darklight03/StackMIAsub huggingface dataset:
Is there an intuitive way to understand the convex duality? If the primal problem is minimization, the dual is maximization over another set of variables - but I would love to have a geometric visualization of this and an intuitive way to understand why this ought to be true. I'd also want to see strong duality present in such an intuition. Textbooks are dense in the math, but I haven't come across a place where this could be imagined in our minds without variables and equations. Could someone here help me out?
If I have two points at different X/Y coordinates, I know that: They are vertically aligned if both are at the same X coordinate; They are horizontally aligned if both are at the same Y coordinate. Based on the X/Y coordinates of one in relation to the other I can also tell the distance between them, etc. Now, how can you tell that the points are diagonally aligned by following the same logic?
We still hang up the phone, even though we really only push a button, not suspend it in a cradle. Sometimes we tape a television series, even though the DVR does the heavy lifting, not the analogue insides of a VCR. Is there a term for these words and phrases? I'm not sure about using words like obsolete or archaic, because the methods they describe may be, but the phrases themselves are not.
Reading the article "Emergence of scaling in random network, by Barabasi and Albert" I faced a lot of results obtained by simulations of the A-B random graph model. I always wanted to do such simulations, but honestly I don't know how to start. There is a better programming language? There are packages? There is a special software to handle heavy data? To put everything in one question: how they do that kind of simulation?
As kind of a real-life example, I'm struggling to write a description of the Crusades from the point of view of a Catholic pope. I know that through the Crusades, the Christians basically "rescued" the city of Jerusalem from the so-called "filth" that inhabited it. (Note: Please do not be offended by my use of the word "filth") You might say there's a tip-of-the-tongue phenomenon going on here.
I'd say both of these uses of "he was shot" make sense: "How did he die?" -- "He was shot in the street" [meaning shot dead] "He was shot in the street, but luckily the bullet only hit his foot." [meaning shot at -- there was a bullet coming his way] Would you agree? And what would you think of a headline "He was shot in the street". Is the man dead or was he just 'shot at'?
As an American, a large part of my impoverished experience of British accents comes from ancient BBC comedy imports on PBS. I'd very much like to identify the regional accents the following actors are using: the farmer Maurice Moulterd in Are you being Served? Again! (aka Grace and Favour) (the second series where they're running a country inn). Alice Tinker and Owen Newitt in The Vicar of Dibley Onslow from Keeping Up Appearances All four have distinct ways of speaking (not necessarily the same, but then that's the problem, I can't tell). Which accent does each of these four use?
In this question different people understood different things when talking about topological manifolds. Some argued they they have to be Hausdorff, some that they have to be second countable and some, both. When I studied them, my teacher showed us examples of non-Hausdorff (the line with two origins) and non-second countable (the long line) manifolds. For me, a topological manifold is a locally Euclidean topological space. What are the different definitions of a topological manifold you know? What it depends on? What author you read when you studied them? Who was your teacher? EDIT: What properties have the topological manifolds if we define them as second-countable and Hausdorff that they don't have if they are only locally Euclidean?
The problem says "In a factory, m workers work h hours to do j jobs. If p new workers are hired, how many hours will the work force have to work to do j jobs?" I worked out the answer logically, but I'd like to know if there's a formula that I can go to to make it simpler and faster when this kind of question arises again. Also I'm really not sure what the type of problem is called, so sorry for any confusion in tagging/titling.
I was surprised to discover my dictionary had this entry for dilemma: a situation in which a difficult choice has to be made between two or more alternatives, esp. equally undesirable ones The notion of dilemma meaning two or more flies against what I was taught about the word. The very idea of a false dilemma is specifically based on the number two. Has my dictionary merely updated its definition to encapsulate the many people who use dilemma for more than two equal choices? Or was someone in my youth being unnecessarily pedantic?
What is the word a deep desire that some external force has kept you from gaining it? For instance in the movie Foxcatcher, the rich guy always wanted to be wrestler but his mother didn't let him because she thaught it was a low sport and it was beneath him and this made a 'deep desire' in him to be a wrestler. Is there a word for that? The word I'm looking has some kind of negative meaning. This 'deep desire' makes you do stupid things and kind of has a bad effect on your personality.
I am learning Mean value property (MVP) of the heat equation. MVP of Laplace equation was relatively easy to understand I think it is because of the spherical symmetry. But I am not able to appreciate the MVP of heat equation. It's not very easy to imagine the "heat ball" in the following theorem from a note: Here are questions: How do I define a heat ball? How does it actually look like?
I have read this is true for all hyperbolic triangles, but I am trying to find an extreme example, or a limit behavior, were the sum of the angels of a hyperbolic triangle are minimized. Is there a min/ inf? Also, why do all hyperbolic triangles have angles sum less than pi (if that is true)? To avoid ambiguity, I am referring to hyperbolic triangles in the open upper half complex plane.
Consider the examples from the Free Dictionary: That summer, she up and died. He had lived here for twenty years, and then one day, he up and left for good. Is this a contraction of a longer phrase, making "up" a particle (as in "get up")? Or is "up" meant as a verb, but mysteriously not inflected according to tense/person? (in which case, how did it end up not being inflected?)
If we can think about the universe as a wave function then many particles should be entangled with many other particles in the universe. The obvious question arises why we don't see those entanglements in everyday circumstances. One standard explanation given is those entanglements average out and cancel so we can ignore those. However, hardly any mathematical justification is given for them to cancel. My question is how much trust one should have on that particular assertion? Is there any mathematical arguments already put forward by anyone?
Do matter and antimatter eliminate each other or release their equivalent energies? I'm almost certain it's the latter as mass can't be destroyed, but when speaking of the big bang it's said if there were equal amounts of both matter and antimatter there would be nothing left. I wonder how that can be true if they don't destroy each other. It may have something to do with how energy decays into matter.
Got curious about polynomials and Galois theory the other day and realized I have no idea how current mathematics treats polynomials (or rather polynomial like expressions) that have arbitrary algebras for the exponents. A quick search yields polynomial extensions like Laurent polynomials but I couldn't find anything that uses any other groups for the exponent, like Gaussian integers, complex numbers, cyclotomic rings, hypercomplex numbers and other algebras. What are these structures called and how is their behavior similar and different with ordinary polynomials?
Let's consider a partition of the words in the english language according to respective use frequency. Looking at the frequency graph it should be easy to find classes of words with approximately the same frequency. Now I'm interested in the size of these classes. I know that the size depends on the relative cut-off points, but I'm more interested in a general classification, i.e. are there more common words, or more uncommon words?
I have recently come across two key concepts in quantum optics: shot noise and back-action noise. This is very important for me to know: first, are shot noise and back-action noise the same? Please let me know if there is any other equivalent term for back-action noise among the quantum optics community. I am also wondering whether back-action is the nature of light beam in vacuum, or is it related basically to measurement detector like homodyne? I really like to know exclusively the characteristics of back-action noise to be able to model it.
There are so many famous paradoxes which are examples of how humans are unable to intuitively understand probability -- there's a discrepancy between their supposed actual experience and the mathematical evidence. There's things like the birthday problem where what we would expect the probability to be is much less than the actual, but also the monty hall problem where the confusion comes in why the answer is what it is. My question is, what is the cause of this? Why are we biased into thinking things are more or less likely than they really are? Why do we find it so difficult to accept and understand the correct probability in the case of the monty hall problem, burnt pancake problem, etc.?
Recently I was proof reading an email that a coworker was going to send to a superior and I pointed out that the valediction wasn't capitalized. He said it didn't need to be because it was the start of a phrase or clause and not a sentence, and that people only do it because other people do it. But in the back recesses of my mind I'm thinking that there is a rule that says that it should be capitalized. Is my coworker right and capitalization is unnecessary in this case? If I'm correct, what rule or guide can I point to, to prove my stance? (T/t)hanks, Jeremy
I've been thinking about this, I want to use this as my science project. The two viable solutions I've thought of so far are magnet or rotary based. Pendulum clocks could be powered once a day and run the clock for the whole day. From the rotary motion, could I easily generate electricity? A magnet on the pendulum could generate energy through coils. Does anybody have any suggestions? I'm just a highschool student so the project should be easy and small. Any blueprints or tips will help. Thank you.
so my goal is to detect an odd-cycle in a directed graph. I know for the undirected graph, the graph contains the odd-cycle iff it's non-bipartile. So I can check whether or not the graph is bipartile. If it is then the undirected graph doesn't contain the odd-cycle, otherwise it does. For the directed graph, does the same algorithm apply? Do I need more condition for the directed graph to have odd-length cycle? Thanks
I have always wondered about the similarity of the two words Astronomy and Astrology that describe two very different things but have their beginning in common and are sometimes confused in everyday language. The linguistic difference (if one can say so) between them is only in the endings '-onomy' and '-ology'. Two further examples are Topology and Topography Geology and Geography where now we have the endings '-ology' and '-ography'. What are the meanings of the different endings '-onomy', '-ology' and '-ography' ? I would also be curious about whether it is a coincidence that '-ology' appears in all the examples above? Does it maybe have historical reasons? And furthermore, are there more such pairs to be found? (I can't think of any others)
In the quote in the title, "of" refers both to the material that makes up the cup and to the stuff that the cup holds. I remember reading that there is a literary device that describes this, but I can't remember what it's called. The device, if I remember correctly, refers to the parallel structure of a phrase whereby a thing is described in two aspects or, as in this case, an aspect and a function. Shakespeare commonly used it, though I can't think of a quote. Syliva Plath uses it in the line: I am silver and exact to refer to a mirror--what it's made from and how it does its job. Could someone tell me what this structure is called.
I am looking for a phrase that is in the same spirit such as "single point of failure", or "bottleneck". Example: Being two engineers short is <-term goes here-> in this situation. If we find two engineers, the project will meet the deadline. Another one: Electric cars are improved enough to be on par with internal combustion engine cars. However, the long charging time is <-term goes here-> behind the problem that electric cars are not as widespread as internal combustion engine cars.
What constructions allow a writer to preserve strict logical coherence and reduce redundancy when conjuncting two noun-phrases? Example Many cultures have used gold or silver bullion as a currency. That sentence could imply that many cultures have used gold -in any form- or silver -only when cast as- bullion, but I intended it to mean that many cultures have used gold bullion or silver bullion as a currency. Moreover, a reader could interpret the sentence to mean that many cultures have used gold -in any form, for any purpose- or silver -only when cast as- bullion -and only- as a currency. How can I construct that sentence to ensure it imparts only the meaning I intend it to impart?
When the word that is used in a sentence to introduce some relative clause it is always an essential element which follows. Therefore, no comma is required. Example: I'm sure that you are lying. When I leave out the word that, it is still a correct sentence, right? Do I have to use a comma then? Because, when you read the sentence aloud, it kind of feels like there is a pause. Examples I'm sure you are lying. I have the evidence right here in my pocket (that) you are lying. Especially in the second case, I would prefer a comma at the place of the that. Is there a strict rule?
In the following sentence, what is the function of "You"? You, go to the store. I know the sentence is in the imperative mood, and that generally means there is an implicit second-person subject. If we dropped the initial "You", the subject would be that implicit subject. While "you" matches that second-person subject, that seems just incidental and it seems like it is just an expression of address that happens to match the implicit subject. Is it the subject, or merely a vocative expression? Or in other words, is the subject the "You" in the sentence, or is it the implicit subject from the imperative mood?
I have to show that if a metric space is path connected and countable then it is complete. I'm pretty lost where to start this at all. I have the basic definitions of complete, path-connected, compact and sequentially compact spaces. Any help how to do this would be great (this is a past paper question-non assesed, just for practice so I think it should be reasonable simple) Thanks very much for any help
can anyone help me by using geometric transformations to solve this problem: construct the triangle whose sides bisectors and their intersection point is given; my professor told me that if I assumed the problem to be solved I would notice that we have compositions such as symmetries, reflections, rotations . I can't really understand what he meant, if anyone can help me with a hint or the solution I would be very thankful
I'm sitting here in the metro station, drinking a bottle of water, and watching how the flow of water out of my mouth changes as air rushes into the bottle. My questions is: in space, obviously the effect would be different. How is this effect different as compared to with earth, and can the change in behaviour be solely attributed to the effects of gravity?
I want to randomly distribute some(in thousands) objects over a surface. This I can achieve with a function say x,y = rand(). This will evenly distribute objects over the surface, but is it possible to have some control over the randomness like having some groupings (some objects close together). I can try to achieve this with multiple iterations of distribution, but that might run into objects overlapping. So was looking for some kind of parameterized algorithm that might help in this area. I do not have much knowledge in mathematics so would appreciate some help. Thanks!
I'm looking for an adjective, saying or idiom for an analogy which makes the things even harder to grasp, that was supposed to make things easier to understand. Examples: A guy makes an analogy to express that playing violin and driving a car is similar, when he teaches driving cars. But since very limited people know how to play violin, it does not make things easier. A guy teaches culinary on Youtube. But he rather than he explains the basics of culinary (say boiling water), he says 'oh this process is similar to gamma radiation'. It is not important if the analogy is good or bad. Just it makes things harder to understand.
I am seeking a word, should it indeed exist, that describes a dramatic or literary device found when a new character is introduced into a story which disrupts the natural equilibrium, driving the story. For example, in J. B. Priestley's An Inspector Calls, there is a natural equilibrium at the Birlings' home. This exists, however, until the Inspector arrives - disrupting the natural order, it seems, and goes on to defining the narrative.
We know that a small object moving fast enough can pass by a planet and escape its gravity. Would this be (theoretically) true in reverse? Meaning a planet moving fast enough past a stationary smaller object would not assert its gravitational pull on the small object? Would this mean that gravity is mitigated by velocity regardless of whether the more massive object is moving as opposed to the small object?
Humans see only a narrow band of light wavelengths. Many animals see much deeper into infrared. Maybe one clue to explain why we don't see IR naturally, has to do with the light intensity as a function of wavelength? How would such a function look like on Earth in daylight and at night respectively? I suppose that shorter wavelengths are less intense, because they are harmful. But what about IR, is it more or less intense than visible light in daylight outdoors?
I'm trying to control a system where the controller sample rate is physically fixed and the plant has significant dynamics on the same order as the sample rate. I understand that one would prefer to have the sample rate considerably faster than the plant dynamics, but the physics of this system are such that this is inherently impossible. I can get some control of the system by hand-tuning a PID, but it seems considerably sub-optimal. Is there a strategy for developing a controller like this? Edit: I should add that the plant is this situation is a relatively complex LTI plant with reverberations caused by pure time delays. The delay cycles are a bit slower than the Nyquist frequency. The plant is stable.
I've been thinking about the following pattern for some time: Linseed oil... soaks into the (visible and microscopic) pores When I was a kid, this wasn't the way I was taught to use parentheses: they go after an idea, and explain it further. Yet it makes perfect sense--"visible and microscopic" is an aside, explaining details. Is this the right punctuation? Is it informal, or only acceptable in technical writing? My gut says brackets might be more correct, but I can't justify it: Linseed oil... soaks into the [visible and microscopic] pores
I'm using the document class scrartcl and appendix. This currently results in a letter instead of a number for section enumeration in the TOC and section title ("A My Code Listing"). I need to change this to "Appendix A My Code Listing", i.e. add the word "Appendix" to the section title. I have found a manual workaround on http://web.reed.edu/cis/help/latex/thesis#appendices but would like to know if there is a way to change this automatically.
I'm going to teach very elementary combinatorics (limited to basic enumeration) during two weeks to middle school students. At the beginning, I want to demonstrate the importance of counting in real life or technology using concrete examples which students are familiar with, so that they appreciate what they are learning. In this discussion, almost all examples are advanced and are not appropriate for middle school students. I'm looking forward to your suggestions. Thanks.
Is there a character in any established alphabet (I couldn't find anything in the IPA) to denote a sharp intake of breath, as if by surprise? I want to include it in a character's name. Initially I thought "!" would suffice, making the name, for example, "!Davis" (pronounced -breath-Davis) based on its usage in demonyms like "!Kung-San", but it seems I have mis-remembered what the exclamation point here does. Googling just gives me information on "a sharp intake of breath", which I'm sure is wonderful but is of little use to me at the time of writing. Thanks.
I recently encountered this word while reading an article and found that its two basic definitions are "Bewildered" and "Unfazed." How can the word mean both these things as they seem to be direct opposites of each other? Should the sentence in which it's used always explicitly reveal the intended meaning? And while many of us might be a little taken aback if Mom showed up at our offices, Secrist is utterly nonplussed, even happy about it. source In the above sentence, it's obvious that Secrist is "unfazed" without even knowing the definition of nonplussed. Instead of adding clarity to the meaning being conveyed, "nonplussed" seems to just add confusion. Then again, maybe I'm missing something. Thoughts? My first post here so please edit/re-tag as appropriate.
The definition of a topological space is a set with a collection of subsets (the topology) satisfying various conditions. A metric topology is given as the set of open subsets with respect to the metric. But if I take an arbitrary topology for a metric space, will this set coincide with the metric topology? I'm trying to justify why we call the elements of a topology "open". If my above question is true, then at least in a metric space, the set of open sets is equivalent to the topology of the metric space. So am I right in thinking that when we remove the metric, we are generalising this equivalence by defining the open sets as those that satisfy the conditions of a topology?
If i put a pen on a table in its horizontal position and then i try to move it horizontally by giving it a small push, so that it would fall off a table, i expect it to move horizontally but my pen ( and all other pens too! ) moves diagonally when it starts moving down the table!When i remove the notebook , the pen moves like,its shown in the picture ( if i keep it horizontally also, it gives the same result)- Why does this happen? Why does it not move horizontally ?
I'm looking for a word that can describe a long-term inhabitant (inhabitant is the best I've come up with so far) of a hospital. Specifically, a soldier living (retained? - again, word might fit here too) in a War Hospital not long after the First World War, however the answer doesn't have to take into account the time period, as I feel there is a word at the back of my mind I simply cannot find right now which means "inhabitant of hospital." I'd like to be able to use it to complete this sentence: The gravel pathway was bordered by short, waist-height shrubberies behind which were the colourful flowerbeds intended to pacify the hospital's ________.
I've got an undirected weighted graph G with c:E(G)->IR. Now I want to find a spanning tree, such that a node v arbitrary, shall be an internal node, and among all spanning trees, in which v is only an internal node, it has got minimal weight. My Idea: Use Kurskal. If v is an internal node than stop. But if v is not an internal node I'm not sure what to do. Do you know how this could be solvable? Thanks in advance.