darklight03/StackMIAsub huggingface dataset:
I am beginning to learn quantum mechanics. Since determining the position of an object involves probing by electromagnetic waves and since i have read a simple derivation of Heisenberg's uncertainty principle which says that uncertainty in momentum of a quantum particle is proportional to the momentum of light (or e.m.) used, I am beginning to wonder whether the theory of quantum mechanics is solely based on measurement using electromagnetic waves? In that case it is not a fundamental law. If we measure the position of a particle using its gravitational field change, does then the uncertainty exist? Pardon me if my question sounds silly.
I was wondering if a library of mathematical expressions in Latex was existing on the web (I don't know if the library term is appropriate) which would help us copy and past them. It would save a lot of time when using, for instance the normal law... PS: I'm not sure of the tag below, tell me it's not the right one, I will change it right away.
A question was recently asked on Musical Practice & Performance, asking what physical properties of silver would contribute to the sound of percussion instruments. It is likely to be off-topic there; I wondered if any of you physicists/material scientists would be able to offer a humble musician information on this site. It would also be interesting to know what contribution solid-silver or silver-plated components would make to brass/woodwind instruments, and what properties of silver are responsible for this.
In many forums, I have seen people keep saying to avoid repetition of the same word in a paragraph. But in the sentence like below, how do you avoid the repetition? Suddenly, the dog stands up and stares at something in the hallway. A shadow of something enters the living room from the hallway. The dog continues to stare towards the hallway. I have to repeat the word hallway three times, and see no way to avoid it. Why and how should I avoid?
I am looking for a word or expression, that describes the specific distance in the space that lets the observer appreciate and completely understand the object of observation. For example, when one is in a museum and stands too close to an impressionist painting, one can only see the brush strokes but not the flowers. But if one stands at the right distance, one can easily recognise the flowers and the whole garden. Is there an expression that describes the right distance to appreciate fully a given object? Thank you very much! anak
I am starting to write my master thesis in latex. So far I have only written article-like texts, so this is my first big document. I would like to start with some good general good practices. Specially since I might go into academia and pursue a PhD. What are good principles to keep in mind?. For example, do you have one single huge tex file, or do you have several smaller files for each chapter?
This was something I understood when we first went over it in class, but my text doesn't really cover it and I cannot find a direct answer online: If I use, say, the midpoint rule on a contour map to get the approximate value of an integral how can I determine if it is an over-approx. or under-approx.? Thanks! I should clarify that I am working with contour maps and double integrals- not single integrals.
I am studying for the Berkeley Math Tournament (BMT) and I was wondering if anyone had any ideas on what I should study to prepare. This is my first math competition and would like to have as much practice before hand as possible. Also, taking a look at last years competition there are a lot of problems that I am unsure of where to begin approaching them, if anyone has any references that would help me learn the ideas and mathematics behind the problem it would be greatly appreciated. Thank you!
Mass appears to attract other mass, irrespective of position or orientation. That is, gravity is attractive no matter what. Contrast that with electrostatic forces which could attract or repel depending on the charges involved, or a voltage between two metal plates which has a specifically directional force on electrons travelling through it. How do we know gravity attracts in all directions at once? What experiments have been done to confirm this?
There's a word, I think that starts with a 'p', that describes doing something to solve a situation before it happens. For example, if a hurricane is approaching a store might take __ action to prepare for the flood of people that might come. In a fictional world, an organization might take __ action against crime based on some foreknowledge of a person's future actions. Edit It's not "preparatory", "precautionary", or "preventative".
I'm looking for a word that is used quite often to mean something that feels real like you can reach out and grab it. Like it has substance. It's used most often around me to refer to user interface or game design. Like when a UI has weight and feels like it has substance behind it you say it's ............... I originally thought of... Visceral Corporeal Ephemeral (although I was looking for an antonym of this) But none of them are correct. But it is a word with the same "al" ending I think.
As the title indicates, I'm trying to find books where the exposition of the main course of thought is done entirely or mostly in outlines of proofs, or as exercises with or without hints. I'm trying to force my reading to be more "active", and I think that such a book would be good training-wheels. No particular topics, but preferably something on the introductory level. I'm particularly interested in basic Differential Geometry and/or Algebraic Topology related topics right now. (I have "undergraduate level" background in Real Analysis, Abstract Algebra, Linear Algebra and General Topology, and I'm trying to get started with Algebraic Topology and Differential Geometry for my own personal and educational enrichment.) Texts on other topics would be welcome for later reference. Much thanks.
I just finished reading (and understanding) Steiner's proof of the isoperimetric inequality. His proof (which is sadly incomplete) seems to rely much on the fact Steiner symmetrization preserves area and decreases perimeter. The only resource I've found which provides proof of those two things are Andrejs Treibergs' beamer slides , however ,they are confusing as he is a bit heavy on notation. Can someone please point me in the right direction on where I could find an alternative resource providing detailed proofs. If possible, a proof if you don't know a resource would be highly appreciated.
Person A says to B: "I thought you were smarter/stronger/better/more trustworthy than that. I should have known better." I was thinking it would be termed passive aggressive, but after reading up on it, that doesn't seem right. I'm tripped up on how focused on the Person A the two sentences are. Typically an insult would be "You're not very smart" and that would be that. But this is "I'm disappointed in myself for thinking better of you." Is there a good term for this sort of insult?
I have been using Windedt with Texlive since many days. But I stopped using it for a while, and when I now compile a tex file, its giving error "The system cannot find the file specified". I don't know wats wrong. I have used this before. I tried re-installing Winedt, no use. I have recently changed the System Path for installing some software. Has it affected in anyway?? Please help me.
Please have a look at these two definitions: Chevalley-Eilenberg complex Koszul complex (German Wikipedia) Both are from Wikipedia pages on Lie algebra cohomology, and they look rather similar. Since I'm not very solid on the notation, I'm unsure about what's the difference between them. Furthermore, since both Wiki pages are about Lie algebra cohomology, and no page defines the "other" chain complex, I'm not even sure whether they are different at all. What's the essential difference between them?
Does a definition need to provide a unique or near-unique description or can non-unique descriptions also be categorized as definitions? For example: Is the statement "An apple is a fruit" a definition of apple? Is the statement "A car is something that gets people from place to place" a definition of car? Are these simply descriptions (or categorizations) of the objects in question or are they also poor definitions?
I've got a sci-fi based Physics question that involved Dark Energy... So I've been watching a lot of Doctor Who recently, and I'm very interested on how his "Tardis" is bigger on the inside. Here you can see the Tardis looks small on the outside. But inside, it's much bigger. So here is what I've been thinking. What if you got a box (like a Police Box), and somehow filled it with Dark Energy! Im hoping that the Dark Energy would expand space inside the box, thus making it "bigger on the inside". My question is, could this actually work? Thanks for your help. (This is just a fun question btw)
Just as the title says: is there a formal name for a convex polygon on a sphere, of which the vertices are connected not by great circle but by small circle segments? My end goal is to intersect two (or more) of such shapes, and find the area of the shape where the two small-circle polygons overlap. It would therefore be helpful to get to know some basic and/or special properties of such shapes, what equations apply, etc.
I'm trying to get the facts straight here. Suppose I'm throwing a ball with no angular momentum. It collides with the ground and Newton's third law tells us that a force opposite to the gravity will be applied to the ball at collision. During collision, the momentum will be converted to potential energy and then become kinetic energy again. Am I right to say that some of the kinetic energy can be converted to angular momentum, thus making the ball rebounce not straight up? (assuming some friction)
It's just a casual observation, so I wanted to check it: A regular spring, when not completely compressed, looks an awful lot like a sine wave. The idea of a circular shape stretched out in the third dimension also seems to support it. But I can find no mention anywhere that such a spring actually is (or isn't) shapes like a sine wave. I don't want to tell my pupils this unless it is more than just an observed similarity. So is a stretched spring, if seen from the side, shaped like a sine wave?
I want to read particularly about diophantine Analysis and Elementary Number Theory from a novice level. The books which I found on net: A Guide to Elementary Number Theory by Underwood Dudley Diophantine Analysis by Robert Daniel Carmichael Diophantine Analysis by Jorn Steuding Help me with good suggestions as I think M.SE. has people from novice to professional users. Thanks. P.S. I have searched M.SE. for this type of question, I didn't find any. If you know someone, you may give the link.
What are some quantities often used to measure the sparseness of a graph? For example, in a graph, with the number of vertices fixed, the smaller the maximum degree is, the more sparse the graph is. With the maximum degree fixed, the bigger the number of vertices is, the more sparse the graph is. For another example, the more sparse the adjacent matrix is, the more sparse the graph is. Then it leads to another question: what are some quantities to measure the sparseness of a matrix? Thanks!
I would like to know if a discontinuous local martingale with paths of finite variations almost surely is a martingale. I feel that it should be the case but can't find a straightforward argument. As noted by Did in its comments below, the continuous case follows easily from the widely known fact that continuous local martingales have paths of almost surely infinite variations. So I modified the question to make it more specifically about discontinuous local martingales. Best regards.
Prove that a) the medians b) the altitudes and c) the angle bisectors drawn from the base angle of an isosceles triangle are congruent. Looking at this problem, I feel that this statement is just false. If you have an isosceles triangle given in the following link Link. Then clearly these are not congruent. Is there something in the problem that I am missing? Thanks
I was told that a dielectric slab inserted into a capacitor connected to a battery (constant voltage) will be repelled, because the energy stored in the capacitor increases when the dielectric is inserted, due to increased capacitance. What is the physical origin of this force? The attractive force by a constant charge capacitor can be explained by fringe field, but why are the two cases different in terms of forces?
What is the official rule when mentioning a city/ state in a sentence? I always thought there was a requirement for a comma between the city and state, however is there also supposed to be a comma afterwards? Tim also enjoys football games, jumping on his motorcycle and being a guide for the Fredrick, Alabama, restaurant scene. I personally think it looks clunky, however I'm told that it is opinionated and that the above is correct. Should the sentence be written like this? Tim also enjoys football games, jumping on his motorcycle and being a guide for the Fredrick, Alabama restaurant scene.
I am new to studying abstract algebra (and math in general). I've been reading Gilligan and Pinter's books. I am trying to improve my understanding by doing exercises. However none of the books I am reading seem to come with exercise solutions. Is there an abstract algebra book with lots of exercise with solutions? I am confused as to why none of the math books come with complete exercise solutions. How do people verify that their answers are right.
Using packages like minted (thanks to Pygments), LaTeX can generate beautifully highlighted/colored source code. Literate programming tools such as noweb and cweb can generate beautifully typeset and readable documentation. Ideally, I would like that the docs generated by noweb and cweb have high quality syntax coloring, and this seems like a problem that someone on either community may have tackled. So here is the question: Does anyone know how to get noweb and related tools to use minted or a similar LaTeX package for syntax coloring?
I saw in my abstract algebra textbook that defines the gcd of a polynomial over a field (i.e. the coefficients of the polynomial is taken from a field). My question is that what happens if the field is not a real numbers? I mean intuitively, I always think of it as real numbers. Is there anything wrong in taking of it this way. Can someone give me an example of a polynomial taken from other fields such that thinking of it as real numbers will result in a misconception. Thank you.
Is there any text that I can use as a short reference for the standard techniques for solving basic ODEs? I currently have been using Boyce and diPrima as my ODEs text, and it is far too wordy for my taste. I'm also not too interested in expositions of applications of physics or phase plane analysis, as I have other books for that. Basically, I'm looking for something short that can quickly remind me how to use techniques like integrating factors, series solutions, etc. which I keep on forgetting.
I have two matrices(the first one is mxm, while the second one is nxn, m>n). They store data pertaining to human speech. The second matrix contains a data segment that acts like an acoustic "signature". I need to find where this data occurs in the first matrix. Which mathematical tool(s) or method(s) can I use to get it done? I know convolution can help me out but is this the best(more importantly fastest) way?
For each relation, determine which of these properties are present: reflexivity, symmetry, antisymmetry, and transitivity: I know the definitions of each of the properties but unclear as to how to apply them to each relation. {(a,a), (a,b), (b,a), (c,c), (d,d)} {(a,a), (a,b), (a,d), (b,a), (b,b), (b,d), (c c), (d,a), (d,b), (d,d)} {(a,a), (a,b), (a,c), (a,d), (b,b), (b,d), (c,c), (c,d), (d,d)} Does anyone know what I would need to do to solve this?
I'm looking for an adjective that describes that tasks should be approached "one-ly". To give some context: [Task] must be performed in one way and exclusively one way. or There must exist precisely one method of performing [task]. I am looking for an adjective that describes this "one-ness". The adjective does not need to specify what the method is, it should merely prescribe that the task should be approached in precisely one way. The closest word I could think of is "uniform".
I just came across the term quantifier-free first-order formula, I first thought that might be similar to a propositional formula, but then after a closer evaluation I realized there are more concepts in first-order logic then just the quantifiers. I believe the difference is the following. A quantifier-free first-order formula can still contain: Function symbols Predicates where as a propositional formula does not have these concepts. Is that correct? Did I miss something?
Please compare He shrugged. and He shrugged his shoulders. Is there anything else that can be shrugged, besides shoulders? To me it sounds like duplication when used in this way. I'm aware of constructs like "He shrugged it off." but that's not what I'm interested in, and it also implies the use of shoulders, doesn't it? So why the need to specify the shoulders as an object? [edit: I also find "he shrugged his eyebrows" but that's rather rare.]
Does the expression "to add another dimension to the situation" imply that the situation has become more complex? In Arabic we would say something like "adds another dimension to the situation that has become more complex". But I know English tends to be very economic and implicit. So if I wanted to express that idea, would "adds another dimension to the situation" be enough? Or do I have to say that the situation has become more complex?
The statement of the Cayley-Hamilton Theorem is fairly straight-forward. I now know how to find characteristic polynomials from a given matrix (or at least a matrix with certain properties that I am unaware of!). I know that the eigenvalues of the matrix are roots of the polynomial. But what does having such a polynomial mean? Wikipedia says that the characteristic polynomial "...encodes several important properties of the matrix...", but once we have switched to "matrix form" of the equation, what can we conclude? In other words, what does the Theorem do for us, besides allowing us to say, "Hey, I know a matrix solution to this polynomial"?? Is there an abstraction of this in abstract algebra (rings, fields, etc.)? Thanks for your time.
Is there a name for the practice of composing sentences in such a way that they don't contain proximate consonants which cause difficulty when read aloud? For example: Under this criteria, "dogs and cats" is preferable to "cats and dogs," because the consecutive d s in the latter are difficult to pronounce clearly and distinctly and will force the speaker to either interrupt the flow of speech or elide the first d.
During a sunny day the walls of my house warm up (no surprise). My question: how much of this warming up (if any) comes from visible light? I associate infrared with thermal energy. If my house was floating in space (to prevent any thermal exchange with its surroundings) and I installed a giant infrared (and UV) filter between it and the sun, would it still warm up (compared to its rest temperature in full darkness)?
Does a matrix with all non-negative, real entries have all non-negative, real eigenvalues? Where might I find a proof of such? Ideas: Perhaps we can multiply a prospective eigenvector so its biggest entries are positive, and then show that it is a contradiction for it to have a negative eigenvalue? I am currently looking at the Perron-Frobenius theorem on Wikipedia, but it seems not to mention this issue. (I suspect my conjecture is not true.)
I think the title says it all. I am planning on giving a talk in a few weeks about the Banach-Tarski paradox and I have some pdfs found online which describe the paradox a little but I am looking for a solid reference which covers the construction from A to Z and on which I can extract the main ideas for my talk from (I understand the ideas beneath the paradox, I am just looking for a formal proof with no details excluded,i.e. a well-structured document). Anyone has a reference in mind?
For instance, would you rather say "It became increasingly hard" or "It became increasingly harder"? From my understanding, both are possible, but their meaning is slightly different. The first simply means that it became "harder". The second literally refers to an increasing rate of getting harder. Though in practice, I believe the second is still used to express the exact same as the first, while sounding somewhat awkward.
I am looking for a specific word to describe a concept such that its meaning is linear and one-way. Such is the case for the title of this question. X would be of this concept and Y would not, Y would be the opposite of this concept. For example, all automobiles are motor vehicles but not all motor vehicles are automobiles. I cannot seem to find any word to relate to this. Any advice/guidance is very much appreciated.
Traditional English prescriptive grammar teaches that these two verbs, to see and to hear, when describing their sensory nature, should never be used in the progressive aspect of tenses. Thus I am seeing you/I was seeing I am hearing you/I was hearing you would be incorrect. But in spoken English, whether it be in the movies or on television, this usage seems to me to become ever more often used. I am seeing you for I see you now I am hearing you for I hear you now When did this usage become so universally accepted? Is it still considered colloquial English? Or is it already considered standard English?
I would like to create a table (cf. attached figure) and use curly brakes to summarize some of the cells. I did a lot of research and found this solution (Curly brackets around a table), but it doesn't help me much as it is only math content and I would like to enter text only. Does anyone have an idea about how to solve this problem elegantly? Cheers
I realize there are questions on the correct usage of "but" and "however". In this case, I am concerned with correctness in a formal context. I have heard it said that however should be used in formal mail communications instead of but because the word "but" has a negative connotation. Which should I use in, say, an email to a client? Examples: We understand the issue you have pointed out, but we cannot consider it as a defect in the application since the current behavior was requested by your team. We understand the issue you have pointed out. However, we cannot consider it as a defect in the application since the current behavior was requested by your team.
As I read on Wikipedia, the Rutherford atomic model is not correct according to classical electrodynamics, as it states that electron must radiate electromagnetic waves, lose energy and fall onto the nucleus. I don't understand this explanation. It is clear to me that with given acceleration directed to nucleus and proper speed, electron can move around the nucleus. I don't understand explanation about energy, but I understand that there must be some force directed to nucleus. Also this force must not be constant because if it is, a larger speed could keep electron moving around the nucleus. So what is that force? Why does this explanation on Wikipedia and on other resources operate with energy, not with force?
I'm reasonably happy with the dictionary functionality in TeXworks but I am struggling to see how I can 'find' all the spelling mistakes in my (painfully long) tex file. I was hoping for a Wordesque spell checker in which I can scroll through each of my errors and accept or ignore the suggested changes. I could install another editor that has this functionality but would prefer not to do this if possible.