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I was reading about different variations of nim game and I'm trying to find the winning strategy in one of them: there are n empty places on the circle. Two players are placing their coins on empty places. They can put their coin only on empty places which aren't next to a coin of the opponent. In one turn each player can place only one coin. The player who can't move loses. Who's got the winning strategy for each n? I think that for even n the second player will win, because he can always place his coins symmetrically to the first player's. But what about for odd n? | 1 |
I would like to have a definition for non-modular lattices which clearly sets them appart from their modular counterparts, thereby focusing on their main distinctive feature. Besides, I would be very grateful to you if you could provide me with an explanation about orto-modularity, which Birkhoff and von Neumann allegedly considered to be the basis of quantum logic, as opposed to modular logics. Is there any correlation between the two types of lattices and this issue of orto-modularity? Thanks in advance. | 1 |
Is a Topological Space an Algebraic Structure? I am referring to the Wikipedia definition: algebraic structure generally refers to a set (called carrier set or underlying set) with one or more finitary operations defined on it that satisfies a list of axioms. Examples of algebraic structures include groups, rings, fields, and lattices. More complex structures can be defined by introducing multiple operations, different underlying sets, or by altering the defining axioms. Examples of more complex algebraic structures include vector spaces, modules, and algebras. | 1 |
This is an exercise from Alhfors Complex Analysis book- to show that an analytic function with a nonessential singularity at infinity must be a polynomial. It seems like it should probably be pretty straight forward, but I must be missing something. If it has a removable singularity at infinity then it extends to an analytic function on the Riemann sphere, and so must be constant by Liouville's theorem. What if there is a pole at infinity though? This was homework some time ago, and I never finished it :/ but have been thinking about it again recently. Thanks :) | 1 |
What is the word for "stealing things during natural disasters"? For example, two guys are listening to the news and hear that there will be a huge typhoon tomorrow, and that there will also be no electricity. So, these two guys decide to steal things from a shop on the day of the disaster. Is there any single word for "stealing things during natural disasters"? | 1 |
I'm looking for a reference for something I thought was easy and well known. There are (at least) two definitions of expander graphs. There is a combinatorial definition via edge expansion, and an algebraic definition using the spectral gap. Neither of these definitions require the graph to be regular. Now, I always thought that the Cheeger inequalities implied that these definitions were equivalent up to the constants. However, when I looked up the Cheeger inequalities it seems that they only talk about regular graphs. Is there a version of Cheeger's inequalities for nonregular graphs as well? In general, is it true that a family of (not necessarily regular) graphs is a family of expanders in the first sense iff they are expanders in the second sense? | 1 |
I am using graphicx to typeset the figures for my PhD thesis. I have large files in .eps format. However, whenever I try to typeset the file (using pdfTeX), the console says "LaTeX error: File 'Figure' not found" It is in the same directory as my .tex file, and the file will typeset if I create it as a .dvi and then convert it to .pdf. I would rather not do this though, because I want to use hyperref. | 1 |
Light as an electromagnetic wave can be polarized in different ways, e.g. linear or circular. As far as I understand it currently this can be compared to the spin direction of a propagation electron (spin angular momentum of light). Now I have learned that an electromagnetic wave can also have an orbital angular momentum, which is described for example in Wikipedia as a kind of shifted wavefront. While trying to get my head around these phenomena I was thinking about other wave-like objects in physics besides photons. Do all particles and/or excitations (e.g. a spin wave) exhibit orbital angular momentum and what are the physical consequences? | 1 |
I'm writing an essay right now and I'm deliberating whether or not I should use Pagan gods instead of Greek gods (to provide variation in the essay). I've looked up the word pagan in the dictionary and it mentioned it was a derogatory term. Would it be acceptable to use it though in an essay or would it be inconsiderate for me to use that term? | 1 |
I'm trying to phrase a sentence in which I'm wishing that something goes easily for someone, but can't get the wording to sound right, and not awkward. For example, someone may be studying for a test and I wish that their studying goes easy. These are the phrases I could come up with. I hope it goes easy for you. I hope the studying goes easy for you. I wish you the best in studying. I'm hoping the studying goes easily for you. Good luck studying. (I don't really like this one since it's a bit vague) Any other suggestions? | 1 |
Does anybody know the source of this idiom or have an explanation of how it originated? I know it means that the speaker does not trust the person in question, but I want to know the etymology of the idiom. How did it mutate from something literal into this? Obviously trust is not measured in the same way as distance, so I want to understand the correlation in this context. | 1 |
Is there any good reference for Poisson geometry/Poisson manifolds out there? I would like to give a deep look to the subject, but all I seem to be able to find are short chapters or interludes in text about symplectic geometry. Looking a bit around on the web, the only thing I found is this book. Has anybody read it? And if so, is it good or is there something better? For those left wondering: the book in the link above seems a good introduction. A more advanced text is given by the book Poisson Geometry, Deformation Quantisation and Group Representations (Cambridge University Press). | 1 |
I'm not a mathematician, but I'm teaching a bit of algebra to some budding logicians, and introducing them to/reminding them of the notions of isomorphism, homomorphism, etc. I'd like to give them an example of an endomorphism which isn't an automorphism, so that they can see the point of there being a name for these separate concepts. I'd also like the example to be as simple as possible, ideally just with some infinite group. But it's proving to be harder than I expected to do this. Every candidate I've come up with turns out to be either an automorphism or not really a homomorphism in the first place. Suggestions, please? EDIT: Should have said explicitly from the beginning, I'm hoping for an example where the homomorphism is surjective. | 1 |
Is the probability space associated with a compact group with Haar probability always a standard probability space? I recall seeing somewhere the fact that if the topology generating the Borel sigma algebra is not metrizable then the probability space is not standard, or something along these lines. If so then any non-metrizable compact group would show the answer to the above question to be negative, but I am unable to find any firm reference for the above fact. Any help with answering the above question would be much appreciated. | 1 |
Please help me determine whether or not to include a comma at the end of the third sentence: "I won't be talking to my ex at the party tonight." -"But what if she talks to you?" "I won't be listening to her either." -or- "I won't be talking to my ex at the party tonight." -"But what if she talks to you?" "I won't be listening to her, either." Thanks! | 1 |
Can anyone provide a word which describes a person who shows a lot of enthusiasm in the beginning but gets bored gradually and eventually leaves the task uncompleted? I looked at jaded, but it doesn't fulfill the criteria. Jaded seems to describe more of an overworked fellow, whereas the word I'm looking for would describe the nature of person. The word I'm looking for would describe a person who always exhibits this behavior. | 1 |
I have a few questions about simple situations. What should I say to another person right after falling? a) I fell b) I have fallen What should I say to another person right after throwing a ball? a) I threw the ball b) I have thrown the ball What should I say to another person right after taking something? a) I took b) I have taken Please provide explanations for your answers. | 1 |
I live in Thailand and we pronounce "w" and "v" the same. When I spoke to American people they told me that the "v" sound was different from "w". They told me to move my lower lip to the upper teeth, then say "v", but I don't get it. I want to know how to pronounce "v" in English. If you can suggest me how to practice it, that would be great! | 1 |
I was looking at the ice formed in my refrigerator and found out there were a lot of air bubbles inside it. The shape of the air pockets seemed strange to me. There were many small spherical ones and the bigger ones were in the shape of vertical ellipses. I am not able to understand what's the cause of these different shapes of bubbles. can anyone explain? | 1 |
The following is from the MIT-Harvard Tournament: You are trapped in ancient Japan, and a giant enemy crab is approaching! You must defeat it by cutting off its two claws and six legs and attacking its weak point for massive damage. You cannot cut off any of its claws until you cut off at least three of its legs, and you cannot attack its weak point until you have cut off all of its claws and legs. In how many ways can you defeat the giant enemy crab? (Note that the legs are distinguishable, as are the claws.) | 1 |
I am a physics undergrad interested in stuff like dynamical systems, chaos theory etc. Is there ongoing research in these fields? I am talking about pure research and not applications to things like weather etc? I hope this question is appropriate for Physics SE. I asked this question, because I browsed through the websites of the physics departments of a few renowned universities (MIT, Princeton, Caltech) etc, but nowhere it mentioned research in these areas. | 1 |
I picked up a copy of G.H. Hardy's 'Divergent Series' a few days ago. So far I love it, as I love the ideas associated with sequences and series, but I am finding it a bit difficult to understand. I assumed I knew everything I would need to understand it(Calculus I/II, etc.), but perhaps not. What would the possible prerequisites for understanding this book be? Also, does anyone have any tactics for getting the best comprehension/understanding of the concepts in this book? Thanks! | 1 |
I know that the proper way to use "not too long ago" is: "Not too long ago, contractors used to build houses and sell them to dealers. It was the responsibility of the dealers to provide financing to potential home buyers." Instead of these two sentences, can I use: "If not too long ago, contractors used to build houses and sell them to dealers, who were responsible for providing financing to potential home buyers, today most builders also offer financing alternatives."? My question is whether "if not too long ago" is correct or not. If it's not correct, I would highly appreciate it if someone could explain why. Thank you, Maria | 1 |
I created a table and it starts from the left and goes all the way to right, which looks really skewed. So I want to center align the whole table but couldn't figure out how to do it. I'm new to latex so I don't know how to use other plugin or macros, but I suppose there's a command for this basic functionality. Can anyone tell me? | 1 |
I am working with certain input-output maps that can be thought of as large RLC-networks. I thought maybe this might be a place to get some thoughts/ideas/answers. My basic question is, given some large connected RLC network (all linear and ideal elements) and two ports in the network, say 'a' and 'b', can the transfer-function between the ports have non-minimum phase zeros? More generally, is it true that every transfer function representing an RLC-circuit network is minimum phase? I suspect the answer is true, but I am having a hard time proving it. Thanks! | 1 |
After taking an introductions to proofs course and abstract algebra, I have been trying to study from Rudin's Principles of Mathematical Analysis. Unfortunately, I still find it very very difficult to read through Rudin let alone do the exercises. Sometimes I spend an entire week trying to understand a proof but get nowhere. At this point, would it be advisible to read a more introductory text in analysis or continue to work through Rudin? Or try reading some more abstract algebra? | 1 |
I am studying English and I have a question. I found it in my text book written by some teacher who is not a native speaker. "Those who came first and in greatest numbers to make their homes on the eastern coast of North America were mostly from England." I do understand the meaning of this sentence, but I cannot understand why the word 'greatest', Superlative adjective, is not accompanied by the word "the". Is there any specific reason for that? | 1 |
How do you parse the following sentence? The lamp by which she read the book grew dimmer. My friend says that "by which she read the book" qualifies "the lamp". So, it would basically mean "The lamp that she was using to read grew dimmer." For some reason, I comprehend the sentence as "The lamp that she was near while reading the book grew dimmer." Can it go both ways, or...? Also, about the usage of "grew dimmer" there, should it be "dimmed" instead? Thanks. | 1 |
Look at the endings of the following words: blight, bought, breadth, brought, caught, delight, depth, fifth, fought, fourth, fright, freight, height, light, plight, taught, thought, width, ... As you may have already noticed, some of the words in that list end in ht, whereas the rest of them end in th. I have some questions regarding those endings: I. Do all words of the English language that end with ht end, actually, with ght? II. Is there any rule of thumb out there that helps one to recall (or determine) when the ending of a given word is th and not ht (or the other way around)? Thanks in advance for your insightful replies! | 1 |
I'm well aware that bulwark refers to something used as a fortification or a defense. However, I was wondering if the word bulwarker is an acceptable word to use in English. I know it's possible to be a bulwark ("He built a bulwark upon the hill."), and I know you can bulwark something from something else ("I will do whatever I can to bulwark the attack."). However, I'm unsure if it is possible to be a bulwarker. | 1 |
I am entering an interesting team based math contest called the purple comet, and quite a lot of questions on this contest involve Diophantine equations. For this contest, you are given a computer, and I was thinking of making a program that solved a linear Diophantine equation. The issue with this is that I can barely solve one by hand, much less make a rigorous algorithm to solve one. I am aware of Euclid's algorithm, but when the numbers get big, this method gets pretty inefficient, not to mention that it would be kind of a nasty thing to program. Are there any other smart algorithms out there for solving a linear Diophantine equation? | 1 |
I was writing an essay when Word picked up an error in my writing; specifically, it wanted to replace "vast majority" with "clear majority." So my question is: is "clear majority" better, more eloquent, or clearer than "vast majority?" If so, how? A similar post here talks about the differences between similar expressions, but I want to know about the difference between "vast majority" and "clear majority." | 1 |
When speaking about turbulence in fluid mechanics many times authors speak about "premultiplied energy spectra" but they never explain what really it is. I have searched for a definition but I did not manage to find it. I guess that is something related about the real energy contained in a region of scales when using a logarithm scale representation but I am not sure. So, what are these "premultiplied energy spectra"? | 1 |
I have been looking around to find an answer to my question, but I was unable to find one that addressed my specific problem. I want to create the following sentence, but I'm not sure whether it's correct. "Not only the world has changed during this time but also we have in particular." I apologize in advance if I have overlooked an easy solution to this. | 1 |
I'm looking for a term to accurately describe a person who can only read but cannot write. While I'm primarily concerned with people who have never learned to write, I would also be interested in any additional terms used to represent people who have lost the ability to write as a result of disuse. Both illiterate and unlettered imply an inability to read as well as to write. | 1 |
I'm a bit confused. QFT is claimed to incorporate both Quantum Mechanics and Special Relativity. Therefore it should address the problem of non-locality caused by entanglement. However when I search for an answer on the Internet, I found nothing. I'm not complaining. But it seems that most people only use QFT to do some fancy particle stuff and forgot we should care more about the more fundamental stuff. | 1 |
I've noticed that, when I'm driving and it's raining, the faster I go the more rain I get on the windshield and the faster I have to run the wipers to compensate. When I'm stopped at a red light I can just about turn the wipers off, but once we get moving again I have to turn them up so I can see clearly. Intuitively I would think that, assuming a statistically even distribution of rainfall throughout the local area, speed should not matter because for every raindrop I move into the path of, I'm moving out from under another one at the same time. But this is definitely not what I observe in actual driving conditions, so what's going on? | 1 |
I am studying Linear Algebra. I have faced a problem to understand Symmetric Matrix with spectral decomposition. After I studied spectral decomposition, the next page in my book talks about a positive definite matrix and quadratic form. I am kind of lost what relationships are there between symmetric decomposition, a positive definite matrix, and quadratic form. Hope I can have some explanations. Thank you in advance. | 1 |
According to Collins English Dictionary, and of course as everyone knows, a doula is a woman who is trained to provide support to women and their families during pregnancy, childbirth, and the period of time following the birth However, the definition in wiktionary says: A support person, usually female, who may not have medical or midwifery training, who provides emotional assistance to a mother or pregnant couple before, during or after childbirth. Is pregnant couple actually an acceptable term for referring to an expectant couple? | 1 |
I'm about to wrap a course in partial differential equations. We've discussed the heat/wave equations and introductory Fourier Analysis. I'd like to do some reading into the field of thermodynamics. Would it be best to start with an introductory text given to most lower-division under graduates or should I begin with something with a little more meat on the bones? By meat on the bones, I mean a bit more rigor and explanation for the fundamental theorems and applications. If this is not clear enough please ask for clarification, I'll be glad to provide it. | 1 |
I know that air pressure and temperature are inversely proportional. Now I saw in a book that "Atmospheric pressure decreases as we go higher and higher." But at greater heights the temperature becomes low, and so the air pressure would be high. But it is given atmospheric pressure decreases with altitude. I understand that air pressure and atmospheric pressure are different. But I can't understand how they are different. | 1 |
Given two (or more) loans of different balances and interest rates and a single amount of funds available per payment period, is there a way to calculate the best way to split the available funds to minimize the amount of money repaid? I'm not really sure where to start to look into this type of question so if someone could point me in the right direction or provide an answer that would be great! | 1 |
In my physics classes, I remember it being repeated a few times that gravity is a much weaker force than the other three fundamental forces, and being told this is an open problem in physics. However, I don't understand why this is a problem. I see no intrinsic reason why the four fundamental forces should have similar strengths in the first place. So why then is the fact that gravity is many orders of magnitude weaker than the other fundamental forces a problem? Note: I've attempted to read the Wikipedia article on the Hierarchy problem, but it is far too technical for me. | 1 |
I'm reading a paper titled "Luminescence spectra of quantum dots in microcavities II Fermions" (link). In section III, the authors introduce so-called closing operators. I don't have enough background knowledge to understand the technique there. So it's natural for me to look for other literature or books on the topic. But it turns out the "closing operator" is defined only by these authors and I couldn't find any literature on this. Could you give me any key words which can lead me to related literature? Or you can point me directly to a literature. | 1 |
Generally speaking when we say "our friend" we are referring to someone who is a friend of ours. However, I have noticed that at times these words are used sarcastically to refer to someone who is actually not a friend but an enemy/adversary. So with respect to the sentence below, is the term our friend used as a form of irony? Our friends the Saudis, who never persecute women, gays and other religious minority groups, have somehow managed to lead the UN Human Rights Council | 1 |
I'm starting my last year of high school, and I will have to do an all year research on a mathematical topic. I'm a really passionate learner and I'm very involved in computer science. I am stuck on finding an idea that will both be challenging and fun. I would also really love to integrate computer science in it, since that's what I want to study afterwards. Thank you in advance. | 1 |
Some dictionaries define a scalar as follows: A quantity, such as mass, length, or speed, that is completely specified by its magnitude and has no direction. -- The Free Dictionary However, it is my impression that in many contexts scalars can be signed, in which case their magnitude (their absolute value) does not specify its value. This definition is even used on a test question here. Is it true that this definition is inaccurate? | 1 |
I'm currently taking a numerical analysis course. We are covering linear algebra topics, the gist of the first chapter of the course being solving systems of linear equations. The lecturer has introduced SVD decomposition, condition number of a matrix, LU decomposition and QR decomposition (using Householder decomposition). In the past I've been used to very rigorous, thorough and well-organized math courses. But I feel like what I'm learning here is shallow since there are very few proofs. So my question is Can you recommend rigorous textbooks or detailed lecture notes that cover the topics I mentioned above ? | 1 |
So I'm trying to prove that the set of polynomials in C([a,b],R) is not open. I understand the definition of an open set, but I'm wondering how to find a point that is not contained in the interior if it's the set of polynomials. Also, Can a subset of a metric space ever be both open and dense? I'm thinking it can, only if the interior is empty. ? Would love help with these! Thanks in advance! | 1 |
Why is a homogeneous function called homogeneous? When I ask this, I don't mean, "Show me how to algebraically manipulate a function whose input has been multiplied by a constant to get the original function multiplied by the same constant." I mean--why do we use the word "homogeneous"? That word in particular must have been chosen for a reason; what is it meant to communicate in this context? | 1 |
I know how to solve linear homogeneous ordinary differential equations with constant coefficients using the differential operator D, by using this method. Is it possible to use a similar method (using the differential operator) to solve more advanced ODEs? I'm thinking of both more advanced linear ODEs, such as Euler-Cauchy differential equations, as well as non-linear ODEs. Are there any articles on the web on this topic, or even textbooks that use this method to solve ODEs? | 1 |
One oddity I notice is that if a random or quasi-random data series such as price data is plotted, it is similar to a random walk, but if the same data series is plotted using candlesticks (open-close, high-low), there appears to be in many cases an undulating pattern. I assume that this is caused by some kind of aliasing. Is there a mathematical explanation for it? | 1 |
I am an mechanical engineering student so I'm kind of ashamed to ask this question but I have a weak math background and am digging into some of my knowledge gaps. So my question is where are all of the constants of integration and why are they generally ignored? Is it simply because they are usually treated to be zero? I guess what I'm looking for is an intuition in regards to integration constants...i.e. how do I wrap my mind around why the integration constant is/was ignored, and how can I truly understand what is going on when these constants are ignored. Any insights or conversation is greatly appreciated. Thanks in advance! | 1 |
I don't know where I've heard such expression. I try to explain (for sales) what our software tool does and I use this sentence: "It helps you to deploy apps in a very simple fashion". And then I describe the steps of how it works. I googled this expression and I found only one reddit post. Is it a widely used expression in the US? Will native speakers understand me? What about non-native speakers like EU folks, will they? Can I rephrase it as "in the simplest possible fashion"? Thanks! | 1 |
My background : I'm currently in my junior year in college majoring in astrophysics. I have taken GR, and some intro cosmology here and there, but nothing in great depth. I had my heart set on taking a full physical cosmology class this spring. As luck would have it, I can't take the physical cosmology class due to scheduling conflict ! I intend to proceed to graduate school in astrophysics, so I would have to take the graduate level cosmology then, but in the mean time, I was thinking of teaching myself undergrad cosmology out of Barbara Ryden's book. My question is : any advise for undergrads teaching themselves this subject matter ? Are there any "go to" resources? is Ryden a good choice? | 1 |
I was wondering if it's possible to construct a table in LaTeX which has a fixed header so when we scroll down the page of the output PDF, we can still read the column names and keep track of what the numbers in the table represent. I have seen in a post here at stackoverflow about how to do this with HTML and someone had linked to this example: http://www.mustafaozcan.net/en/demo/fixedtableheader/jquery-fixedtableheader-demo-en.html I would like to be able to do that in a PDF produced by LaTeX. Is that possible? | 1 |
I was doing some calculations in MATLAB, and noticed a pattern that may be obvious to stats experts, but I didn't notice it before. If I have a time-series, and I remove a linear trend / detrend it, I find that the mean of the detrended data is zero, as expected. However, I was surprised to find out that the standard deviation of both the detrended data and original data is roughly the same. Is this what one should expect? Thanks! | 1 |
I am just beginning to read about the use of "Concave Programming" methods and use of the Karush-Kuhn-Tucker conditions to identify the maximum value of a non-linear objective function subject to inequality constraints. The examples I have seen in the text I have at hand, all involve only linear constraints. Is this method equally applicable to situations where not only are there multiple constraints, but where one or more of those constraints are non-linear ? | 1 |
Wikipedia has the following quote on John von Neumann: Stan Ulam, who knew von Neumann well, described his mastery of mathematics this way: "Most mathematicians know one method. For example, Norbert Wiener had mastered Fourier transforms. Some mathematicians have mastered two methods and might really impress someone who knows only one of them. John von Neumann had mastered three methods." He went on to explain that the three methods were: A facility with the symbolic manipulation of linear operators; An intuitive feeling for the logical structure of any new mathematical theory; An intuitive feeling for the combinatorial superstructure of new theories. And I am wondering what do 'logical structure' and 'combinatorial superstructure' mean in this context? Please explain these methods. https://en.wikipedia.org/wiki/John_von_Neumann#Mastery_of_mathematics | 1 |
I am studying client's request arrival patterns on web and application servers. About web server's request arrival pattern I read that "The request arrival rate on web server follows Poisson distribution". And about application server I read the sentence "The request arrival rate on application server follows exponential distribution. Now kindly explain " is there any difference between Poisson and exponential distribution in the context of client's request arrival pattern on server". Is there any difference between poisson and exponential distributions? | 1 |
I'm working on a project right now and part of the introduction is about energy, and I'm trying to introduce the notion of energy in an unconventional way. Right now, I am looking for examples of situations in physics and chemistry where energy plays a key role. Another way of putting it is: I am looking for questions where the answer is energy. I'm basically trying to motivate the concept of energy and demonstrate why it is important. Does anybody have ideas of seemingly fundamental occurrences where a true answer is provided by the notion of energy? Thanks! | 1 |
When used as an expletive, the name Jesus Christ often gets an H inserted into the middle of it for some reason. I've heard lots of guesses about what the H stands for, the most popular one being Henry, but no one seems to actually know, and I've never gotten any good explanation of where it came from or why it became popular to insert it. Is there any documentation of when Jesus H. Christ as opposed to simply Jesus Christ came into currency as an expletive? Is there any authoritative explanation of what, if anything, the H was originally supposed to stand for? | 1 |
In high school a while ago, I learned a bunch of random terms for words and phrases: synecdoche, antonym, oxymoron, palindrome, etc. There's one term that escapes me but I can give examples of it. I don't love my wife because she is beautiful but she is beautiful because I love her. We travel not to escape life, but for life not to escape us. What is the name of this term? Thanks in advance, it's killing me not being able to remember. | 1 |
D-branes, as I currently understand them, are submanifolds of spacetime on which open strings can end with Dirichlet boundary conditions. On the other hand, type II string theory is a theory of oriented closed strings - the difference between IIA and IIB coming from the choice of GSO projection. Based on these observations, I have the following questions: If type II string theory is built from closed strings, why are D-branes considered in the theory? If open strings are included in type II, does the GSO projection act on the open strings? If so, how? | 1 |
Trying to show that if a sequence converges, it either has a maximum, a minimum or both, I reached a dead-end. Assuming it is not constant, it is still bounded and its supremum and infimum aren't equal. Then I assumed that the supremum and infimum are not in the sequence. I want to show that there are two subsequences that converge to each of them but for that to happen I have to show they are accumulation points. I tried to use definition but failed. I know logically that following my assumption they have to be accumulation points but I can't derive it from the definitions. Any help? | 1 |
I'm working on finding whether sequences converge or diverge. If it converges, I need to find where it converges to. From my understanding, to find whether a sequence converges, I simply have to find the limit of the function. I'm having trouble getting started on this one (as well as one more, but I'll stick to one at a time). I would appreciate if someone could explain how I should start this one. | 1 |
This may not be the correct place to ask such a question. I have read a mathematical paper on multiclass total variation clustering. I wish to use the algorithm in the contents to compare with another clustering result. My question is: Is there a proper etiquette for asking the author(s) of the paper for their code? Is it rude to do so? Should I just try to figure it out on my own? Or is this something that is common? One reason why I want to ask is because I am short on time and may not be able to figure it out by my deadline. Any comments would be greatly appreciated. | 1 |
When writing a book on popular culture, I'm using italics to introduce a film title into my paragraph. In the next paragraph I refer to the film title again. Should I use italics on the second occasion, or stick with normal text? I'm tempted to go for the latter - as over-use of italics would spoil the flow of the text, and the title has already been introduced to the reader. Thoughts? | 1 |
This question may sound naive but still I haven't seen it being discussed in any book. Why do we parametrize surfaces with two variables as opposed to curves? Initially I thought that it is not possible to fill enough points in the space with one variable but there are space filling curves so it is certainly not the reason. Is it because we need to move in two directions? | 1 |
So I've modeled the interactions between the sun and all the planets (and the interactions between the planets) using Verlet integration. I've used data from Wikipedia for masses, distance from the sun etc. I initialized the initial velocities of the planets via the critical velocity equation. This produces nice stable velocities. I'm unsure of how to calculate the initial velocity of the moon so that it stays in orbit around the earth. | 1 |
I just learned from Wikipedia that coproduct of two (commutative) rings is given by tensor product over integers, and that coproduct of a family of rings is given by a "construction analogous to the free product of groups." Can the tensor product approach be generalized to an arbitrary family of rings? (Infinite tensor product?) I'm a little surprised that coproduct of commutative rings requires noncommutative structure (free group). Does someone have a reference which explicitly constructs the coproduct? | 1 |
If I have a binary number W bits wide, initially all set to zero, and I repeatedly pick a random bit and toggle it from zero to one or vice versa, how many times would I need to do this to achieve maximum entropy? I hope I am using the term "maximum entropy" correctly -- what I mean is a point where the distribution of ones and zeros is as random as possible, and no amount of continued toggling will make the distribution any more random. | 1 |
Any given square is always a rectangle, but a rectangle isn't necessarily a square, so squares and rectangles have a _ relationship. I've been noticing this sort of thing everywhere ever since I noticed that I didn't know a good word for it. I've been calling it a container relationship because one class of things is contained within a larger class of things. However, a "container" relationship doesn't sound very good and doesn't really convey the meaning on its own. A more elegant word would be helpful. Edit: A specific definition would be something like: a is always b. b is sometimes a. | 1 |
I'm not a physicist, but I'm really interested in Nanotechnology. I've a question, and I hope that I can be provided by an answer. I was reading some articles about the one-dimensional CdSe nanostructures. My question is why it's called one-dimensional? Is it because of their geometrical shapes or something else? I truly appreciate any hint or a resource could lead to the answer. Thanks. | 1 |
Let's say I have an isolated, adiabatic chamber which is divided into two parts with a massless, frictionless piston. One part has vacuum, while the other has a gas. In the beginning, they are at equilibrium. I release the piston, and the gas expands, thereby pushing the piston towards the end of the box. Since the process is a free expansion, there is no work done by the gas. One could thus say, that the gas applied no force whatsoever, on the piston. Then why did the piston move in the first place? | 1 |
What does the expression "eat shit" represent in the following sentences? Eat shit, I'm not going to do your dirty work. Is this similar to "I dislike doing your dirty work"? Or does it mean "Go to hell."? Eat shit, I am not going to follow you. I found many different interpretations of this expression on Urban Dictionary, so I am quite confused. Please could someone clarify. | 1 |
What I want to ask is what would happen if you split a single light ray (a photon) into two using a half silvered mirror? Would the emerging light rays have half the amplitude as the original one or half the frequency of the original wave? Basically will the frequency get distributed or the amplitude? EDIT I specifically mean a "Single" photon or a single light ray. For those who think a single photon cannot be split, you are wrong. A photon has been split by using special crystals. It is called Parametric down conversion. | 1 |
If the text I am quoting is italicised or bold, does my quote need to include this special font treatment? If I want to emphasise something in the quote, can I make words italic? For example, suppose that the text I'm quoting is: I love apples. I really love them! Can I quote that as "I love apples. I really love them!"? Also, can I quote the beginning as "I love apples,"? Thanks! | 1 |
I don't understand how to solve problems of conditional probability.Here's a problem which I fail to understand."Consider all families with two children and assume that each child is equally likely to be a boy or a girl.If such a family is chosen at random and found to have a boy,then what is the probability that it has another boy."Please help me to solve this problem. | 1 |
I have question which I'm unsure of whether or not I am thinking about it right. If an object is sliding down frictionless incline and it then comes to the "foot" of the incline where it encounters friction, how far would it travel. The foot of the incline is horizontal. The only information given was height of the incline and the coefficient of kinetic friction. I used conservation of energy to find the velocity at the foot of the incline. After, I solved for horizontal displacement using kinetic energy = displacement x mass x gravitational acceleration x coefficient of kinetic friction. Can anyone offer some insight into whether or not this is a good approach? Thank you. | 1 |
The following true/false question was posed: An isomorphism between to vector spaces can always be represented by a square singular matrix. This is not true. I know that in the case of finite dimensional vector spaces: A map is an isomorphism iff it can be represented by a square non-singular matrix. I would like to know whether it is possible to prove this in general (i.e for all vector spaces)? | 1 |
Initially, when the current starts flowing the temperature of the filament is less and thus resistance is less. So, more current flows through the bulb and the power delivered to the bulb is more. As, time passes and the filament starts glowing at a steady rate its temperature has increased which in turn has increased its resistance. So, less current flows through it and thus less power is delivered. Is this the case? Please help me understand the situation. | 1 |
I'm a programmer and I'm looking for a single word that works for the following scenario: I have a list of basic information about people, I call this list the 'user repository'. I need a word for "to view and change more detailed information about a person". I've thought of using words like refine and elaborate, but they don't seem to quite fit the idea that the data can be viewed and changed. | 1 |
Suppose that a person buys a packet of sugar. On the way home, the packet falls off his hands and the sugar scatters on the ground. Nobody is expected to gather the sugar again, but that person does so; of course not for his own use anymore, but to donate it to the poor! Obviously, if the packet hadn't fallen down, he wouldn't have decided to donate it. It goes without saying that this kind of donation and charity is morally worthless and not considered a good deed. Is there any English idiom to describe this kind of charity or donation? Thanks in advance. | 1 |
I tutor student in SAT Reading. One of the SAT tests has the following sentence: "With their dark dungeons and damp living quarters, medieval castles offered few of the comforts to be found in royal palaces." The student thought this must be wrong as "to be" seemed superfluous. To me, there's a subtle difference in meaning if the sentence was changed to "few of the comforts found in royal palaces." The only way I could describe it was that "to be" adds a more theoretical and abstract quality to the sentence. Is there a clearer way to put all this and the change "to be" makes? Thx in advance, J | 1 |
This is something that crops up on the BBC a lot and irks me. For example, from a story today: One woman is critically ill and three others have been injured after they were stabbed near a supermarket car park in west London. To me, you are ill (or sick) if you have, for example, contracted a disease and using it in the sense of someone being injured is wrong. Google gives the definition of ill as "suffering from an illness or disease or feeling unwell." and I'm sure that a car crash or stabbing would certainly make you feel unwell, but I still don't think it's right. Is it? | 1 |
So i am currently learning about double integrals and to be honest i am not really understanding how we compute the volume over general regions. Here is the proof provided in my text book. It all makes sense until the last part. Since we use Fubini's theorem we can change the order in which we integrate. Since that is true wouldn't that mean that the Fubinis Theorem applies to all double integrals? Since this is obviously not true can you point out what am i doing wrong? IF you need any more clarification/photos please comment. | 1 |
I am applying for a new job; I currently work in my family-owned F&B firm. Now, in the job portal, there is a column where I have to mention my current company. I don't want to give the name of my firm as it is not well-known and also, it is not in the same domain as the job I am applying for. I have currently put down "Own F&B establishment" in the column. But the "own" part seems kind of odd to me. Is there any other word or phrase that I can use instead, which would indicate I am not just working there, but am a stakeholder. | 1 |
It is right on the tip of my tongue, and I have searched the online thesauruses but I can't come up with it. What's the word that could fill in the blank: He came to the ___ conclusion that you must be willing to serve if you want to truly lead. The best I could come up with is "non-intuitive", but that just doesn't sound right. I know there's a better one. I want a word that means "this is not what you would expect", "this goes against your intuition". Something that approaches "nonsensical" or "irrational" but without the disparaging overtones, yet more forceful than "surprising". | 1 |
I am struggling on this one question, where it is asking to define an XOR automata which is defined as an NFA and it is defined as the following: N accepts the string x if the number of distinct accepting states that can be reached by a path labeled with x is odd. I'm supposed to prove that any languages accepted by the XOR automata is regular and that any regular language can be accepted by the XOR automata. Can anyone explain to me how I may be able to go about starting this proof? Thanks. | 1 |
My question is simple. I'm an undergraduate student taking Partial Differential Equations. I'm looking for a problem book with solutions. My intent is to just do problem after problem to practice for my final and our assigned PDE book doesn't have the answers, so there's no way of checking. Would anyone happen to know of a good PDE book that has problems and answers (or if possible a solution manual) that I can find online? The book we're currently using is: Basic Partial Differential Equations by David Bleecker and George Csordas. Thank you | 1 |
I'm looking for an adjective that describes the fact that a ship is sailing at sea. Much as "afoot" describes a person being in the state of walking. I was hoping "asail" would be a word, but can't find it from Google. The word would replace the square brackets in the following example: In Plato's ship of state metaphor, a ship is [sailing at sea], helmed by a captain ... | 1 |
The Large Hadron Collider (LHC) "remains one of the largest and most complex experimental facilities ever built" (Wikipedia); it may even be the most complex project in humankind's history (?). Such projects usually have impact beyond their original target and boost science and technology in a non-trivial way. I wonder, then, what kind of impact it has or might have on other science and technology fields, in particular on mathematics (if any), and what specific impact has mathematics had (or might have) on the LHC project (if any)? Cross-post on mathoverflow: Impact of LHC on math. | 1 |
I realize that "kinda" is an informal form of "kind of". However, would "kinda" be appropriate in fiction or dialogue? Or would it be more acceptable to stick to "kind of"? This is for a fiction novel from first person view. Additionally, I found that when I write, I tend to use "kinda" for more informal sentences ("it was kinda freaky") and "kind of" for more serious sentences, I would use "kind of" ("I kind of knew how they felt"). Is this acceptable or would it be preferable to use "kinda" or "kind of" consistently? | 1 |
We know that a Hilbert space is separable if and only if it has a countable orthonormal basis. What I want to ask is If a Hilbert space has an uncountable orthonormal basis, does it mean that it is not separable? Or equivalently, does it imply that the Hilbert space does not have a countable basis? I know that if a vector space has infinite number of linearly independent vectors then it cannot have a finite (Hamel) basis. But here we do not deal with Hamel basis but with a complete orthonormal set, do I cannot apply the usual techniques. Any ideas? | 1 |
I am having lots of trouble with this series. I will upload a picture of what I did. According to Wolfram, the series converges by the ratio test. I also don't know how I would use a different test for such a series. Two of the limits weren't difficult, but obviously I have to do something else, since I am not getting the right answer. We haven't covered Stirling approximation if it applies here, so I'd like some help without using it. Thank you so much. | 1 |
In chemistry we learned about the penetrating power of three common types of radiation: alpha, beta, and gamma. Alpha can be stopped by paper, beta is stopped by a sheet of metal (I think) and gamma is stopped by lead. In the same unit, we talked a lot about nuclear weapons, but not once discussed the neutron radiation that causes the chain reaction in nuclear weapons. What kind of penetrating power does neutron radiation have in comparison to the other three we learned about? | 1 |
I only have a basic, mostly classical understanding of physics and am just starting to learn about photons. Am I correct in saying that, as a photon moves through space, the strength of its electric field varies? If I am correct, what is the qualitative nature of this field? Is it positive (would repel a nearby proton it was passing by) or negative (would attract a nearby proton it was passing by)? Does it switch between positive and negative? Or would it have no effect on a proton it was passing by (the field is neither positive or negative)? If the field is neither, how is it even possible for an electric field to exist without being positive or negative? What would such a field even mean? | 1 |
I know what "begging the question" originally means, but I just can't make any sense of the idiom. The phrase really seems to have nothing to do with its own meaning. The original Latin phrase, petitio principii, is often translated as "assuming the initial point," which quite simply explains the practice. Does the phrase "begging the question" carry any meaning (related to what it's used for)? | 1 |
I was wondering why it is almost impossible to find a geometrical explanation of why adding two linear equations helps us to find a solution of a system of linear equations? Am I right that adding two linear equations will result in an equation of a line which will pass through a point where two linear equations intersect? If it is right then I completely don't understand why such a crucial point in understanding how to solve systems of equations is never properly taught even at a university level. | 1 |
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