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I'm in need to implement Monotone Cubic Interpolation for interpolate a sequence of points. The information I have about the points are x,y and timestamp. I'm much more an IT guy rather than a mathematical person, so I'm looking for an example of implementation. What I need to do with the resulting functions is store them for future analysis. My favorite syntax are PHP, Python, Java, Delphi, VB or a generic algorithmic language of your choice. | 1 |
Lines and conics have clear geometric meanings that are coordinate-free, but cubics seem to rely entirely on cubic equations and coordinate systems. Are there ways to define cubic curves without cubic equations? I thought about this question by trying to generalize tangent lines and osculating circles. Since a tangent line is defined by taking the limit of two points on the curve, and an osculating circle is defined by taking the limit of two tangent lines on the curve, I thought about taking the limit of two osculating circles on the curve, but after playing around with evolutes and involutes, I couldn't come up with anything. | 1 |
I'm an ESL teacher. Normally I teach lower intermediate but I also teach a mixed level grammar review class. I pride myself on being able to explain things clearly but today I found myself in THREE sticky situations all in the same class! I'll explain here the two problems involving conditionals. First Case: Is it better to say... If he knew that I WERE/WAS home now, he would call. OR If he knew that I AM home now, he would call. Does the second verb in the if clause also take the subjunctive form because it is in the if clause or should it take the present simple form because it is not a hypothetical (I am home now is not hypothetical, his knowledge of it is.) | 1 |
I find it really amusing when other people misuse words but my sense of humor fails when it's me. I have always used "notwithstanding" to mean "assuming that A doesn't impact B". For example The delivery will be on time, notwithstanding the holiday. To me, this meant, the delivery should be on time, but you never know what impact the holiday will have on it. Turns out, notwithstanding means almost the opposite: in spite of, regardless of. So my question is, what word should I be using instead? | 1 |
Suppose we look at the twin paradox where the twin traveling at high speed relative to an observer on earth has a clock which counts time by sending photons of light across a distance within the spaceship (perpendicular to the direction of motion) to a detector which counts off 'time' as the interval between photon detections. If the speed of light is constant in both frames, and the distance the photon travels is equal in both frames (no length contraction in the perpendicular direction), won't both observers say the same amount of time has passed in both frames at a later time (suppose the observer on earth uses an identical clock)? Wouldn't a difference in observed time intervals imply differences in the speed of light? | 1 |
A guy walks into a bar. His buddy laughs and says, "Don't worry, I didn't see it either. What is the meaning of this joke? What makes it funny? (Is it supposed to be funny?) I saw this joke in the mood message of a British guy. It is a kind of bar joke but there is usually a connection. (For example: a guy with dyslexia walked into a bra). I didn't get this one. Can it be a meta-joke? | 1 |
I'm trying to analyse the Ballad of Serenity Valley which is the theme song for the tv series Firefly: take my love take my land take me where I cannot stand I don't care I'm still free you can't take the sky from me My interpretation relies on the meaning of 'take' in the second line, being different from the third line, which are a rhyming pair. Is there a name for this scheme or pattern? | 1 |
There is plenty of information about how to encode arithmetic given the lambda calculus. The wikipedia article on Church Encoding seems complete to my inexpert eye. My question is "how about the other direction?" What's a good way to encode the lambda calculus in ordinary real or integer (or even matrix) arithmetic? It would seem that an application of Godel Numbering would do it, but I have been unable to find any writing on Godel Numbering for the lambda calculus specifically. It also seems plausible to encode the lambda calculus in arithmetic in some way more efficient than Godel Numbering; perhaps someone has done that? I might settle for the SKI calculus or some other Turing-complete language that's easier to encode than the lambda calculus. | 1 |
If you are using a word that normally wouldn't start with a capital letter, should it be lower case after an e.g.? Also should e.g. have a capital E at the start of a sentence? Example phrases: Should I always plug in electrical items? e.g. Electric hairdryer, phone charger... Should I always plug in electrical items? e.g. electric hairdryer, phone charger... Should I always plug in electrical items? E.g. Electric hairdryer, phone charger... Should I always plug in electrical items? E.g. electric hairdryer, phone charger... | 1 |
I'm interested in the eigenmodes of the membrane for various mediums, such as vacuum, air, water, etc., which impose a damping effect on the membrane. This cannot be done by merely changing the value for the wave propagation speed, c, because this value belongs to the string/membrane itself, and not to the medium around it. Can the influence of medium be incorporated in the wave equation for vibrating string/membrane? | 1 |
What is the word to describe a person who popularized a sport? The person does not need to be one of the original players nor even currently active. An example is Arnold Schwarzenegger popularizing competitive bodybuilding. There were many superstar bodybuilders before him, like Eugen Sandow, and he has been inactive for a decade. Arnold is, no doubt, the reason why many people started bodybuilding. | 1 |
My English teacher just asked us to write a random sentence in English. Off the top of my head I wrote "I like to eat apples and bananas". She highlighted "apples" and said: "man, this is blatantly wrong". "Uh, what's wrong, M'am?" "It should be bananas and apples. English people always enumerate things in reverse alphabetical order. Always. Just like when they enumerate parts of the body, they always converge to the heart. Always. We do that automatically, without even thinking about it. Not doing it is wrong". Granted, I'm not a native speaker, but I've never heard anything like this before. Bullshit or what? | 1 |
Possible Duplicate: Electrodynamics textbook that emphasizes applications I am a graduate student in applied mathematics and I am looking for a concise introduction to Maxwell's equations / basic principles of electromagnetism. (I have enjoyed the book by Purcell, Electricity and Magnetism, as an undergrad but I have forgotten most of it). I would like something that covers the conceptual details in a quick way and not necessarily a big textbook. You may assume that I have the necessary mathematics background. I am looking for something that will explain the physics, i.e not a huge textbook with intricate calculations but a short book to get a feel for what is going on. | 1 |
So, I finished my undergrad with a degree in applied mathematics, but when reading some graduate level texts and/or papers, I often find myself struggling. I eventually get there, but I often feel like I lack the intuition necessary to be able to come up with concepts on my own. I feel like I'm just missing some pivotal step in the journey to mathematical maturity. Does anyone have any books/references/advice? PS: If this means anything at all, as I was not a mathematics major, I did not take analysis or abstract algebra. | 1 |
The first thing that comes to my mind when I hear the term marketing is a word that is related to advertising, business and commerce. A colleague once said to me that she went to do some marketing. I came to realise that she meant shopping for grocery in the supermarket, only after dwelling further onto the subject. But this is something that is rarely used in such context based on my own personal experience. My question is: Is the usage of the term marketing in the literal sense still appropriate in the English speaking community? | 1 |
Say I had a plastic water bottle that was slightly crushed, I could uncrush it (mostly) by covering the opening with my mouth and blowing air into it hard. Would it be easier to do this if the bottle was full of water? or while empty (full of air)? Why? My thoughts are that it would be easier if it was full of water because water doesn't compress as easily as air and so more force will be applied to the walls of the bottle. Is this correct thinking? Are there other factors involved? | 1 |
Let's say you have a garden hose connected to an ordinary water tap which is opened fully. If you pinch the end of the hose, water leaves the hose at a higher speed (and this can be useful while watering plants, to reach pots which are further away). However when a tap (with no hose connected) is opened only slightly, water flows out at a low speed, possibly even in drops. The actions of pinching the end of a hose and of almost-closing an open tap seem similar, so why the difference in behaviour? | 1 |
The cosmic microwave background that we observe uniformly around us is usually explained by assuming that our universe is the surface of a four dimensional sphere. That way the uniformity makes sense since there is no center. My question is if this is true then what is the explanation that describes the fact that the farther we look into space, the further we look back in time. I can't perfectly picture this and see how it would coexist. Help me out. | 1 |
In my research, I make use of a tool which provides a platform for researchers to investigate phenomenon X in a variety of ways. I want to frame it this way in a paper that I am writing: "Using the --- platform provided by the tool for investigating X, we develop and illustrate a novel method to assess aspect Y of X". I am looking for an adjective to fill ---. "Versatile" comes to my mind. But I feel like there might be better adjectives to use. I don't mind restructuring the sentence if that makes it sound more professional. Any help is appreciated! | 1 |
Given the sentence, We discourage people from committing crimes by using law enforcement, religion and education. I see two possible interpretations: [We discourage people by using law enforcement, religion and education] from committing crimes. We discourage people from [committing crimes by using law enforcement, religion and education]. Of course the second interpretation may not make sense in this particular case, but generally speaking both interpretations are equally valid. So my question is, how to rearrange the sentence for it to be well-structured and have only one clear interpretation? | 1 |
I was reading Frankenstein and I've noticed that the word after the exclamation mark usually isn't capitalised (unless it's a noun). Some of the quotes I've found: Alas! who is safe, if she be convicted of crime? and Alas! to me the idea of an immediate union with my cousin was one of horror and dismay. and Great God! what a scene has just taken place! Why the word after the exclamation mark does not begin with a capital letter? Has the rule for using exclamation marks changed and when did it change? | 1 |
I was waiting on a red light the other day and was wondering. If I'm in my car, not moving and I see a car that's going to hit me from behind. Would I (my body) be safer if I put on the break or if I put the car in neutral? I assume there's no car in front of me and there's no posibility to be hit by an other car. Also, the car crashing into me is going at a good speed. | 1 |
What is an English phrase to describe a video that is not running smoothly, but rather has interruptions in it, becoming sort of like a GIF? This typically happens due to technical problems such as low memory or CPU power, which is why I'm afraid I can't think of a way to demonstrate exactly what I mean (e.g., I cannot paste a link to a video like that). I am not necessarily looking for an adjective; any phrase will do. I would also like to include another related question: what's a word/phrase for almost the same situation but with sound rather than video? I.e., when the sound comes and goes (e.g., over the phone). | 1 |
I need to construct a sentence, in which I'm referring to a feature of each of the animals in a given species. I don't quite know what the possessive of species should be, both in singular and plural. Example: (Talking about a single species with fuzzy ears.) The species' ears are notably fuzzy. Is the above correct? What if I had to mention multiple species all having fuzzy ears? | 1 |
Here are the examples of compound subjects: Everything on the bed and everything in the closet was organised in under an hour. Everybody who witnessed the shooting and everybody in the room were interviewed. Anyone on the soccer team and anybody on the basketball team was eligible for the scholarship. Should I also use was instead of were in the second example? Or the first and the third examples are incorrect that I should use were instead of was. | 1 |
Not all equations of motion admit a Hamiltonian. Several questions and answers on this site concern this correspondence, for example Hamiltonian or not?, When can an autonomous system be written using a Hamiltonian?, and What are the necessary/sufficient conditions for a system to be Hamiltonian/non-Hamiltonian?. My question is who was the first to establish that not all equations of motion can be described in a Hamiltonian fashion? Hamilton himself? Someone else? In which paper or book was this lack of total correspondence first exposed? Who has then developed the details of this correspondence? What is the current state of affairs? (From Hamiltonian or not? I gather that it is still a matter of trial and error to obtain a Hamiltonian from the equation of motions?) | 1 |
Does every convex, nonempty, body have a supporting line at every point on its boundary? This seems intuitively true to me, but I am having a hard time figuring out how to prove it. I was thinking of using a slicing argument. That is, cut a line through the body and then we have a set of curves which are convex. So more generally, do we need to prove that every convex function has a supporting line at every point? | 1 |
What are some interesting applications of the Mean Value Theorem for derivatives? Both the 'extended' or 'non-extended' versions as seen here are of interest. So far I've seen some trivial applications like finding the number of roots of a polynomial equation. What are some more interesting applications of it? I'm asking this as I'm not exactly sure why MVT is so important - so examples which focus on explaining that would be appreciated. | 1 |
I am trying to conform to the British practice (specifically Oxford Style Guide) and I am a little confused which to use to mark a nickname: Andrew 'Andy' Johnson Andrew "Andy" Johnson I know following the rules I should use single inverted commas, however the first one looks a tad weird to me. I have seen the latter option a lot on newspapers and business cards but not the former. I am going to use that for email signatures and names on business cards. | 1 |
I am trying to find a verb which can be used to indicate that someone is acting pedantic. I first considered "pedanticise", but, having found only one source for this, I thought I'd broach the question here. Edit: To clarify, I am defining pedantic to mean: excessively concerned with minor details or rules; overscrupulous. -- Google Or: overly concerned with minute details or formalisms, especially in teaching. -- Dictionary.com An example of this word used in a sentence would be, "Because Ellie spent the whole day ____ing over the grammar choices in her emails, she didn't get any work done!" | 1 |
There is a phrase in Malay that goes "prepare an umbrella before the rain", meaning one must be prudent and proactive of future challenges by making all the preparations necessary. I would like the English equivalent of such a phrase. Thanks in advance, and apologies if this has been asked before! (I checked as much as I could) EDIT: What I'm looking for is the act of preparing a solution to a specified problem before the problem happens. So anticipating rain, one prepares an umbrella. | 1 |
It is generally assumed that there is no limit on how many bosons are allowed to occupy the same quantum mechanical state. However, almost every boson encountered in every-day physics is not a fundamental particle (with the photon being the most prominent exception). They are instead composed of a number of fermions, which can not occupy the same state. Is it possible for more than one of these composite bosons to be in the same state even though their constituents are not allowed to be in the same state? If the answer is "yes", how does this not contradict the more fundamental viewpoint considering fermions? | 1 |
I keep hearing from native speakers the phrases like these: There is a lot of cars (books, hotels) There is a couple of cars (books, hotels) There is five (ten, etc.) of cars (books, hotels) There is a few of cars (books, hotels) Nevertheless, somebody told me that the phrases like above are incorrect for sure and there should be there are instead of there is. Whom could I believe? | 1 |
When someone makes an assertion, the distinction between "how did you know" and "how do you know" seems to be that "how did you know" implies that the person in question is correct in their assertion. "How do you know" is normally an inquiry into the person's credentials, and often expresses that the assertion is incorrect and/or ungrounded. Does anyone know what the reason for this distinction is? Why does simply changing the tense of the verb change the implication so strongly? I suspect that, linguistically speaking, the "did" might be a different tense than the past tense, but I'm not sure what it is, or I could be entirely wrong. | 1 |
I know, that if a polynomial function fails to have any real root, then, by the fundamental theorem of algebra, it must possess at least a pair of complex roots having non-zero imaginary part. The real roots are points of intersection of the curve, with the horizontal axis, on the real plane. My problem is in visualising location of complex roots. Can I make use of Argand Plane in visualising? | 1 |
I found that some theories about quantum theory is similar to Fourier transform theory. For instance, it says "A finite-time light's frequency can't be a certain value", which is similar to "A finite signal has infinite frequency spectrum" in Fourier analysis theory. I think that a continuous frequency spectrum cannot be measured accurately, which is similar to Uncertainty principle by Hermann Weyl. How do you think about this? | 1 |
I study cognitive neuroscience and I periodically run into physics related questions in the context of neuroimaging technologies. My question specifically refers to electric and magnetic fields that can be measured by electroencephalography (EEG) and Magnetoencephalography (MEG), respectively. One interesting difference between the EEG and MEG signal is that unlike the electric field, the magnetic field is unimpeded by differing conductances across brain, skull, scalp and other tissues. I was wondering if somebody could explain what differences between the two fields account for these phenomena. | 1 |
I know that many questions on topics similar to this one have been asked before, but I have read many of them and still not able to solve my problem. You could attribute it to my poor command of English. My question relates to two weird sentences, and I want to know which sentence is correct: I am so hungry, it feels like my tummy is eating myself. or I am so hungry, it feels like my tummy is eating me. | 1 |
Based on my very basic understanding of the Johnson noise, it's not just a DC phenomena, but should change with frequency in a system, where there is a frequency dependent, real component to the impedance. I think both the skin effect and eddy current losses contribute to the effective resistance of an inductor, so Johnson noise should increase at higher frequencies. Am I being dumb? | 1 |
I had a confusion in the diffraction experiment about which I was taught in school. According to the formula we Derived The width of the central maxima decreases on decreasing width of slit and vice versa. But what i wonder is what happens to the max intensity of central maxima in these cases? I asked two physics teachers and they gave me opposite answers-one said it increases on decreasing slit width which i feel is right but the other said it would be the same as light is of constant wavelength(monochromatic). What do you think? Please explain:) | 1 |
As a result of the Ehrenfest Paradox, the geometry of a rotating disc is non-Euclidean. However, while reaching this conclusion, we assumed that "the radius doesn't undergo Lorentz contraction", because "the radius is always perpendicular to the velocity vector", which is equivalent to : "in a circle, the radius is always perpendicular to the tangent at that point." But this is an Euclidean assumption (We have to use the parallel postulate to prove it.) Therefore it doesn't work in Non-Euclidean geometries, and we shouldn't be able to use it. | 1 |
Good evening everybody, I'm stuck with the following problem from an old exam in Linear Algebra. One is given two Eigenvectors with corresponding two Eigenvalues and told that the trace is negative. I figured out a third orthogonal eigenvector and tried to get to the matrix via diagonalisation, using a parameter alpha for the third eigenvector. Then I set the trace of this matrix equal to the sum of the known eigenvalues plus alpha. But my method does not work out; it does not give me a negative value for alpha. Where am I going wrong? How could I make this work? Thank you so much. | 1 |
For example in the models for holographic superconductors we can calculate the conductivity. Also there is an energy gap. I can understand that it describes a superconductor. However I have also heard people talk about superfluidity in holographic QCD. I believe they are talking about the condensates such as the pion or the chiral condensate. Where is the superfluid in holographic QCD (quark gluon plasma maybe?) and how do I know that it is a superfluid? | 1 |
I would like to produce some diagrams (preferably using TikZ/PGF) using the visual notation given in Enterprise Integration Patterns by Hohpe & Woolf. I'm aware of stencils from the above site, based on Visio, but I'd rather be able to compose them directly in my LaTeX documents. Is anyone aware of PGF library packages that I can use, or failing that how I can create reusable symbols for use in a TikZ/PGF figure? | 1 |
Even though I can find this command hiding somewhere on the internet, I though it might be useful to have it up here for the LaTeX community in general. How does one run TeX from the command line interface (Terminal) in Linux? Are there any required parameters? What if the command is part of a bigger script, how does the script know when the TeX processing is done to continue with any subsequent actions needed? Is there a clear manual for this somewhere? A starting point might be: pdflatex [options] filename.tex latex [options] filename.tex xelatex [options] filename.tex | 1 |
If I understand correctly, axioms are those statements that we assume to be true, instead of proving to be true. I have seen that in topology theory, various axioms of countability and separation axioms seem to be definitions of some concepts, instead of being assumptions. So I was wondering if "axioms" in topology theory are really axioms? If no, is this kind of naming rules common in all other branches of mathematics? Thanks and regards! | 1 |
Imagine I have a vertical straw, and that it is partially filled with water. If I were to decrease the radius of the straw at the bottom end, eventually surface tension would allow the water to remain in the straw (i.e. the force of gravity would not be enough to overcome the surface tension and for water to flow out of the straw). What I'm curious to understand is for a certain (small) radius at the bottom, how much force/pressure would be required at the top of the straw to overcome surface tension and force the water out of the bottom of the straw at a certain (volume flow) rate. Any help would be greatly appreciated! | 1 |
If we have two complex numbers, in polar form, as the numerator and denominator of a fraction, and we are asked to write them as a single complex number, is there an easier way to deal with them rather than the usual procedure? (By usual procedure I mean first expanding them by writing the value of each term and then realizing the denominator, etc.) Thank you. | 1 |
Why is Erbium Doped Fiber Amplifier (EDFA) preferred over Erbium Doped Waveguide Amplifier (EDWA)? The question has been asked from an engineering point of view, but obviously I would also be interested in Physics of it. Is it just because of the difficulty of constructing a waveguide, or is there something more? I understand the individual benefits and limitations of a fiber amplifier and a waveguide but cannot understand the preference in this case. http://en.wikipedia.org/wiki/Optical_amplifier#Doped_fiber_amplifiers | 1 |
I have been using TikZ to draw game-trees for my game-theory lectures (mostly using the automata package) but I could not figure out how to draw an arc across the edges the leave a given node. When we want to denote that a player has a continuum of actions available at a node, we usually draw an arc across the edge leaving such node. For example see the arc crossing the edges that leave the first node in this picture: Any suggestions on how I could try to implement this in TikZ? Thanks! | 1 |
We have a car dealer around here with an ad that reads "No Fake Lures". Now, as I understand the concept of a lure, if it doesn't attract attention, it's not a lure. And if a lure does attract attention, it's a lure, so no matter what is used to make the fake lure, it's a an actual lure. Therefore, it's not possible to have a fake lure. What do you call a statement like "No fake lures"? | 1 |
I've been looking around about LCD monitors, and how they polarise light. When a pixel needs to be black, the light is "twisted" so that it can't go through the polarising sheet in front. What happens to this light? Does it relfect back into the screen? Surely that would mean the screen would get quite hot if you leave it on a black image for a while? (but I've never noticed that happen). What happens to the energy (from the electricity used to create the light) when it's blocked by polarisation. | 1 |
I'm currently converting my thesis into LaTeX, and i have an issue: being an IT thesis, I have tons of code quotes. The problem is not about the blocks of code: they are not that many and i can wrap them with {verbatim} tags. The problem is about the millions of inline single terms which should be formatted the same way. Is there a way, for example, to define a macro or shortcut or whatever which, is i select one word and click it, automatically wraps it with {verbatim} (or equivalent) tags? Hope I've been clear. This could really spare me hours of tedious work, thank You in advance! | 1 |
I am writing a novel and am constantly trying to figure out how to describe the action when someone gives a sort of small cough or a quick "huh" in agreement. I suppose it would be the non-word equivalent of "I'll say" or "You think?" To be specific, I'll use it in a dialogue. "He must really hate Ian, then." Clarissa [insert word here]. "Yes." It's usually used when the speaker is trying to convey that the subject is much more serious than their conversation partner is taking it. | 1 |
There are many kinds of integrals, with the most famous being the Riemann integral which is taught in elementary calculus classes. The motivation behind the Riemann integral is to find the area between curves by using rectangles of infinitely small width. When i first studied calculus, i was fascinated by this formulation and thought it was indeed ingenious. My question is: what are the limitations of the riemann integral? What could be the link or the motivation to be able to "create" new ones like lebesgue, or darboux? | 1 |
Heard an English teacher claim that: "Dogs is not my cup of tea" is correct; whereas "Dogs are not my cup of tea" is incorrect. The explanation was that the verb form of 'to be' must agree with the singular noun 'cup' and not the plural noun 'dogs'. Checked Google on this and it appears that this is an extreme minority opinion at best. Nonetheless, can the teacher's argument be authoritatively refuted, or must this person be allowed to continue impressing pupils with their dubious insider's knowledge of the English tongue? | 1 |
I took my son to a science museum where they had a solenoid oriented vertically with a plastic cylinder passing through the solenoid. An employee dropped an aluminum ring over the top of the cylinder when there was no current going through the solenoid. Then they turned on the current going through the solenoid and they aluminum ring went flying up and off the top of the solenoid. What law of electro-magnetics causes the force on the aluminum ring? | 1 |
While studying Electrostatics, I was wondering about whether a charged sphere gains or loses mass while just adding electrons? If it is possible then the negatively charged sphere will have more mass than positively charged sphere, but according to me I think that since the mass of electron is so negligible then there must be no change in mass just because of electrons. So is it possible or not ? | 1 |
For a paper I'm writing, I need a bit of second order logic in order to convey a few steps in an inference. I've completed the introductory and intermediate/advanced logic classes at my school (second order logic wasn't included in the curriculum, unfortunately). I use predicate logic in most of my classes, so I'm comfortable with it. I'd like to learn just enough to properly notate the steps of the inference. Is there a concise tutorial on the subject available online? | 1 |
As far as I know, whenever we talk about a black hole, we refer to a static or stationary solution to Einstein field equations. I know the formation of a black hole can be discussed by the numerical GR, but I have never saw an analytical solution which can describe the formation of a black hole. So do anybody know that there actually exists such solution which has power to describe the formation of a black hole? Even the simplest case, for example, the spherical symmetric collapse of radiation into black hole can satisfy me very well. | 1 |
In Chemistry, an amount of energy has to be supplied for a reaction to occur. This energy, known as the "activation energy", breaks up the bonds between molecues in the substance. It is equivalent to the total bond energy of the reactants. However, in high school I learnt that the energy required to start a nuclear reaction is the difference between the binding energy of the reactants and the binding energy of the products. Why is it that the minimum required energy is not the binding energy of the reactants, similar to a chemical reaction? | 1 |
Which are the differences between Polar curve and Nyquist plot in System Control Theory? I wasn't able to figure it out myself. Are they the same thing? As googling for these two concept returned similar plots, but from the theory I can't find any similarities between them, or I am not able to understand how they are related to each other? Edit: Even though I edited this after more than two years from posting it, I just realized that the terminology that is used at my university, Nyquist plot and Polar Curve mean the same thing. | 1 |
I am curious about the vibration of metal objects as a sign of an impending lightening strike. This is apparently a common occurrence; so much so that a quick google search will yield many pages instructing people to head for shelter if their keys (other other small metal objects) start to vibrate in the midst of an electrical storm. One climbing site even mentions that a vibrating rope is a sign of a lightening strike. Can someone explain the mechanism behind this? My guess is that it a piezo electric effect, though this contradicts my (limited) understanding that atmospheric electricity is static. Thanks :) | 1 |
I collected the following "top eight" text books on computability (in alphabetical order): Boolos et al., Computability and Logic Cooper, Computability Theory Davis, Computability and unsolvability Hermes, Enumerability, decidability, computability Hopcroft et al., Introduction to Automata Theory, Languages, and Computation (thanks to Bill Province) Kleene, Introduction to Metamathematics Minsky, Computation Sipser, Introduction to the Theory of Computation(thanks to Prajwal Kansakar) I know it's opinion-based, but which important text books did I miss? | 1 |
I would like to get the formula on how to calculate the distance between two geographical co-ordinates on earth and heading angle relative to True North. Say from New York to New Dehli , I draw a straight line THROUGH THE EARTH - as they were two points in space. How can I calculate that angle from say New York to New Dehli if I was to draw a straight line through the surface of the earth . What kind of mathematical calculation/formula would be involved in order to do that? | 1 |
There are three Sakharov conditions of baryogenesis: CP symmetry violation. Baryon number conservation violation. Thermodynamical equilibrium violation. In SM the first one is satisfied by CKM phases, the second one is satisfied by instanton-like transitions for zero temperature and sphaleron-like transitions for non-zero temperatures. As for the third one, I've thought that EW phase transition provides violation of equilibrium, but after reading Gorbunov and Rubakov book "Introduction to the Theory of the Early Universe: Hot Big Bang Theory" I've started to doubt. They write that this transition is of second type one; thus it doesn't provide sufficient thermodynamical equilibrium violation. So can EW phase transition provide baryogenesis? | 1 |
I'm interested in the following question: I want to visit where my grandmother was born. To me it seems like a noun clause because I could replace the clause with a noun. For example: I want to visit Ireland. Is this the correct way to check? The definition I read for an adverbial clause states that Adverbial clauses of place modify the main verb in the sentence and provide information about the place that an action takes place. This definition has confused me about the difference between a noun clause and an adverbial clause. How about the following sentences: We can go wherever you want. You can show me where it is. Thanks for your help. Patrick. | 1 |
I can calculate the derivative of a function using the product rule, chain rule or quotient rule. When I find the resulting derivative function however, I have no way to check if my answer is correct! How can I check if the calculated derivative equation is correct? (ie I haven't made a mistake factorising, or with one of the rules). I have a graphics calculator. Thanks! | 1 |
I am teaching English to my cousin, but I am not sure how to explain phrasal verbs correctly. For example "take off". I explain it as two words but a single entity. When I ask her to name a verb in the sentence The plane is taking off, I expect to hear "to take off", not "to take". Do I understand this concept correctly? Update: In the sentence "She put her hands around her hear and squeaked." Is "put around" a phrasal verb or there are separate verb and preposition? | 1 |
Does the demonstratives refer to the next word or previously mentioned statement? The medieval center is Prague Castle and St. Vitus Cathedral. An evening view of these illuminated landmarks is one of the most memorable sights in Europe. In the above sentence, does these refer to "Prague Castle and St. Vitus Cathedral" or to the "illuminated landmarks"? I'm a little confused about this. A clear explanation would be great. Also, what's the difference between demonstrative determiners and demonstrative pronouns? | 1 |
Full disclosure: I'm taking my first complex analysis course as a graduate student and the title of my question looks like a dumb question to me. In any case, there's a problem in my book that deals with a sequence of "holomorphic polynomials" converging to a "holomorphic polynomial". Is this just a redundancy or is there some weird world where certain polynomials aren't (complex) differentiable? | 1 |
Imagine two entangled quantum particles in the singlet state, one held by Alice and the other by Bob. Alice and Bob are both widely separated. Bob measures his spin in some axis and finds it to be up (say). And that puts his particle now into the prepared state of spin up. Entanglement means Alice, if she were to do a similar measurement would find spin down. But assume Alice does not actually do any measurement. So does Bob doing his measurement mean that Alice's particle has immediately and spontaneously collapsed into a prepared state of spin down? Or is the state of her unmeasured particle unchanged? The literature, and popular press, are both vague and inconsistent on this seemingly important point. | 1 |
About a month ago I posted this question about eigendecomposition of a special matrix; and I received an answer. This is not my main field of study and I came to this as part of the proof for a method I developed to address a bioinformatics problem. Now I am interested to learn more about this area. Could anyone suggest some references and relevant literature that I can read. Moreover, I may end up publishing my method. How should I acknowledge and cite the stackexchange users/website ? | 1 |
Suppose you have a set A which has the same cardinality with real numbers R, which means |A| = |R|. Also suppose that you have a finite set B , which of course has finite cardinality. Also suppose A is a proper subset of A union B, I mean there are some objects which are not an element of A but they are an element of B. Now is the cardinality of A union B greater than the cardinality of real numbers, also if so is this cardinality of A union B equal to cardinality of the power set of real numbers ? | 1 |
I often find myself in the situation of wanting to capitalize the phrase "Enterprise IT" due to its frequency of reference as the title of my industry. It feels appropriate when I write: "In Enterprise IT ..." "The Enterprise IT industry..." I would not be surprised if my capitalization is off here. Could one of you help me with a definitive answer to the argument? | 1 |
Forgive me if this is a non-question, but I could not find anything regarding this. I only know parts of GR, and I am not familiar with the math. Since energy and matter density curve spacetime, does this mean that when entropy increases, spacetime curvature flattens? Hypothetically, if the universe is destined to reach total entropy and be in equilibrium, would this mean that the spacetime curvature of the universe be mostly flat? | 1 |
I am interested in the history of functions. Why did Euler introduce them? When and why did they become central to mathematics? I know the second question has something to do with the famous Fourier-Cauchy dispute over the heat equation, but don't have any sense of the details. By the way, I'm asking because I would like to give a short, historically informed explanation to high school students why functions are important. | 1 |
When a trap is set up to be active, is it "sprung" or "unsprung"? I'm confused by the ambiguity of the verb "spring". That is, a trap that is set up and active could be "sprung" in the sense that a spring is compressed and ready to launch, but it could also be "unsprung" in the sense that it hasn't yet sprung to action because its spring force has yet to be released. And after a victim walks into the trap and causes it to spring, the same ambiguity (in my mind) seems to apply. | 1 |
My dad's an author (English books with some Arabic) and until recently has been using WordPerfect for DOS for all his writing. He's been moving to Word and hates the lack of control he has compared to WP. I'm looking for options and LaTeX seems to be a good one. Here are the things I'd like to be able to do: Arabic inline text Support for chapters (as separate files) Support for ebook output (epub/mobi) Cross platform environment (Mac and Windows) Some way to move from WP and Word Is this realistic with LaTeX, and what would be the best way to start for a newbie? | 1 |
I've read 'Axiomatic Set Theory' by Patrick Suppes, and one thing I've noticed throughout is that he seems to be obsessed with definitions, and he tries to allow for urelements. Is this standard for ZFC? I thought in general when we say 'set' in ZFC we really mean 'pure set', and so avoid having to worry about individuals. In addition I've never seen such a fuss over definitions in any other mathematical book I've read, is this something I should get used to in Set Theory? If this is not standard, can anyone direct me to a book similar to Suppes' which builds (from the axioms) all the usual set theoretical structures needed for other areas of mathematics that is? | 1 |
I quite frequently use a word that sounds like "shtook", to mean, trouble with the law or other authorities, as in, "You'll be in dead shtook if you do that" or "you'll be in real shtook if you don't finish your homework", but I have never seen it written, and don't know how it is spelt. Can anyone shed some light on the matter. A search like this doesn't get very far; the real dictionaries don't recognise it and the Urban Dictionary here has only a typically obscene interpretation not in the least bit like I remember it. | 1 |
I am undergraduate in economics. As you may know, most prestigious departments in economics now require their aspirants to have taken Real Analysis (and Linear Algebra, too) before entering their programs. I have time to take these courses but don't know whether any college will give admission in their math program to an econ undergrad. I don't know whether distance learning courses will help me. Can anyone suggest me how to take math courses? Your replies will oblige me. | 1 |
I am learning Fourier transforms, Z transforms etc. in Digital Signal Processing and I can work easily with integrals. However, I don't understand how a Fourier transform converts time domain signals to frequency domain signals or why it is invertible. I also have a very basic understanding of linear algebra, not suitable for fourier analysis. I looked up books on fourier analysis but they don't explain anything I don't already know. So should the next logical step be to learn spectral analysis? Also, which books would you recommend for linear algebra? I already know matrices, eigenvectors, but not Hilbert spaces. | 1 |
I was watching a TV show, and this girl said: I just wish that once, I'd bring a guy home that they actually liked. Shouldn't it be like this? : I just wish that once, I'd bring a guy home that they actually like. Didn't she mean 'I wish they'd like my future boyfriends'? I think this is OK: I just wish that once, I brought a guy home that they actually liked. But the way she said it sounds strange to me. | 1 |
I am writing an article for a magazine about my visit to my village. I want to use a better word or phrase for 'my village' or 'my native place'. The following is the part 'When i heard of stories of hardships and suffering from my grandparents I realized how fortunate I was to live in the city I now call home. When the day came to visit "my village/my native place", I felt uncertain and nervous..' And better word or phrase to make the content more appealing? | 1 |
In Euclidean space, There is a classic Theorem claims that: The length of every rectifiable curve can be approximated by sufficiently small straight line segment with ends on the curve. Now, The question is that: Is there a similar thing happen on plane of constant curvature? I.e., Can the length of every rectifiable curve on the plane of constant curvature be approximated by sufficiently small geodesic line segment? | 1 |
In any cubic meter of space in our solar system there is predicted to be some amount of dark matter. Also in a cubic meter of space is a known average amount of cosmic ray energy. What is the ratio of cosmic ray energy to dark matter energy in our solar system? I'm curious if they are on the same order of magnitude or far from it. | 1 |
Imagine two charges A and B separated by some distance. Charge A emits a photon which is absorbed by charge B. Is the recoil momentum received by charge A always equal and opposite to the momentum gained by charge B? Is this true both for static Coulomb fields and radiation fields from accelerating charges? I suppose there is no momentum "left over" in the EM field after the interaction so that all the momentum lost by A is absorbed by B. Is this how it works? | 1 |
I have always thought it acceptable to say and write, "She looked at me disgusted." However, I know some consider it ungrammatical, saying it must instead be either "She looked at me disgustedly" or "She looked at me, disgusted." Please give me your opinions and explanations as to whether any of the foregoing sentences must be deemed grammatically wrong. Briefly, my own analysis is as follows. It is correct to say, "She looked disgusted." So why would it be incorrect to say "She looked at me disgusted"? (She was disgusted while looking at me--or, she was looking at me while disgusted.) | 1 |
In "Pragmmatic Programmer" by David Hunt and Andy Thomas, there is a sentence: Do you ever watch old black-and-white war movies? To my best english grammar knowledge, present perfect tense should be used here: Have you ever watched black-and-white war movies? Is the version of the authors correct? If so, what's the difference between these two variants and what is the appropriate way to use each? PS. I checked this sentence in the translation of the book in my native language and it was translated exactly as if the orginal sentence was in present perfect form. | 1 |
I read here that there is a general rule to write an adjective order. But I didn't find any explanation if the rule has a specific order for colours, especially for primary colours. This may sound stupid but I'm just wondering. I mean is it preferable to say: red and white flowers Or: white and red flowers Or is there really no grammatical rule to obey? | 1 |
I heard an interesting argument from a colleague recently that went something like this. Whenever we are using an axiom scheme, we are essentially choosing one of the instances of this scheme, and hence, whether or not we include the axiom of choice in our axioms, we are implicitly using some kind of choice principle to choose that instance. My gut feeling is that this argument seems fishy, but also interesting, and I lack the expertise to give a good answer. My question is whether this argument holds or not, and whether it makes a difference if the axiom scheme is uncountable. I realise that the question is somewhat vague, but I hope there can be some interesting answers anyway. | 1 |
An isomorphism indicates that two structures are the same, using different names for the elements. Therefore it's obvious that every (algebraic) property of the first structure must be present in the second. However, homomorphisms only indicate that the two structures are "similar", so it's not quite as obvious that every property will be preserved. Yet all the properties I've ever seen are preserved under homomorphism: commutativity, cyclicality, solvability... What are some examples of properties of algebraic structures not preserved under homomorphism? Feel free to use any algebraic structures you like, but I'm particularly interested in your garden variety structures: group and rings, say. | 1 |
This is potentially a very stupid question but I'm going to ask it anyway. With all these huge buildings such as the Abu Dhabi Mosque, where an unbelievable amount of materials such as marble was moved from one side of the earth to the other, is it possible that if we 'shift enough stuff' that we could change the earths centre of gravity, and potentially alter its orbit? | 1 |
There is no "action at a distance" in nature. Attraction of a piece of iron by a magnet, attraction between distant electric charges of opposite sign, have to be mediated by something. The virtual particles are proposed as an explanation. If they have an observable effect, it seems like they must exist. If so, why do we call them virtual? It can't be that they have short lifetimes, as there are short-lived particles (resonances) that we don't call "virtual." On the other hand, some people say that the so-called virtual particles only exist on paper, or that they are just a technique to help us handle our equations. So what is the meaning of the word "virtual" here? Do these particles really exist, or not? | 1 |
Why it is said that the Microchannel Plates can be operated in vacuum? What is the maximum pressure in which it can be operated? Also, while it is not operating, should it be kept in vacuum? Is this because the semiconducting property of the channels can be affected by the atmospheric pressure? Or while operating the gas molecules can be ionized and burn the detector? | 1 |
A friend of mine corrected my sentence but I couldn't understand it. Just hoping someone can explain it properly for a non English speaker. My sentence is: "Finally your passport GOT ready for pickup" My friend (native English speaker) corrected it to: "Finally your passport IS ready for pickup" Or "Finally your passport got processed and is ready for pickup" Why can't i use "got ready" in the above sentence just like in sentences "We got ready for bed", "Alpha team got ready to play" Thanks in advance. | 1 |
I'm looking for a single word to indicate a point in time which is either the beginning or end of an event. Edit, for a better example: A bell rings at the start a round of boxing. A bell rings at the end of a round of boxing. Assuming the bell rings at no other times, we can say the bell always rings at the BLANK of a round. Currently, for BLANK, I'm using the phrase "start or end." It feels clunky. I'd like to replace it with a single word, if possible. | 1 |
I couldn't clearly understand the phrase "credential mongering" as used in an article in the New Republic about the Ivy League. The extract, from "The Trouble With Harvard" by Steven Pinker, is as follows: Admission to the Ivies is increasingly seen as the bottleneck to a pipeline that feeds a trickle of young adults into the remaining lucrative sectors of our financialized, winner-take-all economy. And their capricious and opaque criteria have set off an arms race of credential mongering that is immiserating the teenagers and parents (in practice, mostly mothers) of the upper middle class. Is it to do with attaining qualifications by any means? Or is the phrase itself imprecise? Thank you! | 1 |
This suggests that the current MLDA is not effective. However, the estimates in this paper challenge that claim and show that the effects of the current MLDA is statistically significant in all cases we observe. This suggests that the current MLDA is not effective. However, the estimates in this paper challenge that claim and show that the effects of the current MLDA is statistically significant in all cases that we observe. | 1 |
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