darklight03/StackMIAsub huggingface dataset:
Connes's non-commutative geometry program includes an approach to the Standard Model that employs a non-commutative extension of Riemannian metric. In recent years I've heard physicists say that this approach does not hold significant interest in the physics community. Is this, in fact, the case? If so, why? I do not mean for this question to be argumentative, but instead would like clarification.
We were taught at school that if we want to make something plural, we should add "s" at the end. Later on, I learned that there are uncountable nouns. Not so much familiar with it. Can you please give some examples?
I learned how to use bibtex from the LaTeX wikibook, found here. They say that to compile a LaTeX file that uses bibtex, you need to call pdflatex once, followed by bibtex, followed by two more calls to pdflatex. I'm wondering: what's actually going on at each of these steps? Why do I need to run pdflatex and bibtex in that order?
If physics is the study of the physical universe, wouldn't that mean chemistry, biology, neuroscience, zoology, history, economics, sociology, etc, wouldn't they all be subfields of physics? I believe they are. If anyone can convince me otherwise with a good argument, the answer will be accepted.
I need to figure out this property of Hermitian / Orthogonal projections "A is a Hermitian projection if and only if it is an orthogonal projection" Your assistance will be highly appreciated. Thank You
Photons travel at the speed of light. Is there a known explanation of this phenomenon, and if yes, what is it? Edit: To be clearer, my question is why do photons travel at all. Why do they have a speed?
I'm having some problems determining which of the following is more grammatically correct: The season that I like the best is Winter or Winter is the season that I like the best I know that both are technically correct, but when would you use one over the other?
One of the requirements of my English final includes removing all prepositions from a previously written essay. I'm having trouble getting rid of prepositions like "to", "in", "of", and other common preposition that seem like a requirement in writing. Could someone point me in the right direction? Thanks.
I recently came across this proposition that the eigenvalues of a product of square matrices are invariant under cyclic permutation of the product order. Is there perhaps some group theoretic way of proving this proposition? I've tried a few cases and it seems to be true, but a direct proof has proven elusive. Or is a proof not so simple?
I've read that the characteristic function of a probability distribution always exists because it's bounded. However, the characteristic function is still Taylor expanded in terms of the moments of a given probability distribution. Given the the moments don't necessarily exist, why is it that the characteristic function still exists?
I'm trying to wrap my mind around the semantic differences between the words "Register" and "Apply". For example, are there any real differences between these two sentences: "I will apply for this event." "I will register for this event." What is the best way to think about the meanings between the two words?
From my experience, it seems that although unstable is more commonly used, instable is often preferred in engineering and scientific contexts, e.g. "aircraft instability", "instable algorithm". Are there any differences in the implied meaning of the two terms? Should unstable be preferred?
I saw a few groups on the web. A group's name is "Non alcohol ~" and another one is "Alcohol free ~". But I don't know the difference between "non alcohol" and "alcohol free". I think that "non alcohol" and "alcohol free" have the same meaning. Am I right?
In fluid mechanics the terms 'pure straining flow' and 'pure rotational flow' are often thrown around (see e.g. here). I have tried looking for a formal definition of these two but have not been able to find one (or in fact anything you might call a definition). So how can we formally define these two terms?
In the spin Hall effect, electrons with different spins accumulate in opposite directions without any external magnetic field. Broadly, the reason behind this is the spin-orbit interaction. But, the question is how? How does the spin-orbit interaction leads to this. A physical explanation will suffice.
Is there any connection between fluctuation dissipation theorem and Kramers-Kronig relations? They are often described together under linear response theory but I do not see any exact connection (like one being special case of another).
The force of gravity is constantly being applied to an orbiting object. And therefore the object is constantly accelerating. Why doesn't gravity eventually "win" over the object's momentum, like a force such as friction eventually slows down a car that runs out of gas? I understand (I think) how relativity explains it, but how does Newtonian mechanics explain it?
I am trying to find the equation for the form that is in the picture. Basically it is an infinitely extending roller coaster loop. I just can not find the magic words in Google. Any suggestions? What is it called? What is the equation?
When referring to a U.S. state in a formal document, is it correct to capitalize "State," or should it remain uncapitalized? For example: This school is accredited by the State of Maryland OR This school is accredited by the state of Maryland
I have a doubt about the Hermite Spline. Is it the interpolation with the minimum value of curvature among the possible interpolative functions between two points? Is it possible to demonstrate it? Thank you very much!
Dirac delta function can be defined in several ways. I know two definitions. One is as a distribution and the other is as a measure. I found many materials on the derivatives of delta function as a distribution. However, I couldn't find materials dealing derivatives of delta function as a measure. Could someone point me at any materials or explain it?
Would you please tell me which of these four sentences is correct one? I am so confused with them :( Action movies are three times as popular as comedies for men. Action movies are three times more popular than comedies for men. Men watch action movies three times as many as comedies. Three times as many men watch action movies than comedies.
I'm aware that the Milky Way has a dark matter 'halo' around it, presumably a spherically symmetric distribution. But I'm completely ignorant regarding the theories explaining dark matter... Is there any reason to not expect a star-sized object to also be made of dark matter? I know they'll be extremely difficult to detect, but I'm wondering if it's even physically possible to exist.
How many triangles in this picture: I know that I can just count the triangles to solve this specific problem. I would be interested to know if there is a systematic approach to doing this that can be generalized to larger diagrams of the same type.
I'm having trouble obtaining the answer for this practice-test problem. I'm taking the volume of the whole cylinder as if it weren't cut then subtract the portion cut off. But I'm not getting any of the answers below. Any hints will be greatly appreciated. Thank you all.
After listening of some lectures of Leonard Susskind about black holes, he mentioned that conservation of information is one of the foundations of physics. After searching the web I cannot seem to find how we came up with this theory. Could someone explain how we know this is true and/or how did we come to this conclusion?
According to a book I'm reading, the Fourier transform is widely used in quantum mechanics (QM). That came as a huge surprise to me. (Unfortunately, the book doesn't go on to give any simple examples of how it's used!) So can someone provide one please?
I want to know if I can determine the time where the sun's azimuth is at a given value. In other words, I want a function that takes the sun azimuth along with longitude or time zone and outputs the time. Is there anything like this?
After reading definitions of universal and k-universal (or k-independent) hash function families, I can't get the difference between them. Also, I couldn't find any examples of hash function families being universal, but not k-universal (it's written, that k-universality is stronger, so they must exist). Could you please clarify the subject to me, or give a good piece of literature/articles to read about it?
A recent arXiv article measures the variation of gravitational potential in a local region around the solar system, and from that it tries to infer the mass density. Are there any valid counterarguments to their conclusion, i.e: that there is no dark matter near our vicinity?
I rarely need the ancillary files TeX produces when compiling a document (.aux, .log, .out, .synctex.gz). In fact, I've only ever had to read the .log, and that's only a few times. Is there a way to write them to a separate directory, so that my working directory only contains .tex and .pdf files?
I'm looking for a package in which you can create nice bar and/or line charts in LaTeX. Currently I'm plotting the charts in Calc (OpenOffice), export it to a PDF document, crop it and then including it as graphics. I reckon there should be some more efficient way of doing this, preferably entirely in LaTeX.
In special relativity, when two observers move in respect to each other, each observes the other's clock tick slower. An observer floating in space far from gravitational fields, observes earth clock ticking slower; at what rate is the clock of the floating observer ticking as observed from earth?
Where does the word "crack" originate from in the phrase "Give me another crack at that"? Curious to know if it's in reference to driving horses? Perhaps a derivative of "craic" in Irish? Or in a structural metaphor about material splitting? Cheers.
Do you use a question mark when a sentence starts as a question but then turns into a statement? For example, "Can you explain this to me, because I don't understand the second part." "What did he just say, because I couldn't hear him over the noise of the television." I usually use a period but don't know if that is correct.
I'm trying to use different distance metrics like Euclidean, Manhattan, cosine, chebyshev among other distance metrics in my k-means algorithm to calculate distances between the data points and the centers. In what situation would one distance metric be more useful over the other in a clustering scenario? [Comparing all the above mentioned distance metrics]
Let I be an open interval that contains the point c and let f be a function that is defined on I except possibly at the point c. Suppose that lim |f(x)| as x->c exists. Give an example to show that lim f(x) as x->c may not exist. Not really sure of an example for this?
I'm modeling the flight trajectory of a golf ball, and using angular velocity to calculate the Magnus force. Currently, I'm assuming angular velocity to be fixed throughout the ball's flight. How accurate will this be? How much will the angular velocity of the ball be affected by air resistance?
I got really confused about the graph of the relationship between wavelength and intensity of black body radiation. What does the peak stand for? And what does the graph tell us? How can we analyze it?
How would I go about computing the volume of an ellipsoid with spherical caps removed and a cylindrical hole through it? I'm thinking about finding dV of a cross section (the ellipsoid has a circular horizontal cross section). Would this be the best way to go? I need to find if the volume is dependent on the radius of the sphere.
I'm looking for a proper English word to say "conversational partner". Is "interlocutor" a word an average person would understand? Are there any other words or shorter expressions which could describe a person you are having a conversation with, but who is not your friend and is basically unknown to you?
Is there a polynomial time algorithm that gives the extreme point as output for which objective function is minimized/maximized ? I am not looking for any solution that minimizes/maximizes the objective function, but an extreme point of the feasible region for which objective function is minimized/maximized.
I have read that in projectile motion both vertical and horizontal components are independent of each other but i don't get it that how it is possible i think that they are dependent. If they are not could someone explain with a mathematical relation.
On a yoghurt advert, the voiceover claimed that you have infinite combinations with it. However, given that there is a finite amount of matter, is it possible to have infinite combinations with the yoghurt or just a very large number of combinations?
In the Lagrangian path-integral formulation of QFT, an anomalous symmetry is defined to be a symmetry of the action which is not a symmetry of the measure of the path integral, and therefore not a symmetry of the partition function. How do we define an anomalous symmetry in the Hamiltonian formulation of QFT, where this is no path integral or partition function?
Speaker A: We want to ask you some questions. If you don't mind, of course. Speaker B: [He opens the door of his house] Sure, be my guests. Is the idiom being used correctly? If not, what would be a better alternative?
He missed out several important facts. He omitted several important facts. I think these two sentences are the same meaning. Is there a slight difference? A few days ago, an American native speaker explained to me that "omit" means intentionally take out whereas "miss out" means mistakenly take out. Is it true? Could anyone clarify the difference to me?
There are several PR firms, lobbying groups who specialize in mud slinging, making wild allegations on behalf of their clients. Is there a word that describes such a person whose job is to make allegations against others?
I looked all over but could not find anything. Is there a package out there that has a symbol/dingbat of a calculator? I know there probably isn't, but I've seen much stranger stuff out there before...
Suppose there are two light beams. One is red while the other is violet. The energy of both is the same. Which one of these beams has a larger number of photons, or is the number of photons relevant?
I am sure there has to be a more precise word to describe a person that is not giving up on her beliefs no matter what other says. You could say consistent in her beliefs, but I am looking for something more elaborate. An example of such a person might be Margaret Thatcher. Thanks
What is the origin of the idiomatic expression rub someone the wrong way? Is it correct to use the idiom in reverse, i.e. rub someone the right way, possibly meaning to calm or to please?
I know of at least three equivalent formulations of QM: The "normal/standard" one, dealing with Hilbert spaces and state vectors. The Feynman path-integral formulation. The Wigner-Weyl phase space formulation. My question is: what is the usual name given to the first, "normal" formulation that everyone learns as an undergraduate?
I know the differences in the meaning of word "trash" and "garbage" but how about "take out the trash" vs. "take out the garbage"? Can both these expressions be used interchangeably? What is the difference in meaning if any?
My textbook states that "Laser communication is much faster than microwave communication." But, how can that be? Both are electromagnetic waves with different frequencies but, how can the speed be different? Or Is the statement referring to any kind of processing speeds involved?
I might be mistaken, but I feel odd calling the following "wooden handrails", since handrails are supposed to be made of metal. Is it OK to call it "handrail", "guard rail", or a "wooden handrail"? Or is there a better term for it?
Today, my teacher proved to our class that every convergent sequence is a Cauchy sequence and said that the opposite is not true, i.e. Not every Cauchy sequence is a convergent sequence. However he didn't prove the second statement. Is there an example or a proof where Cauchy sequence is not convergent?
Is there any good word/phrase/idiom for that feeling of scorn when you're accepted by someone/something after getting rejected the first time? I remember a phrase being quoted by Nathan Fillion in Castle when Richard Castle's daughter is rejected to Stanford and later gets in. Still can't remember the lines, just the situation.
I'm fairly well-versed in calculus but I would like to explore beyond calculus. I have looked into the basics of some topics in higher mathematics such as group theory and abstract algebra and they intrigue me. I am wondering if there are any recommended methods or resources I should use to learn more about these topics. And is there any recommended starting point?
I'm a complete beginner at LaTeX, and I'm trying to typeset a complex layout. How should I go about building a page like the one shown below. Edit I was able to replicate the layout using minipages with the multicols package. The images were embedded using the graphicx package.
I came across several forums and articles saying that criteria is plural and criterion is singular. Some gave me the impression that criterion is used to denote a set of rules. What is the correct use of these two words?
I have somehow managed to lose all my document classes and hence cannot compile anything. I have tried re-configuring and re-installing to no avail. I am on a university computer and cannot edit the program files.
"If they would have been painted this afternoon, the walls would be completely dry by tomorrow evening." The quoted sentence is ungrammatical. I believe it has something to do with tense, but I do not believe that the 'if...would be' structure requires parallelism. So what is wrong with this sentence? Thank you.
Is solving problems quickly an important trait for a mathematician to have? Is solving textbook/olympiad style problems quickly necessary to succeed in math? To make an analogy, is it better to be a sprinter or a marathon runner in mathematics?
I have had real difficulty with permutation/combination questions in probability and statistics texts. What I have real difficulty with is transforming word problems into mathematical form to solve. Are there any recommendations for a good text that might help me to do this? Or any suggestions for how to tackle these sorts of problems. Thanks
Is there a word that works as a milder version of strenuous? Strenuous is defined by Oxford as something "requiring or using great effort or exertion." I'm looking for a word with a similar definition except for the "great" part.
I am confused on how to properly describe an all expense paid vacation. Is it an all expenses paid vacation or an all expense paid vacation, and are there any hyphens between all, expense or expenses, and paid? I ask because it seems to be all over the place on google search.
What exactly is meant by Lorentz invariance? Is it just an experimental observation, or is there a theory that postulates it? What quantities do we expect to be Lorentz invariant? Charge? Charge densities? Forces? Lagrangians?
I've heard many people use the term "goose bumps"; in my family, they were "goose pimples," but I don't know if this was peculiar to us, or if others also use it. My wife's family's saying for this was "Chilly bumps." Are there others? Is one considered the "most correct"?
I've read a few different explanations of how hovercrafts hover, and they all mention a low-pressure cushion of air. This confuses me though: If there is low pressure under the hovercraft, why doesn't it get sucked to the ground? Also, if air is being forced into the space under the craft, why is this air cushion not high-pressure?
It is known that in general, a mixed state can have multiple pure state decompositions. However, it has a unique eigendecomposition in the absence of degenerate eigenvalues. What is the special significance of this eigendecomposition over other pure state decompositions for the same density matrix?
As the title suggests, Can the effects of a person's mass upon the local gravitational field be detected and measured remotely? I am aware any mass produces and effects gravity but couldn't find anything in my searching if it is possible or theoretically possible to detect this effect remotely.
I used to pronounce 'detail' as ['di:teil] with accent on the first syllable. However, these days I hear people (and on the radio) say [di'teil] with accent on the second syllable. Is my pronunciation incorrect? Is there a regional preference for this?
I'm a high school teacher and someone asked me this in my class, and to be honest I'm quite stumped! I haven't done any high level math in such a long time, and I'm really not sure how to approach this. Is the solution even approachable to a highschool student? Thanks for the help.
I am going to learn some math about functionALs (like functional derivative, functional integration, functional Fourier transform) and calculus of variation. Just looking forward to any good introductory text for this topic. Any idea will be appreciated.
That would not have happened if John had completed his work. That would have not happened if John had completed his work. The former seems correct. The latter doesn't seem incorrect. Are there any cases where one ought to use the latter instead of the former?
For example I've written: "I have an interest in rock climbing and am a member of the mountaineers Society." My friend thinks it has to be: "I have an interest in rock climbing and I am a member of the mountaineers Society." which I think sounds bad. Which is right?
What is the past perfect of "have"? Is it "have", "had", or "had had"? And if it is "had had", doesn't it sound weird and awkward? when and how do I use it? Thanks.
I have a problem that I need to prove using induction. Prove that a surjective function has at least as many members in its domain as it does in its codomain. Do I begin by using the axiom of choice? Thanks.
In Arabic, the expression "Summer cloud" is usually used to mean that "this is not going to last for a long time" or "it won't last as long as you think it will". Is there an equivalent phrase in English?
So I'm essentially trying to find an explicit description of the smallest subfield generated by a subset of the field. I know that if s is an element of the subset, we must also have its additive and multiplicative inverse. Is there a succint way of describing the subfield set-theoretically? Again, the intuition seems clear, but I'm struggling with a formal description...
This morning I heard the word "constitutionality" being used by a journalist with regard to the debate over the legality of health care reforms here in the US. This grates on my British ears as I would simply use 'constitutional' in this context. Does 'constitutionality' have a different meaning? Is this a recent Americanism?
When measuring blood viscosity, the literature claims that we generally use a cone-and-plate viscometer. Why is this; is there any way to explain this mathematically in terms of the shear rate, etc? Does it have to do with the fact that the shear rate is constant in this device? Why won't it work with a parallel-plate viscometer?
What does the phrase "begging the question" really mean? And does it even matter if I use it correctly? Almost everyone just uses it as a synonym for "posing the question" these days.
Is there a good template for software release notes? I typically cover new features, bug fixes, and enhancements. I'm currently using HTML but its ugly and not easy to distribute. Ultimately, I'd like to produce a single PDF.
I've been going over the algebraic topology part of Munkres and this question has stumped me. If we have a complete metric space that is not compact, must it be simply-connected (path-connected plus trivial fundamental group)? My intuition tells me no, but I can't come up with an example.
This may be trivial, but I want to be sure I understand correctly: Is it true that the interior of a simple polygon is always a simply-connected subset of the plane? I.e, is it eligible for the Riemann mapping theorem?