snippet
stringlengths 143
5.54k
| label
int64 0
1
|
|---|---|
I was wondering if we could use background radiation to produce electricity (even a tiny amount). However, I've read somewhere that solar panels absorbing infrared (and lower frequencies photons) wouldn't be very efficient, as they are limited by the laws of thermodynamics. The arguments states that the panel needs to be cooler than the temperature of the body emitting the photon. How is this true? I cannot explain why it would be that way with the traditional band diagrams I've learned. As far as I understand it, the only limiting factor would be the band gap of the material that is used, and it needs to be low enough to capture low energy photons. | 0 |
Recently, I find an interesting paper that mentioned the Definition of curvature of an affine optimal control system. It suddenly reminded me that many textbooks on Riemannian geometry only tell us about metrics, geodesics, parallel transport, and curvature tensors and son on, using some special surfaces with constant curvature as examples. So for a general control system, how do we calculate its curvature tensor? Is this a problem worth studying? Are there any more examples? Thank you all for your comments and help! | 0 |
I have learnt that the intuitive idea behind inner product space is finding angles between vectors. But what does inner product actually mean physically or intuitively when it comes to matrices.Can I link inner product of matrices to concept of angles?.I can't imagine angles between matrices as I do for vectors. I really want to learn visually and not just theoretically. As I am amateur in this area my understanding might be wrong. So please do correct me. | 0 |
I have a .pdf file, in which I have to embed all the fonts. I found out that I should use this command: gs -q -dNOPAUSE -dBATCH -dPDFSETTINGS=/prepress -dPrinted=false -sDEVICE=pdfwrite -sOutputFile=edited_file.pdf myfile.pdf but the pdf file loses its interactiveness. For example, I have hyperlinks that jump to references, or clickable table of contents that becomes not clickable anymore after executing this command. Can you please help me to find a solution.... I have only linux, so everything Windows-related is not an option. | 0 |
If neutrino has mass, then it can change it's helicity. But all registered neutrinos have negative helicity while all anti-neutrinos have positive. Does it stands for all registered neutrinos including cosmic ones? I.e. does it mean that cosmic neutrinos had not enough time to switch their helicity? Or it was checked only for neutrinos in accelerator experiments, i.e. only for "young" neutrinos? What about solar neutrinos? Is their helicity known? | 0 |
I keep coming across the term storying in articles on narrative research. The authors however do not explain how the term storying is different in meaning and connotation from the term storytelling or story. I am keen to understand the various theoretical angles that I need to explore to understand the term Storying? Should I connect the concept of reflexivity to the concept of Storying? | 0 |
I'm working on a project that aims to discriminate semi-visible jets (SVJs) in a QCD background, through learning from simulated data in the context of the LHC. I know that these are related to hidden valley models, and probably also to dark matter. Can someone provide an intuitive explanation (even with some technicality) of why SVJs are important, and how these are originated? Also providing some insights about dark sectors, and potential implications for the discovery of dark matter. (sorry if I'm using an improper language, but I'm not a physicist.) | 0 |
The problem I'm working on has a region that's largely accurately modeled by a GP model using a squared exponential kernel. However, there is a large region in the "truth" model that is uniformly zero, with all samples taken from this region being zero as well. However, the GP model in this region oscillates from positive to negative when it's necessary for the problem I'm working on that this region is accurately modeled as uniformly zero, or at least negative when the remainder of the data is positive. Adding a dot product kernel to the squared exponential kernel to create a custom kernel helps somewhat but can't eliminate the spurious oscillations. | 0 |
this is my first post on Stack Exchange. I need a study guide for linear algebraic expressions. I am good at vector analysis and calculus, but not so good at linear algebra. Image : In the image above, is the part I have colored in blue a linear algebraic expression? I am having trouble searching and learning this. I can't type expressions by math symbols into the Google search bar. I can't find a proper interpretation of the formula and just figure out what it means from the context. I'm not even sure if that's a linear algebraic expression. Is my only option to take my time and study a linear algebra textbook sequentially? I apologize if this question doesn't fit into the Stack Exchange. | 0 |
If we place a point charge in a grounded metal box and view a slice of the box, the lines of equipotential deform from circular (immediately around the point charge, as we'd expect) to square at around the perimeter of the box where it is grounded. Is there a mathematical relationship we can derive for the morphing of the field lines from circular to square? I am unsure if the change is a linear combination of the two functions. | 0 |
For some reason, TexShop started autocompleting any ampersand & by adding a period/full stop, which is not a feature that I consider desirable, given that I almost exclusively use the symbol for tabular and align environments. I feel that there is probably a simple way to turn this behavior off in the preferences, but I couldn't see how to do so. How do I change the default behavior? | 0 |
When we think of functions, we refer to their oscillations or periodic components in terms of frequencies. The Fourier transform allows us to decompose a function into its constituent frequencies, providing a way to analyze the function in the frequency domain. For operators that act on infinite-dimensional function spaces, is there an analog of the frequency concept? Is there a transform or methodology that lets us analyze operators in a similar "frequency-centric" manner? I'm curious about both theoretical constructs and any potential applications such a perspective might offer. | 0 |
From what I have read and seen online. The explanation of why there is a net reduction in the speed of EM waves through a medium is due to the interference with the oscillating EM fields produced by charged particles caused by the EM wave passing close by. I hope my understanding, if at least a base level, is correct so far. But would there be any reduction in the speed of light passing through matter made up entirely of neutrons? Either a neutron gas or possibly neutron degenerate matter in the cores of neutron stars. Thank you for your time. | 0 |
I was wondering if there is an easy way to create diagrams like the following: where a, b, c are colors and strings connect like colors. In the paper I am reading, they don't allow crossings, but I would like to allow crossings between different colors. So something like this would be allowed (two colors red and blue) I tried to do this with the braid package, but the problem is that I don't know how to make those semi-circles Thanks in advance! | 0 |
I'm writing an online game, and I want to tell users what their highscore is since the beginning of the hour. But I don't want to say something wordy like: Your highscore since the beginning of the hour is... At the moment I've got: Your highscore this hour is... I have 'today' and 'this week' for the other timeframes, but it still feels very unnatural. Is there any pithy phrase I'm overlooking? Many thanks! | 0 |
Is there a ready-made LaTeX package that produces a calendar in a format known as Familienplaner in German speaking countries: Each month is set as a table on one sheet of paper. There is one row per day, and there are additional empty columns to be filled in (between one and five, typically). Sundays are specially marked (e.g., by red colour of the date, or by a grey row instead of a white one). Nice-to-have features: German language support for day-of-week and month names, week numbers, German holidays. P.S. Searching the net for "Familienplaner" results in a lot of free pdf offers for such calendars. P.P.S. The Familienplaner layout is different from the monthly calendar layout of this question: Calendar in LaTeX | 0 |
I was wondering if the book Contemporary abstract algebra was suitable for self study. I've heard from people that the level is somewhat low and that things such as polynomials in several variables, particularly theorems on symmetric ones. Also,ive heard that applications from abstract algebra to linear algebra are lacking as well. Is this true? if so, which books would you reccomend for abstract algebra self study? | 0 |
I am currently working on a BSM model for unification where I am adding scalars for unification. I add many scalars, so finding the most general gauge invariant lagrangian is becoming difficult. Is there a tool kit where I can enter the particle content, and under what representation of the gauge group they transform and get out the most general gauge invariant lagrangian? I have heard SARAH can do it, but I am unsuccessful with it. If anyone knows how to implement this in SARAH, that would be helpful, too. | 0 |
Recently, I watched small dominoes toppling over, until they push over a massive one. However, I am slightly confused why this doesn't violate conservation of energy. Consider supplying some amount of energy to a small domino, eventually when it topples over the large domino, that large domino can do significantly more work, and should have more energy. This clearly cannot violate the laws of physics. So what is wrong with my logic? | 0 |
Googling and Wikipedia, gives only the following construction A golden rectangle can be constructed with only a straightedge and compass in four simple steps: Draw a square. Draw a line from the midpoint of one side of the square to an opposite corner. Use that line as the radius to draw an arc that defines the height of the rectangle. Complete the golden rectangle. Question: What are the other known methods of constructing a golden rectangle with a ruler and compass? | 0 |
I saw this solution to a problem on twitter, and the solution seems to of used the direct comparison test for the improper integral. I asked my professor about it, but they replied with "yes, just make sure to follow the given conditions." However, they didn't mention what conditions we would need to follow. If we can use Series Tests for Improper Integrals, how would we go about using them?enter image description here | 0 |
I want to make a commutative diagram in the tikz (or tikz-cd) environment to demonstrate the universal property of the pullback. To be precise, I want to make the following diagram in LaTeX (the arrows on top need NOT be curved): I am not sure how to draw this. I know how to make general commutative diagrams, and there are answers to making pushouts with universal property diagrams (How to do the pushout with universal property?) but I can't figure out how to make the above pullback diagram. Any help will be appreciated. | 0 |
I came across this question while studying for the SAT. After World War I, Percy Spencer was hired to work in the research _____ later known as Raytheon Manufacturing. A) lab of American Applicance Company: (a colon) B) lab of American Appliance Company-- (em dash) Though the answer choice states that B) is the correct answer, it does not specify the reason why A) is not preferable over B). I wonder if the usage of the colon in this sentence is correct. (As it sounds, to me, a little awkward to place a phrase like 'later known as --' after a colon.) I'd appreciate it if you could enlighten me. Thank you. | 0 |
As in the picture, we have a room with vents at the bottom to let cold air in and at the top to let hot air out. Normally the air flow is limited by the temperature gradient (correct me if I'm wrong). If we place a hot object in the vent on top, won't that create a faster draft? That way we could get very high "wind" speed indoors to replace fans. Is this possible, and if yes, what's the limit for air flow per second? | 0 |
Consider the following sentence Your time is limited, so don't waste it living someone else's. When I put it into a few grammar checkers like Grammarly, I get no errors. But I feel that there should be an error - like a word following "else's" (e.g., "Your time is limited, so don't waste it living someone else's life.", a quote due to Steve Jobs) Is there some sort of grammar error here, and if so what is it called? | 0 |
Is Aristotelian categorical syllogism (as in Copi's Introduction to Logic) a special case of the first-order logic? (This is my thought after making efforts.) Is it exactly the specialization of the first-order logic without any function symbol (but only predicate symbols)? (This is my thought after making efforts.) If it is still a specialization of the above specialization, what kind of specialization is it exactly? How would you define it as a formal logic system? Thanks. | 0 |
When a nucleus decays it is finding a more stable configuration, as all nature is. But is there a way of finding whether a specific configuration will decay? I know that there is a specific proton-to-neutron ratio range, of which outside nucleus decay. This can also be seen on the nuclides chart. I have also looked into concepts like nuclear binding energy and gluons. However, I never found a definitive answer to my question. My question: Is there a way, given the number of protons and neutrons (and electrons if need be), to find if the nucleus in this configuration will decay? (Please don't hesitate to use math to explain the concepts. In fact, I'd prefer it if I ended up with a formula.) | 0 |
Today I was explaining to my friend about opposite categories, and how the definition of monomorphism leads to defintion of epimorphism in opposite category. He asked me quite an interesting question. If we have a morphism in a category, how does that relate to the morphism in the opposite category? For example, let's consider that category Top, and a homomorphism between two topological spaces. What would be exact expression for arrow in the opposite category? I think it'd be something like the inverse function but I am not sure. | 0 |
This might be a very simple question, but the answer is not entirely obvious to me and I've been unable to find it stated anywhere. Consider two sets of generators (vectors), which are reduced in the sense that no two generators are parallel to each other (if one starts with two parallel generators, reduce that set by adding them together to make a single one). Then, if these two sets are not identical, can they possibly represent the same zonotope? I believe the answer is no. Am I wrong? A proof one way or the other would be appreciated. | 0 |
Outlook is questioning "equipment register" and asking me to double check if I am using singular or plural (error underline on the word register). This has me really confused and I can't find any information about what could be wrong with this phrase. For context, the phrase is part of a list of other items and I am using it to mean a register of equipment, like you would have a register of users, or a register of stock...etc. I get no grammar errors if I replace "equipment" with other words (although obviously I haven't exhausted all possible words!) If I write "An equipment register" the error remains. If I write "One equipment register" it goes away. Thanks! | 0 |
It is well-known the notion of weak limit in category theory. To obtain it, just take the notion of a limit and drop out the uniqueness property in the universal property. Now, as the universal property is crucial when proving the uniqueness (up to isomorphisms) of a limit, I expect the non-uniqueness of weak limits, in general. Well, it is possible to find an explicit example of category that admits weak pullbacks, where a cospan diagram admits two non-isomorphic weak pullbacks? | 0 |
While starting out on Lang's Algebra I have encountered the term "exact" sequence of homomorphisms. And I understand its definition and all the demonstrated examples but I would like to know more on this, like what are the things we get to know out of an exact sequence and does it aid in any kind of constructions or whatsoever. Is it possible to generalize them and how does that look like ?. For my background, I have only been introduced to Groups, Rings and Fields in my introductory algebra course but I would be delighted in seeing a bigger picture on these structures. | 0 |
I understand the fact that if there was no metallic ball in it, then when the ice melts, the level of water would neither rise nor fall. Now let us consider the case where there is a metallic ball in it. When the ice melts, the volume of water added to the vessel would be less than the volume displaced by the ice structure when it was floating. This should mean that the water level will fall if i am not mistaken, further which the metallic ball would sink. When that happens, it is displacing the same amount of volume as it did when it was within the ice. So shouldn't it mean that the water level would fall ? | 0 |
My intuition: In a system without air resistance, I would expect an arrow shot at an angle with its head pointing upwards to follow a ballistic trajectory without rotating around the horizon - because gravity can't induce torque on the body. So the arrow will impact the ground on its tail - not its head. Is this correct? If yes, what causes the same arrow to impact the ground on its head when there is air resistance? | 0 |
I don't think I understand correctly what it means for a Boolean formula to be reversible. By my current understanding, if a Boolean formula is satisfiable, then there exists a setting of variables such that the formula evaluates to true. If you were to reverse said formula, simply flipping each variable in the setting would also satisfy the reverse formula. You can similarly show that the reverse formula is satisfiable if the original formula. Overall, the reversible formula is satisfiable if and only if the original Boolean expression is. Since the author claims that determining reversibility is NP-complete, I think I'm missing something here. This is from the paper: On the Complexity of Polyhedral Separability | 0 |
Working on a thesis, I was wondering how to correctly hyphenate (if at all) the term "high data rate" in the following sentence: High data rate ECUs are connected directly to the backbone. The term "data rate" as such is not hyphenated. But compounds with "high" are hyphenated, e.g. as in "high-income", "high-stress". However, writing "high-data rate" doesn't seem right to me. What would be the correct hyphenation in this case? | 0 |
I've been reading a bit about how it is necessary to consider anharmonic effects in crystals if one wants to properly understand things like thermal expansion etc. So for example here: So the cubic term is said to represent 'asymmetry of mutual repulsion' and the fourth-order one 'large amplitude weakening' of vibrations. How could one come to understand these intuitively? How does one look at a cubic etc. term and come up with this explanation? | 0 |
I heard a while ago that the negation of the axiom of choice leads to the existence of a partition of the real numbers, into more partitions then there are real numbers. I found this post which says You don't want non-measurable sets? This means that you can partition the real numbers into strictly more parts than real numbers, but no part is empty. Yes, let that sink for a moment: you can partition the reals into more parts than numbers! I looked for a proof of this online, but could only find the result mentioned. A couple referenced this link, but it's locked behind a paywall. So, why does the axiom of choice lead to this counterintuitive result? | 0 |
So I was searching online for methods to approximate Pi and found this continued fraction that supposedly approximates to Pi when continued infinitely. I've tried searching all over the internet for how this was derived or why this works but could only find something similar but not close enough. I've got some basic knowledge of continued fractions but do not have experience with numbers that change throughout, how would one derive this equation? Thanks | 0 |
To compile my document (even a little one), my computer needs to load a lot of packages. During compilation (with pdflatex) I can see in the terminal that most of the compiling time is used to load the packages. It would save me lot of time (and ressources) if it was possible to keep the loaded packages in memory and resume compiling operations after that step when I don't modify the preamble. Is this feasible? | 0 |
Suppose one measures the position, then momentum, then position of a particle, and that all these measurements are done in quick succession of one another (ie. arbitrarily close to zero-time as possible). After the momentum measurement, the particles position is very uncertain. Therefore, the second measurement of the particles position can be quite different from the first. But does this not violate causality, since the particle can move a great distance in practically no time? | 0 |
The energy that an electromagnetic field can deliver to a system is proportional to the square of the field. However, we use the terminology watts per meter square to represent the amount of energy going past to represent the intensity of EM waves. How do you give a physical meaning to the 'amount of energy that the field carries past us per second' if you are only given the amount of energy that an EM field can deliver to a system? Why is it necessary to adopt watts per meter square for intensity, whereas I believe the energy that can be delivered to a system is perfectly fine for defining intensity | 0 |
In the case of a direct bandgap semiconductor, the recombination of an electron and a hole generates a photon that has energy equal to the bandgap of the semiconductor, accounting for energy conservation. But in this case, as the electron and hole have the same momentum, 'K' there is no difference. But the generated photon does have a momentum. So how is the momentum conserved in the radiative recombination in the case of direct band gap semiconductors? | 0 |
There is a Spanish joke, Ella es mi amiga vieja, disculpe, mi vieja amiga. The joke basically says, "She is my friend that is old, excuse me, my old friend", making fun of the person's age. Would there be a way to translate this into English? Of course, saying something like "She is my friend old..." doesn't work in English, though the joke does also work in languages like French. The translation I wrote may be considered to work, but I was looking for something smoother. Edit: my attempt: She is my old af friend, I mean my extremely old friend, I mean my old pal. | 0 |
I would like to be able to understand what the fission process is like (ideally, from total ignorance). What references could I read? Would it be more convenient to read chemistry books than physics books? From what I understand, the fission process involves "breaking" the nucleus of an atom. Regarding this: Is any atom fissile? Is there some non-fissile atom? Can this process be understood mathematically? Thank you so much. | 0 |
I couldn't find any similar topics and was curious if anyone had thoughts on the following: Could a magnet (ceramic and/or neodymium etc.) have an adverse affect on a Police Taser, if held to the Taser or held in proximity to the Taser. If yes, is there a material that the magnet could be covered in, to insulate those effects? (i.e. by effect, meaning unintentional discharge of the Taser, or causing the electronics on board to malfunction.) Thanks for any color you may have on this, much appreciated. | 0 |
What I was wondering is this. If I had a tube with water in it, with one end open and the other with a piston-like device attached to it, I can imagine that if I was to give the water a pulse, this would transmit down the tube as a mechanical wave as particles collide with each other - something like sound. But if we picture a scenario where instead of a pulse, I begin moving the piston down the tube at a constant velocity, what would the motion of the particles look like? Also what would this look like with air? | 0 |
I think I understand Ampere's law in the way it was taught to me by my instructor. But as the idea was given that how Gauss's Law in Electrostatics relates to electric field lines produced by charges inside the gaussian surface under consideration. We weren't given any idea that how magnetic field lines even relate to Ampere's law. I have already searched for it on the internet including the posts present here but found nothing. All I ask for is idea that how Ampere's law relates to Magnetic field lines?. Thank you | 0 |
I imagine that people will instinctively say, "There is no masculine or feminine speech in English," but I am not so sure. For instance, the stereotype is that men speak roughly and women speak softly. Then there is the usage of tag questions, fillers, and raising one's voice pitch so that the sentence sounds like a question. Then again, it may be a question of assertiveness. I hope someone knows what I am talking about! | 0 |
Suppose we have a causal curve and we can cover the causal curve by convex normal neighborhoods. We also know that, in convex normal neighborhood there will exist a unique geodesic inside the neighborhood, connecting any two points in the neighborhood. So, my question is: Are we making the curve piecewise geodesic? If a curve is piecewise geodesic, can we say that the whole curve is a geodesic? | 0 |
I have been trying to prove the stability of a queuing system (stochastic), and the state-space I have obtained is uncountable. I am aware of the Foster-Laypunov criterion, but as far as I know, it applies to systems with a countable state-space. I want to enquire of stability conditions for the case with an uncountable state-space, and also if Foster's criterion can be extended to this case. Please let me know! Thank you. | 0 |
I recently stumbled upon the word biggety, meaning conceited or vain, and when I went to look it up, it seems the word is regional, which might explain why I'd never heard of it, except for one region it's supposedly used (Southern US) in is the region I've lived for over four decades. So, how common is it in the Southern US? How common is it in Midland US? | 0 |
According to https://en.wikipedia.org/wiki/Closed_manifold "In mathematics, a closed manifold is a manifold without boundary that is compact. In comparison, an open manifold is a manifold without boundary that has only non-compact components." Closed manifold is a compact manifold without boundary. Open manifold is a manifold without boundary that has only non-compact components. Questions: Is open manifold opposite or antonym of closed manifold? (It seems not, but why not?) How do we call "compact manifold with boundary"? What are the differences between open manifold and non-compact manifold? How is the concept "open" in open manifold compared with the "open" in open set in set theory with topology, and open cover in topology? These open seem to mean different things. | 0 |
Godel's incompleteness theorem says that in mathematics there will be always true statements that cannot be proved and that adding that statement as a axiom generates other unprovable true statements. So, mathematics clearly has logical inconsistencies. I was wondering if it it is possible to find a language that doesn't satisfy Godel's incompleteness theorem or, to put it more simply, such that all its true statements are provable? | 0 |
A thin charged wire conductor, with a semidiameter of a is placed into a vacuum at height h (h >> a) above a big grounded conducting plate. The wire is placed parallel to the x axis, and the area of the plate lies in Oxy-plane. The potential of the conductor compared to the plate is V. Find the equation for the areal charge density in the coordinate system (O). I tried solving this problem, I could find the equation for V using method of images but I don't know how to find the areal density. Can you help? | 0 |
Is the Heisenberg's microscope gedanken experiment valid when considering spacetime kinematics? That is, if we consider a small region of space and try to measure its curvature, then we may use photons and see how the trajectory changes. On the other hand, the photon's energy changes the very curvature that we are about to measure. Here I assume that a high energy photon "maps" curvature more accurately. The ultimate goal would be to find an uncertainty principle that connects curvature and the rate at which the curvature changes. | 0 |
I've gone to Wikipedia and watched a few videos regarding Linear Codes, and from what I see, the Parity Check Matrix is always given, and because of that the Generator Matrix (consisting of Identity Matrix, Parity Matrix) can be made. But what if the Parity Matrix isn't given, and instead, only k and n? I understand the general layout, but I do not see how to figure out the actual contents (or identity, I believe its called) of the Parity Matrix. I should add that the specific scenario I am asking about is in binary, so maybe its only doable there? | 0 |
I've recently started learning about the physics of fluids and I've found that euler's equations exist and that I can use them to compute the flow of fluids with zero viscosity. But I have a problem that I don't see any easy way of adding an obstacle to a compessible flow as shown in this gif How should I do it? Is something similar possible also with navier-stokes equations? (I am aware that this questions is probably a duplicate of some older question, because this sounds as a really basic problem, but I've search for the anwer for some time and I even asked on the physics discord server and I found nothing) | 0 |
Is there a way in TeX (preferably plain XeTeX, but other engines are fine) to automatically choose between different options (e.g. between "and" and "&") so that the badness of a paragraph is minimal? For example, for a small hsize, the following is fine | I read a book by Smith & John. | But if we increase the value of hsize, we have to add space: | I read a book by Smith & John. | So we prefer to use the other variant: | I read a book by Smith and John. | If I remember correctly, the first printers used this kind of trick to avoid line breaks. | 0 |
I've heard about solitons in dense mediums (water), sparse mediums (acoustic) and optical fiber. But I can't find a good overview work on solitons in radio spectrum. Something like generating EM solitons with a peculiar antenna setup. It seems like an obvious thing for people to be working on, but looks like I just lack proper terminology to google it. Is there something that can be recommended, preferably with an experimental setup described? | 0 |
Davisson and Germer's experiment confirmed the wave-particle duality of matter. In this experiment a slowed down electron beam is reflected by the surface of a nickel crystal, which is able to split the electron beam into several parts, each of which is characterized by a reflection angle, rising a diffraction pattern quite similar to that of the X-rays. Is what I'm about to write right? This phenomenon is possible because the surface of the nickel crystal is not regular, but is formed by microscopic grooves capable of rising to the phenomenon of diffraction. | 0 |
I understand it is possible to find the shortest distance from a point to a straight line, but how do we extend this to any function. For a straight line it is simply the equation of the perpendicular which intersects the point of interest. If we have a cubic or a quartic function how would I model the shortest (straight line) distance to that function from somewhere on the plane? I anxiously wait a response. | 0 |
Is there a way to make meaning of it? I was thinking that maybe because the covariance is divided by the percentile rank of std dev of A, the magnitude of A is to a degree bounded. But how does it change the covariance, as covariance is about the co-directions of A and B rather than the magnitude in the first place. Essentially, what does "covariance(A,B) divided by percentile rank of std dev(A)" reveal? Any thoughts would be greatly appreciated! | 0 |
I have learnt that a planar graph is a graph which can be drawn on the plane without any of its edges crossing. What exactly is "the plane"? In plane geometry, we define a plane to be a flat surface of two dimensions; however here the use of "the" suggests we have a particular instance of a plane in mind, not just any plane. Is there a certain specific type of plane which is meant here, other than the general plane from plane geometry? | 0 |
I am reading the paper "REPRESENTATION AND INDEX THEORY FOR TOEPLITZ OPERATORS" by Gerald Murphy and came across this passage: I was wondering why we care about the strict topology or why is it important for multiplier algebra. So I know how these are defined but I've never understood why we should use it. Am I supposed to assume we are talking about the strict topology every time I see the multiplier algebra? Now for this specific example given below for the Toeplitz matrix, why is it better to identify the operators on Hardy space with the multiplier algebra when talking about convergence? | 0 |
Based on my intuition, once light is monochromatic it will stay that way unless you actively try to change its frequency. My intuition stems from the intricate optical laser setups in my lab that sometimes (often?) work with monochromatic light. Sound, on the other hand, seems to change its frequency easily when it interacts with the environment. Again, this is based on intuition so I'm not sure if its true. So my questions are Does light stay monochromatic once it is created? Does sound stay monochromatic once it is created? Why? Under what conditions do waves stay monochromatic? | 0 |
Considering no air resistance, the acceleration time graph for a free falling object would be a horizontal line as the acceleration remains unchanged. When we do take into account air resistance, the graph becomes a curve with negative gradient. However, to me, this is unclear. I understand why this must be a negative relationship, but why can it not be a negative sloping line. When we graph acceleration against air resistance, we see this is a negative sloping line. Why must this be the case? I am looking for both an intuitive and mathematical answer. | 0 |
We have a sentence like this: Transients are individuals just passing through, not contributing to the local population and its demographic rates, and they are thus very unlikely to be recaptured. Is it possible to remove "they are" behind the comma? So it would sound like this: Transients are individuals just passing through, not contributing to the local population and its demographic rates, and thus very unlikely to be recaptured. It would be much more elegant. But the catch also is that the "thus" doesn't refer to the most proximate sentence "not contributing to the local ....", but to the one at the beginning - "just passing through". Is that a problem somehow? | 0 |
In this quote (from this essay), Russell talks about a theorem showing that "three or more lines meet in a point". "In geometry, instead of the tedious apparatus of fallacious proofs for obvious truisms which constitutes the beginning of Euclid, the learner should be allowed at first to assume the truth of everything obvious, and should be instructed in the demonstrations of theorems which are at once startling and easily verifiable by actual drawing, such as those in which it is shown that three or more lines meet in a point. " What theorem is he talking about, and what is its proof? | 0 |
I'm new to manifolds and in my Computer Graphics class, we briefly explored the topic superficially through visual examples. From my intuitive understanding, we should be able to place a Euclidean grid on a manifold's surface or it should appear flat locally. However, I'm puzzled by how a pyramid with sharp edges and corners can still be a manifold. When we zoom in on the edges or corners, we only see flat areas along the faces of the pyramid, in any other direction it doesn't look flat. What is the difference between this case and two pyramids sharing a vertex (as an hourglass shape), which we classified as non-manifold? I'd appreciate if someone can explain what I'm missing in my intuitive understanding. | 0 |
I've been looking into profinite groups, their topological subgroup lattices, etc. I asked the question does every profinite group admit maximal subgroups? I can't find an example of a profinite group which does not admit maximal subgroups, though I also cannot prove that each must have one. I think that if this is true, then it is related to profinite groups being residually finite, something about being able to tell apart elements using a projection onto a finite group, which must admit maximal subgroups. Can someone answer this question with the affirmative, or give a counterexample of a profinite group which has no maximal subgroups? | 0 |
I know how to perform the double slit experiment in high school: a dark room, a source of light like a consumer electronics laser, a black board, and a card board with double slits. Is there way to extend this experiment to the one where we observe from which slit the photons pass (and causes them to not create the interference pattern anymore) without sophisticated measurement devices? Something that we can perform at home or at a typical high school? I have searched a bit but haven't found the answer. Does observing which slit the photons pass through require sophisticated measurement devices? | 0 |
I recently found that a rope suspended from two points forms the shape of a catenary curve, which brought me to another question: What is the shape made by a rod of uniform density when only one of its ends is held horizontally? Obviously the material and width would affect the strength of the rod and thus the shape it makes, however I assume they must all resemble the same curve. (similar to how all shapes and sizes of ropes will resemble a catenary curve when held at two points) I would love any help with this question! | 0 |
Suppose light from a laser passes through a single vertical slit. The width of the slit is certainly a factor how the light scatters after it goes through the slit; the thinner the slit, the wider the scattering. But my question is about the material surrounding the slit. How does the depth of the material influence the scattering pattern? And how does the composition of the material itself influence the scattering pattern? Does the nature of material around the slit significantly affect the scattering pattern? | 0 |
I know that slope is the tangent of angle of inclination. But are they just two ways of defining the same thing? Or do they have any significant differences regarding what purpose they serve in mathematics? The way angles are defined as arc divided by radius, while slope the height divided by the base, doesn't show much difference. I only have a basic understanding of calculus. | 0 |
So on the german wikipedia page of topological vector spaces it is written that, if a topological vector space is a Hausdorff space, then translation by a vector and dilation by a scalar are homeomorphisms. However, I have looked at several lecture notes and it is always stated (and proofed) that these two mappings are homeomorphism for general topological vector spaces (even those that are not Hausdorff). So I wanted to confirm that it is true that for any - possibly non Hausdorff - topological vector space the translation and dilation are homeomorhpisms. Also, can anybody think of a reason why on the german wikipedia they have restricted that statement to topological vector spaces with the Hausdroff property? | 0 |
I have heard that light is a transverse wave which is necessary for effects like polarisation, but I am unsure of what exactly this means. Is this saying that light's electric and magnetic components oscillate in perpendicular directions of three dimensional space? i.e could the electric (or magnetic) component literally oscillate say 'up' and 'down' making the electric field strength of points in space above or below the wave stronger or weaker according to the light's phase? If not, then what could it mean for light to be a transverse wave, and how does polarisation work in this context? Thanks in advance for any help with understanding this. | 0 |
Where do the electrons in a lightning bolt come from? There are problems with the explanations given up to at least two years ago. The explanation that the electrons come from inside the thunder cloud or are derived from cosmic rays are inadequate. There are a lot more electrons in a lightning bolt than those that come from these sources. Is there research which shows were the electrons actually come from ? Thanks. | 0 |
So I know that the main trig functions are sine, cosine and tangent, while cosecant, secant and cotangent are simply known as the "reciporicals", but wouldn't it make more sense for sine, SECANT and tangent be the main trig functions while COsine, COsecant and COtan be the secondary ones? After all, secant is just the reciprocal of cosine, so everything you can do with cosine you can do with secant. | 0 |
I was reading geometric optics when I came across the concept of virtual objects. I found the concept counter-intuitive, as far as reflection goes. (I perfectly understand the formation of such an object when the light ray is refracted through a glass slab.) Attaching the definition provided in my book: My confusion: A mirror forms an image when the rays originate from a certain object. So, how can an image of a virtual object form if the rays do not diverge from a particular point in the first place? What are some real-life examples of such a situation, as depicted by the figure below: I have checked answers to similar questions but my doubt is not cleared. | 0 |
I don't know exactly how boomerangs work, but I imagine that the fact that they are less symmetric than a sphere is part of the reason they can be thrown in such a way that they return to whomever threw them. Eggs also appear to lack some symmetry, because one side is usually pointier than the other. Of course eggs aren't ass aerodynamic as boomerangs and here it is claimed that aerodynamics plays a vital role for how boomerangs work, so probably the answer to my question is no: Will boomerang work in vacuum chamber on Earth? But I am still curious as to what would happen if you did throw an egg (shaped object) really fast like a boomerang. Does anybody know? | 0 |
Please correct me if I am wrong. Almost all materials are made up of atoms with electrons. If we rub two different materials, like plastic scale and oily hair on the head, then static charge develops on the surface of scale. This charge can attract tiny bits of paper. Also during lightening tiny droplets of water and ice crystals rub against each other to create static electricity. However if I rub my hands on the wall then no static charge develops on the hand. I checked it, as my hand did not attract tiny bits of paper , which means no charge developed on my hand due to rubbing. My question is : On which atomic factors of the materials does the phenomena of static charge depends ? | 0 |
In mathematics, scalars are defined as elements of a field. Are scalars in mathematics invariant under coordinate transformation? In physics, the way they are defined, I know they are. Since in physics, they are defined to be quantities having only magnitude and no direction, they are invariant under rotations or translation. Some sources say that in mathematics, scalars are, by definition, invariant under coordinate transformations. Can anyone please explain how defining scalars as elements of a field would intrinsically assume invariance under coordinate transformation? If not, can you give an example of a field whose elements may not be invariant under coordinate transformation? | 0 |
I am currently studying Analysis on manifolds for my thesis. I am looking for some references about the McKean-Singer conjecture and Patodi's proof. I read with much attention to detail his paper: Curvature and the eigenforms of the laplace operator. However I am having difficulty over some of the arguments. I would like to kindly request some references about this specific paper, for example some extra details or maybe if this is contained in a book. Thanks in advance. | 0 |
I am a chemist currently trying to dive in to details of random motions. I have been studying Einstein-Smoluchowski treatment, and want to learn further (Fokker-Plank's equation and Langevin treatment etc). Although I am comfortable with mathematics some of the textbooks I came across include lot of symbols I am not aware of, and hence it gets overwhelming. Could someone please recommend me textbooks which provide detailed conceptual and mathematical treatments, assuming I am not aware of all the symbols or denotations? | 0 |
Most objects in the universe cycle around their centre of mass: earth, sun, galaxies. Even galaxy clusters. However, the whole universe doesn't possess an angular momentum. It can't: If it had one, the centre would be a special point (which isn't allowed) and the velocities of the outer regions would easily become infinite. How does the angular momentum vanish with increasing scale? Shouldn't the laws of nature that lead to cycling for smaller objects also hold for larger objects? | 0 |
The Doves Press was one of the major players in the early British private press movement, hand-printing books in Hammersmith that were known for the absence of any illustrations and a focus on the aesthetics of beautiful type. Below is the famous first page from the Doves Press Bible. Can anyone provide some guidance on how to replicate this "I" that extends downwards to the height of the text? I find this quite interesting because there are several letters that could elegantly be extended vertically by stretching the vertical strokes of the letterform while leaving the proportions of other parts unstretched (I, J, H, E, P, L, F, T, Y, U, M). | 0 |
I read the paper Example of indeterminacy in classical dynamics. I understand the paper: Because the differential equation does not satisfy the Lipschitz condition, its solution is not unique, and thus there is indeterminacy. But is it really possible in physics, as in the example described in the paper, for the ball to rest at the origin to suddenly deviate to the left or right from the origin, which violates the law of causality? Or does the physical world not follow the law of causality? | 0 |
Are electric and magnetic multipole transitions are classified based on the nature of change in angular momentum of an electron during a transition between two states? In electric multipole transitions, the electron changes its orbital angular momentum, leading to transitions between different electron shells or orbitals within the same shell. In magnetic multipole transitions, the electron changes its spin angular momentum, resulting in transitions between different spin states. | 0 |
I'm looking for examples of dramatic typos - where a minor edit can dramatically change the meaning of a phrase, and would like to know if there's a name for this phenomenon. Paronyms are a similar concept, but seems to incorporate pronunciation - "love" and "loathe" might be paronyms but they're not especially similar in spelling. For example, "symptomatic" and "asymptomatic" are one letter apart but have opposite meaning, "heroin" and "heroine" have very different meanings. By edit distance, I mean the similarity of the two words - the number of single-letter additions or substitutions to turn one into the other. | 0 |
I did find the proof of pseudo torque about the center of mass of a body in combined rotation and translation being zero, and thus I'm convinced that in this frame of reference, we can conserve angular momentum. However, although the net torque about the point of contact in rolling is zero, I don't understand how we can conserve angular momentum about the point of contact in rolling motion, even though this axis itself is not fixed and constantly translating. Any help is appreciated. | 0 |
I have a question which asks me to compute the mapping matrix, but I have no idea how to do this. I understand the concept, but I am unable to understand how I actually solve problems. Would appreciate if someone gave me a step by step explanation of how I would tackle problems like these. Would it be the same method for finding a change of basis matrix as well? Here is the image of the question: Mapping matrix question | 0 |
If the axis of rotation is not passing through the centre of mass but some other point of a rigid body then how do we define the direction of angular parameters that is angular velocity, angular acceleration and angular displacement. For example : This is a sphere with a void in between rolling on a flat surface.C is the centre of mass and O is the axis of rotation. So basically my question is, will the angular velocity of the point A be perpendicular to OA or CA? Also will the angular acceleration of A be parallel or antiparallel to the angular velocity and correspondingly the centripetal acceleration would be perpendicular to the angular velocity right? I am confused about this. | 0 |
In the article about Coulomb's law There is following sentence: Coulomb's law is an experimental law of physics that calculates the amount of force between two electrically charged particles at rest. However in the Griffith's Introduction to electrodynamics Introduction before explaining Coulomb's Law, there is following sentence: To begin with, we shall consider the special case of electrostatics in which all the source charges are stationary (though the test charge may be moving). What i'm confusing is: Wikipedia applies to two charges at rest but Griffith's book applies to stationary source charge. They collide with each other. Which is correct one? | 0 |
I tried to implement Kruskal's minimal spanning tree algorithm and I found that the output is essentially a set of the edges... The output is not a tree at all. In my opinion, a tree can be represented by a parents array, and each node associates a key which is its parent. For a tree we need to know which node is its root at least I think. But the output of Kruskal's algorithm are just edges. How to fill this gap? | 0 |
All ferromagnets have domains in which the magnetic atomic dipoles are alligned. However, soft ferromagnets like iron respond quickly to the external magnetic fields while the hard ferromagnets(permanent ferromagnets) don't. In atomic view, what causes this difference? My fist guess is that in the hard ferromagnets the atomic dipoles are stronger and their density is higher so that their greater interaction keeps them more alligned compared to the soft ferromagnets. So,the hard ferromagnets are not affected by external magnetic field as easily as soft ferromagnets? I would appreciate if anyone please help me with that. | 0 |
Given two positive semidefinite matrices X, and Y. My question is, can we use von Neumann or the log-Determinant divergences to measure the distance between the two matrices. Most Manifold measure distance require two positive definite (PD) matrices. In this paper, the authors used the log-Determinant divergence with two positive semidefinite matrices (PSD). However, from what I know, the two divergences are for measures involving positive definite matrices (PD). Any insight please. | 0 |
Consider a mass rotating in a plane around a fixed point O at constant speed. In such case the angular momentum with respect to O is constant and its time variation is zero according to the fact the torque is zero.But if you change the point to which you evaluate torque and angular momentum, the time derivative of angular momentum is not necessarily zero. So? | 0 |
I have been brushing up on real analysis recently and, knowing nothing about topology but having seen some very general YT videos on the subject, I have developed a vague feeling that it somehow is very closely related to real analysis. For instance they both seem very concerned with continuity and continuous maps. Could someone please elaborate on the contact points between these branches of math? | 0 |
I was taught in my image processing class that when a mean filter is applied infinite times on a given image, the intensity of each pixel reaches the same value. I understood this that time entirely on intuition. But looking back, I tried to come up with the formal proof of this result but couldn't make any progress. So is there a way to actually proof this notion. Any help would be appreciated. | 0 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.