to follow their trail. In that case, "hence" is a time forward from a point in the past as made clear by use of the past perfect ("had left me"). Is that appropriate usage, or can "hence" only refer to the actual future, not a future relative to a point in the past? | 0 |
There is a closed continuous loop, and you have a stick of a random fixed positive length,so that You can slide the stick on the loop. Take the stick's midpoint. It's track will form another closed continuous loop. Take another stick of another random fixed positive length. Slide it on the new loop again. It's midpoint will form another loop. Do this again and again. Will the shape of the loops tend towards a circle(well, the area of the loop may decrease, but you can magnify the area to not let it become a point)? Or could it become another shape? The thing I found was that circles and ellipses will tend towards a circle, and I think the question is intuitive, because this operation of sliding sticks round's spikes and makes concave shapes convex. | 0 |
Imagine a ball with diameter "a" at rest and another observer at rest at a distance of 'l' w.r.t to the ball in this rest frame.Say the ball suddenly starts moving at velocity v towards the observer .(Assume it accelerates instantaneously).What does the observer measure the distance between them?What does the observer measure the diameter of the ball to be?If the diameter is contracted by gamma factor then why is not 'l' contracted by the same?Because acc to me by time dilation,as the time interval is zero wrt to the observer between the events (ball moving and ball at rest),so the distance moved is zero acc to observer and hence observed distance remains 'l'.I asked my professor,he also said that diameter would contract but distance of ball wrt observer wont , but I didnt understand why this partial treatment of two lengths ?.They are identical in properties with regard to lorentz transformations so if one contracts wrt observer the other should also. | 0 |
Maybe this belongs on "Linguistics" but since it's about an English word, I suppose they'd only send me here. Over time, some words gather more and more meanings to themselves. Ironically, these words are often small like, "by". Other words seem to shed meanings, or rather, they devolve meanings to new words. In the New Testament, Jesus tells people to "arise" from their bed, elsewhere "the resurrection" appears. But this is actually just the noun form, i.e. "the arising." Now, no one except by poetic license would refer to their "resurrection" from bed; it has become a specialized form of "standing up" (from death.) Is there a pair of words to describe on the one hand the accreation and on the other the fragmentation of words and their meanings? | 0 |
In my current understanding, I have been told that the spin of quantum particles is simply intrinsic to them. That, particles are simply right-handed or left-handed... just because they are. To me, that seems then that we should then treat handedness like it is just as distinguishing of a property as mass, or charge, or color charge. Almost like the standard model should be doubled, or mirrored. Like, right-handed, blue, up quarks should be considered as a wholly different particle from a left-handed blue up quark. But wouldn't something HAVE to catalyze the spin? Like a ball rolling down a hill hits a rock, and how it first strikes that rock determines whether it continues its rolling spinning to the right or to the left. Could spin be acquired, for instance, during the big bang, by the first interaction of a particle as it "hits" the higgs field? And some characteristic of the particle to that point determines which way it "glances" off of the higgs field? | 0 |
At the end my document, I get a new page that contains, Temporary page! LATEX was unable to guess the total number of pages correctly. As there was some unprocessed data that should have been added to the final page this extra page has been added to receive it. If you rerun the document (without altering it) this surplus page will go away, because LATEX now knows how many pages to expect for this document. I know that by just recompiling the document, I can get rid of this error, but I was wondering why does this occur and what unprocessed data that LaTeX couldn't process. For citations, table of contents, table and figure references, LaTeX needs to be run twice, but I have never ever seen this "Temporary page!" page before. | 0 |
As we know, in EM wave, with the oscilation charge (for simplicity, charge was moving at constant speed, then accelerated and then continued moving with constant speed again), kinks are produced. The funny thing is as the kink moves outward, its length actually increase(the joint vector between the new field line and old field line) due to the fact that new field lines move at a higher speed then old ones. I wonder what we exactly call a wavelength of wave then. Is it the kink's size ? but if it's kink's size, then it means with just one acceleration, kinks size increase and wavelength increases as well which seems to me wrong. one acceleration only should produce one wavelength. So what's the connection between kink and wavelength? If there's no correlation between kink and wavelength, then wondering what's the wavelength truly is in terms of EM wave? | 0 |
I want to simulate typewriter style typesetted math articles. There are a few major requirements: All characters in all environments be tt style and of the same size and width (including super and sub scripts in math mode). In math mode, sub and super scripts should be one character higher than the base. All emphasizing should be replaced by underline. Spacing between all kinds of lines, including spacing between lists or figures and texts, should be always integral multiples of character height. The multiple can vary according to the height of inline equations (e.g., when too many levels of superscripts, should leave space for superscripts to avoid overlapping). All spaces being the same width as characters, no adjustments to fit line breaking. If a word cannot fit in one line, leave it to the next line. To conclude, all elements should be arranged as if the page is separated into "grids", each grid of the size of a tt character. All elements should be placed exactly fitting one or multiple grids in both vertical and horizontal directions, there is no "half" space or something like that. Is it possible to fulfill these requirements in LaTeX? | 0 |
We know that when the wave model of light was being used in physics there was Thomson Scattering Model to explain the interaction between a free electron and a light. The Thomson Scattering was explaining the force that acts on an electron when a light hits it, with the force that the electrical field component of that light possesses. (Rather than billard ball explanation) However, I do not understand Thomson Scatter in relation to Doppler Effect and Low-Intensity waves. For the wave model of the Photoelectric effect, it was clear for me to understand where was the wave model wrong when explaining the necessity of the quanta of energies. But, How was Thomson wrong when talking about Doppler shift and low-intensity waves not being able to explain the movement of electrons? I know for a fact that low-intensity waves were insufficient to supply energy for an electron to have the speed and kinetic energy it is supposed to have. I am not sure how built-up energy by low-intensity waves have been thought to be a supply of energy for the acceleration of electron in the first place and how is this related to the Doppler shift by Thomson. | 0 |
I am trying to have better understanding of localized wave functions. Apparently free particle de Broglie waves are NOT normalizable and act as delocalized functions which was the original rationale behind their use for explanation of electrons in double slit experiment. so far so good ! But then we use Fourier transform to make them localized that they can represent a particle and behave normalizable . Here is what I can not understand: if wave function gets localized ( say to the size of an electron - which actually is supposed to be point-like ) , then such wave can not cover the distance between both slits to be able to make interference patterns in the double slit experiment, .... and if wave function remains delocalized , then it will not be able to get normalized and consequently its wave function will not present accurate probability amplitude . The only way I can think of this is to have a localized wave function that is substantially larger than the slits distance but vanishes at the infinity, but it will be much much larger than a particle - let alone a theoretically point-like particle. My question is: when making a localized wave function, how big the particle size or wave area should be to make interference patterns and be normalizable at the same time? are there known limits for that Fourier section? | 0 |
I want a tool to easily make geometry diagrams. For example, say I wish to overlay two circles, and then fill their overlap with the color red, whilst coloring other areas with other colors? Let's say I want to make a triangle with curved sides and a flat bottom side; that could be done in no time with the right tool. I could insert a square and then delete circles from its upper two quadrants. To be more clear, here are the list of features I'd like: A gallery of shapes that can be sized and colored as one wishes. The ability to fill any area enclosed by lines with a color. The ability to draw lines between highlighted points on shapes, like the centers of their sides, their corners, points between the quadrants of the circumference of a circle (allowing the drawing of diameters), etc. The ability to insert text into the diagrams. Is free to use. To give examples of close contenders: Draw.io has all features except number two. Microsoft paint and sketchpad has all features except number three. Does an app that has all features exist? | 0 |
Much of physics education focuses on equations of known possible reactions, how to balance them, how to predict the result if certain elements happen to react with each other. What I don't see a lot of is an explanation of what chemical reactions are likely to happen in a complex system. Assume I was building a physical simulation where I know the position/velocity of any number of elements or compounds. What would the process be to determine which chemical reactions are most likely to occur? Given my assumption: Treat the collision of each atom as a sphere of varying size depending on the size of the type of atom's valence field (sphere collision is to reduce computational complexity). Calculate magnetic attraction/repulsion between local atoms and manipulate the velocities accordingly. If the valence fields of two atoms overlap (or are near each other?) due to attraction, electrons are exchanged, and other atoms that are the least magnetically attracted are either re-positioned or rejected from the compound depending on the magnetic forces and electron availability. I assume "heat" based reactions can be derived from velocity of a collision? Would this be a sufficient model to predict an arbitrary chemical reaction or non-reaction? | 0 |
I am studying the Newton's Law's of Motion, and really confused about one thing. I know that bodies of very small mass get attracted to our earth due to a force it exerts, due to its huge mass. So that, according to the Newton gravitational equation, a given small mass on earth will be attract by a certain force and depends on the distance of separation from earth's core. Right now I am dropping a pen on a table and observing the sound. Higher the height from which I drop it more the sound it makes, showing that (I believe) more force is being exerted. Although from Gravitational equation of Newton, we can observe that the same force is being exerted on the pen because I am dropping the same pen from heights not so far away from each previous drop. My question is that from second law of Newton, change in momentum causes force. But from gravitation law of Newton, the same force pulls the pen down. But the change in momentum is happening due to gravity, but the gravitational force is constant so that, the pulling force is constant, thus, why every different drop do I hear a different sound. What is the right thing here? I am really confused... | 0 |
This question is perhaps more on the use of certain parameters in BibTEX than on the use of TEX/LaTEX itself: nevertheless I think it could be of some help to other persons who, like myself, need to redact large bibliographies. In order to list information on the existence of a review in the ZBmath database on a bibliographic item, I am aware of the existence of the following three parameters: ... zbl = {}, zbmath = {}, zblnumber = {}, ... Until a few years ago, only the last one seems to have been used (possibly my opinion is biased by the heavy use of Jabref I do), therefore I'd like to ask why the other ones have been introduced, if there's one of them which is preferable to use. P. S. Finally, let me point out that the American Mathematical Society always codes the analogous information in the univocal parameter mrnumber = {}, which works perfectly in many bibliography styles. | 0 |
We know from molecular spectroscopy that incoming light on a molecule can change a molecule's rotational, vibrational and electronic energy levels. If the incoming light is, on the far-infrared and microwave region the molecule gets rotational energy.(microwave spectra) on the near-infrared region the molecule gets both rotational and vibrational energy.(infrared spectra) on the ultraviolet & visible light region, the molecule gets all energy levels rotational, vibrational, and electronic energy (electronic band spectra) We also know that, Rayleigh Scatter does not excite electrons of atoms to another electronic level but only causes them to oscillate. Thomson Scatter happens when an electron is free or quasi-free and it also makes the electron oscillate and more, accelerate. Taking into account that both Rayleigh and Thomson most probably happen at low energies and vibrational and rotational energy changes of molecules happen at microwave and infrared spectra: QUESTION: It is clear that, Thomson Scattering can not cause rotational spectra or energy build-up, which requires the whole molecule to rotate since Thomson Scattering is about free and quasi-free electrons. But what about vibrational energy spectra, or energy build-up on such a free electron? Rayleigh Scattering happens on the atomic level so it begs the question, "can it cause both rotational and vibrational energy level changes in atoms or molecules?" | 0 |
For a given n dimensional chaotic system such as a chaotic attractor or really a time dependent chaotic dynamic system does there exist a higher dimensional representation where the behavior is in fact deterministic? This question comes from a data science problem in multivariate time series forecasting. Most real world behavior is chaotic in nature, such as the stock market or Earth climate cycles (milankovitch cycles etc.). Lets say I could build a really big model that takes into account everything that might impact the system of interest, would there be some set where all the chaos would just go away? Take the TV show foundation based on the books by Isaac Asimov. In there they postulate the Abraxis conjecture which is solved by folding space and is critical to the success of psyco-history (which is really just data science). One of the steepest challenges with time series forecasting is the ease at which it is possible to leave conditions where your inital state no longer applies. If chaos could be eliminated then this problem could be pushed out. Effectively with infinite information we could forecast for infinite time (in the theoretical limit only). | 0 |
While playing with GeoGebra a few days ago I came up with an initial property of my Cardioid curve, I heard this curve is well studied so I'm not sure on my guess if it's already discovered or new, adding references would be appreciated You have a Cardioid and its circle of perpendicular tangents The red point is an arbitrary point of the circle of perpendicular tangents The violet line is a right angle bisector The blue line is the hypotenuse of a right triangle The green line is the reflection of violet with respect to blue The brown line is the reflection of blue with respect to green The brown line is tangent For giving me Cardioid. I don't have progress on it yet, but I do have other cardioid guesses that I can include in a follow-up question on the site. | 0 |
I tried lots of research, but still couldn't wrap my head around the difference between free and mobile electrons. Free electrons, from wikipediaLink(I mean free particle bullet point, because other bullet points are not really free electron - as an example valence electron is not free, but mobile) are electrons that don't experience any external force, hence it experiences zero "electric field" from others. as for the mobile electrons, they are loosely bound to the atom (valence electrons). Though, even if these electrons are ejected from the atom, they still experience some electric field from other atoms and could jump into their orbitals. If the above is correct, how can both of these cases exist? how can free electrons not experience any electric field, while mobile electrons do? I know that in sun's core, there're free electrons moving through material. Why don't they then experience the electric field of other atoms? | 0 |
For some extended context, this is how Heads Up Displays (HUDs) and Reflector Sights work: However, as far as a I know, a lens will take collimated light and focus it to a very small point called the focal point. And since the reverse is also true, only the focal point can be collimated and "focused to infinity" to create the virtual image in a HUD. The reflector sight diagrams clearly show a source reticle that is larger than a focal point, and HUDs in general usually use an LCD display to create the initial image. Although modern HUDs use several optical elements to correct for aberrations and other distortions, most early HUDs and all reflector sights used a single large convex lens to collimate the image. Is this merely an issue of lens diameter? Would using a larger lens allow for the focal point to be larger in diameter too which would allow for a small display to be completely collimated? | 0 |
If we bring a separable dipole (say a single ammonium chloride molecule) from infinity to the center of a capacitor, once the dipole stabilizes and the rotational energy is lost to electromagnetic radiation, the net work done is negative. If the capacitor plates be perforated and the field be strong enough to separate the dipole and the ions pass through without collisions, they then may be accelerated in the same direction by two other capacitors with perforations, in the same direction and then may recombine after exiting because of their electromagnetic attraction. Once they combine, they still have the velocity gained by the two additional capacitors but none of the three capacitors lose their charge. The dipole gains some kinetic energy so where does the energy come from? The capacitors are not connected to batteries and are pre-charged, the entire setup is in vacuum and gravity is non existent | 0 |
Recently, I play a game of Turing completeness where I utilize various gate circuits such as NAND, AND, and NOT to construct a circuit that satisfies the given truth table. I didn't learn digital circuits or relevant content. When I play this game, I want to know whether there are any theory to deal it. For example, given a truth table, is there any theory to get the circuit with least basic gate (or only Nand gate). It seems to be a bit like graph theory (but the vertices are special). On the other hand, I know a little about retina from From Neuron to Brain. The retina responds to certain shapes of light, such as a ring of light. I've always wondered how build a neural network with neurons that respond to ring of light but not solid circle light. Of course, I'm not really asking for the details of these questions. I just feel they may are the thing not liking analysis and algebra. If I want to deal these questions, what book I should begin from ? | 0 |
A parabola is supposed to be a conic section, obtained by slicing through a cone with a plane, like this from Wikipedia: But if you do this, what you get is just part of an elipse, since if the cone and the plane were bigger, eventually you'd end up with an elipse. And a section of an elipse is not a parabola - there is no possible focal point that satisfies the condition that all points on the curve are equidistant from the focal point and the directrix - at least not when I try to construct this in my CAD software Answered by JonathanZ, the key thing was the parabola needs the slicing plane parallel to the slope of the cone (not illustrated or explained clearly in either Wikipedia or Wolfram IMHO). Here's what it looks like in my construction: | 0 |
I've attached an image that describes the light-rays refracted through a thin lens. P' represents the first real image that is created when light is refracted through the first convex mirror. But how does this translate to the second image point P'' through refraction? I understand the convex mirror formula and how if you plug in the numbers it just works out that Q'' is where it is, but intuitively, this does not make sense. If the image P' is what P'' "sees", as it is the image, how can the refracted image (P'') be on the same side as the object image (in this case P')? As far as I understand, P' acts as a real object for the second surface (the right side of the lens), and the rays that diverge from P' are what get refracted onto P''. But how is this possible, if they are both on the same side? As far as I understand, the model above depicts virtual object through refraction. How is this shown in our case? | 0 |
The reason we can see the color of objects is light rays undergo scattering in the subsurface of a material, and in their walk in the material lose some wavelengths, and finally exit at a random direction (link) However, aside from this, you see white highlights on an object from the light source. These can be diffuse or specular depending on surface roughness (I'm assuming they're both from surface interactions) Look at the highlights on the shoulder here for what I mean. Not where the arrow is pointing. However, I just found that that aside from metal, most common surfaces, even when highly polished, specularly reflect only a few percent of the incident radiation. How are these highlights then so pronounced, especially for the diffuse highlight case where the light is distributed in all directions. | 0 |
(Edit: This was closed because it was marked as "opinion based" and I was asked to edit the question so that it could be answered by facts and citations. @Fumblefingers gave citations, thank you. On re-reading several times, I think yours is the correct interpretation, rather than assuming the existence of some actual physical flag. It's like as if we referred to captains & sailors dying in the line of duty as a "badge of honour", there's no physical badge. In my opinion, expecting facts about poetic allusion is a bit unrealistic. Thank you @KillingTime, I hadn't known about the literature forum. I can ask such questions there, and keep this forum to linguistic questions. ) ORIGINAL QUESTION: Does any English literature expert know what kind of pennant Walt Whitman was referring to by "a pennant universal" in the poem "Today a rude brief recitative of ships" in "Leaves of Grass" ? Flaunt out O sea your separate flags of nations! Flaunt out visible as ever the various ship-signals! But do you reserve especially for yourself and for the soul of man one flag above all the rest, A spiritual woven signal for all nations, emblem of man elate above death, Token of all brave captains and all intrepid sailors and mates, And all that went down doing their duty, Reminiscent of them, twined from all intrepid captains young or old, A pennant universal, subtly waving all time, o'er all brave sailors, All seas, all ships. | 0 |
I am aware that in the theory of classical infinite sums , one can not generally interchange the order of a double sum or do other infinite sum manipulations. However, these infinite sum manipulations can be valid if absolute convergence is available. I am working on a problem , where I would like to manipulate a double infinite sum but absolute convergence need be satisfied in my context. I am under the impression that these classically illegal infinite sum manipulations can hold under less strict conditions in the context of non classical summation methods. I would be glad if someone can write an answer that discusses when interchanging the order of a double sum is allowed in the non classical setting and direct me to a place where I should read about this. Thank you a lot. | 0 |
After verifying that it was a real word, I just posted a chapter named "Processioning". I have begun to wonder what kind of thing that is. As far as I know there has never been a verb, "to procession", and "to process" is something else entirely. Yet, "they were processioning through town" makes perfect sense. I am thinking that there may be a class of such words, apparent verb forms made from nouns. Am I misguided, or simply ignorant of what the heck that is? It is also weird that processioning would not be used as a gerund, because the noun form is procession. I guess it could be an adjective though, "the processioning group". edit: talented musicians an unconvincing argument an enterprising foreign policy a fun-loving guy are sound examples with no corresponding verbs [EA]. | 0 |
Suppose there is a ridiculously large bridge, fixed at either end (light seconds long at least). The bridge is constantly under the influence of gravity. If the ends are severed simultaneously, the whole bridge will fall. I assume simultaneity isn't a problem as the bridge is all in one reference frame? Will an observer in the middle register the change of inertia, but be unable to see or detect any damage to the ends of the bridge until the light from each end or the signal from electronic sensors has caught up at light speed? If so, does this mean that they can infer from the fall that the ends must be severed I.e. have they recieved information about the state of the ends faster than lightspeed? Or will they not begin to fall until the information about the severed ends has caught up? | 0 |
Usually in a Cartesian form of derivation in math and physics, I have seen that a particular formula is derived for simplicity by taking concerned points say in the first quadrant. Few examples are the derivation of mirror formula, lens formula, lens maker formula, distance between two points. Later, they extend the formula to all cases and say : "The formula is valid for all cases independent of quadrant and position because we have taken proper care of signs". For example, see the case of mirror formula derivation in the book (especially the pointed last paragraph): Similarly here for distance formula in SL loney. I do not understand deeply that why do this happen ? I know that it can be proved in the above cases by actually deriving for all cases and observing that it is confirming, but how can we say it generally? So the question is : Why do the sign convention in coordinate geometry work the way it does ? | 0 |
I am an undergraduated student from a non-native English speaking country. In my country, when doing math, which in many contexts that we will be proving something like a theorem, a proposition. What matter is I feel like we don't have a variety of words while doing math. Everything we used in our assignment are just around "we have, we get, hence, thus, therefore, we have this, we have that, we have and we have ...", which is kind of boring to me. I love math and I love solving math problems, but I would love to bring my product with an abundant style of words, just like it's not simply a proof of math, but more like a nice essay of math, to make my products more lively, agile, elegant, refined. So I really appreciate if you guys could enlight me with your knowledge. My very thank you. | 0 |
We are extracting transformation matrices for different joints from ARKit. These are relative to the parent joint. Since the positions are not very accurate, we have developed a machine learning model that corrects the positions based on ground truth (Vicon data). We only use position data in the model, so now the rotation part of the transformation matrix is no longer valid. My question is: Given that we have the initial transformation matrix (I can have the rotation, scaling, translation separately) is it possible to get an updated transformation matrix that uses the positions of the model? My end goal is if possible to calculate the Euler angles of the updated position for the initial coordinate system. I have checked the Rodrigues' rotation formula but I am not sure if I can use it somehow. | 0 |
Have an excel financial model, that pretty much is a time series of assets and liabilities. I would like to know what the optimal liability structure / mix is, subject to multiple balance sheet constraints. My objective function is to minimise funding cost. I tried to optimise using Excel Data Solver, but encountered the following issues: Excel may not arrive at a solution (can't converge at times even though there is a solution) Solution is not consistent, eg same starting point (ie initial guess) but different end points (not all are optimum) Solution may not be global minimum Am open to using other softwares like Matlab or Mathematica, with my own "constraints" I won't be able to simplify this down to an analytical equation so will need to be in the format of a financial time series model Ideally arriving at global minimum Scalable Are there any guide you can point me to? Open to software suggestions, algorithms, approach, etc... Thanks | 0 |
In Meissner effect we say that below critical temperature there is an expulsion of external field lines or field lines do not penetrate inside the specimen. But here is what I am not able to understand, if the sample creates a mystical force which do not allow field line to pass then it can be imagined as if there is an field due to specimen which cancels its effect. I know experimentally field lines are expelled, but why they are expelled I want to know the reason like who are the one that causes no fields to penetrate inside it. Somewhere I have read that a persistent current rises in such a way that it creates a field which cancels the external field. Now how is that possible that a superconductor inside in it already has a field? | 0 |
I've been told numerous times in high school that "first and second person pronouns in academic writing" should be avoided. This supposed wisdom is echoed in various style manuals as well. However, if you look at any authoritative text, like The Stanford Encyclopedia of Philosophy A simple search of "we" will yield countless articles using the first pronoun all throughout. Given this situation, is it realistic to teach anything stylistically related to using first pronouns? Also, based on experience, trying to stick to this kind of rule damages the entire paper in many ways It takes time to conjure up passive tense sentences which usually is all but required to avoid you/we completely Some concepts more effectively expressed through these words may fall between the cracks and never see it to fruition, which is truly a shame Grades may even suffer trying to stick to the rule -- an irony given that adherence to rules are always motivated by desiring praise and getting good grades, etc. ad nauseum... | 0 |
Background: ZFC in classical first-order logic. To make a definition, we first need to proof something does exist. So, this question is actually about proving something exists based on a recursion. I know that when you want to prove the existence of a certain function with the domain of ordinal numbers, you can use the transfinite recursion theorem. But our things are not always a function of this sort. For example, when we define the truth value function on the set of formulas in predicate logic, we usually define it recursively based on the number of the logical symbols in a formula(or complexity). But for a certain complexity of the formulae, there're many cases to deal with. I can't figure out how to prove such a definition does make sense, aka the function does exist. | 0 |
Good day, everybody. I program a simple computer game and there is a "dumbbel" inside of it, which should using some kind of rocket engine. The engine is fixed on one side of the dumbbel and creates a constant force F, which is ALWAYS orthogonal to the dumbbel. Since the dumbbel is ideal, the both sides have only mass m and zero size. The junction is absolut hard, has the length l and doesn't have mass. S. also this figure: There are no other forces than F (especially no gravity) and there are no other bodies than the dumbbel. Therefore no collisions or bumping. The motion happens flat. How can I calculate the trajectory of the "dumbbel"? Is there an analytical or numerical approach I can use in my game program? Thank you very much! | 0 |
For all the words I know, I can't seem to find the right word for this strange emotion. Some words I have tried come up short in one way or another. Confusion lacks the underlying hatred, annoyance ignores the triggering bafflement, skepticism is to forward to properly describe the abhorrent serenity caused by this mixture of emotions. I tried looking on Google and several other sites for some synonyms for each of them, but my results kept coming up short. Even my 'Better-words-for-authors' guides proved insufficient. I'm starting to think there might not even be a single word in the English lexicon for this emotional mixture that is hatred and anger caused by disbelief. Example of how it could be used: He couldn't help but feel [blank], had the youtuber really sunken below rock bottom. - or - [blank] began to well up inside of her. The others had resorted to Orwellian new speak to justify their problematic behavior. | 0 |
The normal proof goes as follows: if H(f) is a program that takes the source code of any program f and return whether it halts, we define G to be if(H(G)){ loop forever } else { halt } Which is a contradiction if you run H on G. My problem is the unjustified assertion that a program like G even exists, as presumably it is able to print its own source code and run H on it (or something analogous to that) and halt or not halt based on that. My intuition tells me this violates some information theoretic result I am not smart enough to know about. Furthermore, since we have no idea what H even looks like, this proof only works if you can prove that for every program P, there exists a program G which can print its own source code, run P on it, and then do some stuff based on that. Since the mere existence of Quines, which still conserve information, is already a deep and complicated result (from what I can tell), the truth of Gs existance is sketchy to say the least. | 0 |
Suppose I have some process that I believe to be the result of a differential equation. It would be reasonable to regard this as the path of a point particle in some notional space. Suppose further that I know the exact shape thaat the path follows, and it is one with a simple description, such as a conic section or a polynomial in two dimensions of low order. Is there a determinate series of steps that will give me a differential equation which has my specified shape as a solution for some initial value, or produce increasingly good approximations of that shape on iteration? If there is an exact solution tell me how to find it. If there is a way to find increasingly good approximations to a numerical solution, describe that way. If the answer or answers to the questions above are reasonably clear and straightforward, but hard to describe compactly, I will accept a citation to a work that contains such answers. However if it is a citation to a book-length work, I want a page range or small number of chapters that contains the answer. | 0 |
In ceveral textbooks it is said that an ideal LC circuit does not lose its energy, it just bounces from the capacitor to the inductor coil back and forth. On the other hand, any system where charges are going to be accelerated radiate energy (that's should always happen when involved charges are going to be proper accelerated, which is a consequence of Maxwell equations). But then due to this, even an ideal LC circuit should lose after any cycle a certain amount of its energy as radiation, since the charges there are accelerated at all? Therefore I'm confused at that point: Does Bremsstrahlung not occur in an ideal LC circuit (why? That does not make any sense, the charges there are going to be accelerated, so this should give by Maxwell theory radiation losses)? But if this accelerations of charges takes place there, then the energy loss cannot be ignored even in this ideal case, or can it? Does anybody see how to resolve my confusion? | 0 |
Everywhere it is written that electrons flow through through wire of an eletric circuit, and the reason given is that the battery maintains high potential at one end, and low at another. But, if you think about it from first principle electricity& magnetism, then one would realize by intuition that the provided reason only would imply that the electron would move from the high potential region to the low potential region, not that it takes the specific route of the wire. To find a specific route, it would involve solving of the differential equations. In regards to solution, many places I've seen have written that the eletric field caused by the battery only exists inside the wire, but how do we know that/justify this approximation? I have found this related question, but I felt the answers quite unsatisfactory in regards to the above problem. Also, I Understand that to study circuits, we need more than Maxwell's equations, that is a theory of the matter (charges involved and such) as discussed in this question, but my question is, what is the basis for the justifying that the eletric field is confined to the wire? | 0 |
Central idea of Michelson and Morley experiment was that if single speed of light predicted is speed of light relative to ether, then as the earth moves through the ether, light travelling along the direction of motion must travel at a different speed relative to the earth and light moving at right angles to the motion. If I get the argument then something like saying say velocity of ball is fixed in air. Then someone watching the ball from a moving train will see the velocity of ball different in the direction of motion. But in the experiment, the measuring apparatus ( equivalent of person measuring speed of ball in train) and the what is being measured i.e. light are in the same frame (frame of earth). Why should the velocity come different in that experiment as they thought? The argument could have worked if someone to look at this experiment outside earth frame? I know I am missing something just not able to pin point. | 0 |
I don't know if this site is a suitable place to look for examples, but I have a lot of ideas that I would like to find a good example of, and I try to organize these things in a later book. I hope I get to a place where I can discuss my thoughts so that I find people taking these questions seriously, and I think they are thoughts of many people. I am searching for an interesting example/example of a theorem, issue or case in mathematics, in which there is a specific variable that affects the result, while the intuition tells that the result is independent of this variable. In other words, I would like a case where intuition fails to estimate the effect of a factor on a particular problem and one thinks it is ineffective, while reality is otherwise. Are you welcome to find examples of searching for examples on this site? | 0 |
Urban Dictionary includes one explanation of "play" : Anything to do with sexual relations: fooling around, making out, oral sex or having intercourse. However, most of the formal-language dictionaries don't include this explanation, only interpreting the word as "to tease" which can describe something childlike such as flirtation, except the phrase "play ground" meaning: Having sexual relations with other people who is not your partner. Merriam-Webster Dictionary also suggests "play (n.)" as "flirtation", which can be converted into "flirt" with "play (v.)" Is this a difference between the formal language and slang? This question also leads to an answer which regards "play" as a synonym of "flirt". word for a person that flirts with everyone? Does the slang term have a much broader meanings than the flirty activities implied in the formal language? Does the term imply being unfaithful? | 0 |
Any introduction of relative simultaneity usually is like this : Alice on a train car shines two beams of light towards both ends where two clock are. She sees both clocks see the light at the same time. Bob on the station looks at the same event and says the trailing clock was hit before the leading clock. I have no doubt about what Bob is measuring, but if speed of the light stays independent of the source, then it should not matter if the frame of reference is moving with the targets -i.e clocks- or not , both Alice and Bob should see clocks are being hit non-simultaneously . Is there any actual experiment that proves Alice is seeing simultaneous clock hit ? I mean has anyone placed clocks on very fast moving objects to prove light hits both leading and trailing sides at the same time ? Or do radio signals arrive at different times to equidistant Eastern and Western stations due to rotation of the Earth? | 0 |
This question has come up with me in two different Final Fantasy games, where you want or need to collect every memory or skill through random selection where not all memories/skills are available until late in the (main) game (not in the random selection "game"). Collecting a memory/skill does not remove it from the set (you can randomly land on it again) My question is: In terms of getting every entity in the set, does it help (in terms of the expected number of plays to pick every entity) to play this sub-game before all entities have been added to the set (assuming even probability distribution over all entities)? If what I am asking doesn't make sense to you, please ask let me know in a comment and I will try to clarify the question. | 0 |
I'm trying create a new single-item selection system that has either identical or close to the identical probability of an existing multi-item selection system. The current system has multiple "tables", each containing multiple items. Both a table and each item inside of that table have a selection probability. That is to say we determine if a table is used based off of its probability, and then we go through each item in that table and determine if that item is selected based on the specific items probability. Using the new system, I want there to be only one table containing one item. The one table should have the combined probability of ALL the old systems table probabilities and the one item should have the combined probability of ALL the old systems item probabilities. Would this mean that I would simply find the average of all the tables and the average of all the items and that is the new probability for the table and item? I'm also curious if there is way to shift the old systems table probability on to the item? That is to say, the table would ALWAYS be selected, and the probability of the item in that table would adjust based on the tables previous probability. Is this possible? | 0 |
In the book To Have or to Be Erich Fromm claims using "have" in English increased due to the rise of the market economy and Protestantism. Where one is alone in the market, with their personal relationship to God, rather than being part of a feudal economy and church where they are taken care of. How well is another conversation, but the point is they didn't talk in terms of how much they personally have so much, unlike in the market economy, where what they have is all they can depend on, with the rise of private property. He wrote that this is the cause of "have" being used in more cases such as "I want to have a party", instead of "I want to make a party", as one may see in other languages. England was ahead of others in the assimilation of a market economy (besides the Dutch). I'm not sure how English compared to others concerning amendability to change though. I did not see similar explanations in the etymology of "have". So the question is, how accurate is his explanation? This question can be answered with examples of people changed lifestyles of people along with changes in language. Things happen for reasons, the answer would give the reason, whether agreeing with the question or not. | 0 |
When I try to solve a hard problem, I have no idea on what to do before I write anything on the paper: apparently, only after I spent hours on a particular problem I find the key idea by just a coincidence. This makes me feel that training myself by solving tons of hard problems on integration or geometry etc... is a waste of time since for the most of it I randomly run into the solution by coincidence and that is what I mean by randomness when solving a math problem. So my question is: how to overcome that? Should I try to solve each problem on my head without writing down any thing? Or what do you advise me to do? And is this a thing that I can solve or I am just not smart enough? | 0 |
The main statement is: the EM coupling constant is energy dependent, and the fine structure constant (FSS) is the low energy limit. This means that the flow of the coupling constant vanishes when the energy does not suffice any more to create the lightest charged particles, electrons and positrons (there only remain the classical tree diagrams). Below the electron rest mass energy virtual electrons and positrons are frozen out. Consequently, the FTS is a function of the electron mass, and if the electron mass comes from the Higgs coupling, of the Higgs coupling. All QFT literature is about the scaling limit and high energy (where the electron is effectively massless), and and no clear statements about low energy can be found anywhere. But in statistical mechanics terms the above statement appears to be the only reasonable. | 0 |
The problem arose of choosing a direction for studying and working within the framework of this topic: neural networks as universal approximators for solutions of partial differential equations. At the moment, as a rule, neural networks are used to obtain more accurate numerical approximations, stable, compared to classical difference schemes. Today, there are many different libraries for training models and predicting solutions. My problem is mainly that I want to try, based on already selected numerical approximations, using neural networks, to obtain a number of analytical solutions. The question is: is it possible in principle to obtain a similar result, and are there any practical problems described in scientific articles in precisely this context (not refining numerical solutions using neural networks, but approximating already obtained solutions and obtaining analytical expression). That is, maybe there is some small problem that has important practical significance, the solution of which can be presented in this form? In fact, my question is quite targeted, since I am not asking for an overview of the available methods for solving partial differential equations using neural networks, but rather solving the inverse problem. In this case, I am more interested in the mathematical formulation of the problem and the mathematical aspect of its solution. If possible, please provide an answer, links to similar topics, and possibly literature. Thank you very much in advance! | 0 |
I have proven this question but somehow I feel like maybe I have done something wrong or I have been reckless somewhere would you please help me to verify my answer If S is a set with least upper bound and greatest lower bound property assume X and Y are nonempty subset of S such that every element of X <= every element of Y so prove Sup X <= Inf Y I have proven this in the following way from the hypotheses we can conclude everything in Y is an upper bound of X and vice versa. so Sup X and Inf Y exists in s and lets denote them by a and b now lets prove this by contradiction lets suppose a>b since b is infimum of Y everything greater than b is not lower bound and this is in contradiction of a not being a lower bound of Y because a is supremum of X and since everything in Y is an upper bound of X . is my proof true or I am missing something in somewhere? | 0 |
It is said that if one would attach a load physically to the rotating disc from center to rim no current would flow because both in the load wires and the disc itself currents would be generated in the same directions, everything would cancel out, right? But I don't understand why this is a problem? there is a simple workaround: The wires can lead out of the field or extend far away from the magnetic field range, like so: The blue arrows symbolize induced force vectors when disc with shaft and wires rotates, current should flow from the rim to the center of the disc just like in Faraday brushed version, the upper part of the shaft and the wire does not cut the field lines. However I have build this and no EMF was detected, I don't understand why, the voltage induced in the shaft should not block the current coming from the rim to the center of the disc? | 0 |
Like 'pretty ugly'. The most used meaning of 'pretty' is contradictory to 'ugly', and it could feasibly be used to mean something like (if it were an oxymoron), 'someone who may be considered ugly, but is actually kinda pretty'. But of course it actually means, considerably ugly. Is there a term to describe such pairings? Edit: I'll add more examples as I think of them: Don't trust casinos, they're fairly rigged. I'm an f'ing celibate. The doctor gave me a sick healthy report. I'm a bad good kid. -- Like they are morally good, but are bad (not morally bad) at actually making much out of it, as some role-models may do. Like they are comparing themselves to others. As opposed to a kid who is generally a good kid, but does still get into trouble some, so they may be teetering on the edge of not being considered a good kid. Which would actually be an oxymoron. | 0 |
This is a question from an interested amateur. Math welcome (as I or another may investigate it some day) but don't expect me to understand it in your answer. Consider a star emitting light. In order to talk about it simply, think of a point light source, and ignore spatial perturbations (for the sake of phrasing the question). At at time t, the light emitted at a single instant at now-t forms a sphere at a distance from the source. What is the density of photons in the surface of that sphere? Perhaps the reply is that the energy is traveling as a wave, but I understand light energy is quantized - that is, the energy has no representation described by infinitesimals, but will be in minimum quantities. How much must the sphere expand so that there are gaps in the image when sampled at different locations on the 'instant-sphere' image? Or, is there an explanation as to why the energy is quantized, yet can manifest at any separation (due to distance) despite the energy density falling below the quantization when the sphere is of sufficient size? What if the source is a candle? Is the original source always sufficient to 'map' adequate photons to any sphere that may be created in the dimensions of our universe? Are there objects we cannot see because they are so far away (or dim) that we are 'in-between' the photons that form their expanding image? Of course, I may simply not understand, but the explanation would be welcome. | 0 |
I play football. However, I dislike going and sometimes I just dont want to play it. But whenever someone tells me that i do not have to do it or that I can stop when I want, I put all the work into it. One reason I can assume is that my father played ball and I am the last son, he and my mother want me to play but I have "mixed" feelings to say the least. Whenever I constantly tell my parents that I dislike football, they obviously get very saddened and I dont care about that in particular. The strange thing is that when I get the choice alone and with nobody around, I always play ball because it makes me happy. But whenever I'm told that I have to, it feels like a chore. I can't explain this to my parents and I feel the need to get this off my chest as I am heading out soon. | 0 |
As we know, In a circuit, simple or complex, electric fields created by surface charges move electrons which creates current which creates magnetic field which can be coupled to other lines and induce voltage if it is changing by time, which also creates current and this current also creates magnetic field and voltage drop along where it is coupled so on and so forth. Voltage and electric field are related just like currents and magnetic fields are. Changing electric fields create magnetic fields and the opposite is also true. I mean what is the independent variable here? Everything is like being affected by one another continuously. Is it power or energy or fields? What variable or thing I must I hang on to or take as starting point for better analysis of circuits? | 0 |
Currently the proven theory is the quantum field theory. This theory defines fields in "all spacetime" and particles are disturbances in these fields. These particles are punctual and interact through virtual particles. But string theory is not clear to me. This defines the strings (bosonic or fermionic) as the smallest entities and these "strings are in a spacetime" but they are not defined unlike the fields in all spacetime. How is it possible? How is the zero point energy then described? So we must understand that at every point in space there is at least one section of string? Here the difference is analogous to the first quantization with the second quantization. Is a string field already confirmed in all string theories? Is there talk of virtual strings? If I take a field, for example the Dirac field or the EM field, these are defined in all time space. It may be that there are disturbances that we interpret as particles, but if there are not, the field exists the same and has a zero field energy value not equal to zero, with virtual particles being created and destroyed. Or for example, the higgs field directly has a non-zero energy in all space. Do we have a defined string in all space? | 0 |
I am wondering how heat loss happens in sound waves through air. First of all, for wave energy to be transformed into heat, absorption should happen by a medium. But why wont absorption implicitly translate to faster vibrations which would state that even though wave energy was translated into heat vis absorption, that again must have transfered back into wave energy. My logic is that some particles that absorb wave energy will in turn increase their their own kinetic energy, and those that dont absorb wont. So some particles will vibrate more, some wont. Then due to this difference between particles, redistribution energy will occur and since particles that absorbed energy, they might not actually vibrate in a pattern but randomly start moving who knows where. I believe this random motion and not in direct vibration pattern is why we say energy of wave was lost due to heat conversion. Correct ? But I wonder why absorption(even though it increases KE of particle) does not implicitly give it more vibration in the same pattern as it had before the absorption ? | 0 |
We call G the formula that in the formal axiomatic system employed by Godel to formalise arithmetic has the meaning of: "I am not provable in this system". We know that this formula G is true in that axiomatic system since we can exclude that it is false. But why can we say that it is also true in arithmetic itself? After all, within arithmetic such a formula is only a set of symbols, and even if well formed it can still be a false formula. How can we say that such a formula is also true within arithmetic and not only in the aforementioned formal system that formalises arithmetic? We come to this conclusion because the formula G also within mathematics retains the meaning of: "I am not provable in this system" or are there other reasons for considering it true within arithmetic? | 0 |
In security, we speak about different strategies of protection. Mainly, there are three to consider. First kind, usually called shell protection corresponds to the act of preventing the intrusion before the access. For instance, a door, fence, password on a website or silver galvanization of the utensils. That's usually very powerful and easy to maintain. Occasionally, there's a breach and then, we have problems, unless there's also the other kind of security implemented. Here, we're talking about smoke dispensers, mazes, ambulating patrols, honey pots, fake repos etc. What would be a good term for that? (Extra great if it's formal'ish.) The one I've been using is impregnation protection but I'm not sure if it makes sense, let alone is correct linguistically, let aloner comprehensible to regular people. (The third is deterrent protection and not relevant to this question.) | 0 |
I have seen videos that interview accent experts, like on why Americans do bad English accents (a reason given is a lack of exposure). But are there something like references that one could point to to rate accents? I would think at least one should survey native speakers to get a rating (I met a Kiwi who said he would get mistaken for British by Americans even). Maybe AI could do ratings nowadays if trained on enough. I figure one would need to do individual ratings for each case, even if a reference existed, like having to break down examples, showing where they messed up. If ratings were compiled somewhere that'd be easier though. Like something one could use to show how bad Americans doing accents in lotr were, except like wormtongue, which one may figure influenced having less in the hobbit. | 0 |
As oppose to a cylinder in two pieces rotating against each other, as in O'Neill's cylinder, what if the cylinder were all one piece and an external thrust, like rockets, set the cylinder in motion, rotating it, would it rotate indefinitely? Would inhabitants of the cylinder experience artificial gravity indefinitely, or would their movement against the rotation of the cylinder slow it, or would movement with the rotation of the cylinder even it out? Or would neither effect the closed system because they'd be pressing against the cylinder from inside the cylinder? Would friction from the air inside slow the cylinder over time, or would the air turn with the cylinder and artificial gravity? If any of the above would slow the cylinder, how frequently would the rockets around it have to add more momentum to keep the craft spinning? Would it at least be a number of years? | 0 |
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