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I am tasked to simplify this circuit to one source and one resistor, which is equivalent to the original but obviously easier to solve. My problem is the fact, that I don't know how the nodes A and B affect the process. I'm more used to the circuits where the A and B nodes are on one end of the circuit, but these are in the middle. Not sure how this is supposed to be interpreted. | 0 |
I am wondering if this statement about parallel circuits and conservative fields is true?: The voltage drop over resistors in parallel is the same because the electric field is conservative, so the work done on a charge only depends on the start and end point. The field is conservative because the force it generates consists of the electrostatic force (Coloumb) and a magnetic force. We can show that the electrostatic force is conservative, and the magnetic force on moving charges is perpendicular to the velocity vector, so it does not do any work on the charge. So the only force that does work on the charge is the electrostatic force. Is this statement correct? | 0 |
I'm playing around with modeling an archway of a building using a solid modeler, and have come to a problem that exceeds my mathematical ability. Given an ellipse that has a known major radius, and is tangential to a line of a known length, angle, and offset on the Y-axis, can I find the ellipse's minor axis? It's been decades since I took a math class. I can handle basic trig, but I can't figure out how to get started on this one. Edit: Thanks everyone! You can see your solution in the flying buttresses of this (very preliminary) render. | 0 |
The company "Fluke" makes a DMM that they claim can measure AC voltage by simply clamping the connector around a live wire, and using the E-field to induce a voltage/current into the capacitor. I can understand the concept if we assume the person holding the DMM is grounded and the measuring loop is sufficiently sensitive. But what if the person holding the DMM is not grounded, or is in a vacuum, etc. Some people on the internet claim it works even if the DMM is hanging from the wire in open air. I have my doubts... So, I am wondering if someone can explain to me if current can flow in a capacitor that has no path to ground. It seems like an obvious "no." | 0 |
I am trying to understand the Von Neumann decomposition, according to which every Von Neumann Algebra can be uniquely decomposed as integral (or direct sum) of factors. More specifically, I am trying to connect (if possible) the Von Neumann decomposition to the GNS theorem. Can someone please help me answer the following questions? Given a normal state, is it true that its GNS representation is always a factor? The answer would be different if the dimension of the algebra is either finite or infinite? Is it possible that the algebra obtained by applying GNS theorem on a irreducible state is not a factor? From the quantum mechanics point of view, why is the Von Neumann decomposition important? | 0 |
There's a clip going around on the internet of the driver Ross Chastain, 'wall riding' in a race that allowed him to pass many opponents on one turn. Here is the clip. What I do not understand is how did this work? The only explanation I can think of is that the normal force of the wall acted like a centripetal force, which meant he didn't have to brake on the turn, but this doesn't make too much sense to me since the frictional force of the wall on the car would slow him down quite a lot. | 0 |
I'm working on a project involving non-standard dice where each face can have a different size, but the overall shape and weight distribution of the die are uniform. I'm interested in finding out how to calculate the probability of the die landing on a particular face based on the size of its faces. Assumptions: The die maintains a uniform shape and weight distribution. The die has 'n' number of faces, each potentially with a different area. We ignore the complexities of rolling dynamics and assume the die lands flat on its faces. I am looking for an equation or a model that can accurately calculate the probability of landing on a face, given the area/dimensions of each face. | 0 |
Does anyone know where I could find a copy of Ron Graham's PhD dissertation, titled "On Finite Sums of Rational Numbers"? I found this paper, with a similar title, but I could not find Professor Graham's dissertation. I need to double-check some detail(s) in Professor Graham's dissertation which may not be in the published version. This is in consideration of my (current) approach to odd perfect numbers via Egyptian fractions. | 0 |
I am not a pure mathematician but an engineering professor. Right now I am going through the first chapter of Topology without Tears by Morrison. One of the questions is as follows. A set T consists of a set of real numbers, the null set and the closed interval [-r,r] where r is irrational. The question is whether (T,R) form a topology where R is the set of real numbers. The answer seems to be an obvious Yes irrespective of whether r is rational or irrational since both intervals can be infinitely large and can contain arbitrarily large numbers. But I am suspicious as it seems to be too obvious and I think the actual answer is No. | 0 |
I am new to linguistics and am currently learning how to figure out phrase markers for sentences. I am unsure about this sentence: She went off in search for her hedgehog. I know that "she" is a noun phrase, but I am unsure about the VP. Is the VP "went off in search for her hedgehog"? And does that split again into the three phrases: went off, in search and for her hedgehog? Does it look like this? | 0 |
I am trying to find the directional vector to hit a moving target. For example, as seen in my drawing, Lets say a space ship at position Sxy needs to fire a projectile to hit the moving asteroid (currently at position Axy). The asteroid is moving with a linear velocity vector Av. The projectile has a constant speed (magnitude) of Ps. How can I solve for the projectile directional vector Pv? Both the asteroid and the projectile have a radius. | 0 |
I am studying simplicial homology and I am a bit confused about the definition of an orientation of a (finite) geometric simplex. The definition says that two orderings of a simplex are equivalent if they differ by an even permutation, and so we get two equivalence classes - two orientations. My question is, what is an ordering of a simplex? Is it just a permutation of the vertices or does it have to satisfy some other rules? If it's defined to be a permutation of vertices, then we draw paths between vertices indicated by the permutation of vertices (I am thinking geometrically), then my lines might cross each other. Is it that this will not happen because vertices of a simplex are in general position? Thank you! | 0 |
I've been studying the Lax equivalence theorem . I've learned that it allows you to establish the convergence of a scheme through proof of stability. The Wikipedia article says that the method it's important because "it is ordinarily difficult to establish [convergence] because the numerical method is defined by a recurrence relation while the differential equation involves a differentiable function". I used the equivalence theorem to establish the convergence of the Crank-Nicholson method in an assignment. I was wondering what a direct proof would look like (I'm assuming it depends on the scheme). Can you please provide any references for this? Thank you in advance! | 0 |
With some formal systems, it's possible to enumerate all the theorems. This is the case for instance in propositional calculus or in some first-order theories with a recursively enumerable set of axioms (e.g. group theory, field theory, Peano arithmetic, etc.). I'm looking for a software that would implement such an enumeration. Or more basically, a software that would produce random theorems (which may or may not be of interest). A software doing that in any of the formal systems listed previously would be acceptable. | 0 |
My teacher taught us that a square matrix is called a diagonal matrix only if all the entries besides the ones on the principal diagonal are zero. He further cautioned that there is no restriction on the entries of the principal diagonal and that they may be zero or non-zero, BUT there must be atleast one entry on the principal diagonal that is non-zero. We were specifically told that null matrix is not a diagonal matrix as there simply is no entry along the diagonal. However, most if not all sources on the internet say that null matrix is also a diagonal matrix as all the non-principal diagonal entries are zero. Which one of the above definitions is correct? | 0 |
Imagine the following conditional: If washing machines are humans, washing machines are quadrupeds. It seems to me that the truth value of the conditional as a whole is ambiguous. Since its antecedent is false, logic tells us that the conditional is (vacuously) true. But in fact, the conditional as a whole does seem false: if we grant that washing machines are humans, then washing machines are clearly bipeds. But how can the same conditional be both vacuously true and (at least intuitively) false? | 0 |
I just read this answer to "What exactly is a Photon?" which has me a bit confused. It seems to be arguing that "photon" is just a catch-all term for any sort of interaction with the EM field and the implication is that it's not even a particularly useful concept, in contrast to the fundamental particles of other fields. But how is that any different from other elementary particles, when all particles are just excitations in quantized fields? I also found several threads talking about whether photons have wavefunctions or not, such as this one: Wave function of a photon? and I'm seeing conflicting information. If photons don't have wavefunctions, are they even particles at all, in the sense of being localized disturbances in a field? | 0 |
I am doing some interactive plots about cosmological horizons and in my research I stumbled upon the sound horizon, the baryonic acoustic oscillations and how it had an impact on the formation of the first structures in the universe. Some people have calculated the radius of the sound horizon at the time of recombination using the same equation used in the particle horizon but with the speed of "sound", which itself is a function of the density of matter and radiation. But I've never seen anyone actually plot the radius into the future like some have done with other cosmological horizons. Is there a reason for that? Does it not play an important role in the universe anymore? Was it only important at the time of recombination? | 0 |
The nlab claims that the maximal ideal theorem in Heyting Algebras (i.e. for every proper ideal in a Heyting Algebra, there is a maximal ideal that contains it) implies the axiom of choice. Sadly, it does not cite any proofs and I've been unable to prove this, I'd appreciate any proofs/references. I find this particularly interesting as it's known that the maximal ideal theorem for Boolean Algebras is strictly weaker than the axiom of choice. Yet, the same theorem applied to the apparently slightly bigger class of Heyting Algebras suffices to prove choice. | 0 |
I have difficulty understanding when we use "an analogy", "a metaphor" and "a figure of speech". I feel like in a casual conversation, people just use any of these words to say something that is different from its normal use. Does a native English speaker distinguish the difference between them in a casual conversation?. Is it correct to say: "I am like a bee in a bottle is an analogy" or "I am like a bee in a bottle is a metaphor" or "I am like a bee in a bottle is a figure of speech" | 0 |
In the study of the geomagnetic field, an expansion in spherical harmonics is used to represent the scalar magnetic potential: the first terms give the dipole approximation, then the quadrupole, etc. For instance, we can find here (International Geomagnetic Reference Field) reference data for the magnetic field, given as coefficients of a spherical harmonics expansion. My question is: how are those coefficients calculated? I was thinking of the Monte Carlo method, but I couldn't find any information on that. Note that I would also accept answers related to the gravitational field as the question also applies there. | 0 |
I'm an English learner, and sometimes I cannot understand why some words are used to express a meaning. For example, the word "Down". What's the difference between "I walked on the street" and "I walked down the street" or "Alan drove down the street" and "Alan drove on the street" ?? As far as I know, these verbs are not phrasal verbs, so how can I know when to add this "adverb particle-like" with a verb ? | 0 |
I saw this in a textbook and I want to confirm if it's true If a body of mass m rolls down an inclined plane of height h and length l (hypotenuse), the work done is mgh. It is the vertical height of the inclined plane that is used in the calculation, not the length (hypotenuse) of the inclined plane. Please how true is this because I believe we should be using a little bit of trigonometry since the object also moved a horizontal distance. Please if true, how? | 0 |
I'm trying to understand how car wheels work. In a perfect world the bottom of the wheel has no velocity. The wheels are in a state of pure rolling, which means there is no static or kinetic friction because the bottom contact point is not in motion. This would mean that in a world without air resistance a driver wouldn't have to push on the gas pedal, as there aren't any forces opposing the cars forward velocity. Is this right? | 0 |
I have a question about the EPR phenomenon of the quantum-mechanics. When you observe the EPR phenomenon, you separate two spins in the singlet state. Then, you and your fellow independently observe the direction of each spin, and you compare the directions. If one spin is in New York, and another is, for example, in Tokyo, how do you assign the directions? Because the earth is round, I do not know which direction is opposite to another. In reality, it is difficult to make such a large separation without losing correlation. However, in principle, it is irrelevant how large the distance is. Thank you for your attention. | 0 |
I found this problem online somewhere (cannot remember the exact source, sorry) and initially I thought it looked fairly simple and fun to solve. I've now sat for several hours and even asked some friends to help, but none of us can actually solve it (without complex algebraic equations). I am by no means an expert on geometry or trigonometric (or mathematics for that case), so I would assume there are some identities or theorems that would make this problem easier to solve that I just don't know. Can anyone help please. The problem is to solve for x in the below diagram (excuse the bad drawing in Paint): | 0 |
Generally speaking, the universe is electrically neutral and the universe abhors an unbalanced charge. Wherever there is a positively charged object, you can bet there is a negatively charged object not far away. However, no laws of physics prevent the accumulation of positive charge, say, so long as the negative charge is sent somewhere else. This must be true on a cosmic scale as well. Hence my question: What is the most electrically charged celestial body in the universe, and what is its charge, i.e. positive or negative? Dipoles don't count. | 0 |
From many papers I've read in condensed matter physics, it seems "breaking time reversal symmetry" is often equivalent to "applying an external B field", while "breaking inversion symmetry" can be done (but not limited to) by "applying an electric field". Is this true in general? A side question: if a perturbation breaks the inversion symmetry of the original Hamiltonian, does that imply it mixes states of opposite parity? Similarly, if a perturbation breaks time-reversal symmetry, does that mixes time-reversal pairs? Looking forward to any counter-examples. Thanks! | 0 |
At first glance, it seems like the "many" in "There are as many A's as B's" is an adjective. However, we can't substitute an arbitrary adjective in this sentence. Compare: "There are as many A's as B's." (correct) "The A's are as many as the B's." (incorrect) "There are as numerous A's as B's." (incorrect) "The A's are as numerous as the B's." (correct) I'm curious about how to describe the reason why two of these feel 'correct' (to me, as a native speaker) and two of them do not. Is 'many' here a different part of speech than an adjective? Or is "as many as" just its own grammatical construction with its own rules? | 0 |
David Cameron, the previous Prime Minister that has been away from politics for many years, has just come back as the Foreign Secretary. The BBC refers to him as the "old new face". Politics aside, just as an English grammar question, I wonder why it's "old new face" instead of "new old face": is there some convention/rule to determine the order of the two adjectives? Or is it just slang? I did some searching but was overwhelmed by face recognition AI links... | 0 |
I have an anodizing rack that has hundreds of prongs. These prongs are made of titanium and need to be squeezed together in order to place the parts on the rack. I am wondering how I would calculate the force needed to make the prongs touch so that parts can be added? I have seen some people saying to use F=kx treating the prongs as a spring, would this be the best way? Any help is appreciated. | 0 |
I was at a jewelry workshop today and saw somebody place a gold ring under an intense flame. Weirdly, the ring looked normal when underneath the flame, but glowed "red-hot" as soon as the flame was removed. The latter behavior is what I expect of a hot object emitting blackbody radiation. It makes no sense to me why the ring would not look like a blackbody object in the presence of the flame (where it could only be hotter). Maybe ions in the flame are affecting the physics at the surface and making it effectively opaque? I didn't capture the effect on camera, but this video sort of shows the same thing happening, though not nearly as clearly as what I saw in person. | 0 |
I'm trying to construct a table that looks like the following: I know I need to use multirow package in the tabular environment, but I can't figure out how since I couldn't find examples that are similar to my need. It seems like I need to use a multicolumn environment inside multirow for the 'Experiment' cells. Can someone guide me in the right direction? Thank you! | 0 |
As I read on Wikipedia, a phosphor coating of a CRT screen lights up because an electron in one of the phosphor atoms emits light when it goes down from its excited state. When a single electron hits a phosphor coating, is it the case that exactly one atom of the screen will glow? If not, what is the shape of the spot on the screen for a single electron? | 0 |
If we create a pair of rotary wings like those on a helicopter, and spin them in a vacuum, would it be possible for a virtual particle and anti particle pair to spawn, be split by an approaching wing, and take opposing paths around the wing, before re-combining and annihilating? Would this create a pressure differential as it does on macro scales in fluid dynamics? Does the particle and anti particle pair even need to be split or is it sufficient for multiple such pairs to spawn and move around the wing before annihilation? If we rotate the wings at relativistic speeds, does this increase the rate at which this occurs and the pressure difference generated? | 0 |
Given that our best models so far suggest that the universe has been expanding a lot ever since the time the CMB was emitted, I'm wondering: How large was the (visible) universe back at the time it became opaque and emitted the CMB? Specifically, I'm curious as to the ("original") circumference of the spherical shell we "see" out there, in comparison to how far the light from it has traveled to reach us. | 0 |
I was trying to figure out some details about a specific decay channel for a generic particle accelerator experiment. For instance if I have a proton proton collider with fixed energy, I would like to figure out what is the average decay length of a B meson, what would be the energy of its decay products (for a chosen channel) and similar things. I know there is a lot of MC software used in high energy physics but I was just wondering if someone had a recommendation for one which is free and is not hard to use and configure when doing such simple things. | 0 |
In his classic poem which pretty much everyone knows by heart, Edgar Allan Poe writes as follows: Ah, distinctly I remember It was in the bleak December, And each separate dying ember Wrought its ghost upon the floor. Why? "... a bleak December" would have sounded (or would it?) more logical: not all Decembers are bleak. Or: "This occurred in bleak December" would have scanned just as well. What gives? | 0 |
I have recently moved to an institution run by the British government where staff use the term "indent" as a noun to refer to an inventory exercise done to work out what they need to buy. This is consistent with several dictionaries, such as Merriam Webster: chiefly British a : an official requisition b : a purchase order for goods especially when sent from a foreign country Does anybody know where this usage comes from? | 0 |
I was reading a book, the author described the scenery of a certain place, and then said: "You're hooked for life." The search engine told me it means, you have been fascinated by this scenery all your life, "for life" represents the duration of the action of fascination. My questions are: Can this sentence only be used after the previous sentence describes the charm of something? If I want to express people's obsession with life itself, can I use "hooked on life"? Your reply will be greatly appreciated! | 0 |
I've recently read about a subject field called "Boolean differential calculus", which discusses changes of Boolean variables and functions. This subject defines the derivative of a Boolean function, its minimum/maximum, etc. While the field sounds very interesting, I couldn't find much about its applications. I found a book by Steinbach and Posthoff called "Boolean Differential Calculus" which describes applications, but it's under a paywall. For any of you familiar with the subject, what are some interesting applications that can be done with it? I would also be interested in sources that are open-access. Thank you in advance! | 0 |
I don't have any physics background aside from intro physics so apologies if my question sounds very shallow. If lens power is based on focal length, but our eyes adjust its focal length based on the distance of the object we are observing, how do we know that our lens prescription is correct for all distances? Most eye tests I have done involve focusing on objects at a far distance. If our lens prescription is based on focal length when we focus on objects at a far distance, is it incorrect to be using this prescription when doing near distance work? | 0 |
I'm curious, if based on what we know with Newton's law, can we determine if a random planet, knowing it's mass and gravitational pull, can hold a moon in it's orbit. Or to phrase it another way, is there a gravitational force "range" in universe where if a planet has a force less than that range, a moon won't stay in orbit and just escapes and if the planet has a force more than that range, the moon is pulled into the planet. | 0 |
Let's say we have an undirected graph G, where V = number of nodes and E = number of edges. In this graph, there are vertices with odd degrees as well as even degrees, but I have to transform the graph to one with only even degree nodes and I can do that by removing some edges. How do we find the number of ways to remove the edges so that there are no nodes with odd degrees left (this could also mean removing all edges altogether)? Thanks a lot! | 0 |
The elongation of light waves occurs not because galaxies are moving away from each other, but because light waves are stretching along with the fabric of expanding space (cosmological redshift). Although the Milky Way is held together by gravity, space expansion occurs everywhere, including within the Milky Way. Since space expansion occurs in the Milky Way and light stretches due to space expansion, why don't we observe cosmological redshift within the Milky Way? | 0 |
In the derivation of potential energy of two-point charge system, we define the potential energy of the system as the work done in giving both charges to their present configuration, and while doing the derivation, we assume the work done in bringing the first charge to its desired configuration to be zero, but I think it shouldn't be like that. Why is the force = qE acting on the first charge due to the second charge being ignored while calculating the work done in bringing the first charge to the desired configuration? | 0 |
How can I learn General Relativity? Am a undergrad student, who happens to be interested in general relativity. I want to learn it by heart. What are the prerequisites for it? As a fresher who just got into undergrad, what resources are best for me? Feel free to suggest any YouTube playlist which can help me understand the math of relativity and any book that teaches me from scratch presuming I know nothing. | 0 |
I'm doing 'longitudinal' qualitative research, and to avoid continually being accused of assuming that I will find change, I need a term that covers both change and stasis - so I can say that I'm looking for instances of [change-or-stasis] in particular areas of experience over a particular period of time. One researcher gets round this by saying that stasis is a type of change, but I'm not sure that works. Any thoughts gratefully received! | 0 |
I have been curious about intuitionistic logic for some time and I want to know about it and I have a question, the law of the excluded middle and double negation elimination seem completely logical to me and I think they are always correct. But intuitionistic logic does not accept these two laws. What is the cause of this? Are there really propositions in mathematics for which these two principles do not hold? If so, please give examples of propositions that are examined in intuitionistic logic and the law of the excluded middle and double negation elimination does not work in them. | 0 |
I have been trying to get my head around this proof, but i just don't manage to do so. I am ok with the first two lines, it is just the definition. But on the next line, how is Cauchy-Schwartz inequality exaclty applied? And on the next line, I also don't understand how is Taylor's Theorem used. Update: I just managed to figure out the usage of Cauchy-Schwartz. But I still don't understand how Taylor's Theorem was used. | 0 |
The Nyquist limit for interpolation by trig functions states that one must give at least two data points per wavelength, because data just above and just below this "folding frequency" cannot be distinguished. I am currently playing with Hermite interpolation, providing the first few derivatives as well as the function values, and find that the Nyquist limit no longer applies. This cannot be a new observation, but I don't find anything about it online. Maybe I have not got the appropriate vocabulary? | 0 |
I've been reading a lot of various classic literature, and at times there is the sort of casual misogyny or racism that was commonplace and (within certain cultures) the social norm at that time. Such things are no longer so commonplace and generally aren't tolerated. I wish to have a concise adjective or noun to describe those things when discussing them that isn't so oblique and timid as "outmoded" or "archaic", but I cannot recall one nor find it with my (perhaps feeble) attempts to search for it online. Has anyone come across such a word? If not, I'm open to a suggested synthesized word or a potential loanword that might one day make it into a dictionary if we use it enough. | 0 |
I wonder how can I constuct a sphere inscribed in a tetrahedron using GeoGebra? I've thought I can construct it using the intersection of three planes bisecting angles between some pairs of faces in a tetrahedron, but when I contructed it, it didn't seem to work. Is this construction valid and I made some mistake while constructing the planes, or is it not a proper construction? If it is the latter, what is the proper way? | 0 |
If amber and cloth are rubbed together, it is known that some electrons are transfered from cloth to amber. In this case, cloth acquires a positive charge and amber a negative charge. If these two have opposite charge, shouldn't there be electrostatic force between these two ? So, the next time you rub these two items, shouldn't the electrons be transferred from amber to cloth? | 0 |
A solid sphere rolls without slipping up and then down an incline. Why does the static friction force point up the incline both when the object is rolling up and also when it's rolling down? I know it's necessary for the force to point up when the object is rolling up, because then it's the only source of torque on the object, and for the object to roll back down the incline, there must be a torque which acts in the opposite direction of the initial angular velocity. However, I don't understand why this is the case. Why does the force need to point up the incline to create the necessary torque, particularly when the object is rolling back down the ramp? | 0 |
"Mill" is usually used to describe the process of making flour (grinding), to describe a wind or water mill, or a factory. Since the process of milling or grinding consists of making small pieces or powder out of objects, I was wondering if the word "mill" can be used figuratively as in kill, destroy, obliterate or tear to pieces? For instance, in the context of a competitive computer game, would it make sense to say something like "I was milled" as in "I was obliterated" when losing a game as a kind of way to add a bit of color to the expression? | 0 |
According to the S-B Law, an area of mass will radiate out heat energy equal to the fourth power of its temperature in degrees Kelvin. If energy cannot be created nor destroyed, how can a body give off more heat than it receives? I understand how a magician seems to make a pigeon appear from nowhere, but I can't understand how so much more heat is being radiated out than was absorbed by the mass. How is this possible? | 0 |
I'm going to take an introductory class on dynamical systems at the level of Guckenheimer & Holmes, or Arnold's ODEs book, but I don't have any topology background. I know analysis at the level of Stein's Fourier and Complex analysis, but have not had exposure to full-blown measure theory or manifolds. Is there a book that covers basic point-set topology in an accessible manner but perhaps without unneeded generality? Thanks! | 0 |
I'm reading through the paper "Lagrangian Intersection and the Cauchy Problem" by Melrose and Uhlmann, and I'm having trouble with the definition of intersecting pair of Lagrangian manifolds. I am aware of the definition of conic Lagrangian manifold, but what is a conic Lagrangian manifold with boundary? Do we require the boundary to be isotropic or is it that if a conic Lagrangian submanifold has boundary then the boundary is always isotropic, or do we just define it to be such that the interior is a conic Lagrangian submanifold? | 0 |
I have a circle and a line with the length of its circumference. One end of the line is attached to a point on the circle circumference, forming the shape of the lowercase 'b'. Now, the line begins to wrap the circle clockwise, until it completes one revolution around the circle, where there's no more "line". What is the path created by the free end of the line? | 0 |
I've always thought of a transformation as "the movement of a mathematical object through space", but I found this definition that seems to be better: "An operation that changes the status of a (mathematical) object to another state." Does anyone have a better definition that works for both dilations and isometries and also with more advanced math like linear transformations? Or, what would be the best way to combine these definitions? Is the "space" part important? | 0 |
The proof is quite obvious but how do you write it down nicely? I have this problem a lot with graph theory proofs where I don't know how to write them down so that they are rigorous enough. The proof itself would go something like this: Let C be a cycle in G.If we remove the edge e = {u, v} from C then C becomes a path between u and v. C is still connected so G is also still connected. | 0 |
I am looking for a word that describes advice that is too obvious to be helpful. Imagine asking for advice, and someone responds with simply saying to "do what is desirable" or "avoid what is undesirable" in the context of the advice. For example, if you asked someone for exam prep advice, and they simply said "don't fail", or if you asked for advice in marathon preparation and someone said "don't get tired". One might use the adjective as follows: "Please spare your ____ advice" | 0 |
I'm not a physicist so I'm asking you guys. We have been told that a device ("medical"...) uses a laser to irradiate a biological body (human, animal,...). The laser should apparently penetrates through metal and concrete (without destroying it). Can a laser penetrate through metal, concrete, ... without destroying the material? I don't believe that. After all, laser is light and light does not penetrate through steel or concrete. Except it's super thin, so the density would not be enough. Am I right with that? Thanks! | 0 |
I've only started my own studies on grammar recently and as I was reading CoGEL by Randolph Quirk, I came across this category called 'Catenative verb constructions'. According to the analysis used in the book, catenative verb constructions cannot be interpreted as verbs followed by a nonfinite clause acting as a direct or prepositional object. However, 'manage to' is also included yet when I look up the dictionary, 'manage' can be transitive even when used with the meaning 'to succeed in doing something, especially something difficult' like in these examples: In spite of his disappointment, he managed a weak smile. I don't know exactly how we'll manage it, but we will, somehow. Shouldn't 'manage to' be listed elsewhere then ? Or am I misinterpreting something ? | 0 |
I am trying to use the Poisson process for BLE(Blueetooth Low Energy) neighbor discovery. In this context, there are two devices called Advertiser and Scanner. The advertiser and scanner emit and listen to beacons in a duty-cycled fashion. This leads to longer discovery latency sometimes and I want to use the poisson process for the scanning and advertising patterns and prove the discovery is going to happen. Basically I want to merge two poisson processes and make sure there are two events within a small interval delta. | 0 |
I recently used a shear interferometer for aligning two lenses in an optical setup (a Galilean beam expander to be precise). I was able to align the lenses such that the vertical stripes were perfectly vertical (i.e. the beam is collimated). But I noticed that the image showed slight fanning: With fanning I mean that the stripes seem to be expanding when going to the right. Does anyone know which type of aberration causes this? I'm using this shear interferometer: | 0 |
Is it possible to find the highest "noise" value along a line segment defined by two endpoints within a Simplex (or Perlin) function by using an equation? The reason I ask is to avoid expensive ray marching. It's fine if there are multiple points along the segment with the maximum value. It would be preferred if it could work with multiple octaves of Fractional Brownian Motion as well. I'm fairly certain it's possible but it might be too difficult to derive. Corresponding code for the simplex (snoise) function can be found here. I've added a rudimentary image to show what I'm trying to do here :P | 0 |
I have a background in acoustics and do more and more of quantum mechanics. I wonder why don't we use more often the bra-ket notation in acoustics and vibrations like in quantum mechanics? In modal analysis, we deal everyday with Hilbert spaces, inner products and linear algebra so I think that it would make sens to use the notation in the same manner. Is it because the notion of state vector is less important in those contexts? | 0 |
Reading through wikipedia's page on international law, I noticed that there is never a definite article "the" before the phrase. It is a set of rules, norms, and standards generally recognised as binding between states, so it should be quite a definitive thing, right? So why is there no definite article? Compare: the constitution, the second amendment, the Bill of Rights, the Defense of Marriage Act, the Non-Proliferation Treaty. | 0 |
Is there more than one definition to "polarization" in the context of waves? In some cases, I've seen the term "direction of polarization", which I presume it refers to the direction of oscillation. In other context, I see this word use as a process of turning unpolarized waves into polarized waves. Also, there are times whereby people say that "polarization only occurs in transverse waves", which implies that polarization is a property/phenomenon of transverse wave. So is polarization a property, a process, an adjective to describe the direction of oscillation, or is it all of the above? Is there any other definition of polarization I'm missing here in the context of waves? | 0 |
I am studying about fibre bundles. If a fibre bundle is locally trivial then I understand the fibres are locally isomorphic. Also I understand that any compact Hausdorff base space cannot have a disjoint finite open cover for if I have a disjoint finite open cover then base space is disconnected. My question is, if my base space is connected, then are all the fibres isomorphic to each other? | 0 |
I have been watching videos of WIMP's and have a simple question.. The larger the particles, the shorter their lifetime. A top quark is so massive that it cannot form a "stable" bond with any other particle to form a meson or baryon. If WIMPS are too massive to make in a particle accelerator, how can they still be around today to affect gravity of galaxies? Wouldn't they have decayed by now into things we could see or detect? | 0 |
I have an enclosure mounted to the chassis of a vehicle. There are multiple points where the enclosure is fastened to the chassis as well as areas where it rests on the chassis without being fastened. Is there any point in putting vibration pads on the areas where the enclosure rests on the chassis? Logically I feel like anything fastened rigidly to the chassis would vibrate the same as the chassis. | 0 |
Could anyone help me to understand the difference between the usage for and to in the below sentences. They will be more interested in the struggles of the downtrodden, in those who are fighting to obtain the title deeds for respectable humanity. They will be more interested in the struggles of the downtrodden, in those who are fighting to obtain the title deeds to respectable humanity. Ideally, both the sentences are correct, however the preposition for is mostly followed by a noun whereas the preposition To is mostly followed by verbs. So, why is "To" correct in the second sentence in comparison with the first sentence? | 0 |
On plotting the angle of deviation vs the angle of incidence for a prism, we find that the graph dips only at one point. It is this result that is later used to prove that for minimum deviation to occur in a prism, the angle of incidence must be equal to the angle of emergence. But why exactly does the graph have only one minima? Are there any mathematical or physical reasons behind this phenomenon, or is it a purely empirical result? | 0 |
In his famous hit Working Class Man, Jimmy Barnes sings: He believes in God and Elvis He gets out when he can He did his time in Vietnam Still mad at Uncle Sam I can't make sense of the second line. What could it mean? What does he get out of? I thought that the line in question might be some idiom or slang known among workers, so I looked in dictionaries, but found no idiom or slang that would fit the context. Maybe it's something obvious to native speakers, but I am not one. I humbly hope that users of this SE can shed light on this mystery. | 0 |
I am a beginner to Lie groups and Lie algebra. Recently, I learnt that the dimension of the Lie algebra generated by a Lie group is the same as that of the Lie group. I have known for a long time that the space of vector fields on a manifold (even when not considered a Lie group), forms a Lie algebra. Is there any conclusion that can be made about the dimension of this Lie algebra? It seems to me that the Lie algebra generated a Lie Group (space of left-invariant vector fields) is the subalgebra of the Lie algebra generated by the underlying manifold (space of all vector fields), so their dimensions should not be the same. Any enlightenment is greatly appreciated! | 0 |
While scrolling through an online document, I came across the statement, "If charges carried by the black hole are large, the curvature at the horizon is small." How is this so? I tried to think of an answer to this. My thinking goes this way: I know curvature is related to mass. If an object is more massive, it bends the spacetime fabric more, producing large curvature. So curvature small means mass small. So how does a large charge mean a small mass for a black hole? What is the relationship between the charge and mass of a black hole? | 0 |
Is there, or has there ever been, an unambiguous word for "the leftmost extreme" or "the rightmost extreme"? Such words exist for the other two dimensions. Imagine you are floating in a cube in space. You can go up until you hit the top. You can go down until you hit the bottom. You can go forward until you hit the front. You can go backward until you hit the (back/rear). You can go left until you hit the _______? You can go right until you hit the _______? | 0 |
In an acute-angled triangle ABC, let us denote H as its orthocenter and I as its incenter. Let D be the perpendicular projection of I on the line BC, and E be the image of point A in symmetry with center I. Furthermore, F is the perpendicular projection of the point H on the line ED. Prove that the points B, H, F, C lie on a circle. I think the idea here is the circumcircle BHC is the reflection of circumcircle ABC respect to BC. But I don't know how to proceed, can anybody help? | 0 |
So, the uncertainty principle states that one can not measure momentum and position with accuracy simultaneously. However, we know from relativity that simultaneously is something frame dependent in nature, so how can we reconcile these two in relativistic quantum mechanics or even QFT? I know that in QFT we define observables in different points in spacetime such that their Lie bracket is zero, but I'm not really sure how to go from this to an answer. | 0 |
I noticed that whenever I bunch up aluminum foil (into a ball), it becomes extremely hard to compress. If I use another piece of the same amount of aluminum foil, and keep folding it in, I arrive at a much smaller volume. It is full of air and much lighter than the same shape of solid aluminum, though, it is still extremely hard to compress. Question: Why does bunched up aluminum foil become so extremely hard to compress? | 0 |
I am a graduate student in mathematics studying algebraic logic. For quite some time now, I have been meaning to study physics -- it turns out that some ideas in foundations of mathematics have found promising applications in theoretical physics (topos quantum theory and quantum logic come to mind). I want to get a somewhat rigorous picture of classical and quantum mechanics, so that I can contextualize some of the things I will be reading later on. Is there a good resource that I can use for this? I would prefer to read something that has a careful development of ideas starting with classical mechanics, eventually culminating in a broad formulation of quantum mechanics. All suggestions are welcome! | 0 |
I came across some interesting dialogue in a tense scene in a novel, Salvation Lost by Peter F Hamilton: "We'll know exactly what the other [people] are seeing and doing." "Doing and seeing," "What?" "Better grammar." "Jesus, man; keep it relevant" Though this is intended as comic relief, it has me wondering if there is any reason why "doing and seeing" is preferable to the reverse. Is there any actual guideline/grammar or does it just sound better to have the more active verb first? | 0 |
We recently attended a concert in a protestant church in England that was advertised as "free admission with retiring donations". The concert was indeed free with a voluntary (optional) donation. What is the meaning of retiring in this context? Googling without quotes gives results for people retiring from work, which is obviously not meant here, and googling with quotes returned similar events being advertised as such. | 0 |
A friend has pointed out that in an Oxford comma separated list, either every clause needs a verb, or each clause must be the object of the first verb. This seems to make sense to me, but would this mean that this sentence is a comma splice? "Next week, I will go to the gym, beach, and get a haircut." The above sentence might be ambiguous, but are there any strict grammatical rules that this is violating? Does each clause have to have a verb, like so: "Next week, I will go to the gym, go to the beach, and get a haircut?" | 0 |
Everyone knows this experiment: You mix salt and pepper and use a charged balloon to separate the pepper from the salt. I never really understood how this works. In school (long time ago) we learned that unlike charges attract each other while like charges distract each other. In the experiment the negatively charged balloon attracts the pepper. Does this mean the pepper has a positive charge? Why is pepper charged? How can I predict for given particle if the balloon will attract, distract or not interact with it? | 0 |
I have often read that our universe was once small enough to be subjected to quantum mechanical effects, potentially altering how our universe turned out. This is a large theme in Laura Mersini-Houghton's Before the Big Bang. Michio Kaku also mentions this in his book Parallel Worlds. What exactly are they referring to? The initial singularity? The observable universe shortly after the big bang? The inflaton particle that inflated space giving rise to our universe? It is my understanding that the universe might have always been spatially infinite after emerging from the initial singularity so I'm not quite understanding what aspect of the universe was subject to QM. | 0 |
I have started to study formal languages, especially finite automata and regular languages and I encountered some difficulties, i.e. Is this true: Automata will be called isomorphic if, by changing the names of the states, one moves from one automaton to the second. Let be a regular language. How can I Prove that all minimal automata for the language are isomorphic? Thank you for any hints and answers! | 0 |
I am dealing with a PDE and I am trying to characterize the solutions: Galois differential theory might be of help, but I can only find books about this theory applied to ODE. Are there resources, books or papers, on the application of Galois differential theory to partial differential equations? I know the basis of the Galois differential theory applied to ODE as explained in Magid's Lectures on differential Galois Theory and Galois theory of linear differential equations by van der Put and Singer, and I am looking for something along the same lines, but maybe with more examples and at least at the graduate level. | 0 |
If I have two identical magnets of equal strengths producing equal repulsive forces between them, and if I replace one of the magnets with a stronger magnet (everything else remaining the same), how would the forces on both of them change, i.e. will they exert equal repulsive force on each other or not? Why? Also, does the size or strength of the magnet affect this conclusion? In other words, replacing one of the magnets with a significantly larger or stronger magnet will produce uneven/unequal forces on both the magnets? | 0 |
Lately, I observed a rainbow-like ring forming in my window during nighttime when the light enters from a street lamp. Interestingly, the sequence of colors in the rainbow seems to be reversed from what I anticipated. Normally, I would expect the inner part to be red and the outer part to be blue due to the greater refraction of blue light (like a sun halo). What could be the reason behind this color reversal phenomenon? Edit: To clarify, the window has a decorative film on it which causes the rainbow. The core question is still the same: Why would blue be on the inside and red on the outside? | 0 |
I am trying to understand the logic of negative exponents and I stumbled upon the video "Negative Exponents" by YouTuber JLC. He says negative exponents are "defined". But why is it defined the way it is? Is there some kind of international agreement or some kind of international organization that maintains this definition of negative exponents? What if I make my own definition of negative exponents? Please enlighten me, many thanks. | 0 |
I am trying to figure out what this phrase deconstructs to. Does it imply a logical OR, like: "attention-deficit disorder" OR "hyperactivity disorder"? For additional context, there are different types mentioned here: There are three main types of ADHD: Predominantly inattentive presentation. Predominantly hyperactive/impulsive presentation. Combined presentation. ...which seems to indicate that it is always both, but a little more of one than the other. If this is the case, does the grammar check out? Also when it is spoken as: "attention deficit hyperactivity disorder", or abbreviated as "ADHD", the slash is dropped, which loses meaning and adds confusion. Would there be a better way to phrase it? Would there be a better way to say it? | 0 |
Does anyone know a simple and accurate way to measure the size of an iron core using a magnetic sensor? Imagine having a collection of identical iron plates. I expect the strength of the magnetic field around the core to increase with its size. Would it be possible to determine the number of stacked plates by measuring the magnetic field strength using e.g. a Hall effect sensor placed on top of the staple? Are there better sensors/methods? | 0 |
This sentence is an excerpt from The Economist website. The Kremlin denied the advance, saying that Russian troops had repelled Ukrainian attacks in the region. What is the grammatical rule that's governing the "saying that Russian troops had repelled Ukrainian attacks in the region" in the sentence above? I've been looking into the types of clauses to find any applications that match this, but I think I'm lost. | 0 |
I am wondering if anyone happens to know the computational methods - and hence the computational complexity - of simulating the distribution of an electric charge (how electrons distribute) over a surface. In particular, I am curious about the computational difficulty in simulating the distribution of electrons over a highly asymmetric and non-uniform surface (like the surface of a rough rock). How does the simulation complexity scale with the complexity of the surface and the precision/accuracy of measurement? | 0 |
I am trying to write a proof regarding the following question and am stumped on this particular version of the problem. I believe that I have written a correct proof when asked if the columns of A are linearly dependent. That is solved by showing that the non-zero vector y can be used as a nontrivial solution of linear dependence. But I don't really know how this information translates when analyzing the rows of A instead. I tried to look for a counterexample that IS linearly independent but cant find one. | 0 |
I've recently read that what most people learned to think of as the 'speed of light' is actually the 'speed of causality', and that light just happens to travel at that speed (through free-space.) I'm also aware that light travels measurably slower through transparent materials such as water or glass. This leads me to ask: is light traveling slower through such materials, because the speed of causality is reduced in such materials? And if so, what does this tell us about how the speed of causality is determined by permittivity and permeability of various materials? | 0 |
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