darklight03/StackMIAsub huggingface dataset:
In the following statement, I am confused with the meaning of "whether" in the second sentence. Could you please advise which one is the meaning of this statement? a or b? The statement: "For the grant of the permanent Partner visa, you can be either in or outside Australia. This is the case whether you lodged your original application in or outside Australia." The meaning: a) You can be either in or outside Australia for the grant of visa and it is not important where you have lodged your application. b) If you have lodged your application in Australia, you have to be in Australia for the grant of visa and if you have lodged your application outside Australia, you have to be outside Australia for the grant of visa. Many thanks, Kourosh
An inertial frame of reference is described as being a frame of reference in which the first law of Newton (the law of inertia) holds. This means that all events as described with respect to this frame of reference must have a zero net force acting on it and therefore traces a straight line with a uniform non-translatory motion. But, I have read in some books, especially "Introduction to Special Relativity" by the well-known Robert Resnick, wherein his definition of an inertial frame of reference also refers to such a frame of reference as being an unaccelerated system. This is where I am confused. How can we describe a frame of reference as being unaccelerated if we occupy the frame of reference itself? No mechanical experiment conducted solely confined to a single frame of reference can determine the absolute motion of the frame of reference relative to another frame of reference. All that can be understood is that there is a certain uniform relative motion between frames of reference and no more. Is Robert Resnick saying that the inertial frame of reference is unaccelerated with reference to another frame of reference?
I am currently a senior in high school, and I have been studying mathematics for about nine or ten years now in my personal time outside of school. I am not familiar with academia or in general higher education, but I do know that I want to continue studying mathematics or something in a related area. I am having a lot of trouble pinning down which universities I should consider going to, I don't think I am even ready to start comparing, so despite the 'softness' and vague nature of this question I feel I don't really have any where else to start then by asking which universities should I be looking into for mathematics? I have read many articles that rank schools according to some criteria, articles with titles like "Top Universities for Mathematics" or "Best Mathematics Programs", but I really want to get the opinions of people who study mathematics frequently. Any school suggestions would be greatly appreciated. I am trying to gather a list so don't hestiate. I live in California and am willing to go anywhere on the planet, so location is not a problem for me.
What would be an idiom or word or name for someone that is an initial tester (like a beta tester). I am writing a speech for my younger brother's engagement and want to say how I have always been the first to try everything in my family--schooling, learning to drive, college applications, etc.--because I was the oldest son. My parents basically used me as a trial run to test the waters each step of the way in their parenting. They tweaked and refined the process with each of my two brothers. Now for his wedding, he's being sent out to scout for the proverbial mines for the first time. So I'm looking for a better term than beta tester to describe what I have been my entire life. I was kind of like a "lab rat", but that sounds horrible. Here's the line: "Throughout our life, being the oldest, I was sent out as the front line to test the waters." I really hate that line. I hope having a better term for "beta tester" would make that line make more sense and sound better.
Possible Duplicate: When is it okay to end a sentence in a preposition? So we've all heard the admonishments from our teachers not to end a clause with a preposition A plumber visits a wealthy estate to fix a clogged toilet. As the butler opens the door, the plumber barks out,"I'm here to fix the toilet. Where's your bathroom at?" "Please try to speak with more discretion. We do not want to disturb our neighbors with the details of our plumbing issues. And we most certainly do not end our sentences with prepositions, sir. So the plumber lowers his tone and says more cordially, "I'm here to fix the toilet. Where's your bathroom at, asshole." Anyway, back to the matter at hand. I have come under the impression that this is a rule of thumb to help the elementary student avoid mismatching case for the target of the preposition rather than a hard rule. For example by placing the preposition closer to its target, you avoid constructs like: "Who did you give the invitation to?" instead of the proper "To whom did you give the invitation?". Moving the preposition closer makes the incorrect case sound absurd. No one would ever say "To who did you give the invitation?" All of this introductory text leads up to this simple question: Is this phrase correct "Whom did you give the invitation to?" or is it still incorrect english even though we addressed the issue of case?
Background: I am an upper level undergraduate physics student who just completed a course in classical mechanics, concluding with Lagrangian Mechanics and Hamilton's Variational Principle. My professor gave a lecture on the material, and his explanation struck me as a truism. Essentially, he argued that the difference between the Lagrangian evaluated along the parameters describing the true path and the Lagrangian evaluated along parameters corresponding to a mild perturbation of the parameters by a function an(x), where a is a scale factor, is zero. Where exactly is the profundity in this statement? I understood it as "If we deviate the parameters away from the parameters that minimize the integral, and then take the limit as that deviation vanishes, the difference between the path described by these two sets of parameters is zero and the path must be the true path." Well of course this is true. What am I missing? Alternatively are there any decent texts that outline this principle at an undergraduate level?
I am a high school senior and I am interested in doing a math research. I hope someone can recommend areas or topics of research that are challenging, rewarding, and yet do not exceed my capability. (I acknowledge this is quite hard) My math background: a. I have done competition math (Elementary number theory and combinatorics, Euclidean Geometry, and Algebraic manipulation) and I'm fairly comfortable with proofs. b. I had my first courses in Multivariable Calculus, Differential Equation, and Linear Algebra (Familiar with fundamental concepts, basic techniques and motivations) c. I have learned a portion of Abstract Algebra on my own and in summer programs including topics like Lagrange theorem, Vector spaces, Polynomial Rings, and Morphisms. d. I don't have a good background in statistics and probability e. I have been exposed to Knot theory and Chaos theory f. I do have basic programming skills in python and Mathematica, and I can work with LaTeX. I really appreciate your help!
I am planning to take a graduate Geometry course next semester. The preliminary syllabus does not specify any textbook but has the following descriptions: Catalog Course Description: This course studies higher geometry including triangulations of polygons, Voronoi diagrams and Delaunay triangulation, algorithms in computational geometry, Euler characteristic of geometric objects, conics, elements of differential geometry of curves. Topics Covered: inequalities, Helly's theorem, power of a point, inversion, Voronoi diagrams and Delaunay triangulations, algorithms in computational geometry, Euler characteristic of geometric objects, conics and their affine and metric classification, elements of differential geometry of curves, polyhedra. I would like to study early taking advantage of my downtime. Is there any textbook that you would like to recommend for my self study? Thank you very much for your time and pointers.
Fluid dynamical instabilities are present in many different everyday things. The famous tears in wine for example are a classical example of a Marangoni effect, where surface tension gradients due to evaporation cause an instability. I recently came across an instability that occurs when you have just emptied a glass with yoghurt drink and have only a film of the drink left on the walls of the glass. A tear-like pattern emerges over the time of about a minute that looks like shown below: I have been thinking what can cause this effect. It seems somewhat similar to a Marangoni effect, but given the ingredients of the yoghurt drink I think we can safely rule out evaporation on this timescale. Another potential effect explaining this would be viscous fingering, but for that to happen I believe the gas phase has to be driven, which it isn't here. Or perhaps it is a 'surface-version' of a Rayleigh-Taylor instability? Or maybe it is related to the non-newtonian nature of the yoghurt drink? To summarize: I don't know which instability I am looking at and I would love to know what causes this pattern on the glass with yoghurt drink! Does anyone know what is causing it?
There's an old debate going on in the guitar community about how much does wood choice and body shape affect the sound of an electric guitar. No one denies that there's a difference acoustically (how the guitar sounds unplugged) because in this situation it's the wood and body shape that amplify the sound made by string vibrations, but when we're talking about the sound as it comes from the pickups, things get much more uncertain because there are a lot of variations even in supposedly identical guitar parts, and accounting for all of them for the purpose of doing an experiment where the only difference between two guitars is the wood is difficult (I certainly haven't heard of an experiment that was satisfying enough, but feel free to prove me wrong). I'm interested in a way to circumvent these practical difficulties using a theoretical explanation: Since the pickup only sees the string's vibrations, the question basically becomes "does body shape and wood make enough difference in the way a string vibrates that it changes the sound in a noticeable way", and this sounds like something that may be possible to figure out mathematically, or at the very least should be much easier to test because there are less variables involved. My question is: Is what I'm describing possible to calculate/test, and has this been done before?
Let's say I am at the train station and I missed the train, I still see it driving off. I would naturally say to myself: 'Damn, that was the train I was hoping to get.' Would that be wrong? If not, why is the past progressive used here? I have been taught that you use the past progressive when you are either talking... about a longer action that was interrupted by a shorter action about actions that were happening at the same time about an action that was in process at a specific time in the past However, my sentence doesn't follow any of the rules above (at least I don't see that). Another sentence that I can't gramatically explain... Context: You told your friend David that Fred would not behave good when he is drunk before going to a party at which Fred gets drunk and then behaves bad. Later you say to David 'See? That's what I was talking about.' What's the grammatical explanation of this? Can anyone give me a rule why these sentences work? Thank you in advance!
My friends and I were playing a game where you roll dice and you bet money on what picture it's going to land on and I began reasoning with myself that if I tallied up what pictures the dice landed on that the ones it has not landed on were more likely to come up in the next roll of the dice. So I began a process of observing two rounds and tallying up the results and then on the third round betting on the pictures that have not come up yet hoping that they would make their appearance on the next roll. Although I do not have any mathematical proof to verify this. Does anyone know what this phenomenon is called if it is even possible or if it is possible? Edit: I figured it out its called "Gambler's fallacy"
Is "family" both plural and singular? or would I have to say families for the plural form? For example, which of these is the best option: "A majority of those whose family were unaware of their sexuality..." "A majority of those whose families were unaware of their sexuality..." "A majority of those whose family was unaware of their sexuality..." Edit: Here are some full sentences to give some context. Participants whose famil(ies) were aware of their sexuality were predominantly feminine and identified as gay, homosexual, drag queen, or a combination of these identities. All those who assumed their famil(ies) knew about their sexuality were gay identified and a majority identified as feminine. A majority of those whose famil(ies) were unaware were masculine and identified as non-gay, straight, down low or did not identify with any label.
I'm reading Chris Hecker's third article on rigid body dynamics http://chrishecker.com/Rigid_body_dynamics Quoting... "More importantly, if our collision detector supplies us with a 'normal vector' for the collision (denoted by n, and pointing toward body A by convention), we can define the 'relative normal velocity' as the component of the relative velocity in the direction of the collision normal." Which he defines as vAB . n where vab is the relative velocity of points A and B and n is the normal vector for the collision. I read Understanding Dot and Cross Product which explains that the dot product gives the length of one vector in the direction of another, which I think is what is being applied here, but I'm having a really hard time visualizing what is going on, specifically what the component is. Can anyone help explain what this component is and how using the dot product helps identify it?
I would like to better understand how neutrino oscillations are consistent with conservation of momentum because I'm encountering some conceptual difficulties when thinking about it. I do have a background in standard QM but only rudimentary knowledge of particle physics. If the velocity expectation value of a neutrino in transit is constant, then it would appear to me that conservation of momentum could be violated when the flavor eigenstate at the location of the neutrino source is different from that at the location of the interaction, since they are associated with different masses. For this reason I would think that the velocity expectation value changes in transit (for instance, in such a way to keep the momentum expectation value constant as the neutrino oscillates), but then it seems to me that the neutrino is in effect "accelerating" without a "force" acting on it (of course, since the momentum expectation value is presumed constant, there may not be a real problem here, but it still seems strange). Any comments?
I've recently learned about ultraproducts, but the source I learned from almost immediately after the definitions restricted to talking about countably incomplete ultrafilters. I know that the existence of countably complete ultrafilters is a large cardinal issue, but aside from this, is there a reason to focus on the countably incomplete case? Do ultraproducts (or even just ultrapowers) with a countably complete ultrafilter behave very differently from the countably incomplete ones? It would be great to have an example of the kinds of differences that happen, ideally in a fairly down-to-earth setting (maybe groups, or fields, or graphs?). The few places I've seen talk about countably complete ultrafilters all seem to be taking ultrapowers of models of ZFC, which is a bit much for me to grasp at this point. Since I just want to see the differences, it's fine with me if some set-theoretic hypotheses are needed to make the examples work.
While my physics teacher was explaining pseudo forces to us he gave the following example : An elevator is accelerating upwards. In it there is a bob strung up by a rope. There are two observers, A in the elevator and B outside of the elevator, on the ground and not accelerating. Due to the action of gravity and the lift's acceleration the rope breaks and the bob falls. Does it do so at the same time for the two observers? The falling of the bob will be registered only when an observer sees a change in its position. This will happen earlier for observer A in the elevator compared with observer B outside. Question: At a particular time instant, is it possible for the rope (which holds the bob) to be both broken and taut for different observers?
Is there a word to describe someone who uses complaints to indirectly brag about themselves? An example would be "I hate going to concerts because people start singing and because I have perfect pitch it irritates me." Perhaps another example might be "I don't like that video game. It's too easy and I get bored." The complaint would be in context, like the discussion is about concerts or the game in question, but the person uses it as an excuse to highlight something about which they want to brag. I don't think I'm looking for narcissism, as it's not necessarily that the person is trying to talk only about themselves, but rather that they specifically use a negative complaint to mask the fact that they are bragging. Is there such a word to describe this behavior?
I think prejudice is too general. The definition Google gives me for prejudice is: "preconceived opinion that is not based on reason or actual experience." - it doesn't specify that this preconceived opinion is due to membership in some group (or, more specifically, perceived membership in a group), although it seems to have that connotation, so maybe that is what I should go with. I think bigotry is too strong. For bigotry, we have (wikipedia): "Bigotry is a state of mind where a person strongly and unfairly dislikes other people, ideas, etc. " Bigotry sort of connotes hatred, not just bias. I want a way to describe the fact that a particular statement reveals an attitude that is unfairly biased against a culturally significant group, which may or may not be intentional or malicious.
In one of the books on algebraic topology (I don't remember exactly which one) there was an exercise to build an example of two topological spaces having two continuous bijections between them which are not homotopy equivalent. To be honest, this exercise confuses me a little because, as I understand, each pair of homeomorphic spaces is homotopy equivalent by construction. On the other hand, the existence of bijective continuous mapping between spaces automatically provides their homeomorphism (correct me if I'm wrong). Thus, in this logic, if we have two continuous bijections between topological spaces this will inevitably lead to the homotopy equivalence between them. I guess, however, that there is a simple counterexample related to the discrete topologies which breaks such a reasoning (see, for example, this: Is a bijective homotopy equivalence with bijective homotopy inverse a homeomorphism?), but I have certain difficulties in discovering it. Is there any suggestion?
One quality or trait that many employer looks for in a leader is the ability to not only perform well yourself but to also elevate the performance of others around you. For example, Steve Nash was an elite point guard and an all-star that made the people around him better. He made Shawn Marion and Amare Stoudemire all-stars and afterwards, when they were no longer teammates, they were not able to play at their all-star levels. You could say that Steve Nash is a great leader but it does not inherently imply that he also makes the people around him. Is there a specific word that describes this? A phrase to describe it would be, "he brings the best out of others", but I cannot think of a word to describe this ability/trait.
I was driving to work this morning when this question occurred to me. I was going up a clover-leaf entrance ramp to the highway. The person in front of me was lazily floating the outside of the curve, whereas I always tend to hug the inside of the curve. Hugging the inside of the curve tends to lead to an apparently higher speed... and I soon had to apply the brakes to avoid hitting the floater in front of me. This made me wonder, why does hugging the inside of the turn yield an apparently faster speed? Is it simply because the inside is a shorter radius and thus you traverse it more quickly, thereby appearing to go faster (something I know track racers take advantage of, thus the expression "he's got the inside track")? Or, it occurred to me that it could be similar to the way a figure skater performing a pirouette speeds up as she pulls her arms and legs inwards. So as you continually pull your car inwards on the curve it actually does increase its velocity. Does the second concept actually come into play here, yielding an actual faster velocity? Or is it simply the first concept, yielding only an apparent faster velocity? (assuming our cars are identical weight, engine power, etc.)
Given the equations of two spheres, how would I find the equation of any plane tangent to the two spheres? I tried something, but I realized that it failed, and I am not sure where to go from here. I have only basic knowledge of cross product, dot product, etc. and have not yet taken calculus. My attempt: I know the centers of the two spheres. I pick any point on the surface of the first sphere. I find the vector from the center of the first sphere to the point I selected. I then scale the center of the second sphere by the vector I just found divided by the radius of the first sphere and multiplied by the radius of the second sphere. Then, I construct the vector from the point I chose on the first sphere to the point I found on the second sphere. I take the cross product of this vector with the vector formed by the centers of the two spheres. I use this as the normal vector for my plane and plug in to get its equation. I noticed by experimentation that this does not work. Is there a way of solving this problem in a similar manner to what I tried above?
Back when I studying the time independent perturbation theory of the Hamiltonian in quantum mechanics, I remember reading that there are only three problems in physics with exact solutions: the free particle, the harmonic oscillator and the hydrogen atom. It was further stated that any given problem (even a simple pendulum) could have its solution determined by applying a small perturbation to the exact solution of another similar problem, i.e., it would be an approximate solution. So I was left wondering: are the solutions to all [a] real life scenarios (where you don't go around neglecting friction, using symmetries, etc.) obtained through perturbation theory? That is, are they all approximations and not exact solutions? In that case, would it be fair to state that physics is inaccurate to a certain degree? [a] With the exception of the aforementioned ones.
I'm a little out of my depth here... I'm trying to understand quasiparticle tunnelling in superconductor-insulator-superconductor junctions. Many books use the "semiconductor model" to explain this: (source: wikimedia.org) These diagrams show the available quasiparticle states (with a large band gap due to the formation of Cooper pairs), the filled states, and the empty states. My question with these diagrams is: shouldn't all the electrons exist as Cooper pairs? I assume that the lower band is filled with quasiparticles, since Cooper pairs would all be at the same energy level and quasiparticles obey Fermi-Dirac statistics, but I don't know where they're coming from. Also, why is there an energy gap in the quasiparticle energy states? I understand that this gap corresponds to the energy needed to break Cooper pairs, but I don't understand why would you need to break Cooper pairs to raise the energy of quasiparticles. Or is this "semiconductor model" not fully representative of the physics?