darklight03/StackMIAsub huggingface dataset:
I'm having trouble with a problem in Propositional Logic Using induction I am supposed to show that if a well formed formula (wff) X has no repetitions of sentence letters then X is invalid. The hint in the back of the book says "Instead of trying to show directly that every wff without repetition of sentence letters has the feature of PL-invalidity, find some feature F that is stronger than PL-invalidity (i.e. some feature from which PL-invalidity follows), and prove that every wff has that feature." What does invalidity follow from?
It is well known that the Lagrangian of a classical free particle equal to kinetic energy. This statement can be derived from some basic assumptions about the symmetries of the space-time. Is there any similar reasoning (eg. symmetry based or geometrical) why the Lagrangian of a classical system is equal kinetic energy minus the potential energy? Or it is just because we can compare the Newton's equations with the Euler-Lagrange equation and realize how they can match?
After a hot shower, the mirror in my bathroom steams up. When I try to clear it with a towel, it immediately refogs. Yet once I use my hair-dryer, it will clear the fog and the mirror will stay clear. I'd like an answer to the mechanics behind this difference. I suppose it got something to do with the heat, and maybe the refogging is only delayed due to it. But that is just me speculating, and I'd like a concrete answer on this phenomenon.
I can see this is true for the sum of two roots of unity with some basic trigonometry (the resulting argument is the half the sum of the original arguments, and so must also be a rational multiple of Pi) but trying to extend this method to the sum of more than two doesn't seem to work. Is there some other way of showing this? It seems related to this question: Sums of roots of unity but I'm not sure if that can be extended to this.
I am studying Hyperbolic Geometry. At this part, I have proved that semicircles and straight lines orthogonals to the real axis are geodesics in the hyperbolic plane. But how I proof that this geodesics are uniques? That it does not exist others geometric places between two different points that minimizes the hyperbolic length? I have seen a topic related to this, but I do not know nothing about Riemannian Geometry. If someone could indicate to me some references to this proof(or the idea behind) I will be very grateful!
I need to show through a proof that the set of nonnegative numbers is denumerable I know a set is denumerable if its members or elements can be put into an order and counted. I am supposed to show this through a proof as well. I was considering using Induction possibly but I'm not sure if this is a viable or feasible method to use. Any help is great appreciated
I have a rather large text file that I'm trying to convert into a table. I'm pretty new to Latex, so I was using this other answer from this site as a guide to help me: save table on a separate file and I got some great results, but I realized that my table needs to be split up across many pages, which they say to use longtable to achieve. I don't completely understand where you would add that in or which part you would replace with that, and I was hoping that someone could explain that to me. Thank you!
We know that gravity affects time. More the gravity, slower the time, and vice-versa. Now consider a hypothetical condition where two people are walking next to each other. One person is subjected to a lot of gravity and the second person to a lot lesser. How would first person see motion of second person? Since time would be running slower at first person's place and faster at second person's, would the first person see the second person to be moving faster than we usually see? Like a video is being fast forwarded?
In the phrase 'in the field instead of behind a / the desk', would you use 'a' or 'the'? It seems to me that 'the' is the more sensible option, as English has other expressions of the 'the N' form which denote an activity associated with the object referred by the noun, e.g. the bar as signifying the legal profession, the pen as in 'the pen is mightier than the sword'. However, a search on Google shows that 'in the field instead of behind a desk' exceedingly outnumbers the other version.
According to general relativity, inertial mass and gravitational mass are the same, and all accelerated reference frames (such as a uniformly rotating reference frame with its proper time dilation) are physically equivalent to a gravitational field of the same strength. Refer: Einstein's thought experiment of a Physicist in an Accelerated Box. I find that the 'How' part of this question is somewhat easy to understand Mathematically but hard to visualize physically and on the 'Why' part I am totally blank.
A chain of some mass, forming a circle, is slipped on a smooth cone. If we consider an infinitesimally small section of the chain, a component of gravity will try to accelerate it along the surface of the cone. So there must be some tension in the string that prevents the acceleration. What will be the direction of the tension on this section of the chain? Will it be towards the height of the cone, parallel to the ground?
In mathematics, we talk about tangent vectors and cotangent vectors on a manifold at each point, and vector fields and cotangent vector fields (also known as differential one-forms). When we talk about tensor fields, we mean differentiable sections of some tensor power of the tangent or cotangent bundle (or a combination). There are various natural differentiation operations, such as the exterior derivative of anti-symmetric covariant tensor fields, or the Lie derivative of two vector fields. These have nice coordinate-free definitions. In physics, there is talk of "covariant derivatives" of tensor fields, whose resulting objects are different kind of tensor fields. I was wondering, what is the abstract interpretation of the general notion of a covariant derivative in terms of (tensor products of) tangent vectors and vector fields.
Let's say you wanted to calculate, for example, the average (i.e. mean) cost per day for a hotel to accommodate a tourist. If only aggregate cost data is available, is dividing the average cumulative cost for one person's stay by the average person's duration of stay an acceptable method? Would using the median cost and median duration of stay be better? Worse? The same? I know the median is less susceptible to outliers than the mean, so if both the median and the mean work the same I'd rather use the median.
Richard Feynman showed that Quantum simulation on a Turing machine will have an exponential slowdown. If that is so, does this put quantum simulation outside of P (complexity class)? I thought quantum simulation was polynomially possible on quantum computers, but there is still no proof that BQP is strictly bigger than P. So either quantum simulation has not been shown to lie outside of P, or it is not in BQP. I can't seem to find the answer.
So I was wondering about the event horizon on a black hole. And wondering if the point of no return for radio waves vs gamma rays would be different. I guess the logic being, since gamma rays have more energy than radio waves, their point of no return might be different. But I'm not sure if gravity has the same affect on all frequencies of electromagnetic radiation. I'm sure the answer for this would lie in gravitational lensing, ie are different colours of light lensed by the same amount? or do higher frequencies lens less?
I was watching a Physics TV show, When someone called Alex Filippenko said that when there was the Big Bang, the Space extended at a speed faster than speed of light. He said that it wasn't against the Theory of relativity because space isn't a particle and can go faster than speed of light. So I wanted to know if that is a fact? And otherwise how could the light go further if space around wasn't going at least as fast as light?
I've been reading my Stewart Calculus book and I honestly find most of the coverage of sequences and series easy to grasp (excluding power series, Taylor and Maclauren since we haven't covered those just yet). However, when the book guides me to a test to use to solve a problem I don't have an issue, but if I'm given a bunch of problems and told to choose a test to use I honestly have no idea where to begin. How can I intuitively know how to attack a given problem? I realize the thought process is quite similar to integration, but I still feel like integration is much easier than determining convergence and divergence of a sequence/series.
I have been interpolating cubic splines to some data, but it is now clear that I need my curves to be monotonic. Wikipedia and StackExchange sources describe how to impose the monotonicity condition while fitting with cubic Hermite splines. However I need my splines in B-spline form and I'm not sure how to translate from Hermite form to B-spline form. Is there a method to do this monotonic interpolation so that the resulting curve is explicitly in B-spline form (i.e. a list of knots and B-spline coefficients)? If not (and this might warrant its own question) how does one take a spline in Hermite form to B-spline form?
I would like to write a sentence to thank a number of colleagues. I would like to express the idea that it was a pleasure to spend time with them. Which of the two sentences below is better? I also take this opportunity to thank a number of colleagues with whom I had the pleasure of spending time these past two years. I also take this opportunity to thank a number of colleagues I had the pleasure of spending time with these past two years. Can you think of an improvement?
if I make a circuit with a battery and a capacitor (with a dielectric inside), how it is possible to get a current in the circuit? If electrons go from one pole of the battery and they arrive to one plate of the capacitor they cannot flow to the other plate of the capacitor because the plates are separated by a dielectric and this dielectric doesn't have free charges, they are bound charges. How can I explain a net flow of electrons in this circuit? Thanks.
I have been told that industrial mixing machines (say, for cake batter) switch directions periodically, first stirring in one direction, then the other, because this mixes the material more thoroughly. I imagine (but don't know for sure) that stirring in only one direction will tend to create helical structures in the mixed material, where each helix is more or less uniform but two helices might be quite different from one another; and that switching directions tends to break up and mingle these helices. Is this at all correct? Is there a way to quantify the effectiveness of different methods of stirring? If so, how much better is it to stir in alternating directions, and how often should one switch directions?
I am thinking of a (greatly simplified) computer simulation of a universe that followed something like Newtonian rules. Inside the simulation are A.I.s that are made from those same rules, and can only use those rules interact the world around them. Would there be some fundamental limits on what those A.I.s could work out about their universe, like their own version of an uncertainty principle? Sorry for phrasing this question in such a convoluted way. If anyone recognises what I am asking, and can point me in the right direction that would be appreciated.
I quoted the following from a pamphlet: Please read the instructions carefully before filling out the application form. The application will be returned to you and the registration may be delayed, if the information is not filled in completely. Does "filling out" equal to "filling in"? The words in and out have opposite meanings, how can they produce almost equal meaning in these phrases filling in and filling out?
I have not idea how to call these things, but I just saw a paper with the following figure and I was wondering how one would go about doing it in LaTeX. The closest thing I saw on TeXample.net was the Ford Circles example, but that's for a very specific case. I would like to see a way use this as a plotting device. At this point, I am not even sure how to do it in "normal" programming language, so perhaps the question is ill-placed. At any rate, I'd love to hear what people think!
Is there a term for when a person is getting really irritated/frustrated by someone, but they don't want to yell, so they do that thing where they exhale sharply through their nose? Say, for example, in customer support the operator has to explain and re-explain a procedure over and over, but the caller can never seem to get it right. To be clear, I'm talking about the act of blowing air out of the nose when angry/frustrated as opposed to breathing an exasperated sigh out of the mouth. It's just air; there's no vocalization or loud sound like a snort.
Is there any difference between the mass defect and the mass deficit? I have read that the mass defect of a nuclide is never negative and have also been told that the mass defect is the same as the mass deficit, which can be negative. Is it purely a sign convention? As a result of this is the binding energy of a nuclide ever negative?
While studying about band theory of semiconductors, I observed that when the electrons were excited from the valence band to the conduction band, they left behind holes in the valence band. From my existing knowledge, I believe that the valence electrons alone occupy the valence band which tells me the valence band is negative. For the holes to exist, the valence band has to be neutral. So, why is the valence band neutral? If my reason for the valence band to be negative was wrong, I would like to know the reason.
I've been watching this little HBO show by the name of Game of Thones. Perhaps you have heard of it. In the most recent episode the following line is used (and also happens to be the title of the episode): Now their watch is ended This sounds foreign to my ear. I would be inclined to say "Their watch has ended". Is there a subtlety in the English language that alters the meaning of the sentence by changing "is" to "has" and vice versa in the context of a simple sentence such as the above?
I have an upcoming statistics exam and I'm studying it on my own. I was recommended Hogg's Introduction to Mathematical Statistics, but I didn't find it helpful. I just want a book which covers basic mathematical statistics and statistical inference: stochastic convergence, estimation of parameters, testing hypothesis, etc. all at an elementary level (suitable for a math undergraduate), with good introduction to the required background for such concepts. Can you provide me a good source?
I was discussing about particle accelerators with my friends and it came to my mind whether it is anyway possible to make a table-top accelerator(accelerator that can fit on a table). I asked this to my professor and he mentioned something about plasma field accelerator.He said that charged particle passing through a plasma created by laser pulse can get acclerated. How can plasma accelerate charged particles? What will be the maximum energy we can achieve using such accelerator?What is the progress towards the development of such science? Will it be really a table-top accelerator?
I have developped a little tool in matlab to fill directly some .tex files and then compile them in a pdf file (I use the command pdflatex to compile). It is well working on my computer because I have MiKTeX installed. Now I would like to make a installer (using Inno Setup) to share this tool but I need to include the compiler in the setup. Does someone know if there is a way to only install pdfTeX for the furure users of my tool or do I need to require them to install the whole MiKTeX?
This is more of a general question rather than anything specific but I was just wondering if someone could point me toward resources which discuss singularities in a PDE rather than in an ODE (by singularity I mean as in https://en.wikipedia.org/wiki/Singularity_(mathematics)). I did a bit of work with singularities in ODEs, but it seems working with singularities in PDEs is harder, and I can't seem to find any material on it. I have a first order PDE so it shouldn't be too difficult (I think) to work with singularities with it, but seeing as how I'm from a more probability/stats background I can't be too sure about it... Thanks in advance.
I've looked up both and seen the answer to "why do we say 'soup up.'" Having always thought myself that the phrase was "to soup-up," I've been lately surprised to see a significant amount of usage of "suped-up" with claims that it's from the term "to supercharge" or "super" and that "soup" is the misspelling. Is there a definitive word on whether "suped-up" is a real term for "supercharged" or if it's a misspelled variant of "souped-up"?
I hear people say things like "inside a black hole the laws of physics are not valid" or "there can be parallel universes with different physical laws" or "before the big bang there was nothing". Can physics really make such predictions? Is not there a logical issue here, namely, is it possible to predict a system where all physical theories break, by using only validated/well-established/working theories of physics?
Is there a difference between "headquarters of" and "headquarters for"? It is the headquarters of many branches. It is the headquarters for many branches. It is the headquarters of the party. It is the headquarters for the party. Intuitively, "for many branches" seems correct and "of the party" seems correct. I can explain the conceptual difference between branches and party, but I can't connect my intuition to any rules. Any thoughts on this? Thanks.
I am working on a project whose object language is in non-monotonic logic. Since the project involves reasoning about the models, I am thinking of translating a non-monotonic problem into a first-order logic, use model theory in first-order monotone logic to solve the problem, then translate the results back to a non-monotonic logic. However, this seems cumbersome. Could you please provide me with a book or paper reference on model theory in non-monotonic logics. Preferably, classical topics such as Compactness theorem, Incompleteness theorems and Stable theories should be included.
I'm interested in the semantic implications of using the words quote and estimate in a business scenario. Here's the situation: When someone wants to purchase a service that I provide, they can fill out a form on a Website with information about the work to be done. Based on that info, they are instantly given a predicted price. This is intended only to be a ballpark. Once I manually review the work order, I will contact them with a personalized, much more accurate guess at the price. My instinct is to use estimate for the ballpark and quote for the more precise guess, but I'm interested in both your opinions and the more subtle distinctions and implications of the two words.
I want to say something like: The system stores the crazygonuts data separately from the data feed. I think this is wrong (maybe I am wrong in that), but I'm not sure exactly why. One alternative I thought of: The system stores the crazygonuts data separate from the data feed. I checked some dictionaries online, and I did not find separate listed as an adverb, so this also seems incorrect. I want to keep the verb (stores) in there. Is there any way I can keep this same sentence structure without sounding silly? If possible, I would like to use the word separate (or something sufficiently close, like distinctly); or is this formation doomed from the start?
Most modern texts spend some time deriving the LSZ reduction formula that connects S matrix elements to time ordered field correlation functions. It seems essential, and really helps clear up what you are calculating. Yet some earlier texts and even some modern texts (e.g. "Student Friendly Quantum Field Theory" by R. Klauber) seem to skip right past this, working everything out in the "interaction" picture. It seems there must be something going wrong with this latter procedure, but I am not quite able to put it together.
I'm trying to read about anabelian geometry and obviously the things to start with is the algebraic (etale) fundamental group. Every now and again I encounter authors talking about the arithmetic fundamental group, especially when they're talking about curves. Are these really the same thing, except the term algebraic fundamental group is used when talking about arbitrary schemes and the arithmetic fundamental group when talking about curves?
Possible Duplicate: [Singular] Is/Are [Plural]? I'm currently writing my master thesis on Bitcoin and I'm not sure which version of this sentence is correct: "The first most important part of the Bitcoin infrastructure are all applications that communicate with the Network." "The first most important part of the Bitcoin infrastructure is all applications that communicate with the Network." Or perhaps both of them are wrong? EDIT: Finished sentences.
Possible Duplicate: Unbreakable block I have a block of text (possibly comprising many paragraphs) near the end of a page. The page break is being inserted in the middle of this block--how do I prevent that? (How do I tell LaTeX that this block of text needs to always stay together on the same page?) This question should apply to all formats, but in my case I am using the memoir class, and am willing to include any necessary packages.
Currently i am reading about bandgap engineering in zinc oxide. I read that using external dopents likes magnesium or cadmium we can increase or decrease bandgap of zinc oxide,thus giving unique optical and electrical properties to zinc oxide. But how adding an external dopent causes changes in the bandgap of zinc oxide. I tried to search research article regarding this but was unable to find a mechanism for this phenomenon. Advance thanks for your help
If the coproduct of a family of objects of a Poset (seen as a category) is the least upper bound, who is the coproduct of a family of objects of a Preorder (seen as a category)? My intuition tells me that is the lub again but I'm having trouble writing the proof formally due to it is my first time with category theory and I'm not a mathematician, can you help me?
I am a physics undergrad and thinking of exploring quantum information theory. I had a look at some books in my college library. What area in QIT, is the most mathematically challenging and rigorous? From what I saw in the books, most topics were just simple linear algebra. I am looking for an area which is mathematically richer, and uses maybe more concepts from theoretical computer science, number theory, discrete maths, algebra, etc. Classical cryptography is an area on the interface of maths and TCS which uses many areas of maths such as number theory, algebra, elliptical curves. Is the quantum cryptography also rich in mathematics? What are the prerequisites? If not, please could you suggest some areas that I are mathematically rich in QIT?
Is the phrase "item is ignored for deletion" grammatical and idiomatic? The context is a software program. I have a list of items to be deleted from a database, and if an item from the list is not in the database, I want to display a message saying that the item is ignored. Since this message can appear among other unrelated messages, I want it to be as informative as possible but laconic.
Can the word dear replace expensive, as in "That new T.V is too dear"? The dictionary says so, but I was completely unaware that it had that connotation. I want to use it in writing because it's a shorter, simpler sounding word with a regular comparative/superlative, dearer and dearest, but it doesn't sound idiomatic at all. No one round these parts would say that. Does anybody else in the English-speaking world say this? I tried searching a corpus but all results came back with dear used as a term of endearment.