darklight03/StackMIAsub huggingface dataset:
According to the current Big Bang with inflation cosmological model? I was under the mistaken impression that there was very low volume, very high temperature/pressure, very low entropy and the Big Bang (perhaps prompted by the high pressure) resulted in an expansion of volume where energy didn't change much so temperature went down and entropy went up. Now I've learned about inflation and how there is no conservation of energy at cosmological scales and that the universe gained an exponential amount of energy during the inflationary period. How did this happen with a decrease in temperature? Inflation was a period of supercooled expansion, was it not? Why was positive pressure not enough to cause inflation such that we need a negative pressure in the form of the inflaton field (or later dark energy) to explain the expansion of the universe? Thanks for your time
You can obviously move a solid at a different speed along the surface of another solid, so how come the velocity of the fluid at the fluid-solid interface must be equal to that of the solid? What physical property dictates that the no-slip is valid for fluids but not solids? The Wikipedia page has the following: Particles close to a surface do not move along with a flow when adhesion is stronger than cohesion. At the fluid-solid interface, the force of attraction between the fluid particles and solid particles (Adhesive forces) is greater than that between the fluid particles (Cohesive forces). This force imbalance brings down the fluid velocity to zero. which didn't make sense to me since I'm not sure how they prove that this is true for any fluid-solid interface.
A long time ago I was thinking about how the Imperial system of measurements is arbitrary and annoying, and I decided to design the best system of units ever (I wasn't very old then). I worked on this idea occasionally for years without making any progress. When I finally got serious about it, I discovered Planck Units and that seemed to settle the issue. Now my problem is that Planck Units are so small that they can't be used for "normal" things without huge exponents, most of these being very different depending on the quantity being measured. Solving human-scale equations with these units by computer would thus either be very inaccurate due to floating-point errors (for numbers that are even within range) or very slow due to the need for extended precision. They also go "up" but not "down", which renders almost half of the possibile signed floating-point values as useless. I considered the idea of creating a new system by raising each Planck Unit with a standard exponent or multiplier, but I think this would bring some into an acceptable range but not others. So what I want to know is whether a system of natural units exists that uses units that are appropriate for work with technology that humans can interact with, or can be made appropriate without introducing too many arbitrary elements.
My friend has a tendency to wear mismatched socks, because he "Can't be bothered wasting time matching them, so he just pairs them up at random". One day I noticed he was wearing matching socks, which was apparently not on purpose. This got me thinking, if you have N different pairs of socks and you start matching them at random, what is the probability of putting together at least one correct pair? What first came to my mind was the famous Hat-checking problem, which I cannot generalize to answer this question. I tried programming the problem though and noticed that the chance of getting a correct pair becomes significantly lower with large inputs. It does seem to converge though, but I'm not sure how to find the limit analytically.
I'm currently writing a simulation in python with scipy and matplotlib to reproduce an one dimensional driven diffusive system described in this paper from M.R. Evans et al. The system consists of positive, negative and hole particles. On the left side of the system the positive (negative) particles are produced on the left (right) side with a possibility a and destroyed at the right (left) side with the possibility b. In some cases the system should show a flip between positive and negative high density states and I'm trying to reproduce this behaviour with my simulation. But all I can see is an increasing current within my simulation and I can't find any problems in my code explaining such behaviour. Does anyone here have some experience simulation such or similar systems? Cheers, Florian
Sorry if this question is naive. It is just a curiosity that I have. Are there theoretical or experimental reasons why gravity should not be an emergent property of nature? Assume a standard model view of the world in the very small. Is it possible that gravity only applies to systems with a scale large enough to encompass very large numbers of particles as an emergent property? After all: the standard model works very well without gravity; general relativity (and gravity in general) has only been measured at distances on the millimeter scale. How could gravity emerge? For example, it could be that space-time only gets curved by systems which have measurable properties, or only gets curved by average values. In other words that the stress-energy tensor has a minimum scale by which it varies. Edit to explain a bit better what I'm thinking of. We would not have a proper quantum gravity as such. I.e. no unified theory that contains QM and GR at the same time. We could have a "small" (possibly semi-classical) glue theory that only needs to explain how the two theories cross over: the conditions and mechanism of wave packet reduction (or the other corresponding phenomena in other QM interpretations, like universe branching or decoherence or whatnot) how this is correlated to curvature - how GM phenomena arise at this transition point. Are there theoretical or experimental reasons why such a reasoning is fundamentally incorrect?
Reading about intellectual history and the history of natural science, I have very often come across the expression to come-to-be as a synonym for to come into being, to start to exist, to originate, and so on. I also see commonly used such verbal expressions as to come to know (for to learn, to acquire knowledge of) or to come to see (for to realize), and so on. My question now is twofold: If one is allowed to write to come-to-be and to come-to-know and to come-to-see, is there some definite end to this or am I allowed also to write to come-to-converge, to come-to-acquire, to come-to-X? If I am allowed also to use other combinations, then what about the dashes/hyphens in these expressions. I usually see come-to-be with dashes, but the to come to know without (I think). Why is that so? Should one be consistent? Or has to come-to-be become a lexical entity that warrants a particular use of dashes, whereas the other expressions are simply compound verbs that do not warrant an equal use of dashes? What about "to-come-to-converge` and other less usual instances of such combinations?
Feynman Path Integrals are a way of calculating the wave function of quantum mechanics. It usually integrates every possible path through all of space. I wonder if there is any study of Feynman path integrals through a space with holes in it - with regions of space excluded from the integration process. More specifically, I'm wondering about points or regions of space where the amplitude must be zero. I assume that a point or region that is exclude from the path integral means that the amplitude will be zero there. I've heard described elsewhere that a space with holes in it can result in curvature in that space. And I wonder if the classical limit of a particle path will become curved due to nearby holes. This might result in the curvature of general relativity. So I wonder if there has been any study on this.
I think the wave function of a free electron is nonzero almost everywhere. In particular there are regions of space arbitrarily far away where the electron has positive probability of being found. If I prepare an electron in a particular position, then wait a small amount of time and then check to see if it has appeared in a region that is too far away for it to reach even if it traveled at the speed of light, there is a positive probability that I (or my assistant, who is coordinating with me) will find it there. What have I missed? This seems a lot like spooky action at a distance, but with spooky action no matter/information actually moves faster than light, wheras in this situation the electron actually moves a greater distance than light could in a given amount of time.
I'm working on ray tracing and I'm trying to understand the impact of the angle at which a light-path intersects the surface of a light source on the amount of light that source delivers to the path (per unit time, of course). My assumption for an ideal diffuse light source is that light rays leaving a particular point on the surface of the light source are uniformly distributed, in which case the angle of the path is irrelevant. I think that in essence, this assumption models each point on the diffuse surface of the light as an individual point-light source. Is that a fair assumption for something like a frosted light bulb, where I'm modeling the light as coming directly from the surface of the bulb, not the filament? Or alternatively, if I wanted to actually model the filament itself, would the same assumption be relatively valid? Are there any light sources for which this assumption would not work? I'm assuming lasers would not work this way, with most of the light leaving in one particular direction, but I'm not really worried about modeling laser light. For spot lights, I believe this is still just an ordinary "diffuse" light source which uses mirrors, an aperture, and lenses to direct the light once it has already left the light source so I could model it this way (though I suppose a more efficient model would encapsulate all of this and take the angle of the path into account).
Is there a game which is perfect, that is: always provides a decisive victor, and involves no component of luck Possible games which would be perfect or near-perfect might involve the pie rule. https://en.wikipedia.org/wiki/Pie_rule For the purposes of this question, a 'decisive victor' means that there is no tie, draw or stalemate- the game always ends with one player winning and another losing. 'Luck' includes any arbitrary decision outside the strategy of the players, such as deciding who gets to go first by flipping a coin. In other words, what I'm asking is: is there a strategy game in which neither player has an advantage due to luck, but one of them must win. It seems to me that there cannot be, because otherwise if two 'perfect' players played against each other, what could be the result?
In an electric circuit, how does the excitation of the free electrons to higher energy levels translate into net forward motion of the electrons to the positive terminal? My concept of electrons being excited by the electric field is that they have a higher orbital but they are still localized around the nucleus of a few atoms (especially in a more resistive element). But I know there must be a small net forward motion for there to be current. I need to marry the classical model of the colliding electrons and atoms of the medium with the Quantum principles involving the excitation of charges to higher energy bands and emission of photons. Also, a second question is what causes the electric field in the conductor to be practically zero (compared to that in the resistor) in a non - electrostatic model (i.e., when there is a current). Thank you so much for your help. I have scoured the internet for insight but I have not found a site that marries the classical to modern theory clearly for me.
For class I'm supposed to create a PDA state diagram that is capable of generating an infinite language with no state q such that q is reachable from the start state, there is no cycle within the diagram that starts at q and ends at q, and there is not path from q to and end state. Essentially, I'm trying to prove that a PDA does not need looping states to create an infinite language but I do not know the first place to start. I know that a PDA can make use of lambda transitions which could possibly be to my benefit, and I know that there can be multiple paths resulting from the same transition but I cannot wrap my head around an infinite number of possibilities without any sort of loop. I suppose I'm not looking for a definitive answer, more so something to get me pointing in the right direction. Thanks!
I have the following question, and given few proofs (provided by friends, professors, and my myself) which seem to work, I suspect the answer is yes: But I am still not completely sure. The question is: (A): "For any given value x, are there uncountably many (countably infinite) binary sequences (ones and zeroes) whose limiting relative frequency is x" Is this an open question? I ask this because all of those whom I've asked, had either not thought about the question nor knew the answer until they came up with their own proof. So has (A) been proven in the literature, and if so where? I am interested because if the answer to (A) is no, it can be easily shown that the Kolmogorov formalization/calculus of probability is undermined. This holds because the Kolmogorov calculus seems to require that (A) is true. That the Kolmogorov calculus requires (A) can be easily shown given its axiom of countable additivity, and its theorem: the strong law of large numbers (ie, simply consider that any infinite sequence of independent and identical random variables/trails has probability zero, if the individual outcome probabilities on each trial is less than one). Even if non-standard analysis is applied (so that infinite sequences composed of individual independent and identical random variable with non zero probability are assigned infinitesimal probability values, rather then zero probability values), it appears that this result (ie (A)) is demanded by the Kolmogorov calculus
I am struggling with the concept of tension in a rope. Below specific questions. I am understanding tension to be an elastic force between rope molecules. If so, is it fair to say the net tension on each rope molecule is zero (if rope is in rest) but there is a net tension for the rope whose direction is opposite to applied force? What is the direction of the tension. I am reading conflicting answers for it. If a mass attached to rope is hanging. I think tension in rope is equal and opposite of weight. is that true? Kleppner seems to mention that tension has no direction which is confusing me. Also, does the tension vary. Mass attached to rope and hanging. does value of tension vary throughout the rope?
Here is an old but interesting task from a math book, but I'm completely clueless: A teacher stands at the chalkboard and draws a line, starting from the left side of the board, towards the right. The line is ten centimeters long. Then he draws, without interruption, a second line with half of the length of the first line towards the right. Then a third, with a third of the length of the first. Then a fourth with a quarter of the length, and so on and so forth. The teacher works very carefully. With pointed chalk, he adds a new line per second. The chalkboard is one meter and ninety centimeters wide. How long the teacher needs, to arrive at the right side of the chalkboard? As the teacher finished, he constructed a square on each line. The side length of the squares corresponds to the length of the respective lines. How big is the surface area of all the squares together, approximately? Can't even tell if it is about a convergent respectively divergent series. Can you help? Thank you!
I'm using LyX for writing my article. And I want to add a bibtex library to add references for it. I can do that and then add citations from that library without a problem. But the thing is, I'm writing the article and adding references as I write. I don't have a ready-made library of references beforehand. On every paragraph I would like to add a citation that was not there before. But as far as it works in LyX, you add the bibtex library to your file and then add its citations to your article. So by every new reference I want to add, I have to remove my bib library and reload it for the new citation to be added and this is a bit tiresome because I'm going to have a lot of references. So I was wondering if there's something I don't know or is there another way of doing that. Would appreciate it.
I know how to use LaTeX (not an expert, but still quite some experience - wrote couple of papers and my thesis, can make TikZ pictures etc.), but I don't have the slightest idea, what XeTeX, LuaTeX, etc. are. For an invitation card I'd like to design I found this beautiful font named zapfino. But it's for XeTeX or LuaTex. This website has a nice example: http://nitens.org/taraborelli/latex#glyph I downloaded that tex code, but I can't compile the code on my ubuntu machine (with texlive) - neither using LaTeX (no surprise there), nor xetex, nor luatex, nor xelatex. I always have issues. Best works xelatex, it only complains about the font not being found before it exits. I downloaded the font from <removed> and put the .otf file into /usr/local/share/texmf (where the TEXMFLOCAL variable points to), but that does not change anything. What do I do wrong? Is there a possibility to make zapfino work with latex? and if not, how can I compile that small example on my machine, what do I have to do? Furthermore - is there a way of combining XeTeX (for the font) with LaTeX (for TikZ-tricks)?
Let A and B be linearly independent subsets of a finite dimensional vector space. I want to show that if |A|>|B| then there exists an x in A s.t. B union {x} is linearly independent. My proof is ' Let |A|=n and |B|=r. Suppose B union {x} is linearly dependent for all x in A then span A is in span B. Since |B|=r , vector space spanned by B has dimension at most r. And vector space spanned by A has dimension at most r , since span A is in span B. But then it is contradict to A is linearly independent , since |A|=n > r implies A is linearly dependent. Therefore our assumption is false ' Is that right? And, someone have another proof? I want to prove it by using linearly independent but dimension of vector space.
There're other previous questions about using a color background with fancyhdr so that you get a colored header and/or footer. However, they discuss either using a different color box for each part of the header, or working with a single part header (i.e: a header with just the center part, for example). But what if I have a complete header with three parts (left, center, and right), and I want all the three parts inside a single colored box? Ideally, the colored box should have no margins, but the three header parts should keep their original margins, so I guess I cannot use the fancyhdr margin parameters for that. I really need to use fancyhdr for the header. I can add more packages if necessary, but the header must still be created with fancyhdr.
In short, I'm hoping for some reading recommendations. I'm starting to do some work with Calabi-Yau manifolds, though my prerequisites are fairly minimal in differential geometry. I've taken a relaxed reading course on differential geometry, hopping around Spivak, and I'm taking a full course this semester. I've also taken a reading course on elliptic curves and a full course in algebraic geometry, building up to Riemann-Roch, in case there are some reads that build from that angle. So, does anyone have any recommendations for good reading material for my situation? Mostly I'm asking because I've been informed I have to read papers and present (relaxed) talks on the material, and I'd like to not fall flat on my face on the very first talk! Thanks! (Also, any recommendations on presenting material you very not familiar with is welcome.)
Please note that I am posting this question because I'm still not sure if I understand the difference although I did a comprehensive study of a great number of answers to the "for versus to" questions. This issue turns out to be much more complicated than I expected. I chose to pick this among many and different questions still to be made. (A) It is important FOR me to speak proper English. (B) It is important TO me to speak proper English. (A) It is important FOR me to speak proper English. Could this imply that he or she is an English learner and wants to improve his or her English very much, making it possible to rephrase it as "it is important that I speak proper English?" (B) It is important TO me to speak proper English. Could this imply that he or she, presumably a native English speaker, expects English to be spoken properly no matter who the speaker is, making it possible to rephrase it as "it is important to me that English be spoken properly" or "speaking proper English is important to me?" My guess is that they wouldn't be interchangeable and could have different meanings as above. I would appreciate any advice, hopefully including any rule of thumb.
Consider the following sentence: I have a lot to talk about with John about his project. Since I can swap the position of the first about to make it 'I have a lot to talk with John about', then I would end up with: I have a lot to talk with John about about his project. My question is, can I consolidate the two instances of about, giving me: I have a lot to talk with John about his project. Or do I have to keep two prepositions there, but change the second about to something else in order to make it sound less-awkward, as in: I have a lot to talk with John about regarding his project. Related question (now that I'm thinking more...er...about this): is the first about really an adverb, in which case, of course, I cannot ever consolidate the two?
I'm studying the first chapter of Hartshorne's Algebraic Geometry by myself and I found this book really hard for a beginner like me, but my advisor said to me that I had to study Algebraic Geometry by this book during my vacations. Then any part of the Hartshorne's book which I find very dry or superficial I search the same subject in another books or notes available online which are easier to read and have more examples. So my question is if there is some book or pdf to accompany Hartshorne's book? I mean the same contents but more detailed, if there isn't such book, it can be a book for each section of the first chapter. In this way, the first chapter of Hartshorne's book for me would be more a route to follow for an introduction of algebraic geometry, than a book to study. Remark: I know there are a lot of posts asking requests of books in algebraic geometry on this site, my question is more specific, I'm only asking this because I couldn't find any good resources with I need. Any suggestions would be really appreciated. Thanks in advance
Notes for context: I am a native BrEng speaker. I have read "Each of these is" vs. "each of these are", How does "each" change "are" to "is"?, and What should I use between "triple" vs. "all"? and I understand the general concept of "Each of them is" and how "each" always takes the singular. Reading my daughter's bedtime story this evening, I came across the phrase "They each have a bag of equipment". It made me wonder why the following seems naturally (to me at least) to be true: (Correct) Each of them has an X (Correct) They each have an X (Correct) Each of them is a Y (Incorrect?) They each are a Y I would never say (to use the examples from one of the posts I linked) "I have three pens. They each are green.", but "I have three pens. They each have a lid." is fine. Is "to have" different from "to be" when it comes to using it with "each"?