darklight03/StackMIAsub huggingface dataset:
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?...
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?
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!
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?
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.
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?
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"?
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?
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.
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
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?
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?
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?
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.
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.
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?
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!
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?
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.
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?
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".
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?
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?
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.
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?
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
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.
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.
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.
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?
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).
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 ?
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.
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.
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.
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?
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.
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?
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.
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.)
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?
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?
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?
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.
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?
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.
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?
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.
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?
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?
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.
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.
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?
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?
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.
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?
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
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.)
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?
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"?
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?
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?
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.
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.
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.?
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.
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.
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?
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?
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!
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?
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)?
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?
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
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.
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?
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.