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"Half of the time I was working from about eight in the morning until eight at night, and the other half I was incapacitated by excruciating pain." This is what I have currently. Is this correct or is there a better way to approach this sentence? To be specific, I am wondering about my comma usage, and whether or not more commas should be added, however, all tips are welcome. Thank you. | 1 |
I learned a lot from prof Tao's notes and books because unlike many authors, he seems to prefer writing more words, explanations and intuitions rather than just mathematical formulae. His approach is also very pedagogical, and quite often, when talking about one concept, he also talks about similar concept in other fields, like group theory, differential geometry, etc. (due to his very broad areas of expertise). This makes me understand (superfically) how mathematical concepts are related to each other. I would like to know if there are some books or blogs on probability theory, stochastic processes, Monte Carlo and convex optimisation, with similar writing style and approach. Many thanks!!! | 1 |
I'm new in this study and I don't know much about the foundations of mathematics, so I have a question. If I'm doing category theory, and I need to talk about "small categories" , "locally small" and etc, I need to have some set theory foundation like NBG where I can talk about this things, right? But, if I want to take the category of all categories, I will have some problem in this context with NBG as foundation? | 1 |
I'm looking for a foundational book that builds up ideas like transcendental functions. For example, how the trigonometric functions are truly defined when plotted as continuous functions. I believe Shilov briefly touches on this in his "Elementary Real and Complex Analysis", but I'd like a more broad and in-depth treatment - book that, in general, deals with mostly functions (and maybe continuity/their limits). Meant for a freshman mathematics major. Books that are entirely dedicated to this topic are preferred over others wherein this topic is only treated in passing. | 1 |
We all know that it uses less energy to go by wheeled transport than walking if the terrain is smooth and there are not too many hills. We also all know that when going up steep hills we get off whatever wheeled transport we are using and walk. To make things concrete, let us consider a child's scooter. How can one calculate the steepness of the hill at which point you would use more energy to scoot than to walk? | 1 |
The phrasal verb "sit on sth" means "to be a member of a group of people". Well, according to Longman, "to sit in / on sth" means "to be a member of a committee, parliament, or other official group", the same thing. I don't know why my phrasal verbs book "says" just "sit on sth" and doesn't say the "in" too. Perhaps Parliament can only be used with "in" with this meaning, I don't know. When I found the meaning of "sit on sth" for the first time, I realised that I could say "To sit on a Parliament" and not "To sit in a Parliament". Is my phrasal vebs book incomplete? Can "sit on a Parliament" be correct? I hope you understand my question. | 1 |
I was wondering how one would actually calculate how much oxygen would dissolve into water given the necessary initial conditions, and what those initial conditions would need to be. I assume they would be pressure, and initial concentration, but I really don't know where I would go from there. Clearly air and water have different concentrations of gases and liquids, despite having been in contact for thousands of years. And once in water, is oxygen still considered gaseous? I assume it is, but why is it called gaseous-what quality of it deems it a gas despite being surrounded by liquid? | 1 |
I'm designing a space ship for a comic I'm writing. I was just finishing up the first sketch when I thought whether such a design would actually be possible. Hence my question: A spaceship is located in deep space. A propulsion system (let's make it a rocket) is attached to the side, and thus not in one line with the ship's center. Would this spaceship travel in a straight line, or rotate? | 1 |
Let S be the intersection of diagonals in a cyclic quadrilateral. Let p be a circumcircle of a triangle ABS and it intersects BC in M and q is a circumcircle of a triangle ADS and q intersects CD in N. Prove that M, N and S are collinear. I tried proving that vectors NC and DC are the same, and also that vectors CM and CB are equal but nothing seemed to work. I'm probably not thinking right. | 1 |
Question: Why is ionic lattice energy inversely proportional to the radius of the atom? Most heterogeneous covalent molecules are polar to some extent. The degree of polarity, or the dipole moment, depends on the difference in electronegativity difference between the two atoms. The larger the dipole moment, the higher the ionic character. What I know: Electronegativity decreases as you go downward in a group, however, the size increases, usually, as you go downwards in a group. Thus, ionic character will increase upon going downward, but the ionic lattice energy will decrease? This seems contradictory. Is this true? And if it is, why is it so? | 1 |
As far as I know, a magnetic field can only be produced by a moving electric charge, or from a particle's spin (this is how a permanent magnet works, all the spins are in the same direction) What is strength and direction of the magnetic field of a stationary electron at the origin with spin oriented straight up? I suspect a function of cylindrical coordinates is most convenient. | 1 |
I would like to know the status of the following problem: Given a simple graph, is there a walk traversing each vertex at least once and each edge at most once? (I am asking for a complete trail, a sort of cross-breed between Eulerian and Hamitonian walks, in a way.) In particular, is that problem known to be solvable in polynomial time, or NP-complete? Or is it suspected to belong in NPI? More generally, what is known on it? Variants: One could also ask for a circuit rather than a trail, and/or consider oriented graphs instead. Thanks in advance! | 1 |
Sometimes I'll look at a word for too long and I become convinced that it's spelled or pronounced incorrectly. This happens most frequently with "spider" (I think that should be pronounced "spih-dur" [like "spitter"], not "speye-dur") and happened just now with "finger" ("fin-gur", not "feen-gur"). There's a similar variant to this (discussed here), but that's related to a word losing it's meaning. To me, the word just looks incorrectly spelled, or I convince myself that everyone's pronouncing it incorrectly. Is there a difference between what I'm describing and Semantic Satiation? If there is a difference, does this one have a name? | 1 |
I'm currently studying Single-Variable Calculus independantly through MIT OCW. I can only focus on one course at a time independantly since it takes up so much time, and I really want to study Linear Algebra next instead of Multi-Variable Calculus. My question is simply this: after understanding Single-Variable Calculus, would I be able to continue into and understand Linear Algebra, or should I do Multi-Variable Calculus first? | 1 |
I've just been wondering about how atoms and molecules can be quantum mechanically thought about, and I have a question. It is often said that intermolecular bonding is purely "electrostatic". I hope what this means is that it is easier to consider molecules as point charges that are attracted, but in reality, there is some sort of orbital superposition, but the small distances between different charges within a molecule don't really matter. Is it correct to say that the essential physics is captured by considering the particles as classical Coulomb charges? | 1 |
Are binary systems (in case of stars and other celestial bodies) more favorable than independent existence? I've been going through an article regarding pulsars, where it was stated that 'many pulsars are found in binary systems.The companion of pulsars have been found to be normal stars, planets, white dwarf stars, neutron stars and even another pulsar. So what are the criteria to form binary systems ? I know that their sizes should be comparable, and that leads to the equilibrium of the gravitational attraction between the bodies, etc. As it is a known fact that neutron stars and pulsars are quite heavy and dense, how are they able to co-exist as binary systems with other stars, planets, etc.? Search this @ http://outreach.atnf.csiro.au/education/everyone/pulsars/ | 1 |
Source: gradestack.com This is a problem I am trying to solve for a long time. But still not able to proceed. After spending some time, I got a doubt whether this question is correct. Because, in a rhombus, diagonals bisects each other. Here PA=PC. That means, P is the center point of diagonal AC. So PD must be equal to PB which is not the case. Why I am wrong here? Please give pointers in how to solve this problem. thanks. | 1 |
I am interested in why many small animals such as ants can lift many times their own weight, yet we don't see any large animals capable of such a feat. It has been suggested to me that this is due to physics, but I am not even sure what to search for. Could someone explain why indeed it is easy for smaller objects/lifeforms to support several times their own weight, but this is harder as objects/animals become larger? | 1 |
A set of r marbles is selected from an infinite supply of red, blue, white and yellow marbles. A selection must satisfy the condition that either the number of red marbles is even and the number of blue marbles is odd, or the number of white marbles is even and the number of yellow marbles is odd. Does it mean a selection is invalid when both red is even and blue is odd as well as white is even and yellow is odd ? Do we discard this case while counting the number of selection ? | 1 |
I am looking about similar triangles and I always see the word corresponding but I always forget to include it in the definition. I am trying to think of an example I can use to show the importance of the word corresponding. So here is the definition: Ex: "If the measures of the corresponding sides of two triangles are proportional then the triangles are similar." So if the word corresponding is not in the definition: "If the measures of the sides of two triangles are proportional then the triangles are similar." but what is so important about the word corresponding? Any ideas? | 1 |
Most of the proofs of the Cauchy-Schwarz inequality on a pre-Hilbert space use a fact that if a quadratic polynomial with real coefficients takes positive values everywhere on the real line, then its discriminant is negative(e.g. Conway: A course in functional analysis). I think this is somewhat tricky. Moreover I often forget its proof when the pre-Hilbert space is defined over the field of complex numbers. Is there a more natural proof (hence it's easy to remember) which is based on a completely different idea? | 1 |
Autorefractors are being used by eye opticians for eye diagnosis. I searched internet for articles and wiki page as well but I wasn't satisfied. I am interested to know how do they actually work. How the machine is able to focus sharp on retina automatically. How do they figure out spherical/cylindrical aberration for human eye. I even asked optician as well but he tricked out of this position saying it does all happen automatically. LOL! A detailed answer would be much appreciated. Please don't hesitate to write any technical details or mathematical derivations. I would love to know how these machines actually work. Thanks in advance! | 1 |
I received an e-mail including the following sentence: I am not asking for a facetious grade change, just one that would allow me to pass. What the writer means is that the request isn't frivolous or petty. This use sounds wrong to me, but the literal dictionary definition doesn't contradict it (the dictionary definition includes, for instance "flippant"). My question is whether this is a use typical in some situation or dialect I'm not familiar with, or if it's actually completely nonstandard. | 1 |
The product of nonempty sets is nonempty. I am fascinated that such a simple and seemingly intuitive statement can lead to rather astonishing results such as the Banach-Tarski paradox or the solution to this riddle. I am also intrigued by the seemingly innocent results that rely on AC (the existence of algebraic closures, any ideal is contained in a maximal ideal) and I wonder if I am missing some intuition to see how truly remarkable they are. My question: What are other examples of seemingly magical results whose proofs rely explicitly on AC, and what are examples of seemingly innocent results that rely on AC that upon further examination turn out to be fairly remarkable themselves? | 1 |
Let G be a finite planar graph, then there is a natural walk around the outer (i.e. the unbounded) face of G. It might happen that a vertex v is visited more than once by this walk. Proof that this is a cut-vertex. This is a task which might be obvious at first glance, but I wasn't able to do it rigorously, i.e. by citing any of the used arguments from a book and proving everything else. I would also be satisfied with a book which I could cite. Thx. | 1 |
I am looking for a good mathematical rigorous introduction to solid state physics. The style and level for this solid state physics book should be comparable to Abraham Marsdens Foundations of mechanics or Arnols mechanics book for classical mechanics or to Thirrings Physics course for quantum mechanics. Any recommendations? Edit: As a reaction to Peter Shor's comment, I try to narrow the scope of the question a bit and give some more specific subareas of solid state physics I am in particular interested in: semiconductors and applications the quantum hall effect superconductivity | 1 |
Is there any way to tell how many clusters there are with respect to all the roots of a polynomial? Specifically, I'm after the multiplicity of each root but since I would like to work in floating-point arithmetic I'm afraid I have to deal with clusters. I don't mind any method of finding out: be it by numerical-iterative means during the convergence, a priori/a posteriori guess, maybe some matrix method would help..? If I have to set some small disk radius, that's ok, too. | 1 |
Example: The three picked up their chopsticks and started on the food. The scene seemed strangely normal to Naomi. It was as if everything were OK, and her mom were perfectly healthy. In fact, she looked more lively and energetic than Naomi remembered. The whole illness issue seemed like a distant, bad dream. Something that belonged to another reality. Still, Naomi couldn't take the thought out of her head, so she decided to ask. If I changed still for yet, would the sentence mean the same thing? | 1 |
As I've been trying to wrap my head around the principles of decoherence and quantum behavior I am left wondering why fundamental particles are 'allowed' to exhibit quantum properties even in ideal conditions ( close to absolute zero and in a 'box'). If a particle/photon behaves in a probabilistic superposition state as seen in the double slit experiment then wouldn't we expect the multiple coincidental states of the particle to interact with each other and thus cause decoherence? This would in turn lead to an innate instability of any system above a zero point energy thereby making quantum properties not identifiable at all..but indeed we do have verifiable and replicable evidence of quantum mechanics. | 1 |
This will depend on whether he's suitable for the job. This will depend on whether he's suitable for the job or not. This will depend on whether or not he's suitable for the job. It is still not defined whether we're following that approach. It is still not defined whether we're following that approach or not. It is still not defined whether or not we're following that approach. "Or not" doesn't really seem to be needed to complement "whether". Why do people use it then? Is it redundancy and nothing more? Or is it for emphasis? Or are there cases when "or not" is required for the sentence to be grammatical? | 1 |
Please see the sentences: I scheduled to stay after school with you today, but yesterday I was assigned a detention for today too. I scheduled to stay after school with you today, but yesterday I was assigned a detention for today also. The sentence ending in also sounds better to me, but I am not a native speaker, and I don't know it it's correct to use also at the end of a sentence. Which one is the correct form? | 1 |
Wikipedia defines the notion of a pure set as follows: a hereditary set (or pure set) is a set whose elements are all hereditary sets. Why does this definition make sense? It seems to be circular. Also, wikipedia says: The inductive definition of hereditary sets presupposes that set membership is well-founded (i.e., the axiom of regularity), otherwise the recurrence may not have a unique solution. Why does the definition sometimes not have a unique solution? Is the problem the existence or the uniqueness? Can you give an example of a situation where the recursive definition from above does not have a unique solution in a setting where we don't assume regularity? | 1 |
The original sentence is "The Spaniards brought horses to the Americas." I recently have made a final-term test question like this: Q: Where did the Spaniards brought horses? A: ______________________________________(Make sure to use the 'it-cleft') Not a few students answered like this: "It was the Americas that the Spaniards brought horses to." But, I think that only "to the Americas" is a right answer. Does the preposition 'to' need to be next to the noun? So, Separating 'to' and 'the Americas' seems to be awkward. What do you think about it? I'd really appreciate it if you could help me... | 1 |
We have terms like 'high culture' and 'high art'. They are used to describe things deemed of a higher quality, or held in higher esteem, than products of popular culture. We also have terms like 'art music' and 'art film'. What I'm looking for is a similar term to describe literature. Like high literature or art book or art novel, none of which I've heard being used. For example, we can say: John wouldn't like Transformers. He only watches art films. But what about: Harry wouldn't like Tom Clancy. He only reads ..... (what?) | 1 |
I'm looking for a way to truncate outliers in a time-series graph. Some context: I'm plotting two different metrics on a single graph. It's important to understand what portion of "Metric A" takes up respective to "Metric B". "Metric B" can at times spike to a high value thus increasing the Y-Axis scale which then minimizes the visibility of Metric "A". Are there any good formulas that help normalize this data or visual treatments that can make the graphic honest as well as accessible? See screenshot for more context. The blue area is "Metric B". Thanks! | 1 |
Context: I'm programming a system for exams, each exam has people on it, in the industry we would call one of these people a 'Delegate'. Unfortunately in the programming language c# 'Delegate' is a reserved word and I can't really use it without my code looking terrible. I need a word to represent a person who will be on an exam. A colleague suggested ExamSitter but I think that might have been tongue-in-cheek | 1 |
How does quantum electrodynamics actually explain HOW reflection occurs on a microscopic scale? Note that Feynman's QED lecture series/book is not sufficient, as he only assumes that light DOES reflect ('turn around and go back') in order to expound his path integral theory. My question is why does light have the propensity to turn around in the first place. Is it just the absorption and re-emission of photons, and if so, why does it happen so uniformly (i.e. on a shiny thing, entire scenes are reflected near-perfectly). In essence, why are flat things shiny? Are all the molecules arranged at exactly the same angle? | 1 |
I'm not very advanced in LaTeX. I don't know what e.g. XeLaTeX or LaTeX->dvipdfmx are. I only use ShareLaTeX and used to use Overleaf. I need to be able to insert thumbnails in a document which when clicked would display their bigger version in a popup or something. This gif is a perfect example of what I want to achieve. Is it possible to achieve something like that in one of the mentioned sites? If so, how? (if there's a way to achieve it online but on a different site, I'm still interested) | 1 |
According to Wikipedia, the past tense (and past participle) of the verb to output is either output or outputted. Are these two forms entirely interchangeable? Or do they have certain nuance in meaning or context (e.g. in programming one of the forms is preferred)? Instead of correct results, my program output/outputted garbage. Which one should I choose? My logical sense tells me output is better because it derives from put, but intuitively I tend to use outputted when I speak and don't have time to think. | 1 |
So one of the exercises I am doing is to prove (or disprove) that 'Every compact set on a metric space is bounded'. Verbally, I can 'prove' this by simply stating: "If the every compact set on a metric space is not bounded, then there exists an infinite number of open covers, and if something is compact, there are only a finite number of open covers. This is a contradiction, and thus every compact set on a metric space is bounded." Two questions: is this argument right? And if so, how to I learn how to represent this formally? | 1 |
I've heard people using this idiom, such as "each day is better than the next", or "you hope that each experience you have is better than the next" (heard this one on a TV show not long ago), apparently in a positive way. However, if taken literally, I find the meaning very negative - if the current thing is better than the next, then the next thing must be worse, so things would just keep getting worse and worse. How do you explain this phrase/idiom? | 1 |
Linkin Park sings "wash the poison from off my skin" in Castle of Glass. Shawn Mendes sings "ripping all the skin from off my bones" in Mercy. As far as I can remember these are the only two occasions where I have heard that expression. To me it sounds like it should be "off from" (if at all). Is this normal, or did the artists just do it to get another syllable for their rhyme? | 1 |
I have been on and off of this problem for three days and need to present the proof tomorrow. I am thinking that because I know for any element in the additive group of integers modulo n the order for that element is the ratio of n and the greatest common factor of that element and n then I can say,[...chirp, chirp, chirp...] and my mind goes blank. What can I say? I have also tried using the division algorithm to say the order of any element in the group can be written as a multiple of n and some other integer but I am coming up blank. There is something I do not fully understand and would like for you to point out my oversight. Thanks. | 1 |
"My female cousin working for a finance company was dismissed. Disappeared along with her job were her confidence and smiling face." There is a very complicated system in Chinese for naming different relatives. For example, in Chinese, different words are used for a female cousin and a male cousin. Also, the word for an elder female cousin is different from the word for a younger one. I'm having some trouble writing this sentence in English. I used "female cousin" in the first part, to translate the word that actually means "elder female cousin" in Chinese, but it still sounds awkward. I suspect that the "female" may be redundant too, because in the second part I use the pronoun "her". | 1 |
I am trying to implement Microsoft Excel's GROWTH function in JavaScript. This function calculates predicted exponential growth by using existing data. What makes it tricky is that it must work with multiple sets of known_x's values. I could not find any reference equation. Any suggestions? The part that might be relevant is the reference equation. I cross-posted the question here because someone suggested it in response to the same question originally posted on stackoverflow. Thanks in advance for your help. | 1 |
I'm interested in writing a numerical integrator to solve the motion of systems of pendulums. For example, a simple case would be the double pendulum. The motion can be quite complex in general. Is there a way to determine if a system of pendulums is going to produce stiff DEs before actually trying to integrate them? Usually the masses and lengths of the pendulums are considered to be identical for the classic double pendulum system, which I suspect makes the system quite tame. But I have nothing to back that up. | 1 |
I am fairly new to this so apologies for informal terminology. After I discovered what space filling curves are, I came to the conclusion that any point in any number of dimensions can be represented as a single number along a space filling curve, given that the curve covers enough space. I also imagine that it is possible to rewrite any operation on these points in terms of movements along the curve. Is this correct to assume? | 1 |
I've found plenty of blog posts and papers where the authors claim that the Higgs mass divergence (usually presented with a momentum cutoff) doesn't show up under dimensional regularization. Unfortunately I've never seen a book or paper which explains this with any more detail: it's usually just stated as a fact. Is there some specific reference that people can point to for this? I'm well aware that dimensional regularization just hides the hierarchy problem until physical particles are added, but I want to include a reference to motivate the introduction of new particles without going to through dimensional regularization. | 1 |
I need some assistance with a calculation I'm trying to do. I have access to surgery waiting times data (date arrived, date completed) and I want to figure out the expected waiting time for a new patient - this should take into account the number of patients already waiting and those who have completed (I think). I've tried looking at the average time to wait for the past three hours but this doesn't seem the right way to do it (too simple I think). I've also thought about perhaps looking at the average wait time for the same day of the week for a previous week...would that be sensible? There are so many variables to consider but I need something relatively simple... | 1 |
People on Reddit often comment "I lost it" while quoting the funniest part of a joke to highlight how funny that part is. As I don't speak English much, I am not sure if this is Reddit-specific, but I guess not. Where does this come from? Is it related that laughing from a joke is similar to "losing your mind"? That seems far-fetched. "I lost it" would intuitively mean "the joke stops making sense here" (i.e. "I lost track of the joke here"), which is the exact opposite of what it actually means. What is the etymology of this phrase? | 1 |
I've searched the question in the forum, and found the following conclusion : - "In electromagnetism, electric flux is the rate of flow of the electric field through a given area. Electric flux is proportional to the number of electric field lines going through a virtual surface. But, It doesn't make intuitive sense to me, that electric flux is just something that we can count like no. of lines, I don't think electric field is passing in lines literally, so what exactly is Electric flux? and Rate of flow suggest that it's moving like water flow in river. These ideas are difficult for me to grasp, please clarify. | 1 |
I've heard mentioned in various classes that neutron stars, like superconductors, are described by BCS theory. I know that in superconductors a key element in forming cooper pairs is a net attractive force between the electrons which would normally repel one another. That attractive force is accounted for via lattice vibrations (phonons) created and "absorbed" by electrons. So my question is: what provides the attractive force between neutrons? just gravity? If it is true that neutron stars follow BCS theory, by what means was someone able to verify that? | 1 |
I have to submit some paperwork for the approval of an activity. However, I have already got approval, the paperwork is only necessary to submit the specifics (the date, people involved, and other details which have already been approved) for sign-off. What is the word (or expression, but preferably a single-word) to describe this kind of action? Examples: I already have approval, so submitting this paperwork is a ____ act. I already have approval, so the paperwork is just ____. It's not "futile" as it's still necessary, I'm not "going through the motions" as I really mean it and my heart is in it, so how can I describe this paperwork? | 1 |
I've been studying the representation theory of groups from Tung's "Group Theory in Physics." I understand Young symmetrizers of different Young diagrams are essentially primitive idempotents in the group algebra of the symmetric group and then all inequivalent minimal left ideals as well as all inequivalent irreducible representation can be obtained. However, the construction seems unintelligible to me, while the property of Young symmetrizers is so striking. What is the idea behind the construction? | 1 |
What is the meaning of the text quoted below? In the physical world, if a system is described by an equation that is first order in time, the system is general dissipative (has energy loss). If the equation is second order in time, the system may be non dissipative. Such a system has time-reversal symmetry. Can somebody explain what it really means to be first order and second order in plain English? | 1 |
I'm thinking of those old U.S. wartime movie-theater newsreels that celebrated victories, but combined with aspersions and taunts on the enemy. "We're great and those guys are idiots." Not necessarily in film format like a newsreel; maybe a printed publication. Example: The Mouth of Sauron Magazine, the ??? of Mordor, celebrates its victory at Minas Morgul and continues to mock the armies of Minas Tirith. | 1 |
Several people I know were good in mathematics when they were in high school and they loved it but when they joined a university (specializing in mathematics) they felt mathematics is hard and that they were somewhat deceived because this wasn't the type of mathematics they loved and joined the university to learn. How can we overcome this problem in contemporary curricula? and why there isn't a universal mathematics curriculum? (I mean mathematics is not country-dependent like languages or history) | 1 |
After reading this answer about the gravitational force I wondered how that applied to the electric force, since both have the same basic form - product of the masses or charges over distance squared. If I was in a charged metal-walled elevator that was "falling" in an electric field, would I be just as oblivious as my friend who was in another elevator falling in a gravitational field? | 1 |
I asked a question on one of the stackexchange sites and one user edited a sentence I made from "We were relocating so we...." to "We were moving house so we....". As an english speaker, I have never heard of "moving house" in context of relocation in a sentence before. Presently I am even doubting if relocating is correct in the context of : "Moving all your belongings in a house you onced rented into a newly rented house" | 1 |
In many mathematics texts I've seen "ordered n-tuple" appear, and in such texts, there isn't any mention of just "n-tuple". So I'm wondering: are there really cases where one writes "n-tuple" and somehow it's not ordered? If not, I'm thinking the "ordered" in "ordered n-tuple" is really not necessary and can be shortened to just "n-tuple". Please let me know if there is significance is writing "ordered n-tuple" that I'm not seeing. | 1 |
I had to edit my question because I think it led to misunderstanding. For me, the definition of "immunity" is quite different from "impunity", and I know the differences. But what I don't know is that is the law the thing that draw the line? It seems to me they both refer to exemption from punishment. for example, a police officer can kill a criminal, whereas I cannot. Another example is that a diplomat raped and tortured two women but nothing happened. But if a man who has a powerful and wealthy father did that, the word impunity would be said. So, here is the question: Does only the law define the differences? | 1 |
Which is the better verb to use with data: feeding or entering? Furthermore, which is more common in the literature of the field and which do people who work in the field say more often? Are they used for different kinds of input systems? If the data are automatically continuously input by a machine (e.g., the Mars probe), is feeding data used, but if the data are individually input by someone at a keyboard (e.g., entering data into a user database), is entering data used? | 1 |
I want to use beamer (Madrid style) for a presentation I'm giving next week, but I am forced to use the institutional title page. That means that the whole background is filled by an image and the title itself cannot be in a coloured box. In the worst case I will have to pdftk the title page onto the presentation, but I'm sure there must be a way to force LaTeX to do it. I've tried using a PlainFrame with a TitleGraphic, but I can't get the image to stretch across the whole page the title itself will still be in a coloured box Any ideas??? | 1 |
My teacher made an example to explain DFA, it was about paths (URL paths), the rules were as follows: S ::= / S ::= /O O ::= [a-z] O ::= [a-z]R O ::= [a-z]S R ::= [a-z] R ::= [a-z]R R ::= [a-z]S Examples of paths could be: /foo, /foo/, foo/bar and so on. However, I don't understand why you would need the R rules since they are equal to the O rules. Can I write it without the R? If not, why? | 1 |
The problem is, that I fail to unambiguously understand this phrase. There are two ways in which I can understand it (and a number of similar phrases): I may never be able to do this = It's impossible for me to ever do this ('never' negates 'may') I may never be able to do this = It's possible that I will never be able to do this. ('never' negates 'be able') Which is the correct one? | 1 |
According to Newton's laws, if net force is zero on a particle then the particle is at rest or in uniform motion, and if it is not zero then it is accelerating. So when a car moves on the road, friction helps it to accelerate. If the acceleration is zero, (i.e) it is moving with constant velocity, the net external force must be zero, so friction is zero. Then with friction equal to zero how is the car moving on the road? | 1 |
I have to do a final project for my PDE subject and last year I did one about Game Theory (specifically, Prisonner's Dilemma and Snowdrift game) for my ODE subject, which the rest of the students enjoyed and which my teacher thought it was a fun approach to the contents of the subject. I want to do a similar thing, but every Game Theory problem I have seen only involves ODEs. Until now we have seen first order PDEs (both linear and non-linear) and second order (hyperbolic, parabolic and elliptic) PDEs. Also wave equation and heat equation. What would be some fun PDE related problems to discuss? (I hope I put the right tags, because it is the first time I ask a soft question). | 1 |
The title gives away pretty much the entire question except for the fact that the class of functions I am interested in is a subset of twice continuously differentiable functions. I think that if an odd function (defined on the whole real line) is concave on the positive real line, then it is convex on the negative real line. If it is supposed to be convex everywhere, then it is linear on the negative real line. The argument goes also the other way. So it is linear everywhere. So maybe I don't even need the monotonicity property. This is the first question I am posting here that has no equations. So I hope that is allowed. Is my reasoning correct? | 1 |
Do you know if the concept of chemical potential can be properly defined for nucleons in the nuclei? I mean, if I can picture the nuclei like an interacting gas of nucleons, then may I think of a chemical potential for nucleons, similarly to the case of an electron liquid. Of course the nature of the interactions is different for the two cases. My idea is related to the liquid drop model of nuclei. | 1 |
So imagine you're at the beach; you go into the water and the moment you enter the water you stop hearing anything from the outside world. The same happens vice-versa: your friend shouts at you from inside the water but you only hear the bubbles rising to the top. So the questions are: Why does that happen? Would it also happen if you used a hydrophone? | 1 |
I am writing a title and I was wondering whether I can skip the second article just like you would say a pen and pencil. Can I say, "A cap and tie for Zed," or must it still be "A cap and a tie for Zed?" Have been searching the net and books for some answers but have been unsuccessful. Would appreciate a quick response from some Grammar Genius! Need clarification here to finish up my work. Thanks ya. | 1 |
The usual solution to fix lines that overflow is to rewrite it. However, that hardly works with bibliography entries that experience the same problem. So what can I do to fix it? I can't rewrite anything since the information needs to be "as-is". I can't provide a minimal example because if I take the entry that overflows in my document, then the problem fixes itself as the font, font size and margins change. EDIT Even though I've accepted an answer, please submit more answers if you have a good approach for addressing this issue. Maybe it can assist someone else who have the same problem and don't want to resort to using "ragged right". | 1 |
I have studied in a course several algorithms to integrate ODE's numerical: Runge-Kutta, Predictor-Corrector methods, Taylor... However the teacher failed to show which is the best for every particular situation. The only thing I know is that implicit methods are appropriate for stiff systems. But how do they compare Runge-Kutta (of any order) with predictor-corrector methods or with Taylor method? Which is best for each situation? Heuristic answers based on experience may be good enough! | 1 |
I have a paper copy of some old LaTeX notes, but I lost the source file. If I scanned them as a .pdf, does any OCR software exist that could convert the scanned .pdf to LaTeX source (.tex)? I also have a paper copy of some old notes created using Microsoft Word's Equation Editor. While I am considerably less hopeful, I ask the same question -- does an OCR software exist that could convert a scanned .pdf to .tex? Thank you for your help. | 1 |
I came across a problem where I have to find out the longest path in a given graph. I have list of edges ( eg.{AB, BC} ) which states there is an edge between vertices/nodes (A,B,C). Now i want to figure out the longest path possible (not repeating the vertex) such that it covers maximum nodes starting from any vertex/node. What can be the best way to solve this? I have to implement this as a program. I looked up google for Minimum Spanning Tree, Dijkstra's Alogorithms , hamiltonain path( which i think suits- but not sure ) and many more. but can't figure out what would suit best for this problem. Any help or reading references would be much appreciated. | 1 |
Here is an example sentence, written by a pupil of mine: Through the British Empire, which resulted out of Britain's urge to build up its economy, Britain was connected to a lot of different countries The sentence clearly has several issues, but I am only interested in one of them here. I would only use "result from", as a native British English speaker. My pupil has one American parent and one German parent, and lives in Germany. Would "result out of" be acceptable in written, academic American English? Can it be said at all? | 1 |
What are the possible applications of Countable Infinite Sets and Power Sets in areas that are not strictly mathematical? Also I want to know the significance they carry. What was not possible before the concepts of countability and power sets were introduced and what became possible afterwards? How did the introduction of these concepts change our thinking and outlook and the areas they affect? Please explain in plain language, possibly with examples, as I am from a non-mathematical background. Thank you in advance. PS: The applications need not be in strictly practical fields either (as Asaf Karagila keeps pointing there aren't any). Please help! | 1 |
What is the best word or way to describe a person who just has to try and do everything themselves because they think, either rightly or wrongly, that only they are good enough to do the task in hand? The type of person I'm thinking of will attempt to take over any situation. So if you're having a BBQ only they are good enough to cook the food or if you're planning a day out then they decide only they are good enough to drive you there. | 1 |
My understanding of irony comes from the movie "Reality Bites": It's when the actual meaning is the complete opposite from the literal meaning Frequently people use the term incorrectly, applying it where the actual meaning and the literal meaning are surprisingly similar in unintended ways. A perfect example of the incorrect usage is the picture below. It's definitely not irony, so what word can we use? (Just in case the link has broken, it's a picture of a building with a plaque saying "George Orwell Lived Here". Pointing out in front of the building is a security camera.) | 1 |
Why is it true that the lower sums of f with respect to some partition is less than the lower integral (which is the supremum of the lower sums) I think what I'm confused about is the difference between a lower sum and the lower integral, how can the lower integral be the supremum of the lower sums when a lower sum is a single number? | 1 |
Gravitational force is mediated by graviton exchange. If I am standing outside a black hole, I can of course feel the attracting force towards the black hole. This should correspond to gravitons mediated between the matter inside the horizon and myself; but then these gravitons should cross the horizon from the inside to the outside. My question is: how is this paradox precisely solved? I guess a starting point for an answer is that these gravitons are off-shell, much like in QED where photons exchanged between electrons that feel each other are virtual. But still, this confuses me a bit - is there some references explaining this in detail? | 1 |
I'm writing an essay for a grad school application detailing my unique characteristics as an individual. I am leaning towards words & phrases like "thirst for knowledge" and "earnest curiosity". I feel these phrases are underselling this attribute though - I feel so genuinely interested and invested in how things work and how people think, and thus how others perceive stimuli in comparison to my response. Is there a word for this constant absorption of external data in order to think critically and formulate theories for why the world works? | 1 |
I am trying to understand the following question: "How much experience do you have gathering data for web analysis?" I understand the concept of "web data analysis", and I understand "gathering data from the web for analysis", but the above question is not clear. Perhaps I am being too literal or picky, but the question sounds like I would first gather data, then put it on the web, and then analyze it, which is not logical. If you have any ideas, could you please provide a specific example of what kind of work would satisfy the question. For example, maybe the question means I would download Apache Server logs from a website, import into Excel, and perform analysis? | 1 |
Is there a word to describe the co-opting of a well-known phrase in the course of regular conversation or writing? For example, a sentence regarding death might refer to "shaking off the mortal coil" without mentioning that the phrase is taken from Shakespeare (perhaps assuming that the audience will be familiar with the reference). If it's not an exact quote, this could be called a "paraphrase" of Shakespeare. But what could it be called if it is an exact quote? Example: What adverb could be employed to complete this sentence: The phrase "shuffled off the mortal coil" was made famous by Shakespeare, and is used by this author ______y. | 1 |
The book < Geometry and the Imagination > (written by David Hilbert) introduces a property of a Quadric Surface without a proof. Property : The cone consisting of all the tangents from a fixed point to a quadric cuts every plane in a conic, and the points of contact of this cone with the surface form a conic. Moreover, the quadrics are the only surfaces having any of these properties. It was easy to prove the property itself, but i found it difficult to prove that it is a sufficient condition for a surface to be a quadric. (the statement starting with "Moreover, ...") I would like to know the proof of this statement. | 1 |
Ok, so I am trying to computationally model a Carbon Nanotube FET and I need to know a lot about the actual equations and PDEs(Partial Differential Equations) involved while modeling such a material. I had taken a course in material science in my sophomore year , but that just covered the basics of CNTs and its applications. I would really like to know if there are some good books out there that give an in depth understanding about CNTs ( structure, properties, behavior in presence of Fields, Equations and PDEs, Fabrication and applications, etc) | 1 |
I am having a hard time figuring out how to configure TortoiseHg to do colored word diffs for my TeX and LaTeX documents. I found the following two threads How to use Mercurial for version control of text documents? Good strategy for line breaks with paragraphs of LaTeX source but they don't go in detail how to to set this up on TortoiseHg. I was wondering if anybody in the TeX/LaTeX community has figured this out already? | 1 |
Given an urban area such as a shopping mall, is there a statistical model that estimates how often during a working day the area becomes depopulated and what is the maximum time of depopulation? By depopulation I mean that the number of people per unit area becomes zero. In particular I am interested to know the answer to this question: Can we say that typical urban areas are usually populated (during the working day) and there is an upper-bound for the depopulation time? any article that exposes some research regarding this subject would be useful. | 1 |
In the following paragraph, is it appropriate to use the term "transversely" to describe something that has the opposite effect? Tests have shown that the lower the range, the more likely that a submatrix will be singular. Transversely, the larger the range, the least likely that a submatrix will be singular. If not, is there another word that I can use instead? I know that, in this instance, I cannot use the word "conversely" as this means something totally different. | 1 |
This was an experiment I saw in my son's workbook. It said to mark out the top of your forehead and the bottom of your chin on a mirror using a whiteboard marker. Then slowly move backwards, and investigate what happens to the size of the reflection subjective to the two marks made. It actually got me quite flabbergasted. I always thought the reflection would get smaller as you moved away from the mirror. Why is this? | 1 |
While explaining the quantum adiabatic theorem recently, I appealed to a thermodynamic analogy: when slowly contracting the walls containing a classical gas, the relaxation timescale can be taken to be fast, so the system remains always in thermal equilibrium. By analogy, the quantum system remains always in a stationary state. The hidden assumption here is that stationary states (eigenstates of the Hamiltonian) are in some sense attractors of the system: that a system in some energy-superposition will, over time, relax to a single energy eigenstate. Is this actually true? It seems like maybe it isn't, since for example coherent states of the harmonic oscillator are stable (?). Maybe it's true in neighbourhoods around the stationary states only? | 1 |
She will (or already has) leave for Jamaica soon. She will leave (or already has left) for Jamaica soon. I'm uncertain which of these (if either) is more correct. Should I simply not use this language construct, opting for this instead: She will leave for Jamaica soon, if she has not already. I find the previous constructs, despite being awkward, do a better job of conveying the uncertainty of tense. Is there a better way to construct the parenthetical version to avoid tense conflicts? | 1 |
As I understand: Accelerating electrons generate electromagnetic waves. An emitting antenna have an alternating current (electrons are moving) which generates an electromagnetic waves. The electromagnetic waves reach the receiving antenna and makes the electron inside move. Greate, the communication is done. However, since the electron in the receiving antenna are moving too, the receiving antenna is generating an electromagnetic wave too. How is this not affecting the incoming wave? Does it have a different wavelength? | 1 |
I'm looking to communicate the idea that performing a task would be less costly (more than just financially; technically, or when risk is considered) if you start from scratch or anew, instead of attempting to alter or change some existing object or entity. The closest phrase I can think of that satisfies this is "it may be cheaper to build a new house than to renovate an old one". What other sayings exist? | 1 |
Is it always true that projective objects are retracts of free objects? I know that retracts of projective objects are always projective, so in particular, retracts of free objects are projective. To prove the converse for modules, write your projecive module as a quotient of a free module, and then take its kernel to get a short exact sequence. This sequence splits because it ends with a projective object and so by the splitting lemma our module is a direct summand of the free module. How to generalize these to an arbitrary algebraic theory? I guess we should somehow look at the kernel pair of the quotient map? | 1 |
A question regarding drawing checkers pieces and boards using TikZ has been asked here previously and I'm aware of the chessboard package. However I want to draw a Chinese checkers board: I want to draw it as opposed to using an image because I want to be able to edit the locations of pieces. The question is how I would go about drawing the board. Two options I see are: Draw the board as rows of circles and then draw the outline similar to the above. Draw the board as rows of equilateral triangles as seen here. Either way is fine, but drawing either one is a mystery to me. Any tips? | 1 |
When a sensor registers electromagnetic radiation, such as that used for the transmission of communication like light or radio waves, does this radiation "abrade" or "erode" the material of the sensor? Are there any traces of the received radiation that can be detected, even if only theoretically? An example from a biological background would be that high energy light (such as that in the UV range) destroys the pigments in the eyes, which is why animals that live longer than a few years cannot see in the UV range. Maybe something similar happens with man made sensors for different wavelengths of electromagnetic radiation. | 1 |
I was about to use this word in an email to refer to its recipient, as in: I was the guy who nabbed you as you were leaving to ask about ... I'm going for a friendly, familiar tone. Is my usage of 'nab' inappropriate? Looking it up in the Oxford Dictionary: verb (nabs, nabbing, nabbed) [with object] informal catch (someone) doing something wrong: the Feds nabbed a suspected terrorist take, grab, or steal (something): Dan nabbed the seat next to mine | 1 |
I'm currently studying Action. I've been reading about how a particle has particular probabilities of ending at an infinite number of events. Say I have a free particle that isn't experiencing any external forces (no potential, or friction). I give it a particular kinetic energy, whilst it is at some arbitrary event A. Why doesn't the particle stay at position A, "lose" its kinetic energy and reduce the action to a minimum? Why does it travel in a particular straight line? You can't argue from conservation laws since they are dependent on the idea of the stationary action principle. I'm curious to know the answer, cheers! | 1 |
Today, in the midst of chatting on other SE sites, the term "bum buddies" was used. Some other users took this to be offensive, saying that it was just a slightly less egregious version of "butt buddies". I was not offended by the term, but others informed me that it has homosexual connotations. I always remember using the term to refer to close friends, almost as a synonym of "bosom buddies". Can someone guide as the correct usage (so I can avoid using inappropriate terms in the future)? If there is any history on the term that could be useful as well, please include it. | 1 |
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