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I see that the Oxford dictionary has a plural dice for "a small cube with a different number of spots on each of its sides, used in games of chance". However, there is no plural listed for "a block with a special shape that is used for shaping pieces of metal" (both definitions summarized). Researchgate has a photograph of "Two dies arranged side-by-side". Is dies the correct plural of this meaning of die? Why do the two meanings have different plurals? Which was in use first? | 0 |
For a new book I am writing with two friends, I like to include three biographies (mine as well as the other two friends) after the preface. Ideally, we like to keep three photos (A.jpg, B.jpg and C.jpg) on the left and our biographies on the right.. The book is in single column format, and I don't know how this biographies page can be done in double column format. Also, the biographies need to be aligned with our photos. We are OK with any format or style in a professional way as long as we can post our biographies along with the photos. Your suggestions are most welcome. Thank you. | 0 |
I have a pretty strict requirement for a document (I'm currently using memoir), which must: use biber/biblatex in the usual way based on a primary bib file (e.g., main.bib), and sort the resulting list of refs by author then year. at some other point in the text, I want to print out a list of all the refs of type article from a secondary bib file (e.g., extra.bib), sorted by youngest to oldest. Is there some biblatex voodoo that would make this easy-ish? | 0 |
This particular example comes from a peer-reviewed publication with authors who seem to be native speakers: This trend is both popular and has presented a variety of challenges I wonder if this is grammatical? If this sentence didn't have "both", we would parse it as follows: This trend ((is popular) and (has presented a variety of challenges)) But with "both", what do we have? This trend is both ((popular) and (has presented a variety of challenges)) but this gives us "is has presented", so this parsing is incorrect. Alternatively, we could try This trend ((is both popular) and (has presented a variety of challenges)). but then "both" goes inside the first coordinate. This is different from, say, You and me both where it's at the end. | 0 |
How or where can I find the Absorption cross-section of Gaseous Ions? I have looked over the internet and can only find it for neutral atoms. Does it increase or decrease for ions? I have found formulas but they include the imaginary part of the refractive index of the specific medium and I can't find how to calculate or get a relative order of magnitude for it even for plasmas. Scattering cross section will do too Please help. | 0 |
Let ABCD be a convex quadrilateral with AD = BC. Show that AD and BC determine congruent angles with the line passing through the midpoints of sides AB and CD... MY IDEAS MY DRAWING As you can see i noted some points. Okey, so, i thought of similar or congruent triangles. But i don't know where to start. Hope one of you cn help me! Thank you! | 0 |
There is literature on the lie symmetries of quantum harmonic oscillator differential equation. The generators satisfy certain lie algebra. On the other hand, we have ladder operator method. The relevant operators satisfy some lie algebra. I was interested in knowing if there might be some connection with the two approaches. Is there some relation between the two lie algebras. Cause if there is, it might help me explain ladder operator method better. | 0 |
In the Einstein field equations, the only tensor that shows up is the Ricci tensor and the metric tensor, together with the Ricci scalar. The Weyl tensor though is a tensor that is a part of the Riemann curvature tensor as well (the off-diagonal part). It represents tidal forces, which are non-local. Why doesn"t the Weyl tensor show itself in the Einstein field equations? Is it because gravity is based on the equivalence principle, which is a first-order equivalence? | 0 |
I had recently come across "Russian for the Mathematician" by S.H. Gould, and saw it as a wonderfully useful resource. I have very little experience in Russian (only skill is ability to read Cyrillic), but I saw it as a useful introduction to the language, in the sense that I would be able to decipher Russian language math literature without the need to be entirely fluent or understand every word. Reading through a preview, I like how it breaks apart the words piece by piece to I was wondering if there were any resources for other languages in this similar vein, e.g. learning French or German with the main focus of reading scientific or mathematical literature. Downloadable here | 0 |
I hear this kind of false implications pretty often, e.g.: If you're smart you'd agree with me People who understand the situation would all agree that ... Anyone who says something else must be trying to confused us These often come up in social deduction board games, where the good team is trying to gain information and the evil team is trying to spread misinformation. If someone says one of these lines and I disagree, they can say "see, he disagreed, so he must be on the evil team". Is there a term for this kind of faulty logic trap? | 0 |
Is it possible to use magnets to lessen the force of a pull that is associated with Cervical Dystonia (spasmodic torticollis) which is causing an involuntary pull of the head over one shoulder. Having the magnets attached to clothing on one side such as a shoulder pad and more on a collar. Would the strength of magnets keep the head from pulling to other side ? As a person with Dystonia I'm trying to find a way of creating some sort of "crutch" to allow the head to look straight :) | 0 |
Imagine a tank that accelerates towards a relativistic speed. As the caterpillars are at rest with respect to the ground, the caterpillars will show no length contraction there. But the tank body above it will. The upper part of the caterpillars, on the other hand, will show more contraction than the tank body does. What will happen? Will the lower parts of the caterpillars slide along the tank body to "deliver" an extra piece of caterpillar for the upper part which contracts more than the tank body? Will the caterpillars snap? I'm not sure. | 0 |
This question may have been asked a bunch of times, but I have not found exactly what I was looking for. I say calculus, but mathematical/real analysis works as well as long as it does not have calculus as a prequisite. I have been looking for books that take an inquiry based approach, where the theory and everything else is build by solving problems with minimal explanations from the Author aside from introducing some definitions (Bogart's "Combinatorics Through Guided Discovery" is exactly what I am looking for, but for calculus/analysis). I am aware of jiblm, but I was wondering if there are published books on calculus/analysis using this approach that may be more suitable for independent learners? | 0 |
According to MathWorld, the probability distribution of the length of lines between randomly selected pairs of points inside a cube has a very complicated form. In particular it is not uniform. This distribution relies on the fact that the pairs are chosen uniformly and independently. My question is - is there a way to do a reverse engineering and enforce uniform line lengths density? Namely, say I want the probability distribution of the length of lines between randomly selected pairs of points inside a cube to be uniform, from what probability distribution should I sample my pairs? In particular, I want this sampling to still be independent, but not uniform. | 0 |
If I use a transformer the get a high voltage, the power of the transformer remains the same, as the current is reduced proportionally. However, according to ohms law, the current through a resistor connected to that secondary side of the transformer will be the voltage divided by the impedance of the resistor. But that is impossible, because this way both the voltage and the current felt by the resistor will increase, meaning an increase of power, while the power of the transformer remained the same, compared to the first side of it. Please sort out my confusion over it. | 0 |
Yesterday I heard this: suppose you have a rubber hose, in which you inject helium, which replaces the air which was there before. Now, because there is no helium in air, so the partial pressure is zero there, the helium escapes through the rubber into the surrounding air and creates vacuum in the hose (insofar it is possible in a rubber hose, effectively you'll get substantially lower pressure than before). Is this correct? If so, se can create vacuum using a solid membrane, which permits the gas (that we used to replace the air inside) to escape to the outside world, where its partial pressure was zero/low? | 0 |
I have found a sentence that goes like this: "Serenity may be the name of the company, but it doesn't describe the company." Someone translated this sentence to my language as if "may be" meant there was a possibility that Serenity was the name of the company (and a possibility that it wasn't), but I feel like the sentence really means "While Serenity is the name of the company, it doesn't describe the company". Is there a specific name (akin to "non-continuous verb" or "inclusive or") for this usage of "may be"? I want to be able to say "This sentence is using a [...], so the correct translation would be...", chere [...] might be something like "comparative may" or "comparative auxiliary". | 0 |
[A partial groupoid (half-magma) is a set S equipped with a (single-valued) partial binary operation, as in Bruck's Survey of Binary Systems.] This question may be nonsensical, given that the duality between Cayley graphs and groups is deeply related to the mutual complete-ness of each structure. If that is the case, perhaps what I am really asking for is a common diagrammatic representation of partial groupoids. Here is a crappy mock-up of what I'd expect from diagrams of half-magmas in the latter case. If Cayley graphs encode the abstract structure of group, is there a similar type of graphs that encode the abstract structure of a partial groupoid? If there is not, is there some other commonly used diagrammatic representation used for partial groupoids? Thanks! | 0 |
There is a medical specialty called obstetrics and gynecology. In the UK I have only heard this truncated to something like the first syllables separated by a truncated "and". This could perhaps be written as "obs 'n gy-nee". I have multiple times recently heard this specialty referred to by Americans by spelling out prominent early letters, an initialism. This could perhaps be written as "oh bee gee why en" (as in one spelling out OB GYN). Is this a UK/US difference? Is there a "right" way to abbreviate this specialty? I am particularly interested in how it is said, as opposed to how it is written. | 0 |
While solving inverse function problems, I got confused in a part, like for any Inverse function to be defined, it must be one-one and onto, then in many questions why the codomain is given more than the Range as if we know that the codomain must needs to be equivalent to the Range for the Inverse function to be valid or defined, then why does they gave us the codomain different from the range? Kindly help me solving this doubt. | 0 |
So I understand that matter emits EM waves when hot. And that the higher the temperature, the shorter the wavelength, so cooler flames start off orange and the hotter flames reach light blue and white. What I'm wondering is if, hypothetically, you could take that blue-white flame and could make it considerably hotter, would the emitted wavelength reach UV thus making it invisible to the human eye? If so what temperature would need to be reached? | 0 |
I am interested in modeling the populations of low-lying, long-lived "dark" electronic states after excitation of an atom in the ground state with a laser. Using just a regular rate equation solver, I get nonsensical results. Provided there are no interactions between the low-lying states and the branching ratios to these states are known, is something like an Optical Bloch Equation solver needed to determine their population as the laser irradiates the atom? | 0 |
I downloaded a nice latex class, but I'm having trouble with one aspect of it - every page's header gets marked with either the chapter name or section name. As you can see, it makes the page look really cluttered. The code for the class is here. I've tried for a really long time to solve this, but I can't. I searched online and found that some commands containing mark have that info, and I've tried commenting out lines containing such commands. Still no luck and could use some help on this - I just want the page numbers to show in the header. | 0 |
If a block of mass m is attached to one free end of a spring and is performing simple harmonic motion of some amplitude A . Now if a wall is placed at some distance x (x < A ) from its mean position . It collides elastically, how is its amplitude going to change ? [ Will it be different in the side with the wall or uniform throughout? ] | 0 |
We know that sound travels through a medium through vibrations in the form of longitudinal waves. An example of it is here: We also know that particles of any medium vibrate when we give them more energy in the form of heat which gives them more kinetic energy. From this a logical inference can be drawn: heating the medium might disrupt the propagation of longitudinal sound waves. Consequently, should the disruption occur, would sound production be inhibited altogether? | 0 |
I am taking the second law of thermodynamics in the 'useful energy minimized' sense, although I am not sure if that is necessarily the most correct. Take the example of two electrons: electron A and electron B. Electron B has a wavefunction. Can we say that electron B's wavefunction will not have high probabilities close to electron A because that would lead to there being more useful energy than otherwise? Otherwise, is there a similar type of 'wasted energy maximized' or 'entropy maximized' for singular wavefunctions rather than groups of particles? Instead of treating entropy as an outcome of different particles, perhaps the wavefunction's different possible positions of particles can do a similar job? | 0 |
I know that the work done by gravity in going from A to C, and from A to B to C is the same. I also know that the work done by an applied force in going from A to C is the same as negative of the work done by gravity if there is no change in kinetic energy. But what is the work done by an applied force in going from A to B to C if there is no change in kinetic energy? | 0 |
It is assumed that a valid QFT, must have states/observables in a Hilbert space, transform according to the projective unitary representations of the Poincare group. I can understand why the observables must transform according to unitary representations of the Poincare group, but don't see any compelling reason for that symmetries must be projective as well. Some have explained it, as it is required for dealing with the phase factor redundancy in the wavefunction,but I guess this redundancy is dealt by the unitary representation itself, as the phase factors cancels out. I don't see why a phase factor redundancy demands the symmetry be projective. | 0 |
Exactly the question above. I've recently posted a question, and the more I look at it, the more it seems like a bug to me. The upstream code base on GitHub seems pretty inactive too (for about two years), having many open issues. I'm missing some experts who could help me or even the maintainer. Do you know whether there are good alternatives for PGFPlots which I can integrate easily into LaTeX and are quick to learn? | 0 |
Imagine spreading double-sticky tape all over the surface of a car or a plane. Would there more significantly more aerodynamic drag as a result of the adhesive 'sticking' to air molecules and slowing down? This would certainly cause more resistance in solid mediums but would this cause more resistance in air or water? If an adhesive surface can drastically increase friction with solid surfaces, could one also increase friction with the air? | 0 |
In finding this article, I questioned my understanding of the word 'gadget'. My current understanding is the word is (and please let me know in your answer if I'm right or wrong on this one) synonymous with 'accessory'. The only difference really being that accessory somewhat precedes the technological age. Hence, 'gadget' carries a sort of electronic/technological connotation (but not necessarily?). The article enumerates a 'backpack' as a gadget. Is that correct? | 0 |
A lever and a fulcrum is able to to multiply the input force to the output force and trade moving distance for increased force. The same happens in automobile transmissions, taking advantage of high motor RPMs. What exactly is the physical mechanism behind this? I am very aware you can mathematically prove it, for instance via an energy approach where energy in roughly equals energy out. Still, is it possible to explain the phenomena down to atomic level? That is, how is it in qualitative terms, that the force on the other side of the lever is amplified? | 0 |
I will have to teach a first course in differential equations. A good motivator might be to promulgate modelling with differential equations but I have seen some teachers have made polemic against modelling. Are there any really good resources on modelling with differential equations? I want something which will have an impact and motivate the learner. I am not really looking for artificial engineering examples but some bona fide real applications. Also, would like to bring in some history of differential equations to motivate the learner. | 0 |
What are local laws? I was reading this line in a book... Newtons second law is a local law. This means that it applies to a particle at a particular instant without taking into consideration any history of the particle or it's motion. What does this mean in simpler terms? Are their non local laws as well? Please explain with an example. I'm a high school student. | 0 |
It might well be that universal constants, say the speed of light, are only constant as far as we can tell in our chunk of the universe - in the same way that the Earth looks flat in the area you live. Are there any ways to tell that the speed of light is actually the same not just in our "neighbourhood" but in all the observable universe? | 0 |
Take a deck of cards, cut it in three, and rearrange the three packs in any order (for instance, the middle goes on top, the top in the middle, and the bottom stays). Repeat as many times as you want with different (and possibly uneven) cuts. What permutations can you generate? Motivation: given a set of symmetric matrices, the trace of their product does not change if they are subject to a permutation generated in the way above. | 0 |
I may be misunderstanding the general idea and the following specific example, but I was told that Dirac predicted the existence of the positron based on a formula for the motion of the electron(?) and then feeding in a negative value or imaginary value and somehow this suggested antimatter being a real thing. Sure enough the particle was soon discovered; perhaps the discoverers were guided by Dirac's work. But just why would anyone expect this? Could it not be that an equation works in many cases but not all? Was Dirac surprised by the discovery of the positron or would not finding such a particle have been more of a surprise? | 0 |
If we consider the addition of orbital sngular momentum L and spin angular momentum S to produce the total angular momentum vector J, then J is a member of the vector space that is constructed by taking the tensor product of the vector spaces associated with L and S. Why don't we take direct sum of the vector spaces of L and S instead to construct the J-space? Why are we particularly using tensor product to combine the spaces? | 0 |
From my textbook, A noun phrase is headed by a noun. Modifiers include articles, adjectives and demonstratives. Qualifiers include prepositional phrases and relative/adjectival clauses. Given the following: Your bag is in your locker What is the grammatical name? I know that its grammatical/syntactic function is the complement of the preposition . The problem is that I suspect it is a noun clause because "your" is neither an article, adjective nor a demonstrative. It is a determiner. Also, a noun clause can be perform every function that a noun phrase can, or so I think. | 0 |
Recently I learned about Markov chains. Consider a simple two-state Markov chain: This looks like a categorical diagram, with states as objects, transition probabilities as morphisms/arrows, and of course, identities as the same state transition probabilities. Although I don't know much, I also came across connections between two separate Markov chains, implying a functor equivalence. I wonder if there is such treatment in literature. Is there any benefit in approaching it this way? | 0 |
Today i studied about mirror formula, its derivation and sign convention used while deriving it, a question which i have is, why do i have to use sign convention while doing the derivation ? focal length, object and image distance all are distance so what is the point of using sign convention ? and while solving problems based on mirror formula why we use the sign convention again ? I have seen some answers on internet, they say that we use sign convention two times to cancel the effect of sign convention, but if want to cancel the effect of sign convention in the end then why do we use it, can't we solve without it ? | 0 |
When thinking about a "random" atom in space (say a Hydrogen atom), should I assume that the electron is in a ground state (or any particular excited eigenstate) or is it in a superposition of all energy levels before I measure the energy of the atom? On the one hand, If the latter is the case that would mean that there is a nonzero probability to measure any arbitrarily large energy for the system, which seems weird. On the other hand, should not any quantum system be assumed to be in a superposition of all the eigenstates before making a measurement, then is there any mechanism by which the superposition of such atom is collapsed even before measurement? | 0 |
I'm not sure where else to ask this since I'm not very familiar with this area. What is the backdrop of a theatre play act called? Like when the actors are behind the curtains and their silhouettes are instead flashed on the white screens or curtains. The play or act is all going on in the background just like a puppet play... What's it called? May I please know if this really is a thing or not? | 0 |
Baum-Welch is an instantiation of the more general Expectation-Maximization (EM) algorithm. But recently when I learned about it I couldn't figure out where the Maximization step is used. Because the Baum-Welch algorithm give me a sense of just iterating between computing some intermediate variables according to old parameters and updating parameters according to computed intermediate variables. Out of the reason, I searched this problem online, but I only find this article useful to me. My problem is a step in the derivative process troubled me(it's shown in the figure below). Could you please explain it to me? I asked my professor and she couldn't help me. enter image description here | 0 |
Consider a vessel completely filled with water and a vertically oriented capillary. If the water vessel was open at the top, you would expect capillary action to occur, lowering the water level in the vessel until a force equilibrium is reached. However, if we seal the vessel, the water would have to increase its volume/reduce its density for capillary action to take place, as no air can enter the vessel to fill up the volume. Does the (high) bulk modulus of water also apply here, as this expansion is nothing else than negative compression, i. e. would the hydrogen bridge bonds mostly suppress capillary action? | 0 |
Order the following functions in terms of little oh notation: where: Im actually confused on how to do it. I think its the functions that confuse me not the method on how to do it. I know that: But either my mathematical skills are failing me or there's a different way to do it, that I don't know. Any help is appreciated. Thanks a lot in advance. | 0 |
I just wanted to bring up some discussion about an apparently essential concept for some fields in mathematics as so as for some in physics, as already mentioned in the title, I'm referring to the word "symmetry". I'm currently studying about Lie symmetry method to search for first integrals of ODE's, and already saw that the main problem would be, exactly, to compute the symmetries, which involves a PDE. In adition, I constantly hear "symmetry breaking" from some working with QFT. It sounds like a joke but, are we trying to find those symmetries for you guys to "break'em"? Despite the kidding, could these two contexts be related in some degree? | 0 |
In an infinite universe composed of single point masses which can be simplified as a uniformly distributed mass density, what is the equation for the gravitational field intensity in Newtonian gravity? I assume that: The gravitational field intensity is constant through space since the matter density is constant. The net force on any test particle must be zero, because all forces must cancel out due to symmetry. The gravitational field intensity is infinite since the its the sum the gravitational field intensity of each mass point, and there are endless mass points at infinite distance. But it must converge to a specific value since contributions of far away point masses contribute less and less with the square of distance. | 0 |
Is there a word that means "lost thing"? Ir perhaps a word for "forgotten thing/ something that has been forgotten"? Similar to how requirement means "that which is required" or necessity is "something necessary"? I'm ideally looking for a noun or other words that are constructed to from an adjective describing something to the noun that stands for it. Here are two sample sentences: This book contains a list of major [lost things] throughout history. The [forgotten things] inspire many mythological stories. I am also okay if there's an archaic or uncommon word for this! | 0 |
I don't know much about this topic, but I read something saying that gravity is not a force using an example of inertial observation. I started thinking about the topic again when I was researching photon spheres and thought why does gravity (if it is a force) curve light when photons have no mass. The only possible answer would be that gravity is not a force but rather the warp of space around mass. Would this be right? | 0 |
I don't understand why you can't invert a hessian matrix using gauss jordan method. Can't you integrate or differentiate an entire row (because they are linear operators) and then subtract/add/swap? To clarify, I mean inverting the generic hessian formulation before it is applied to any function. In this way, I can get the hessian inverse so I can apply it to other functions. otherwise, I'd need to calculate hessian of a function and then invert, which takes a larger time complexity. | 0 |
Can we calculate the total observed time dilation on a spaceship and a planet by combining the planet's relativistic spin velocity and the spaceship's approach or recession velocity from the planet it came from and where it's heading? Would the spaceship see both planets as time-dilated due to their combined relativistic spin and approach/recession velocities? Should we consider both the spin velocity and the apparent recession/approach velocity, or just one of them, in such calculations? | 0 |
As I understand, it is perfectly possible to explain the standard double slit experiment with a laser beam using only classical physics. On the other hand, this experiment is one of those experiments which is mentioned the most when quantum theory is introduced. So at what point of the experiment -- or through which variation -- does quantum theory come in where classical physics fails ? | 0 |
In Baby Rudin a subset E of a metric space X is defined to be connected if "E is not a union of two nonempty separated sets." This may be nit picking, but should this not be E is not a union of two or more seperated sets ? Wikipedia agrees. To be super nit picking, by Rudin's definition (and taking it super literally) a set that is the union of three nonempty separated sets would be connected since... two is not equal to three. | 0 |
According to the argument in this post, a theory of Quantum Gravity should not be compatible with the notion of time evolution. This is also called "The Problem of time". However, the target spacetime formulation of string theory does have a notion of universal background time given by the target spacetime. So it seems like it does not address the problem of time. The CFT part of AdS/CFT is also a QFT with a well-defined universal time. So does String theory not address this problem? If no, then what does it say about it? | 0 |
I heard this dialog in a Western film: Ruffian: Are you Josey Wales? Josey: That['d] be me. Methinks Josey responded That be me and not That'd be me. Is the former even correct? Is That be me. also a sentence in subjunctive mood, just as That'd be me is. If That be me is correct, what would be the difference in meaning between That'd be me and That be me? Please, take note that this question is not a duplicate. | 0 |
The intended meaning is that 'it', described simply, is 'everything'. Would I write: It is in short...everything. Or: It is, in short...everthing. Instinctively, I believe that a comma is needed before "in short". But the confusion arises here: Is it a common enough phrase that the comma is not needed? Is it a publisher's preference situation? Author's preference? I've seen the phrase 'in short' both with and without commas. Normally two commas are used, as it's a parenthetical, but the ellipsis makes the second one unnecessary. | 0 |
In one of our informal math research club sessions we are thinking of hosting a math meme making competition. Our idea is that math memes will trigger curiosity and interest among the participants. This would not only help in questioning and understanding the mathematical ideas behind the meme but the participants will also have fun doing it. Lets say that I go ahead with this idea. What could be a possible way achieve best results? | 0 |
What is the meaning of the phrase, 'as thus construed'? I was writing an essay and felt that phrase was appropriate, but I looked it up with quotes on google and found only references in some legal documents and academic papers. Is there a similar phrase that I am thinking of, or does this make sense by itself? For example, suppose I just described x a certain way. I then say, "x, as thus construed, is Y." Does this make sense? Or is there a phrase that is more accurate here? | 0 |
so I am looking for good text books that treat signed measures, integration thereof and total variation etc. In particular also for finitely additive signed measures. I have found Dunford and Schwartz a little bit too general in that they dont necessarily consider (signed) measures but more generally set functions. I would also like the book to be as standard in notation and the used concepts as possible. So can you give me any suggestions for text books? | 0 |
I am in charge of deciding the name of a skill in a role-playing game that serves as a catch-all for abilities/skills that are otherwise unlisted in our handbook (think skills that will help players flesh-out their character's personality, quirks, and life). Such a skill could be a profession type, a craft (e.g.,whittling), or something more exotic like hyperlexia. Profession and Craft do not capture the spirit well enough. Ability seems too generic, as are its multi-word variants, e.g. Unlisted Ability. Knack seems closer to the mark but open to suggestions. | 0 |
I am currently studying a paper on Wasserstein Fair Classification. Several places they mention the Wasserstein barycenter, weighted barycenter distribution or the Wasserstein barycenter distribution. What is it? How is it defined? I can only find very deep measure-theoretic explanations, which are both a bit out of my league as a statistician, who never enjoyed analysis very much, but they simply also lack an intuition behind. | 0 |
I was wondering is it possible to try and do optimisation of an ellipsoid given the formulae for its volume and surface area? I would be trying to keep the volume constant whilst minimising SA. This is for one of my maths investigations, basically trying to minimise packaging of a kinder egg, so if this is somewhat of a dead end, what are some alternative approaches I can take forwards? Any help would be really appreciated! Update: Ive derived the equations for the SA and Volumes of an egg shape Would the Lagrangian Multiplier Method work here | 0 |
I happened upon this video purportedly showing a coin on a horizontal table receding away from a lens would disappear from bottom up. The explanation via diffraction resolution limit is wrong. However, I would like to find the correct explanation of the phenomenon. When the camera zooms in and focuses on the coin, the coin appears clearly. This can be explain by the fact that part of the light from the coin still enters the aperture of the lens. However, how would one explain the abrupt disappearance of the bottom of the coin below the table upper edge when the focus of the lens is on the table edge? | 0 |
My question is this: Why can't electric potential energy be defined at one point. Surely a point charge has some inherent electric potential energy cause by force applied by the source field. The applied force would cause the charge to accelerate. The acceleration approaches zero as you get farther from the field, so the velocity could also approach a known limit (depending on the function). That velocity can be used to calculate the maximum kinetic energy, which would equal the original electric potential energy imparted on the charge by the field. I know this is a classical treatment of the situation, but what's wrong with this line of thinking? | 0 |
I have questions about the inner product and coordinate transformation matrix. For F inner product space V, consider vector a and b in V and its inner product <a,b> then the inner product is invariant about changing the Basis of V? And let B and B' be Basiss of V. Then can I think that the coordinate transformation matrix from B to B', denoted by R is a unitary matrix because it preserves the inner product <a,b>? | 0 |
Electrons have an e-field, and a moving e-field causes a b-field. These fields are defined in such a way that it makes calculating things like forces much simpler. Is this just a model and there aren't actual 'waves' traversing around us, but rather mere forces caused by a movement of an electron? If the force caused by a charge wasn't viewed as a wave, would electromagnetism only be a model for calculating the effects of the charge, utilizing waves as a tool? If so, is it fine to propose that visible light is simply our brain's reaction to certain forces caused by moving electrons in a certain frequency? | 0 |
I have always been told that if you press the brake pedal fully and fast it can make the wheels lock themselves, and that you shouldn't do so because it would take longer to stop the car than if you push the brake pedal progressively, why so? I can imagine that when done progressively the car won't start doing jumps due to the wheels block as if you would brake immediately but I can't see why. | 0 |
The existence of dark energy leads negative pressure. Is the pressure can be anisotropic? What situation can cause anisotropy of pressure? Further, Is the pressure can be negative in some directions and be positive in other directions? Such as in spherical coordinates, the radial pressure is negative and the tangential pressure is positive. Will this happen when matter and Dark energy exist at the same time? | 0 |
I want to determine the largest area ellipse inscribed in a rectangle, in order to write a code that can determine the lengths c and d given a and b (see image here). I know the obvious answer would be c and d are halves of a and b, but I want the derivation (and also the maximum area) so I can stop thinking about this, saddly I can't seem to figure this one out. I remember doing the opposite in school (rectangle inside ellipse) but can't do it properly now. Hope you can help me. | 0 |
I'm quite close to release my first game, and I can't decide which is grammatically correct on my first user facing screen. My game will surely have some grammatical mistakes but I would appreciate it if the first screen would be more or less accurate ;P So the title wants to welcome the user into my game but I dunno which way I should go. Welcome to {Game Title} or Welcome in {Game Title} Any feedback is appreciated! | 0 |
i would like to find a way to study physics online and get academic credentials in it and be able to contribute to the research and publish. I know some topics are experimental and require physical attendance, however there must some subfields in physics that can be studied online. Now there are many online masters in STEM fields like computer science from reputable universities. Is it the same for physics? | 0 |
The Wikipedia page for locally constant function says that a locally constant function is constant on each connected component, but that the converse only holds if the space is locally connected. What would be an example of a function that is constant on each connected component but not locally constant? I first thought of the topologist's sine curve, which is not locally connected, but since this is a connected space, such a function would be constant on the entire space and therefore automatically locally constant. | 0 |
I need to prove in graph theory that if L(G)=G then G is a combination if simple cycles. I already did it assuming G is connected, so feel free to use this fact as given. My only issue is that it may be possible that in a non-connected graph not every one of the connected components will satisfy L(G)=G. For example, if the Connected components in G are A,B,C it may be possible that L(A)=B, L(B)=C, L(C)=A. | 0 |
Suppose there is constant diameter pipe where a liquid flows through it, and if pressure of a liquid is due to external force or its weight when it is constrained or semi constrained (according to the accepted answer on this question), how can someone visualize how does pressure drop occur due to frictional losses? Does the force on the liquid decrease somehow or does it become less constrained so it has lower pressure? | 0 |
I am studying the spontaneous symmetry breaking in the mean-field Ising model and it's clear to me the necessity of taking first the thermodynamic limit and then the zero-field limit to see the phase transition, otherwise we only see zero magnetisation even under Tc. I was wondering if there was a phase space approach underlying this result and if the spontaneous symmetry breaking implied and ergodicity breaking as well, as I imagine that the ensemble average is anyway zero, but this is not what we observe physically. Can someone give me a hint? | 0 |
I went through a quite a lot of posts here but did not find the information I wanted. I'm looking for a beginner / introductory (yet mathematically rigorous) book recommendation for differential geometry / topology required for General Relativity. I'm perfectly fine (in-fact I like) the so-called dry mathematics books (theorem-proof-theorem). What I need is - Very clear definition of Mathematical objects used in GR Crisp / rigorous proof in modern notation I need the book at advanced undergraduate or beginner graduate level. Thanks in advance. | 0 |
Is there any way one can modify a known functional so as to get a solution for another quantity related to it? Because this is too general I would like to make it more clear with an example. Given the classical EM Lagrangian, we acquire the equations of motion for a particle in an EM field. Starting from this, is there anyway one can find a functional that when varied will give the solution for, let us say, the electric potential, for a given charge distribution and known boundary conditions? | 0 |
To understand the attractive and repulsive force between two currents, I am looking at two electrons moving parallel and antiparallel to each other. How can an attractive (or less repulsive) Lorentz force between two charges and its directional dependence be explained? I would like to understand this in terms of dynamical effects of the electric field and not in terms of a magnetic field which is the common approach for correctly treating and not further looking at such details. | 0 |
Pramod Achar's book on perverse sheaves has a quick reference in the back that looks like this. How can I achieve something similar? The important things to me are: the general spacing (although maybe I would enjoy less margins on the outside), the two columns, the numbering and labeling, the horizontal line separators. For language, I only care about English. I don't have any font preference. | 0 |
Consider this fact that we all know from school mathematics: There is a one to one correspondence between real numbers and points of a line. But the problem is I have never seen a rigorous proof of this fact. This is what Apostol writes. And similar is the case with other modern analysis books. So my question is, where can I find the proof of this one to one correspondence. I don't care if geometry is in Hilbert's axioms or Tarski's or anyone else all I care about is correspondence. | 0 |
I'm bit confused about the current flow in capacitors. My question is, let's assume those two electric circuits: As shown in the picture, the only difference is only the capacitance. I'm wondering about the current flow magnitude. In which of the circuits the current flow will be bigger? or will it be the same? To start, I assume both plates of the capacitor are uncharged. My guess is that right at the moment of closing the switch before the capacitors are charged from the voltage source, the current flow will be even. Once they are fully charged, of course, the current will be bigger in the system with the bigger capacitor. But till this point, what will be the current flow? thanks | 0 |
it is said that the time period of a simple pendulum in space is infinite. it is because the gravity in space is zero and anything divided by zero is equal to infinity.how can time period be infinite? also, in space, everything just floats around. how can a pendulum in space do oscillations if there is no restoring force to bring the mass back to mean position. how can a simple pendulum exhibit SHM in space? if it cannot exhibit SHM , how is the time period formula for the simple pendulum applicable to the pendulum in space and what is the meaning of infinite time period. why do the time period of pendulum in space even exists? | 0 |
I was wondering if it is posssible to write my own environment for writing redox equations in form of: O: ... R: ... ___________________________ S: ... O stands for oxidation, R for reduction and S for the summary equation. Also, there is line that should separate O and R from S. I have never written any environment in LaTeX, so could anyone just help me start? I've seen that there are some packages that are about chemistry, but none help me about this problem. | 0 |
In surface integrals the process is to use the dot product of the vector field with the unit normal vector first and multiply that with the area element. In the line integral the process is to use the dot product of the vector field with the length element. Why isn't the unit tangent vector used in the line integral computations while in the surface integral computations the unit normal vector is used? | 0 |
While deriving the Planck's radiation formula, why do we use MB statistics when we calculate the average energy of oscillators? Shouldn't we use BE? Is this because temperatures concerned are very high and quantum stat goes to classical at high temperatures? But again, in a similar calculation, while calculating the lattice specific heat of the solid using Einstein's model or the Debye model, I have seen books calculate the average energy of oscillators using MB distribution only, but we use this formula to predict specific heats at very low temperatures also. So I don't understand, what is the reason? | 0 |
The sentence is as follows: "Isn't it evident who/whom they have in mind for the position?" Depending on how you try to reword it to figure it out, the answer seems different. --Is it not evident that he is the one they have in mind for the position? (This seems to be a case for "who" here.) --Is it not evident that they have him in mind for the new position? (This seems to be a case for "whom" here.) Should it be who or whom? Why? | 0 |
I know multiple singular subjects have been addressed here and singular compound subjects here. However, I came across a sentence with multiple subjects, one single paired with one plural. I could not find this question addressed. For example Does a table and four chairs sound like sufficient furniture for a breakfast room? That doesn't quite sound right to me, but then Do a table and four chairs sound like sufficient furniture for a breakfast room? also sounds a bit off. Which would be correct? Or are both incorrect? Purdue uni subject-verb agreement is confusing. | 0 |
An intuition that I thought of about a year ago, but my level does not allow me to prove it. I think it needs advanced tools to prove it, or just a counterexample to refute it. Who can help, please, thank you. The locus of the point of intersection of the perpendicular tangents of a convex curve is the convex curve Of course, the intuition is only in this direction and does not constitute an obligation, as the cardioid is a concave curve. Despite this, tracing the perpendicular tangents to it gives a circle | 0 |
Using Hugyen's principle and wave nature of light, refraction, diffraction are relatively simple to explain but I have been visualing a mental model for a couple of days where the photons on reach the boundary of two media, experience a difference in the structure of the medium of propagation and hence some sort of collision or change in the overall velocity vector of each photon occurs which leads to refraction. Can someone help me understand these phenomenon using particle nature? | 0 |
how one would know that the given frame of reference will be inertial or non inertial, without the use of 'accelerometers'. earlier physicst has defined this concept and I am sure that they define it without the help of accelerometers. I just want to know about the logic behind the whole concept. And I will be not getting any accelerometers in my exam and not able to conduct any experiment in the frame. i want to know how teachers just say that this frame will be inertial or not without any accelerometer. | 0 |
How come there is no loss due to coupling between the superconducting channel and the single particle channel? I imaging the two channels being two parallel wires, so the magnetic field from the current running in the superconducting state, should fully inclose the single particle channel generating a electric field, that at least would create a displacement current and introduce a loss. Why is that not so? Also is there no current fluctuation due to the current being carried by discrete charge quanta? I would assume that, that would also create a electric field fluctuation in the single particle channel causing a loss? | 0 |
I posted about monoid coproduct to try to understand the correct way for constructing them. In the process and from the answer I got, I am further confused whether the product and coproduct of plain monoids compare free monoids, what are the subtle differences in terms of what they look like. I understand in both coproduct of monoids and free monoids, the process of word reduction to strings are applied. I don't know anything beyond that. I am hoping someone can explain to me their subtle differences. Thank you in advance. | 0 |
If we add a constant to both sides of an equation, we will get a new equation with identical solutions. This is mostly true for multiplication and square roots, but there are some minor complications/exceptions. Taking the derivative of both sides will result in entirely different solutions. Is there a formal way to show how performing some operation/action on both sides of an equation will affect the solutions of the resulting equation? | 0 |
This is a question about grammar, in particular about a specific language syntax. In the german langage it's legit to write negative prefixes in braces like "Die JSON (De-)Serialisation wurde implementiert." Is this valid in english? "The JSON (de-)serialization has been implemented." As a software developer I need to document the work I've done and the software functionality itself. I often have a lot of language constructs similar to the one above. And if it's legit to use this syntax of negative prefixes it would save me a lot of time. | 0 |
I wonder whether there is a space filling curve that looks like the following if the width of the domain has an odd number of cells and looks like the following if the width of the domain has an even number of cells. I would like to fill a three dimensional grid none of whose sides (lengths) are guaranteed to be a power of two or even. | 0 |
How is it paradoxal that a set of all sets exists in set theory? Russel's paradox is about the set of all sets that do not contain themselves cannot exist, that I understand. But what about the set of all sets, in a unrestricted manner? Is it the fact that it contains itself (which may be what allows to define the paradoxal set of Russel's paradox) that is problematic? | 0 |
Is the result of a contour integral around a closed loop path unique? I'd think it'd be similar to a definite integral, which is unique. This came up regarding the proof of uniqueness of a Laurent Series - if the contour integral is unique, then the definition of the Laurent Series can be used to prove its uniqueness. Edit - as pointed out below, the Laurent Series aspect may be a limiting case, as it's within a specified annulus, so for any of the Cauchy coefficients, the same analytic annulus is used, so the same number of poles will always be within the inner radius. | 0 |
Is it true that if a curve is increasing, Euler's method will always underestimate an actual solution? So if a curve is either increasing and concave down, or increasing and concave up, we can simply ignore concavity and justify the answer based on the fact that it's increasing? Euler's method will therefore underestimate whenever the function is concave down and increasing, or concave up and increasing? | 0 |
There are two machine learning models, A and B. Model A classifies samples into 'O' and 'G'. Model B classifies the samples determined to be 'O' into 'S' and 'C'. Each model shows the probabilties of classification. Input samples pass through model A first, and if the result is O, then they enter model B. (If not they don't) In this case, how could I get the probabilities of classifications, G, S or C? | 0 |
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