darklight03/StackMIAsub huggingface dataset:
This question related to Why are magnetic lines of force invisible? and is motivated by a comment of @BlackbodyBlacklight, based on that, the illustrating example may depend on that linked question as context to be clearly understandable. A remote magnetic field, in the sense that it is not at the location of measurement, could influence the location of measurement in some (possibly indirect) way that allows to derive information about it's structure. This is comparable to deriving information about a remote temperature profile based on properties of the local electromagnetic field, like when using a camera, or just seeing something glow. It might well turn out that it is fundamentally impossible to derive information about a remote magnetic field, (given some sensible constraints). In this case, an Answer should ideally explain why that is the case. What is described above is roughly comparable to human perception, which was the context where the question came up originally. Therefore, I will illustrate my initial ideas in that context in the section below: Establishing the context for the question (The biological aspects referred to are part of the illustration, not directly related to the question): The motivating idea was: "We can not see magnetic fields, but that may be because it was not important during evolution to acquire this capability." Could it be possible, in principle, to "see" magnetic fields? Now, if it would have been helpful during evolution - what kind of perception is possible purely from the physical side of the question - assuming "perfect evolution". The linked question asks about seeing magnetic field lines - so could something like eyes for seeing field lines have evolved? I assume not, so we do not need to go into details whether to see them on surfaces, as lines at a fixed distance, etc. (Feel free to make creative assumptions as needed regarding how to "see") What did evolve, in some birds and bacteria, is perception of the field of Earth in terms of direction of the local(!) field lines - something like "feeling north and south". The actual question, related to physics of magnetic fields, in comparison to phenomena for which human perception exists: What are the physical constraints? Seeing a magnetic field like a fourth base color would not work - there is no radiation. Something similar to spacial sound perception? Which would mean to measure from a finite set of "local" reference points to collect measurements on a given remote locatioin. Anything better than measuring a local field vector is certainly interesting.
I have a question about adjoint operator. I have known that bounded linear operator on Hilbert space has a unique adjoint operator, but I am wondering whether there is similar existence result about bounded linear operator on Banach space? Thank you.
I am learning measure theory this semester. The definition for sigma-algebra is "a collection of sets that is closed under complements and countable unions and intersections." I wonder what does it mean by "closed under complements and countable unions and intersections." Thank you so much for your help!
I know that "callipygian" means "having beautiful buttocks"... so I was wondering if there is an English word that means "having beautiful hair". I tried googling this but couldn't find anything so far.
I'm preparing for an exam and I can't seem to figure out the reasoning behind the answer to this question. Why do they use a chi-squared test? Can someone walk me through their explanation? Thanks.
I'm looking for a good textbook for an introduction to Stochastic Analysis, preferably one that focuses on rigour. I am familiar with measure theory and basic probability theory. The direction I am mostly interested in is stochastic differential equations.
I'm terribly confused on the concept of "rank of a linear transformation". My book keeps using it, but it doesn't clarify what it means (or at least I haven't been able to find it). Is it the same as the rank of the matrix? For example, if A is a mxn matrix, what would be the rank(A)?
I've recently been working through a lot of physics problems and a lot of them say to assume that the mass of the string used in a problem involving a pulley, for example, is negligible. Why is this important? What would happen if the mass of the string wasn't negligible?
How do I properly punctuate this sentence: "I prepared, packaged, and priced beef, pork, chicken, and seafood." I am trying to say that I did those three actions to those four kinds of meat, but I am unsure of what to do. Should there be a colon or semi-colon between priced and beef?
I'm not a native English speaker, and I don't understand the meaning of the phrase "in your general direction." I have found its use in the line from Monty Python and the Holy Grail: I fart in your general direction.
This problem is taken from the book Mathematical Circles by Dmitri Fomin, et al., translated by Mark Saul and published by the American Mathematical Society. Can anyone describe what the question actually means?
I'm reading a book on probabilistic robotics and it mentions that "this probability density function is quadratic in x." I haven't heard of the phrase "quadratic in x" before. Can someone explain what it means? Does it mean that the graph has a quadratic shape?
I don't want subsections to appear in the table of contents of my Lyx document. How do I turn them off? I went to Tools -> Settings -> Numbering & TOC, but it won't let me modify anything. What should I do?
I just read this interesting interview with Frank Wilczek and he talks a couple of times about gate symmetry, without ever defining the term. This isn't a term I've come across, and google throws up a blank. What is gate symmetry, and are there any good references?
I have a LaTeX document that contains proprietary information. I need to print a version of the document that has a box around the text with a disclaimer (something to the effect of "Proprietary information of company XYZ, do not redistribute without express consent'). How can I do this? If it matters, I'm using MacTex.
Density Functional Theory (DFT) is formulated to obtain ground state properties of atoms, molecules and condensed matter. However, why is DFT not able to predict the exact band gaps of semiconductors and insulators? Does it mean that the band gaps of semiconductors and insulators are not the ground states?
I'm not a particle physicist, but I did manage to get through the Feynman lectures without getting too lost. Is there a way to explain how the Higgs field works, in a way that people like me might have a hope of understanding?
Is it possible to establish that the lines joining the mid points of opposite sides of a quadrilateral bisect each other. I attempted using mid point theorem of triangles but I couldn't prove it
I am trying to find an English translation of Camille Jordan's work "Cours D'analyse". Only the French edition is on Amazon, so since this is a somewhat specialized topic, I thought perhaps someone in this forum might know. TIA, Matt
I am currently studying Electrical & Electronic Engineering. I wish to pursue Quantum Mechanics or Quantum Computing as my research subject. Is it possible for me to do my M.Tech. and then pursue my research subject? What are the prerequisites for studying these subjects? I would be grateful if you could help me.
Prove that if the real part of an entire function is bounded so is the imaginary part, without using Liouville's theorem. In particular, is there a way to prove this using the Cauchy-Riemann equations?
I'm sorry if I ask this question at the wrong place, but I don't know a better one. I am a Master's student and I am really interested in analysis, but I also want to get into AI. Does anyone know a natural way to combine these two interests? Thanks in advance.
The title basically states the whole question..I was trying to invoke the Mean Value Theorem on it but it hasn't worked..I was wondering if I'm supposed to solve it some other way. I just need hints, please. Thank you.
This has been bugging me. Why is the lower case letter "a" used to spell "abelian group" when upper case letters are used to spell the terms, "Gaussian Integral", "Cantor set" or "Cauchy sequence"? Don't know where else to ask.
As far as I can tell, if a function is holomorphic on its domain, then it's also meromorphic and vice versa. Can someone tell me what the difference between these two properties are (if any)? A counter-example and an explanation of why it's a counter-example would be nice.
I'm reading "The Portrait of a Lady" by Henry James, and I found the following two sentences. "I suppose that after a girl has refused an English lord she may do anything," her aunt rejoined. "After that one needn't stand on trifles." What does "one needn't stand on trifles" mean?
I am making a piece of software which has the ability to send out Emails and SMS messages. My boss has asked for both facilities to go under the same heading in a dropdown menu. But I can't think of a suitable work that encapsulates both. Any suggestions?
We've all seen that label on our passenger side mirrors that says, "Objects in mirror are closer than they appear." Why is this? Further, why does it only apply to the passenger side mirror, and not the driver-side or rear-view mirrors?
Show that Lebesgue measure can be expressed as a countable sum of probability measures. I'm trying to do something with the countable additivity property in order to show this, but so far nothing is working. I don't think this is supposed to be difficult, but I'm not seeing it, so any help you could give would be most appreciated!
I'm trying to compile a LaTeX template to a PDF, but it's not working. The template is available in this link (on the right side in Article Templates). I'm using TeXnic Center. Can anyone please try to compile this and let me know if it's working.
I am trying to use Egorov's Theorem in a proof. However, I only have convergence in measure of f_k to f and uniform integrability of f_k. How can I combine these two to get convergence point wise so that I can use Egorov? Thank you so much for your help!
Is the following sentence grammatically correct? "Symptoms of lactic acid build up in muscles include cramps, spasms, fatigue and sensitivity." Does "sensitivity" need to be qualified, as in "sensitivity to touch"? Can someone point out the "rules" that come into play here?
As a student in a highschool physics class, my teacher has repeatedly told me that photons are massless. Yet, I have also heard from other sources that photons have momentum. If photons were to have momementum, that would mean that they have mass as according to p = mv. Do photons really have mass? Also, how would this mass be calculated?
I heard somewhere that the capacitance of a superconductor is much higher than regular conductors, but I haven't heard or seen anything yet proving or disproving such. So whats the truth? And why?
A colleague asked me this question, and I couldn't come up with an answer that satisfied him, so I'm wondering if anyone can help: Why does a man with a short temper become a short-tempered man? In other words, why do you need the -ed at the end? Are there any special rules for this?
Is there a path connected topological space such that its fundamental group is non-trivial, but its first homology group is trivial? Since the first homology group of a space is the abelianization of the fundamental group, we are looking for a non-trivial group whose abelianization is trivial. Is there such a group?
I got edited on Stack Overflow because I used "I'm", "you're" and "I'd" instead of "I am" etc. Is it considered rude to use contractions like that in informal conversations on the internet? I would not use them in papers but, I thought on Stack Overflow it was okay.
This is probably a stupid question but I will have to ask it. If you had a set of N correlated random variables and knew the correlation matrix, can one compute the joint probability distribution of all variables? Does it make a difference if the correlation matrix was built using Pearson's rho or Kendall's Tau for example? Thanks, Bogdan.
My book says all extensions of finite fields are cyclic, but I could not find a proof (maybe I haven't looked hard enough). If it's straightforward, can you tell me why it's true? Thanks :)
I'm trying to solve this question: I didn't understand why the hint is true and how to apply it. I really need help, because it's my first question on this subject and my experience on this field is zero. I need some help. Thanks a lot
I do know Schreier's theorem, which states that a finite index subgroup of a finitely generated group is finitely generated. Other than this, I have no reason to suspect a positive answer to my question, other than it would be nice.
Could someone tell me if I've worked this out right? I'm unsure of the process, especially the final parts where I convert it to a sinc function. Please let me know if I've made mistakes anywhere else too.
The Shannon-Hartley theorem gives an expression for the capacity of a bandwidth and power limited channel. How would one formulate this theorem mathematically (rigorously)? I understand the formula given, but not how to formulate the assumptions made mathematically.
What is the standard way in latex to display certain objects (e.g. pictures, tables, etc.) side by side, instead of one below the other? I thought about using the tabular environment for this, but I'm not sure if there isn't a better way.
I am reading the book "Lebesgue Measure and Integration: An Introduction" by Frank Burk, and it says the following: If the Lebesuge outer measure is finitiely additive, then it is countably additive. How can I prove this?
Hello everyone, I'm trying to solve this problem, but I'm stuck... i don't quite understand the definition of the norm, If you guys can give me a better explanation, I would appreciate it, Thanks
It is well known that a local ring is a ring containing only one maximal ideal. I was wondering if there is a characterization (or any information) of the commutative rings such that all their non-trivial ideals are maximal. Thanks.
I am an undergraduate student doing a project on rooted trees. I was wondering if anyone would know any easy to understand references that explains Grossman and Larson's Hopf Algebra on rooted trees? In particular, I want to know how the comultiplication, counit, and antipode are defined. Maybe if there is anything that explains their paper 'Hopf-algebraic structures of families of trees'.
I've seen in a documentary that when a star collapses and becomes a black hole, it starts to eat the planets around. But it has the same mass, so how does its gravitational field strength increase?
Which one is correct? Centuries ago, people weren't aware that the planets revolved around the sun. Centuries ago, people weren't aware that the planets revolve around the sun. In my grammar book it has mentioned the first one as "grammatical correct sentence", but it has not done such a comparison.
What lessons do we have from string theory regarding the fate of singularities in general relativity? What happens to black hole singularities? What happens to cosmological singularities? Which points of view on string theory yielded results in this respect? String field theory? AdS/CFT? Matrix theory? I suppose perturbative string theory is not applicable in the vicinity of singularities.
I've always thought "to slumber" meant to sleep deeply or for a long period of time. Several colloquial but less reputable dictionaries agree with me (http://www.urbandictionary.com/define.php?term=slumber, http://www.yourdictionary.com/slumber) but Merriam-Webster and the OED disagree, defining slumber as "to sleep lightly" and "to sleep, esp. to sleep lightly; to doze or drowse," respectively. Which is correct in modern usage?
Question: Which of the following graphs correctly describes the variation of kinetic energy with time of a block when it slides down a smooth inclined plane from rest? The answer is C but I do not understand why. How do we know if the velocity increases as it slides down the inclined plane?
Why must a symmetric positive definite matrix must be invertible? I'm reading a proof of the Levi-Civita theorem in differential geometry but the author states this without proof and I haven't been able to prove it.
I was wondering if it's possible to produce the anarchy symbol (the circled 'A') in LaTeX. I tried googling "latex anarchist" and got nothing but merchandise and porn, and while I'm not complaining, I also wanted the anarchy symbol.
Is there a way to increase the font size in the source window of TeXworks? I guess I'm showing my age, but for me it is almost unusable. It's kind of annoying having to put my face so close to the screen to get any work done.
I'm trying to make a figure environment that can select between multiple images. I am not trying to do multiple subfigures but rather a single figure environment that can cycle through multiple images like a slideshow. At this point I don't have any particular format in mind. I am just looking to see if Latex has the ability to do this. Thanks in advance.
I read the following sentence in the book Options, Futures, and Other Derivatives: Treasury bond prices in the United States are quoted in dollars and thirty-seconds of a dollar. Here is my question: How should I understand the phrase in bold, namely, "thirty-seconds of a dollar"? I think the plural form "thirty-seconds" means several thirty-seconds of a dollar. Does it make sense?
noob question here. I'm interested in reading The Elegant Universe by Brian Greene, but I've read some reviews that say the science has been discredited. I'm a total layman, has the science been discredited?
I have a strong mathematical background and I am interested in the relationship between mathematics and music. I have found some introductory material on the web. Do you know any good books that will broaden my perspective of this subject?
While looking for something on this site I accidentally found a document class which is perfect for a scientific report with two columns layout. Unfortunately I forgot its name. Could someone point me out the document classes which implements two column layout without using multicol packages?
If the universe is undergoing inflation, and there is a minimum scale that things can exist at (the Planck length), does that mean that new Planck-sized domains have to be continuously popping into existence? If not, does that mean that the Planck length is constantly changing?
What do they mean? How should I use them? Which one is more appropriate to what context? I was talking to a colleague of mine and we couldn't get to a consensus about what should we say when referring to drinks, for example: A lemonade is made of lemons. or A lemonade is made with lemons.
If the title of a song ends a sentence, whether a statement or interrogative, where does the period or question mark go? For example, is it: The Beatles sang "She Loves You." or The Beatles sang "She Loves You". Is it: Did The Beatles sing "She Loves You?" or Did The Beatles sing "She Loves You"?
I'm having some trouble understanding the concept of negative work. For example, my book says that if I lower a box to the ground, the box does positive work on my hands and my hands do negative work on the box. So, if work occurs when a force causes displacement, how does negative work happen? Are my hands displacing anything?
How to prove Ampere's Circuital Law in case of any conductor. My text gives the proof of only the special case when the conductor is long and straight. I am trying to prove it, but haven't been successful. Any hints would be welcome.
I've recently come across the following sentence: Round the corner walked Hannah, and nearly bumped into Louise. The first clause sounds clumsy to me. I think the example above should be written like this: Hannah walked round the corner, and nearly bumped into Louise. Is it ever right to put the subject at the end of a clause?
When I was much younger, I remember the press always referred to the U.S. president using the title of the office: "President Nixon" was followed by "President Ford" then "President Carter". Now that seems to have fallen out of favor and the common reference is: "Mr. Obama". My question is: when and why did that change happen? Was it associated with a particular president?
Is there a sequential criterion for differentiability,just like there is one for continuity ? If not then,why so ? I'm studying undergraduate real analysis and haven't really come across one. Thanks in advance !
What does "sit in the back of the bus" in the following sentence mean? It has been taken from Harvey Milk's "The Hope Speech." The first gay people we elect must be strong. They must not be content to sit in the back of the bus. They must not be content to accept pablum.
The Ricci tensor is defined as the contraction of the Riemann tensor in its upper and the second lower index. I was wondering why it is defined this way. What happens if the Ricci tensor is defined as a different contraction of the Riemann tensor? Would it satisfy Einstein equations? Does the usual definition have any physical or geometrical meaning?
What is it called when the subject of a sentence is the same as the object of the previous sentence? For example: I'm going to Freddy's house. Freddy lives down the block. The block is paved with gravel. The gravel is jagged.
I am unable to comprehend why ammeter is connected in series and voltmeter in parallel in a circuit. My book doesn't give any explanation about it nor am I able to understand it from the internet. Can someone please explain this to me (a beginner).
Helium is a scarce resource, as it escapes the atmosphere over time. If we run out of Helium deposits, will it be possible to manufacture more helium through nuclear fusion or another nuclear process? If so, how much energy will be required?
Is it more correct to say 'The picture hung crooked on the wall' or 'The picture hung crookedly on the wall'? My instinct is that the first one sounds better to me as a native speaker, but someone else I was talking to was convinced that only the second is correct. What's better here?
Possible Duplicate: Should I put a comma before the last item in a list? What is the difference between tomato puree, paste, and sauce? OR What is the difference between tomato puree, paste and sauce? Do we need a comma before and in this case?
A Lie group is a group which is a smooth manifold such that the multiplication and inversion are smooth. When does a Lie group become simple? What is the difference between simple and semi-simple Lie group? Just want a quick answer here. Thanks
I'm working on an engineering project, and I'd like to be able to input an equation into my CAD software, rather than drawing a spline. The spline is pretty simple - a gentle curve which begins and ends horizontal. Is there a simple equation for this curve? Or perhaps two equations, one for each half? I can also work with parametric equations, if necessary.
How can I center the titles of the chapters in the frontmatter and the backmatter of a document written using memoir? Keep in mind that the mainmatter chapters should not be affected at all.
I keep coming across the term pseudocubic unit cell while reading about orthorhombic perovskite structures. No clear explanation is given in papers. Can someone please tell me how these structures are generated and what exactly is meant by them?
What does "sanding a doorstep" mean? Does it mean polishing the doorstep? Or filling it in with sand? I read this expression in Charles Dickens' book, The Haunted House where it says, I found the landlord of the little inn sanding his doorstep.
A person who makes desserts is called a pastry chef, but is there a name for the action itself of making desserts? "Cooking" is too general, and "baking" implies bread, cakes, etc. which is not quite what I mean. Any ideas?