darklight03/StackMIAsub huggingface dataset:
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.
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.
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?
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?
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.
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?
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.
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.
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.
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?
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.
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.
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!
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.
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.
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)?
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.
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.
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.
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
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?
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.
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.
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".
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.
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
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 ...
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.
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?
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?
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.
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?
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?
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)?
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.
According to the Bernoulli's equation, if velocity decreases, then pressure increases. I am trying to understand the Bernoulli's effect based on a situation. Suppose we have a stream of water. Let's assume it is an ideal fluid. Imagine the water flows out from a wider pipe to a narrower pipe. Since the area decreases, according to the Continuity equation, velocity of water molecules increase. This causes an decrease in pressure. I don't understand the last part. If water molecules' velocity increase, then their kinetic energy also increases. Wouldn't this causes more collision between pipe's wall and water molecules, thus giving higher pressure?
I hope this isn't an inappropriate question here! I'd like to ask the following (perhaps slightly ill-posed) question: why do we study prime ideals in general (commutative or non-commutative) rings? The situation is somewhat clear to me in some nice cases such as Dedekind rings, but even in slightly more general settings (e.g. general commutative Noetherian rings) the theory becomes rather horrible. What benefit do we gain from an understanding of the prime ideals of a ring? Thank you!
The following quote from Anthony Burgess has a comma after it: There is, in fact, not much point in writing a novel unless you can show the possibility of moral transformation, or an increase in wisdom, operating in your chief character or characters. But this quote from William S. Burroughs doesn't: There is in fact something obscene and sinister about photography, a desire to imprison, to incorporate, a sexual intensity of pursuit. When should you use a comma after "there is in fact"? Is it necessary to put a comma after "there is in fact"?
While learning about shock waves in an introductory Gas Dynamics course, it was revealed that normal shocks are unstable if formed in a converging channel. Even if the local conditions ostensibly require the presence of a shock in the converging section, the flow instead chooses to reinvent itself, moving the shock wave to a diverging section while simultaneously altering the upstream conditions. I can verify that this is a genuine phenomenon, but is there any formal explanation in terms of the underlying flow physics?
We are struggling to find the correct word(s) that describes a list of all messages in the system that are sorted by recency. Trending does not work because what we are displaying is not what is popular in the system, only the most recent. Recent does not work because it implies there is a limit to the number of messages we display. All does not work because it does not imply that they are sorted by recency. Any hints or suggestions are welcome. Thanks!
In an electron gun, the heating filament heats the cathode, releasing electrons by thermionic emission. I've read that "electrons are negatively charged particles and the positively charged cylindrical anode develops a strong electric field that exerts a force on the electrons, accelerating them along the tube". However, I don't think that this explanation is very clear, and I was wondering specifically how the "strong electric field" inside the cylindrical anode is able to accelerate the electrons?
My understanding is that in quantum mechanics the wavefunction may be expressed as a function or as a ket vector (composed of many orthogonal ket vectors). I'm not too sure about the further differences between these two approaches. For example, I am familiar with operating on the wavefunction as a function with the hamiltonian operator, but when you use ket vectors can you use the hamiltonian operator in the same way or do you have to find matrix representations of the operators? I would also be grateful for any links to websites or books explaining the different approaches.
What is the English word for "collecting money for a special event from a group of people"? For example, say some friends are planing a party. Each one has to contribute some amount of money to the event. What is the word or phrase that can be used to explain this kind of activity? I have found "fund raising" to have a similar meaning, but I feel it's more along the lines of "collecting money for some charity event". Is that right, and is there a better word I can use?
I'm trying to write a tagline for my live blogging service, and this is what I've come up with: Live blogs that are a breeze to write, a pleasure to read and are actually updated in real-time. Is that correct grammar or should it be Live blogs that are a breeze to write, a pleasure to read and actually updated in real-time. The completions 'a breeze to write' and 'a pleasure to read' both follow '... that are'. So why does 'are actually...' sound better to me? Doesn't that repeat the 'are'?
Given any problem, how do I know whether it is solvable using Dynamic Programming? For example: consider the rod cutting problem. Now, how do I know whether dynamic programming will give me an optimal answer? Basically my question is: how do I check if a problem follows the "Principle of Optimality" - that optimal solution of every problem involves the optimal solution of a sub problem. And are there any problems that don't follow this principle? (If there aren't, my original question becomes redundant, of course!)
In mathematics we often have statements like a x <= b, where a and b are constants and x is a variable. Now there may be variables satisfying the inequality (that is the statement is true) as well as variables violating it (in which case it's false). However I don't have any words in my vocabulary to express stricter statements: Is there a word to describe that the variable x satisfies the equality a x = b? What about the case that a x < b? I remember having read "x is a root of the inequality" meaning a x = b somewhere, but I can't remember where.
Let's say me and a colleague are going to a meeting and I want to make sure his responses to the questions raised are similar to mine, that we are in agreement and we will responde in a similar manner. Can I say: "Let's make sure our responses are aligned" or, "Please let me know your views cause I want my responses to be aligned with yours."
The words "opportunism" and "opportunist" suggest the ability to take advantage of situations -- but they assume that one is doing so for one's own benefit, which makes the terms pejorative. What is a non-pejorative word in English that means "have the skill and wisdom to recognize and seize opportunities that lead to broad gains"? I am looking for something that is part of the "art" of diplomacy and politics, for example. "Clever" is a somewhat helpful adjective, but there is no such thing as a "cleverist." "Entrepreneur" means is a person who is willing to take on risk and innovate, but lacks the sense of seizing opportunities as they emerge. It seems like an important concept that has no word. Any suggestions?