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In gel electrophoresis, there needs to be an electric field created in the gel. I realized that I have some gaps related to my understanding of electromagnetism because I cannot fully understand in what conditions a field gets created. Are the electrode plates on either side in contact with the gel or insulated, and if so, how does this affect the field? My understanding is two insulated plates with different voltages would still create a field between them. Is the issue that the surface charges in the gel would align themselves to cancel out this field on the gel inside? Thus, do you need to actually pass a current through the gel in order to create an electric field inside? I think this is related to the nature of the electric field in a current carrying wire (where I treat the gel as a really thick rectangular wire), which I also realize I don't understand. Namely, do the electrodes need to span the full width of the gel rectangle to create a uniform field across the width? More generally, what are the possible ways to create an electric field on the interior of a conductive object such as a gel? Do you have to pass a current through it from one side to the other? My other thought is that a changing magnetic flux would also create an electric field, although it would be of a odd shape. But would this induced electric field exist on the interior or also be subject to some cancelling effect as is the electrostatic case? | 0 |
Recently I saw a conversation between Sean Carroll and Slavoj Zizek concerning the MWI. One of the questions that drove Slavoj concerned with this question of Ontology vs. Epistemology, as the way Sean had described the current understanding of MWI is that we merely 'don't know' where we are on the wavefunction which seems to keep the openness of reality at the level of epistemology rather than ontology. The question I have concerns entanglement with new information that an object encounters as it is coming in from outside the object's light cone. In my understanding when entanglement-measurement occurs, some pair (or more) objects in the wavefunction take on a correlated value, but then the price of this is that other values become randomized (so electrons take on opposite spins, but then the spin of each electron is not determined). What I am wondering is as we pass from before the moment of entanglement with new information coming in from outside the lightcone to after that moment, some of the information will be consistent (or not consistent) with our current history - that information gets zipped with (or excluded from) the entanglement event, but all the sort of 'random' information that is really new... is it the case that the wavefunction of our object has a different space (or location on the wavefunction) for each of these random timelines before the encounter with new information - or is that space created at the moment of entanglement with the new information? That is... is it the case that our original object is actually already always split into all of its future possible timelines in a way such that various points on its original wavefunction can be assigned to various final 'futures' - or is that split not possible in principle or in the mathematics from the beginning of the calculation (so that in reality many futures pass through the same original point on the wave function)? | 0 |
I would like to forecast demand count time series of taxi fleets at different locations on the map at different points in time. I.e. multivariate demand Time series forecasting. Given hierarchinal demand time series. where the region level time series is the sum of district level time series at each point in time and district level time is the sum of city level time series at each point. sum of all the city level time series at each point in time should equal region level time series. There are also covariate time series (both numerical and categorical) associated with each city's demand time series. e.g. rainfall level, temperature, traffic level, taxi supply amount, date information like weekday or weekend, holiday information and Time invariant features like type of city. (e.g. industrial, CBD, residential etc. ) Note: The city level time series are quite sparse ( have many zeros). How do I go about using a bayesian framework/statistics to model and predict the mutivariate (city-wide) demand time series? The reason for choosing the bayesian framework is to estimate uncertainty in the prediction. Build a strong prior sequentially over time which can capture the fundamental data distribution/patterns without being affected by noise in instantaneous data. incorporate the various pieces of covariate information together to enhance prediction accuracy. Here are my thoughts: Use summary statistics of covariate time series and response time series like ACF to compare similiarities between and try to explain causation. Try to improve dataset quality by (probably using bayesian a hierarchical model using partial pooling) to combine sparse and low quality (lowly correlated time series to response time series) covariates to model a better covariate. Use bayesian sequential learning to sequentially accumulate learned patterns over time into the prior distribution. Could someone give me your thoughts and suggestions on how to go about doing this? Thanks. | 0 |
When a mathematician says that two categories are the same thing, they may mean there is an equivalence or an isomorphism between them. I am wondering if there is a precise way we can say that two categories that are isomorphic are different categories. I have no idea what I mean, but perhaps it has something to do with models of categories in Set. I just feel there may be justification sometimes when two mathematics feel that two isomorphic categories should be considered independently. Is this possible? Does it ever come up in discussion? For example, consider this language on modules "The concept of a Z-module agrees with the notion of an abelian groups." This language "agrees" really means there is an isomorphism of categories. It seems like the theory of categories simply deletes any way of seeing them differently, but is there another way of seeing them where one might say"No, we consider them differently!" I think this might have something to do with the way computer scientists talk about monads in a different way than mathematicians. If you've ever looked at these two literatures, they are nearly incompatible at times. This may have something to do with the notion of "up to isomorphism" in category theory. When, in category theory, do we say, "no, I won't forget details that are deleted when we work 'up to isomorphism'"? Is there category theory that doesn't work "up to isomorphism"? Which category theory concepts and constructions only work up to isomorphism and which, if any, go beyond this? | 0 |
Where from Hawking radiation actually arise? I would like to connect the answer with the technical derivation along the lines of the original calculation by Hawking (a modern account of which is given in Harvy Reall's notes). I have seen this where the three answers apparently don't agree with each other entirely. i. The first answer points out to tunneling process (whose math I would like to see) or particle-antiparticle production near event horizon none of which isn't directly connected to the original derivation. Well, the particle-antiparticle picture is claimed to be somewhat connected because we can find their mention in many "formal" places (also) including Hawking's original paper. (Somewhere else it is claimed to be wrong/heuristic). In the technical derivation in which step exactly do we utilize this "vacuum turning to particle-antiparticle pair" thing implicitly? I am actually partially convinced with Ben Crowell's answer that the radiation comes not exactly from the horizon but from a region away from it. But then a) How do we justify the use of geometrical approximation far from the horizon in Hawking's derivation? b) In an alternate derivation (for Schwarzschild black hole---not a collapsing spacetime like in Hawking's derivation) detailed in Carroll's book, the author uses Unruh temperature for a static observer and redshift it to infinity to find Hawking temperature; there also the static observer is necessarily near the horizon---otherwise we can't apply the Unruh temperature formula correctly because only the near-horizon geometry of Schwarzschild spacetime is Rindler. These two observation seems to point out the fact that the radiation is necessarily coming from near the Horizon---although the second point seems invalid because accelerated observers do Unruh-radiate in Schwarzschild geometry too. And how do we know that the particles are not coming from a time when the black hole didn't form? If we look at this diagram (adapted from Harvey's notes) used for backtracing things become more confusing (to me) Reading this would be like (according to an observer at infinity)---A wavepacket started from past null infinity away from the horizon at a retarded time after which if it had started it would go inside the hole. It went near the horizon before it's formation at very late times and stayed near the horizon for the rest of it's life while coming to us---the observer. It was joined by another wavepacket coming from infinity which started at a later retarded time, hence heading for the event horizon but got scattered towards future null infinity instead. Much of the results of the derivation follows from the change in frequency of the Schwarzschild modes due to extreme blueshifting near the collapsed matter . So apparently the collapsing spacetime(partially Maimon's POV in the linked answer)/some stuff at past null infinity created the Hawking radiation. So how do we prove that these two are not responsible and the event horizon is the culprit of creating Hawking radiation, from this backtracing framework? As mentioned above, there are reasons to believe in event horizon creating the Hawking quanta but I can't understand how that fits within Hawking's original derivation. This might seem like a duplicate of the linked question but since most of the answerers there are not active members of this community anymore and that many years have passed since the Q/A and (possibly) we have a better picture, I took the risk of reposting essentially the same question but nonetheless with new issues raised. | 0 |
Consider a loop gap resonator for electron paramagnetic resonance which has static (but sweepable) magnetic field in one direction, "x", and a GHz RF magnetic field in a direction "z" that is perpendicular to the static field." I had assumed that I had built the loop-gap such that the H_z field was constant over the sample volume. We get a reasonable EPR signature from it, can identify some hyperfine components, etc. I finally got around to doing a finite element for the field and to my surprise, the calculation appears to show that I am generating positive and largely constant Hz on much of the "left" side of the resonator and exactly the opposite Hz on the "right" hand side of the resonator (i.e. negative Hz, with zero field in the middle). I am now completely confused. I would not have thought such an RF field could give any EPR signature because the spin contribution on the left should cancel that from right. If so then my FEM model is wrong and I need to look there. But maybe not... in which case I need to look into fixing whatever is driving the wrong eigenmode because obviously I will get more signal if all the Hz is uniform. So that's my question can you get an EPR signal from an Hz which is flat over two areas of the resonator but such that the average Hz is zero? Or maybe in math terms: Given a computation of the RF field in a resonator and a theoretical spectrum of a species, how can I determine the corresponding EPR spectrum of the sample? E.g. does it depend on |H_z| or H_z ? | 0 |
In everyday talk we say things like: we must use the fundamental theorem of calculus to calculate this integral; we must use the results of analysis to proof the fundamental theorem of algebra; we must have a function that maps well formed formulas to numbers and that is bijective (Godel beta function); we must have a ring with the fundamental theorem of algebra to be able to proof this result; etc... Sometimes it seems that, when we say this, we are saying that the theorem in question must be made an axiom, then we will try to investigate what results hold with it, or without it, like in the case of the fundamental theorem of algebra. Sometimes it seems that we are saying that to proof some theorem we need to use a central theorem that mobilizes a particular set of axioms, this seems to be the case with the fundamental theorem of calculus, or the case of a theorem that say that some function or property exist and we must use it. In this last case, which is the case I am interested, it seems that the construction we are trying to make needs another construction, that in turn needs a set of axioms. But it's not the case that, if we simply fix it as an axiom, we could see what thing depends or not on it, for fixing it as axiom would turn the axiom system redundant (meaning: one or more axioms could be eliminated). So, my question is: what means to say that a theorem depends on another theorem? Is there some logical analysis of what means to say this? | 0 |
Constant motion can not be detected by neither particles (because of inertia) nor mechanical waves ( because they need a medium ). However when you consider light for example and assume it does not need a medium to travel through you could detect constant motion. For example, when someone is traveling at the speed of light in the x direction, and fire some photons in the x direction the person would see light as standing still while someone who is not moving will see the light passing at c. So why would we consider constant velocity to always be relative and so on undetectable. Clarify: Its obvious that the discovery was made, however for Einstein to actually get anywhere he needed to assume c to be constant. Which is exactly what I am wondering about, how did he come up with this. So that is why I am asking about constant relative motion and trying to come up with a thought experiment which proves the distinction between being stationary and constant velocity reference frames. However every single object with or without inertia which includes particles and mechanical waves are shown to give no proof of one or the other the one being in constant velocity. Which brings me to a light wave traveling through no medium and then would suddenly give us a way to detect constant motion, because now the so called ether wind is not causing the wave of light to go slower because the "wind" is moving in the opposite direction, no, it is now possible to say that light moves at a different speed for one of the two experiments on board the two and then proof that the one where c is slower, is the one actually moving and the one other one stationary. So from knowing this to be forbidden there is only one logical conclusion c must be constant for all observers, its the part where knowing this to be forbidden to c is constant for all observers is where I am stuck. Ps: please don't just give me a mathematical proof, this doesn't really help me, Much appreciated! | 0 |
A 'blunt' statement is when someone says things to the point and factual. But wouldn't 'sharp' (or some other word that implies frankness or sharpness) be a better word than 'blunt'? As blunt has the meaning that it is not sharp. When someone says something that is not direct or something soft (and if I am to make phrases or rules in English) then I am more likely to use 'blunt' for such a thing. All I am saying is the real meaning of the word is not appropriate(actually opposing) for the phrase. Being direct is never 'soft' and can hurt and blunt real meaning is more close to 'soft' and cannot hurt you (compared to a sharp object). Blunt: (of a cutting implement) not having a sharp edge or point. "a blunt knife" (of a person or remark) uncompromisingly forthright. "a blunt statement of fact" Etymology here points to some interesting meanings and usages but none quite explain the usage in phrases . Edit: what I am trying to say explained better in comments by other users "why blunt means what it does, when it doesn't sound like a piercing effect" The most common, physical meaning of 'blunt' is 'dull', 'rounded', or lacking edges - the antonym of this context is, as you say, 'sharp'. But when 'blunt' is used more metaphorically to mean 'direct' or 'unnuanced', the antonyms are very different. Also "Blunt knife hurts more" is creepy thinking and language usages do not take shape on those lines. It is usually simple popular opinions that turn to usages/phrases. | 0 |
According, to definition, provided, as I understand by Newton, there are frame of reference, where all constantly moving bodies keep their velocity constant, untill the force is not applied to such bodies. Some sources, in particular Russian Wikipedia inertial frame of reference article, state, that there is no inertial frame of reference in the world (translated from Russian): Absolute interial frames of reference are mathematical model, and do not exist in real world Or, for example this answer from this forum: When you ask for a "perfect" or "true" inertial reference frame you are asking for something that cannot be answered in physics. But each time sources either do not explain why, probably considering it obvious, or the explanation is not satisfying for me. I do not know, do I understand the reason correctly. Is the condition of frame of reference to be inertial applied for any time? Do constantly moving bodies in such frame should always move constantly if the force is not applied, so if the force even only once is applied to the body, which is linked with inertial frame of reference, that frame will never be intertial? Or frame can variate: for some period it can considered absolutely inertial, even in real world, for some period not? Is there no inertial frame of reference because there is no constantly moving bodies, i.e. every body have at least tiny, yet acceleration? If yes, why all bodies have acceleration? Due to mass, and the fact, that gravity force goes to infinity? Okay, I understand, that massless particle will move at speed of light, but what if there is a particle, that doesn't not affected by gravity or eletric field, i.e. will be "fixed" at space? Will it have intertial frame? Also what about particle with speed of light? Since their speed is constant, don't they have interial frame of reference? (Extra) Also, since the motion, even non-constant (i.e. with acceleration), as I understand is relative, then for some frame of reference, attached to the accelerated body, there are "constantly" moving bodies, that "actually" move with acceleration, but relatively to such frame - constantly. I do not understand why this frame is not inertial? Because, by definition, bodies should move constantly and without a force being applied to them? But how do we know is the force applied? No, if someone punches a ball, okay, but what about fields of something like this? | 0 |
I am in advanced UG (in Elec Engg). I was consolidating a mental model to help in (most of) engineering applications. I read Griffith recently. I learned that there exists no magnetic charge, (although, as Griffith said - how cute the scenario would have been, if they did.) Intuitively so; as Magnetic fields are engendered by time-variance of electric phenomenon (in field or charge (as current)), I never expected their existence. But, why the world needs a concept that is "charge"? The Gauss law, firmly relates the charge concept to the field. Intuitively, the field fluxes out of charge. It may seem that charge is engendering the field. But, let's believe in absence of such concept; the field is inexplicably (concentrated) sourced at "some" places - say S. Here is an argument - It is ambiguous whether the charge carries the energy or field. In the absence of charge concept; the field carries the energy; then the source to this energy are S. Energy is a transient phenomenon; Charge concept could represent the source to these new perturbations in the field. Coming to the title of the question. There is no magnetic monopole. Why is there an electric mono-charge? Clearly, charge represents transfer of energy from other domain of energy into electrical domain. Transfer of energy is relative. Can't we say the other half of the charge exists in the other domain of energy? (imaginary pole). I have an argument to address the polar nature of charge as well. But, I have already revulsed enough physicists here. (Excuse me, I was just thinking.) | 0 |
In Einstein's equations the curvature of spacetime and energy-momentum-pressure density are correlated. Is it clear when changes in matter energy density affect causally to curvature and when changes in curvature affect to energy density? Or can these kind of changes be non-local just as gravity correlated with matter in general? Is orbiting-like repetition needed for causality considered? I'm studying the principle of locality in physics. But the curvature of spacetime means that the fly-by has momentum of spreaded curvature of meeting bodies and those keep colliding into each other early. Where is the source of the cause? The fly-by anomalies has been mentioned. Are there any fly-by research projects that take the principle of locality into account? I appreciate answers that focus on localizing the physics so that time travel or any exotic negative energy etc. is left out. My problem is identifying on what basis something is cause or effect with gravity or when it is a non-local correlation of the curvature of spacetime. For example, gravitational waves act locally, but gravity acts non-locally in general. In which situations do changes in the gravitational field transmit causal information? Especially in fly-by passing: where is the origin of the causal information? Another case. Point-like fermion particles obey the Pauli exclusion principle. Although they appear to be free, they are subject to field forces and together other particles can "feel" tidal forces - if I interpreted correctly what is meant by "feeling gravity". Thus, the local limiting flat tangent space must be considered relative to the surrounding other tangent spaces (even if it is also point-like) and real (e.g. em) forces occur. The farther the particles are from each other, the more significant are the changing field effects compared to Decoherent interaction. How much has been loaded into the finished space-time curvature into the future without the exchange of causal local information and energy? Does it depend on the internal structure of the particles or the size, the mass? On the relationship to the dominant curvature?... | 0 |
The conservation of energy says that it can neither be created nor be destroyed, it can only be transferred from one form to another. i had this doubt in my mind for a long time that why do we need to save energy if the total energy is conserved. Energy can never be destroyed so why do we need to save energy? | 0 |
Is there something we can tell about the function, if we know that its Hessian matrix is the zero matrix? Is it concave, convex? What about quasi-concave and quasi-convex? As I am a beginner on this topic, I would be interested, if there's maybe an intuitive answer to this. Thanks! | 0 |
Why, when calculating contour integrals, we need to avoid the singularities inside the region delimited by the closed path we're integrating over? Wouldn't we need to care only about singularities laying on the actual closed path? | 0 |
I am looking for exercises/examples of "simple enough" morphisms between varieties being flat/non-flat, with solutions. I have only ever found a handful of examples, however very rarely with solutions to check my work. Any help is appreciated. | 0 |
The English word "pepper" comes from Latin word "piper". But why is there a double 'p' in the English word, when there is no double 'p' in the Latin word? Where does the English spelling of the word "pepper" come from? | 0 |
I came across this sentence: The dogs bounded past their leader. What does "bounded past" mean? I know the past tense of bind is bound. But here the verb "bounded" is used. Is the root of "bounded" different from the verb "bind"? | 0 |
Is there a point of balance where the gravitational pull of a sphere of electrons is equal to their electromagnetic repulsion? That is to say, could it be possible to create stars that are made purely with electrons and that are stable and don't fly apart? | 0 |
I initially tried to convert the whole thing into a Conditional via Material Implication but just ended up in a loop of assuming the antecedent and then using DeMorgan's. If anyone has any insight I would appreciate it. | 0 |
Does the word "alumni"/"alumnus" always pertain to a particular university or school, or can you say e.g. "history alumni" meaning all the people who graduated in history at any university (e.g. in some particular geographical region)? Would "history graduates in France" be more correct? Thank you | 0 |
In an integrable quantum system (say XXZ model), where there is an extensive number of conserved charges, does the set of local conserved charges obtained from expanding the log of the transfer matrix form a complete commuting set? In other words, does specifying all conserved charges obtained from the transfer matrix specify a unique state of the system? | 0 |
I have recently started to study quantum information theory on Nielsen and Chuang book, but in order to understand the theory better I need to solve more problems, there are in this book. Can you recommend a book or a book of exercises, where there will be problems on the topics from this book? | 0 |
By reading the first sentence in this article I interpret that, for every projective space, every isomorphism of its underlying vector space gives rise to an isomorphism of projective spaces. Is this also true for affine spaces (and their underlying vector space)? Or, at the very least, is every isomorphism of affine spaces induced by an isomorphism of the underlying vector space? | 0 |
I've been browsing through a bunch of questions here about how diagonalisation fails for Q. What I am finding hard to wrap my head around is how every bijection from N to Q, if used with the diagonalisation argument, will surely yield a rational. I can't really see how we can go about this. I'd appreciate any help. | 0 |
I can't think of any reason as to why one would have a directional derivative using a vector that's not of unit length. It would always "mess up" the derivative by scaling it by the magnitude of the vector, would it not? I tried searching online but can't seem to find any particular purpose. | 0 |
In TexStudio, one can open two or more tex files (or .bib, .aux, etc.) in the same window. But with my little experience with TeXShop so far, if I open a tex file and then a bib file, they open in separate widows. Is it possible to make all files to appear in the same window in TexShop as well? | 0 |
Is the following sentence grammatically correct? The word "if" is not used in this sentence, which I'm not sure is a mistake or not. And if anyone has a link to a reference on conditional clauses within relative clauses, that would be great! | 0 |
Specularity is a value that defines how glossy or matt a surface is. For example, a mirror is highly specular, but a brick wall is not. Is the specularity of a material a fraction of its total reflectance? | 0 |
I am relatively proficient in most material found in high school math courses but one of my weaknesses is in parametric equations and expressions; I really struggle to understand and apply them. Does anyone know of a good book or online resource written by an expert that really introduces and explains them step-by-step from the very basics? Thanks in advance. | 0 |
To estimate the parameters of a truncated distribution (lognormal for example), we can use the Maximum Likelihood Estimation or Method of Moments. For the Method of Moments Estimation, one needs to write down the mathematical expression of the expected value of the truncated lognormal distribution. Is it possible to do so? Or can we use a numerical method? | 0 |
In the textbook I am reading for class it is talking about the interactions of photons with atoms and how when an atom emits a photon it must have the same and opposite momentum of the emitted photon. I am confused on what the book means by "the atom must also have a 'recoil' kinetic energy". | 0 |
Orchestra seats are mentioned in this answer but why are seats closest to the orchestra (or stage) called "orchestra seats"? They are certainly not in the orchestra. What is the history/origin of such an expression? | 0 |
As a speaker of English as a second language, I've long been curious to know why English speakers would choose to say "Easier said than done" over "Easier to say than do". Why should it be said in the passive voice, not in the active one? Or is it simply a matter of being idiomatic? | 0 |
Forgive my naive usage of the term 'classical physicists' but what I mean is physicists who were either unaware of probabilistic quantum mechanics or refused it entirely. I am interested in whether they thought there was an infinite amount of matter in the universe, and whether space was infinite. | 0 |
The parameters is getting updated when you change the project rate. The parameters is being updated when you change the project rate. Is there a difference between these two statements? Which statement is more correct from a grammatical point of view? | 0 |
When the IV drip for a patient is completed, the patient's blood will flow back. This is apparently due to the pressure difference. However, IV needles are inserted into veins in the direction of blood flow. Hence, the blood is flowing against the direction of blood flow. Is the pressure difference so high? Can someone explain this? A non mathematical approach is fine | 0 |
I read on this page that an endomorphism of degree one of a smooth projective algebraic variety must be an automorphism. The proof uses Zariski's main theorem. My question is this: are there examples of nonsmooth projective algebraic varieties having endomorphisms of degree one that are not automorphisms? Note that for a morphism, having degree one is equivalent to being birational. | 0 |
What would you call a place or thing that's well-known or renowned but only among a locality, family, or small group? I've looked into it and have failed to find anything that fits. | 0 |
Could you please provide suggestions on how to include a list of my publications in my PhD thesis? I would like it to appear at the end of the thesis, following the "References" section. Additionally, I would like the title "List of Publications" to be listed in the table of contents, with dotted lines connecting it to the corresponding page number. | 0 |
I'm currently wondering how packages like tikz can possibly work. I've read the TeX Book and found no evidence of TeX primitives capable of drawing things. LaTeX is just a collection of macros so the use of LaTeX cannot provide this capability. Is the pdfTeX engine providing the primitives necessary for producing drawings? If yes, which are those primitives? | 0 |
Let's assume there are two observers 'A' and 'B'. B is at ground and A is moving with an uniform acceleration ('a') with respect to B. Will A be an non inertial observer with respect to B? (As we know that non inertial observers are those which are moving with an acceleration with respect to an observer). | 0 |
The ring of representations of the symmetric group is isomorphic to the ring of symmetric functions. The Schur-Weyl duality relates the irreducible representations of the symmetric group and that of the general linear group. Using the Schur-Weyl duality, is there way to find the ring of representations of the general linear group in terms of the symmetric functions ? | 0 |
I would like to know if there exist concepts of ergodicity and mixing properties for projective representations. If they do, do these properties exhibit similar characteristics to those observed in the context of unitary representations? Thank you in advance. | 0 |
HAMTREFOIL = {(G,s,t,u,v) | there exist paths s->t, s->u, s->v such that every vertex(except s) belongs to one of the paths} I want to prove that HAMTREFIOL is NP-complete by reducing Hamiltonian path to it but I am stuck in the construction part. Any tips or solutions would be great. Thank you. | 0 |
I want to make LaTeX Workshop's PDF preview fit my Visual Studio Code's theme, and I managed to change the background color of the previewed file following this guide, however if I make the background a darker color, the black text becomes very hard to read, and I'd like to modify it to a lighter color, but I'm not sure how. | 0 |
I am studying formalism of QM from the book by Griffiths. He illustrates via two examples that momentum and position operators have no eigenfunctions in Hilbert space. In that case, how can we expand a general state vector (in Hilbert space) in position/momentum eigenbasis, as the eigenvectors constituting the basis do not lie inside the space? | 0 |
I am an art student and I think my work could benefit from broadening my horizons on mathematics. I am mostly interested in Topology, but starting from high school mathematics I don't know where to begin learning. Could you give me an order of subjects to learn before starting topology? Thanks in advance. | 0 |
In UK English, the idiom "more fool me" means something like "and I'm a fool for doing so". But how might you try to understand the underlying syntax? Is "fool" an imperative here? A noun? Is the idiom an ellipsis of a longer phrase? | 0 |
Given a convex quadrilateral, and a point inside it, I want to find all ellipses that are inscribed in the quadrilateral and passing through the given point. My attempt: is outlined in my solution below Your comments, hints, and answers are highly appreciated. | 0 |
Which is considered (more) correct: wracked by [X] or wracked with [X]? Example sentences: He is wracked with grief. He is wracked by grief. The Cambridge definition of wrack contains examples of historical use of both forms. Thanks! (Apologies if this has already been asked; I searched first, but only saw the more common question of rack versus wrack.) | 0 |
The sign of the Jacobian determinant of a two-dimensional transformation tells us if the transformation is locally orientation-preserving (if it's positive) or locally orientation-reversing (if it's negative). Is there a similar interpretation of the Jacobian determinant for a three-dimensional transformation? | 0 |
Could anyone help me understand the use of 'that' in the below sentence? (I took this example from an old book) The morality of Buddhism is essentially that of the Upanishads except in the matter of forbidding sacrifice. What is the role of that in the above sentence? | 0 |
Distinguishing between distinct unitary irreducible representations is important from the point of view of distinguishing between different sorts of particles; the eigenvalues of the Casimir operators provide a way of doing this. I have never properly understood why this is the case. Is there a good way of seeing why any two distinct irreps must, necessarily, have different eigenvalues for at least one Casimir? | 0 |
Consider a location-scale family of random variables. Is the variance of a random variable within the family always monotone in its scale parameter? What if the random variable is also symmetric around zero? I would be interested in a proof or a counter example. | 0 |
Is there a theorem that states that Integer Linear Problems with a Totally Unimodular constraint matrix are solvable in polynomial time? If the answer is positive, is it also valid for Mixed-Integer Linear Problems? And in which books can I find such theorem? | 0 |
I understand that special relativity is what help creates a magnetic field in currents. But what I don't understand is how this plays into how changing magnetic fields lead to electric fields and how changing electric fields lead to magnetic fields or if special relativity even plays into this. If anyone can clear up my misunderstandings, that would be greatly appreciated. | 0 |
Recently I started learning about matrices and what you can do with them. I learned how to add them, subtract them and multiply them, but I found out that apparently you can't divide them. Why is this? | 0 |
Examples: "Two miles is too far to walk" vs "There are two miles" In the first situation, the noun is seen as singular, while the noun is seen as plural in the second situation. What is the reason that allows this noun to be both plural and singular. | 0 |
I'm reading this paper "Billiards In Polygons" by Boldrighini et al. They say that polygonal billiards have zero measure-theoretic entropy, because a given element of the configuration space is almost surely determined by its forward hit-sequence(the sequence of sides it collides with). Why does being so determined imply zero entropy? | 0 |
I know that when a cavitation bubble collapses, heat is given off and a shockwave is formed. What else happens? Is there increased water pressure in that region? Can the intensity of this implosion be measured using a hydrophone? | 0 |
I'm looking for a word to describe a person that is: always trying to treat others nicely, kindly, afraid of saying or doing something that makes others upset, never say or think about what he/she really wants, only try to make everyone happy. This word is usually talking about a child or woman that has suffered from something terrible that made them become this. | 0 |
There is a famous song called Baby I'm-a Want You. The name sounds wrong. Why is it not "Baby I want you"? Auxiliary verb "am" and article "a" look excessive in this phrase. | 0 |
What is the intuition behind Koszul graded-commutative algebras and Lie algebras? Why is it an interesting property to study in commutative algebra? I know why it's interesting in homotopy theory but what about in algebraic geometry or commutative algebra? | 0 |
Why does a changing magnetic flux induce an electric field? When a coil moves through a magnetic field, the induced emf is due to the Lorentz force. But why does a changing magnetic flux produce an induced electric field and emf even though the coil is stationary or there is no coil? | 0 |
I'm a first year graduate student in math and I'm currently studying fiber bundles. The definition is clear and I understand how it generalize concepts as (co)tangent bundles or vector bundles. What for me is unclear is why we are interested in spaces which are locally product of spaces. What is in general its usefulness? Thanks. | 0 |
I assume that the Milky Way has a dark matter halo just like any other. If that is the case, if we look at a huge part of our own galaxy, do we actually see the gravitational lensing effect? How intense is it? | 0 |
When I tried to solve some motion questions, I got complex numbers for time, displacement, etc. And my teacher said my answer was correct. Is it possible to have a complex number solution in the equation of motion? What does the complex number mean in the equation of motion | 0 |
In a, let's say rectangular container, the water surface always aligns itself perpendicular to the direction of net force acting on it. Why exactly does it happen? (For example when this container is accelerating towards left, the surface of water aligns it self in such a way that the right end of the liquid is at a higher level than left end.) | 0 |
While researching rotation curves, I've noticed a variety of velocity behaviors in different galaxies. In some, the velocity decreases, in others, it remains relatively constant, and in some cases, it increases, particularly in the outer regions. Is there a mathematical equation or method to objectively determine these patterns rather than relying on visual inspection? | 0 |
From the movie "No Time to Die": Nomi: The world's moved on since you retired, Commander Bond. Perhaps you didn't notice? Bond: No, can't say I had." Why did Bond use "had" and not "did"? | 0 |
A goat is tethered to a rope of length L. Each end of the rope is attached to a post, the two posts being distance D apart. The rope passes through a ring attached to the goat's collar and can move freely. What is area that the goat can graze? | 0 |
Is is correct to say that, elementary particles have different masses, because they have different coupling strengths to Higgs field? And if yes. Does it make sense to question, why they have different coupling strengths? | 0 |
Newton merely stated the law of inertia as: An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. How does it prove the existence of inertial frames? I see no mention of it in the original law. | 0 |
In mathematical logic, there is a notion of "predicative definitions". I understand what a predicative definition is, intuitively, but I am interested in a formalization of that notion. Has any mathematician ever formalized and made rigorous a definition of predicative? I would love to see such a definition. | 0 |
As per the conservation of mass, matter cannot be created or destroyed. Doesn't this contradict the big bang theory? Like, it states that it all started from a single point. But seeing the massive size of the universe, isn't it weird that a single point held this much debris for the formation of planets, stars etc.? | 0 |
I'm new to Tikz and I've already made a few diagrams. However, I'm having trouble making this one. Would it be possible to help me? It doesn't matter if the colours aren't right, I'm just trying to draw the central block and the two arrows marked "seuils...". Thank you for your help. | 0 |
I am looking for texts that discuss the logic of the game of chess. I am sure there are a few such texts out there. Such a text might formalize chess in first-order logic. I would be very grateful if someone gave me a list of texts on the logic of chess. | 0 |
As the title says I want to know if the result is true, ie, if a linear projection in a normed space is bounded iff its kernel and image are closed. I know the result is true if the space is complete but I cannot prove nor find a counterexample in the non-complete case. Any ideas? | 0 |
I'm a final-year physics degree student and I want to know about QFT, but my knowledge about tensor mathematics and groups of symmetries is really low, as my university doesn't offer us advanced mathematical subjects. So, would you please suggest me some books or any other resource that make it clear and easy to understand these mathematical basics and that digs into QFT? | 0 |
Consider the topological group(s) in https://en.wikipedia.org/wiki/Solenoid_(mathematics)#Pathological_properties This seems like an interesting and bizarre group. It is obviously not a Lie group and obviously not a manifold. However, I was wondering if it satisfies geometric properties like local contractibility? What about its homology groups? Is there a nice reference for the topological properties of this group? Could anyone tell me more about this group? Thanks! | 0 |
I'm currently trying to figure out a function for a real coordinate space, which satisfies all the rules for an inner product, but with which the standard basis is not orthogonal anymore. Does such a function even exist? Or does someone here know an example of such a function? | 0 |
Recently, I'm learning FFT and I want to read this original paper("Theoria interpolationis methodo nova tractata", by Carl Friedrich Gauss. ). But I can't get a valid url from Internet. Would someone give me a valid download url about this paper(or just send me that file via any viable method)? | 0 |
There are many quantum Monte-Carlo methods. Many of them can be used to calculate or estimate the ground state energy. The problem is, is the estimated energy an upper bound of the true ground state energy? We know an estimate based on a variational wave function has this nice property, but is it the case for the QMC methods? | 0 |
When we speak about Discrete random variables we have PMF. When speaking about Continuous random variable we have PDF. So my question is if we already have PDF or PMF with us then why do we use or calculate CDF, what's the intuition behind CDF | 0 |
This is a question about the proper use of the word "thrust." Suppose a freewheeling prop is turning in the wind. Is the air coming out the back (downwind) side properly called thrust? I understand the basic physics. I just don't know if thrust is the proper term to use for the air coming out the back. | 0 |
I was wondering, if I theoretically shake a magnet like a sine wave with a very high frequency (Let's say a frequency in visible spectrum), will I see a visible light coming out of it? | 0 |
I am looking for a verb with the meaning of ceasing to like something/someone. To dislike is not fitting here, as it means the opposite of like, not going back from liking something to having a neutral opinion about it. | 0 |
For a differentiable function f, we know that the gradient is orthogonal to the level sets of f. What if f is Lipschitz continuous? we know that its gradient exists almost everywhere. Is the gradient (when it exists) orthogonal to the level sets? | 0 |
I am wondering when the Legendre transformation is irreversible. I know if Y is a linear function of x, then the Legendre transformation of Y is irreversible. However ,what if Y is a multivariable function? Could anyone give necessary and sufficient conditions when Legendre transformation is invertible? Thanks!! | 0 |
I have to work with the radial velocity dispersion. Could someone help me to understand what this actually is and how I work with velocity dispersion? What happens if you multiply the radial velocity dispersion with the radius? Is this something that is often done? In which systems does the radial velocity dispersion change with the radius? How is it related to the velocity? | 0 |
I know that the purpose of differentiation is to find the rate of change of a function. But i don't really understand how this is concept can be used to find the tangent of a specific point. It would be greatly appreciated if you can explain this to me. | 0 |
You can use the Euler Lagrange equation to show how the shape of a suspended cable with no load is simply a catenary. However, if you suspend a much heavier load (i.e. a bridge) with the cable, the cable forms a parabolic shape. Does anyone know how to show this fact using the Euler-Lagrange equation? | 0 |
Where did the slang term juice/sauce for steroids come from? I suppose that it may be a metaphor because of being liquid or maybe the similarity in colour. I cannot find any information on its origin, can you help me out? | 0 |
I'm typesetting a multi-page text with a fancy frame on each page. As you can see on the attached picture, the inner corners of the frame are taking extra space and I would like to increase the margin for the first/last two lines (or for a certain distance from the top/bottom) on every page. Is there a simple way to do that? | 0 |
I'm trying to find a Scottish colloquial idiom that means that people talk too much (especially in a gossipping, hot air, or inconsequential way). Perhaps this might be along lines of the English 'more babbling than a brook in flood'. I'm ideally after an idiom, not a single word. | 0 |
I'm currently working on proving an iff statement and was wondering is it allowed for me to prove the two statements required to prove an iff statement using two contrapositive statements. (for example, I'd prove if A then B using if ~B then ~A) and similarly for the second statement Thank you! | 0 |
I was wondering if there is any connection between number theory and operator theory. Especially the applications of Hardy spaces, de branges-Rovnyak spaces, Dirichlet spaces in number theory. For example to study modular forms, and etc.Something except Riemann Hypothesis. Does anyone know any books or papers about that? | 0 |
Is it possible to separate fluids or at least alter their relative concentrations in the presence of a magnetic field if one fluid is diamagnetic and the other paramagnetic? If so by how much? Are there any studies or data on this? How could this effect be calculated? | 0 |
If someone uses the name of a book/object with punctuation in it, does one need to capitalize the word after? Do I write: In the book Who's Afraid of Virginia Woolf? the main character... Or In the book Who's Afraid of Virginia Woolf? The main character... | 0 |
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