darklight03/StackMIAsub huggingface dataset:
A friend has pointed out that in an Oxford comma separated list, either every clause needs a verb, or each clause must be the object of the first verb. This seems to make sense to me, but would this mean that this sentence is a comma splice? "Next week, I will go to the gym, beach, and get a haircut." The above sentence might be ambiguous, but are there any strict grammatical rules that this is violating? Does each clause have to have a verb, like so: "Next week, I will go to the gym, go to the beach, and get a haircut?"
Everyone knows this experiment: You mix salt and pepper and use a charged balloon to separate the pepper from the salt. I never really understood how this works. In school (long time ago) we learned that unlike charges attract each other while like charges distract each other. In the experiment the negatively charged balloon attracts the pepper. Does this mean the pepper has a positive charge? Why is pepper charged? How can I predict for given particle if the balloon will attract, distract or not interact with it?
I have often read that our universe was once small enough to be subjected to quantum mechanical effects, potentially altering how our universe turned out. This is a large theme in Laura Mersini-Houghton's Before the Big Bang. Michio Kaku also mentions this in his book Parallel Worlds. What exactly are they referring to? The initial singularity? The observable universe shortly after the big bang? The inflaton particle that inflated space giving rise to our universe? It is my understanding that the universe might have always been spatially infinite after emerging from the initial singularity so I'm not quite understanding what aspect of the universe was subject to QM.
I have started to study formal languages, especially finite automata and regular languages and I encountered some difficulties, i.e. Is this true: Automata will be called isomorphic if, by changing the names of the states, one moves from one automaton to the second. Let be a regular language. How can I Prove that all minimal automata for the language are isomorphic? Thank you for any hints and answers!
I am dealing with a PDE and I am trying to characterize the solutions: Galois differential theory might be of help, but I can only find books about this theory applied to ODE. Are there resources, books or papers, on the application of Galois differential theory to partial differential equations? I know the basis of the Galois differential theory applied to ODE as explained in Magid's Lectures on differential Galois Theory and Galois theory of linear differential equations by van der Put and Singer, and I am looking for something along the same lines, but maybe with more examples and at least at the graduate level.
If I have two identical magnets of equal strengths producing equal repulsive forces between them, and if I replace one of the magnets with a stronger magnet (everything else remaining the same), how would the forces on both of them change, i.e. will they exert equal repulsive force on each other or not? Why? Also, does the size or strength of the magnet affect this conclusion? In other words, replacing one of the magnets with a significantly larger or stronger magnet will produce uneven/unequal forces on both the magnets?
Lately, I observed a rainbow-like ring forming in my window during nighttime when the light enters from a street lamp. Interestingly, the sequence of colors in the rainbow seems to be reversed from what I anticipated. Normally, I would expect the inner part to be red and the outer part to be blue due to the greater refraction of blue light (like a sun halo). What could be the reason behind this color reversal phenomenon? Edit: To clarify, the window has a decorative film on it which causes the rainbow. The core question is still the same: Why would blue be on the inside and red on the outside?
I am trying to understand the logic of negative exponents and I stumbled upon the video "Negative Exponents" by YouTuber JLC. He says negative exponents are "defined". But why is it defined the way it is? Is there some kind of international agreement or some kind of international organization that maintains this definition of negative exponents? What if I make my own definition of negative exponents? Please enlighten me, many thanks.
I am trying to figure out what this phrase deconstructs to. Does it imply a logical OR, like: "attention-deficit disorder" OR "hyperactivity disorder"? For additional context, there are different types mentioned here: There are three main types of ADHD: Predominantly inattentive presentation. Predominantly hyperactive/impulsive presentation. Combined presentation. ...which seems to indicate that it is always both, but a little more of one than the other. If this is the case, does the grammar check out? Also when it is spoken as: "attention deficit hyperactivity disorder", or abbreviated as "ADHD", the slash is dropped, which loses meaning and adds confusion. Would there be a better way to phrase it? Would there be a better way to say it?
Does anyone know a simple and accurate way to measure the size of an iron core using a magnetic sensor? Imagine having a collection of identical iron plates. I expect the strength of the magnetic field around the core to increase with its size. Would it be possible to determine the number of stacked plates by measuring the magnetic field strength using e.g. a Hall effect sensor placed on top of the staple? Are there better sensors/methods?
This sentence is an excerpt from The Economist website. The Kremlin denied the advance, saying that Russian troops had repelled Ukrainian attacks in the region. What is the grammatical rule that's governing the "saying that Russian troops had repelled Ukrainian attacks in the region" in the sentence above? I've been looking into the types of clauses to find any applications that match this, but I think I'm lost.
I am wondering if anyone happens to know the computational methods - and hence the computational complexity - of simulating the distribution of an electric charge (how electrons distribute) over a surface. In particular, I am curious about the computational difficulty in simulating the distribution of electrons over a highly asymmetric and non-uniform surface (like the surface of a rough rock). How does the simulation complexity scale with the complexity of the surface and the precision/accuracy of measurement?
I am trying to write a proof regarding the following question and am stumped on this particular version of the problem. I believe that I have written a correct proof when asked if the columns of A are linearly dependent. That is solved by showing that the non-zero vector y can be used as a nontrivial solution of linear dependence. But I don't really know how this information translates when analyzing the rows of A instead. I tried to look for a counterexample that IS linearly independent but cant find one.
I've recently read that what most people learned to think of as the 'speed of light' is actually the 'speed of causality', and that light just happens to travel at that speed (through free-space.) I'm also aware that light travels measurably slower through transparent materials such as water or glass. This leads me to ask: is light traveling slower through such materials, because the speed of causality is reduced in such materials? And if so, what does this tell us about how the speed of causality is determined by permittivity and permeability of various materials?
I'm trying to reconcile two seemingly conflicting sources of information about Lorenz force. Let's consider a solenoid in proximity to a permanent magnet with the field pointing in the same direction as the axis of the solenoid. From the right hand rule I conclude that the wire should either be pushed towards the center of the solenoid or outside. However, the solenoid also acts as a magnet with poles on each sides and will attract/repel other magnets. How does one reconcile the two explanations ? Is the solenoid both contracting on itself and moving towards the other magnet at the same time ? If yes which force/equations describe the movement of the electromagnet towards a permanent magnet. Thank you!
I am aware there are similar questions already asked, however, I find none of the answers satisfactory, they either do not contain any mathematics at all, or mathematics of a level I am not capable of comprehending. My doubt is that, if the change in kinetic energy is dependent on frame, then how is the law of conservation of energy valid in all frames? One possible explanation I have thought of is that the change of potential energy is also frame dependent, but I cannot think of a suitable example to justify the same. Please answer only using newtonian mechanics I do not know statistical or lagrangian mechanics.
I have recently started to study integrals and faced some difficulties of understanding why we need antiderivatives to calculate area under curve. I am trying to visualize it using graphs but it just doesn't make sense to me. If anyone can explain me if it's even possible to understand them the way I try. here is the image: enter image description here Thank you :)
I was curious if anyone knows the font used by the Desmos graphing calculator. All the formulas are formatted as LaTeX, so I wanted to know if there was a way to use this font in my own documents. It seems at first glance like standard Computer Modern, but upon closer inspection as you can see the "w" and "v" characters are rendered in a style that makes them pointier so that they are much easier to distinguish from omega and u respectively (and imo they just look a bit more pleasant). Here is a side-by-side comparison for context. Computer Modern: Desmos Font: (This is my first time making a post on the site, so apologies if I have made any mistakes!)
What is the interpretation of temperature in the Ising model? Can one describe a theoretical thermometer for the Ising model? As far as I know, in the theory of gases, temperature is interpreted as a quantity proportional to the mean kinetic energy. A thermometer is a device capable of converting the average collisions of particles into the movement of a dial. The higher the mean kinetic energy, the more movement the device registers, and the dial goes up. I can't grasp a similar idea for the Ising model.
I already know the term anaphora exists for repeating the same word for emphasis. I'm specifically interested in a term for repeating a word twice without additional clarification to express that something is especially strong or genuine. Examples "Do you like her, or do you like like her?" "Are you making quick bread, or are you making bread bread? "I'm so excited, I got a promotion promotion, with a pay raise and everything!" I don't know that I've ever seen this in formal prose; it seems unique to spoken English, but if anyone knows of any written examples please add them. If no term already exists, I'd like to coin the term "duplication duplication," to distinguish it from ordinary duplication.
Imagine that Alice is the President of Arstotzka. Alice has a lot of enemies but she's generally an upstanding President so her critics have a hard time building a campaign against her. Instead, the critics are patiently waiting in the shadows until Alice makes a minor mistake - perhaps she misspeaks at a conference or her car driver skips a stop sign. The critics then blow this incident out of proportion and use it to smear Alice before the next election. What's a word or expression specifically describing the act/strategy of waiting for a small transgression to happen?
Can you compute geodesics by treating it as a problem where you want to minimize the length of a curve through two points on a specified surface while having the constraint that the curve must reside on the specified surface? If so, can you explain how one could do so for a cylinder? Or is the calculus of variations the only method by which to do so? I tried setting up the constrained optimization problem for a cylinder but was unable to make any progress, leading me to think that maybe it's impossible to solve the problem without the calculus of variations.
I am working on my thesis and need to convert my paper to a different format. I'm new to using latex, only having started using it for this project, and am struggling to get the base version of this template working. No error occurs, but compilation appears to halt, judging by the fact that main.log log ceases to update after a certain point. The repository hasn't been updated in a while, so I am guessing that the setup may be outdated. I've tried removing some of the references to other sections, but that doesn't appear to make a difference. If someone could help me get this working, or point me in the right direction, I would greatly appreciate it. https://github.com/davidanastasiu/thesis_template-SJSU_CMPE
Show that, given four coplanar points, we can always draw two intersecting circles coplanar with the points, such that two of the given points are diameter endpoints of one circle, and the other two given points are diameter endpoints of the other circle. In this question, "intersecting" means that the circles share at least one common point. Example: I will post my answer. Alternative solutions are welcome. This question and answer serve to provide ideas that might help answer a harder question about five points and two non-intersecting circles.
Ive recently been introducing myself to Gaussian Processes. In Bayesian linear regression, one would expect that when adding new features, the likelihood on the training set would weakly increase due to the larger degree of freedom, of course leading to overfitting most likely. I was wondering if this is true in general for marginal likelihood for GPs, regardless of the choice of kernel/specific hyperparameters? If so, what is formal explanation for this? Can we prove it mathematically? Thanks :)
I heard that natives use Present Cont. to describe things in the future. As I understood, we use Present Cont. when we have arranged an action or there is at least one person with whom we agreed to have plans. But I saw this: I am teaching English tomorrow. I will be teaching English tomorrow. What is the difference and when I should use Present Cont. to describe action in the future?
I work in an office where the airconditioning is not working, so I brought a small mobile airconditioning device: it's a small machine, emitting cooled air. It looks like this: However, according to the laws of thermodynamics, the total amount of heat should always increase in a closed system. Therefore, regular airconditioning systems vent their waste heat to the outside, but this little mobile machine does not have any connection to the outside, so it has no means to discard its waste heat. So my question is: how can such a machine even exist?
Two congruent circles that touch at point H are given. Let the line p be their common tangent that doesn't pass through the point H. Construct a circle that touches both given circles and the line p. The most intuitive thing was to construct an equilateral triangle NOL (such that L is on p, and N and O are on the given circles) and find its circumscribed circle. However, the obtained circle intersects given circles at N and O, instead of just touching them. What am I doing wrong?
If a set is equipped with total order (reflexive, transitive, antisymmetric, strongly connected), does this necessarily mean there exists an injective mapping from that set to the reals? Alternatively, if a set has larger cardinality than the reals can it not be well-ordered? I'm struggling to think of a counter example. Most of the canonical examples of sets with larger cardinality than the reals (all functions, power set of reals) cannot be equipped with total order.
This question is bugging me from a very long time and I don't know whether it can be answered or not but still I am posting to get other's opinions. Is there any inherent property among all the uncountable sets which make them uncountable ? Or more precisely:- If I ever wanted to "make" an uncountable set, what ingredient should I put in so that I am guaranteed of the set being uncountable ? Edit :- My apologies for the wrong terminology used. By "ingredient" , I was just trying to refer to some property which is common to all the well known uncountable sets (e.g. the irrational set, set if real numbers) that I should keep in mind while forming a new set of numbers.
Imagine a uniform thin layer of a viscous gel sticking on a vertical wall. A small sphere is submerged in this gel. The gel has a yield stress (Bingham model). How can I calculate the yield stress that will cause the sphere to start sliding with the fluid on the wall? This yield stress will obviously depend on the weight and dimensions of the sphere.
I'm having a problem with the second part of the question, which shows that the sum of the vectors equals zero. I came up with a geometric proof, but I wondered how to prove it by using complex numbers and maybe links to the first part of the question. I was thinking about the equally distributed roots of unity, but don't know how to move on.
I understand how we can have three coin tosses (or three events if you prefer) such that all three tosses are pairwise independent, but not mutually independent. One trivial example of this would be to just have the third coin be the xor of the first two coins. My question is whether it's possible to have four or more coin tosses such that any two coin tosses are pairwise independent, but any three coin tosses are not independent. If this is not possible, what would a proof be like showing that it isn't?
I am a PhD student working on observational cosmology. My research is based on the experimental side of it (receiver design, etc.) but I would like to get deep into the CMB and CMB statistics. I have found several resources and have read some of the papers but I feel like they are a bit "unconnected". Does anyone know where I could start? I thought of just studying Ruth Durrer's (The Cosmic Microwave Background) book, but I am not sure if it will be complete enough.
I am studying blackbody radiation and modelling a cavity as a blackbody. However, I am encountering a number of confusions in this description: Many textbooks mention that the cavity consists of metallic walls that act as perfect reflectors. Light entering through the hole, after multiple reflections, get absorbed. However, if the cavity walls are perfectly reflecting, how is the radiation getting absorbed by the walls? For studying the radiation emitted by the blackbody, the textbooks model the radiation inside (emitted by walls due to heating) as standing waves. But how are standing waves being emitted by the cavity? Because standing waves are supposed to be confined inside. Can anyone please explain in simple terms?
For example, a carpenter works in carpentry and a plumber works in plumbing. So what trade does an electrician work in? Electrical? I searched the definition for "electrical" and found that it gives the part of speech as an adjective and not a noun like the dictionary does with carpentry or plumbing. This is confusing to me. I would like to understand and know how to talk about the trade for an electrician. I would appreciate it if someone could help clarify and explain this to me.
Imagine a mass hanging from a string attached to the ceiling of a lift and the lift descends with a certain acceleration. From the reference frame of the ground the tension in the string would be smaller than when the lift remained stationery. However, let's say your friend was inside the lift and when asked about the tension would say that the tension was same, regardless of the list ascending, descending or stationery. Isn't that really counterintuitive? Isn't the force not relative and the same, regardless of the reference frame?
For example: It is a thing that works producing stuff. This feels wrong to me, but I can't quite put my finger on what exactly is wrong about it. It seems like it's trying to be a participle phrase, but it's not necessarily modifying the current state of "it", and is, instead, describing what "it" is -- i.e. by working, "it" produces stuff. If it is, indeed, a participle phrase, then it should be able to be written as Producing stuff, it is a thing that works. But, to me, this doesn't seem correct either, so it leads me to believe that the very structure of the sentence is incorrect.
I have been taught that path difference and phase difference are essentially the same thing, except phase difference is measured in an angle unit while path difference is measured in multiples of wavelength. This seems incorrect. I think they are rather different concepts, with path difference representing the difference in distance a wave needs to travel in order to reach a point. Are they really the same thing like I have been taught?
For example, when referencing a webpage: Visit the "The Performers" page to learn about our musical lineup. In this case, I want to tell someone to visit a webpage entitled "The Performers" to find more information, but the repetition is throwing me off. If I were to remove the first "the" before "The Performers," though, then it would essentially read as "Visit page" without an article. So, is it okay to use the article of the webpage title as the article for the sentence, or must I include the first "the" before the webpage title? The two iterations: Visit the "The Performers" page to learn about our musical lineup. Visit "The Performers" page to learn about our musical lineup.
I think something is missing in the definition of homeomorphism I saw. It just said it maps the collection of open sets to the collection of open sets in a bijective way. What exactly makes this preserve topology? I can think of weird situations where each individual open set is mapped to totally disjoint open sets in a bijective way, throwing the topological structure out the window.
The definition of optical path length is the distance that light could have travelled in the same time, in vacuum. So, can we define something analogous for sound waves, like an "acoustical path length", with respect to a specific medium, say air? And if we were to define something similar, how far would it's applications reach? For example, can we use it in doppler effect in cases when the observer and source are in a different media? Or interference, when there is a change of medium in between? If so, kindly guide me on how to do it.
I know foliations as a particular topic in differential geometry. I understand the definition and basic properties of a foliation from the DG point of view, including the Frobenius theorem. While trying to understand why this concept is important I came across this Wikipedia page on integrability conditions for differential systems, but couldn't understand much of it. I do not want to too diverge from my other studies now, yet want to understand this association quickly and completely. Can you suggest me a source that is solely focused on the relation between foliations and systems of PDEs?
I was going through this paper in which the authors state that : In Landau theory, a continuous phase transition is associated with a broken symmetry. The phase transition in a black hole system can also be characterized by the symmetry and order degrees as in a conventional thermodynamic system. The authors don't explicitly state which symmetry is broken for the black hole phase transition. Also, would such symmetry breaking lead to any chaotic effects? Any explanation in this regard would be truly beneficial.
I am attaching the solution of a school question asking to calculate the inverse of a matrix. However, the solution proposed does not fit in anything I ever seen about calculating inverse matrices. I did not found any property that fits the final part of the solution (the one I highlighted in the image below) although the solution is correct, I would like to know which property or reasoning supports the final solution of such a problem. Thanks.