darklight03/StackMIAsub huggingface dataset:
Why doesn't the first line have an auxiliary to make it interrogative? These lines are from Sorry Seems To Be The Hardest Word, featuring Elton John: What I got to do to make you care? What do I do when lightning strikes me?
I'm an undergraduate student and currently I'm approaching tensorial calculus. I was wondering: is there some geometric meaning to the operation of rising/lowering indices (and then if there was any geometric difference between vectors and covectors), or are they only mere formal operations? In case, why don't we simply use only vectors in the definition of tensors?
What are the ways to center headers only without using the titlesec and sectsty packages? If we take the titlesec package, then the question is how to prevent this package from automatically changing header styles?
What is the concept of hypersurface in general relativity? I know it could be characterized into three categories but how do we define hypersurface (in general) in physics? I didn't get what thing it is.
I have always believed --- from somewhere --- that in archaic English, cats were always referred to using feminine pronouns, regardless of what sex they actually were. But I thought to go and find a reference for it and I can't find anything. Was this ever a real thing, or was I just hallucinating?
If I lift a weight to a certain height, where does the gravitational potential energy at that height originate from? is kinetic energy converted into gravitational potential energy as the weight is decelarating as it approaches the maximum height? or is the chemical energy from my body (doing the work) shared between kinetic energy and gravitational potential energy? Hope this makes sense. thanks.
Why do electrons have discrete energy states when they are bound to a nucleas and not when they are free for example in an electron beam. Why doesn't an electron beam have certain specified energies like bound electrons do.
I have seen that a number of packages exist that define symbols. How can I find a list of just the core symbols provided by the Latex Team, but without the use of packages like amssymb, MnSymbol and so on.
I am new, not have expert level knowledge. But I have studied about black hole information paradox. The black hole doesn't kept any information which passes event horizon. Which can break physics. Is there any theory about Information Paradox, to resolve it.
What is a good term for plants whose parts, either as tubers, roots, or fruit/seeds are harvested and consumed? I exclude plants such as hemp and flax whose fibres are used, or, for example, poppies for opium.
i.e. is the comma to signify the boundary between the instruction and the recipient of it (that is to say, "Hey, stupid! Keep it simple"), or is it serving the function of an "and" (as is sometimes used in US English but rare in British).
I have tried to search a lot about the laws that predicted this behaviour of black body. But haven't really found out. And the ones I found like equipartition theorem, i find them contradicting with classical physics itself. How exactly it was predicted that with increase in temperature, there would be increase in intensity of radiation at each frequency.
I've realized that there are many results in set theory rely on the theorem that states "the union of countably many countable sets is countable". However, all of the proofs of this theorem I've found so far, including ones on SE, rely on the axiom of choice. So, I'm wonder without AC is it still true or false or neither provable nor refutable?
What's the difference between these? I will go to the bathroom and brush my teeth I will go to the bathroom and will brush my teeth Perhaps one of these sentences is grammatically incorrect. Which one is desirable to use in technical writing?
I've noticed that both are used though "point in" is seemingly far more prevalent. Is there any difference or it's down to one's preferences? E.g. There's no point in talking to you. vs. There's no point talking to you.
Is there a phrase with a similar meaning to the phrase Don't put all your eggs in one basket which doesn't make reference to eggs? I'm writing a story in which one character is a bird and I feel it doesn't make sense for them to use this specific phrase about eggs, given that eggs are essentially bird pregnancies
If the activity involved only me and one other friend, e.g. playing tennis, I know "I played tennis with Jake" is correct. However, is it possible to also say something like "We played tennis with Jake"? If not, is there a slight adaptation in the structure which allows for the use of "We"?
I've heard of the term escortee, but Googling it doesn't turn up any definition. If not that, then what could I use in this sentence: I escorted the girl through the school; she is a ________.
I do not know exactly what shape is a spoon. I feel like it is an elliptical paraboloid but really I don't know. I really need to do this for my math project. Any help would be very appreciated! Image of a sample shape
Is it possible to give an example of countable set, with uncountable derived set, such that intersection with this set and its derived set is empty? I know that if given set is uncountable, then it is impossible. But what if set is countable?
Do internal forces of an atom lead it to move, or can an atom only move when an external force is applied to it? For example, if we had a perfect vacuum with the exception of one arbitrary atom, would it move due to internal forces?
I am proofreading an article and have come across: "to a focus on a fulfilled (upper)middle-class life". At first I was simply going to put a space between the closing parenthesis and the "middle" but am now second-guessing myself. My question is, in keeping the parentheses, would it be: "(upper) middle-class" or "(upper-)middle-class" or some other form?
When a railway is laid in a cold environment, should tensile or compressive force be applied? How does this work? I think the answer should be tensile. The railways expand while heated so applying tensile force would mean there is less extension and therefore less stress. Is this a correct explanation?
I have a problem where I have to study "the geometric properties of the Brachistochrone curve in non-Euclidean spaces". But I am confused about the definition of the Brachistochrone Problem/curve in any non-Euclidean space. Please offer me some help.
I considered the word "circumstantial" or phrase "circumstantially true" but I feel like there's another word that better describes this. In an example; if you step in a puddle and your feet get wet then that is the truth in your case, but it is not the case that anyone who steps in a puddle will get their feet wet.
How would I go about drawing something that looks like this (please excuse the extremely lousy Paint image) I am sorry I cannot provide any exact code, but I am basically clueless as to how I'd do this. I hope you have understanding. Thanks in advance.
I've been learning about the density wave theory of spiral arms, and also how the gravitational potential of galaxies is non-axisymmetric, resulting in a sinusoidal spiral potential. I've then learnt that the spiral arms/density waves occur at this spiral potential minima. Why is this?
Is there any word for someone who doesn't accept others' favors? They have no reason for it, they just say no. Perhaps it's because they would feel insecure. Example: -Why does she always say no when I offer her snacks or drinks? -You know she is a [word]
I've been learning spectral methods mainly through reading the book "spectral mehtods in matlab" by Trefethen. I have a simple question: Could spectral methods solve first-order differential equations? It seems using spectral methods requires two initial conditions.
Recently, I was reading about a article which tells about something known as "Susskind Complexity". The article states that the interior volume of a black hole grows forever. How/why does the internal volume of a black hole grow forever? What is the mechanism/reason behind this?
How to prove that a Hilbert space is the directed colimit of its finite-dimensional subspaces? Does this imply that the category of Hilbert spaces (and bounded linear maps) is the Ind-completion (see here) of that of finite-dimensional Hilbert spaces?
I am looking for a distribution whose mean and median are different, preferably a distribution that share some properties with Gaussian distribution. I kinda know that there is something called skewed distribution or alike that probably would work but I have no idea how it is defined and/or how the expectation/median is estimated. Thanks a lot.
I know "No, it can't be" can mean "It's impossible that it is", but I don't think "No, it may not be" can also mean "It's impossible that it is". I know that "No, it may not be" can mean "It's possible that it is not", but can't the sentence mean "It's impossible that it is" like the case of 'can'?
So, I'm preparing for a PTE test and came across this problem in the Fill in the Blanks section. Gators can move through the water oh so silently, barely ___ (making/creating/adding/showing) a ripple. Why is the answer creating the ripple (not making the ripple) here? I just wanted to know the reasoning behind selecting the word "creating" instead of "making".
Can I use parse as a verb in this example? The clouds began to parse and the day opened up. Meaning the clouds began to separate from one another and dissolve. Parse is commonly used to describe analyzing text or sentences but can also be defined as to resolve into its elements.
If we have a beam of photons (high energy X-ray) and a beam of protons both with the same energy, which one will get further inside the human body and why? Can this be explaind due to LET (Linear energy transfer)?
In a problem, I have the expression of acceleration and velocity in Cartesian coordinates , and it ask me to calculate the tangential and normal acceleration, so we don't know how I can do that, can any one help me?
I have a problem, where I am asked to give a precise definition of the Sierpinski-triangle. The problem describes the usual algorithm to construct the triangle. However, I am clueless on how I should give a different definition. Is there some definition using the union of the points of the Sierpinski-triangle?
From what I 'understand', Noether's second theorem applies to infinite-dimensional symmetry groups. A classic, even historical, example is the invariance group of Riemannian spacetimes, i.e. the set of spacetime diffeomorphisms of GR. Does Noether's second theorem also apply to quantum field theory (= the 'gauge groups')? Or is it confined to general relativity?
I'm wondering what native English speakers call a person (man or woman) who is attracted to a no-make-up look and dislikes it when people wear a high amount of makeup. I can think of no-makeup lover or not into makeup. But is there a specific word being used?
It is well known that the quaternions, octonions, and sedenions are well studied, but I don't find any articles or books in which other hypercomplex numbers are studied. Does anyone know a book or an article in which other hypercomplex numbers are studied? And if so, what is the usage of numbers like pathions, voudons, etc...?
Looking for a reference for a textbook that discusses classical conditions for contraction mapping, such as diagonal dominance. It should contain theorems similar to the one in the picture (which I found on this post without a source).
Basically it means that the vowels must come in the order - E, U, A, I, O and can be place anywhere in the word. I tried to do it by assuming that each of the vowels can come in five different spots. But I didn't get anywhere...
We don't pronounce "th" in "pothead" as a single logical sound, or "ph" (as "f") in haphazard. They are consecutive letters pronounced individually. Is there a term to describe such a language phenomenon? I'm guessing no but it can lead to some humorous situations (I think on the Simpsons, policeman Lou said "poth-ead" which I found entertaining).
What is the adverb that is commonly used when describing something rapidly/drastically increasing? It's on the tip of my tongue and I can't get it out. It's not tenfold, rapidly, drastically, dramatically, stratospherically, etc. but similar. I think it has a connotation of quickly multiplying. (It's a single word.) It's driving me insane--any idea what it is?
My understanding is for a rigid body the angular velocity between two points fixed on the body is the same for all points. In other words the angular velocity vector would be the same. I can't find a proof of this. To be clear I'm talking translating the origin on the body, not relocating the secondary point you're computing the angular velocity of.
I know that a charge moving parallel to a straight current carrying conductor experiences a force towards that wire due to magnetic lorentz force. I am more curious about the idea where the charge is stationary and the wire is moved parallel to it in the opposite direction at the same speed. Will there be a force on the charge this time?
In Spanish there is a suffix, -udo, that's used for "in adjectives derived from nouns, it indicates abundance, big size, or intensity of the meaning of the root." Is there something like this in English?
I'm thinking of doing a project with some undergraduates soon involving edge ideals, particularly binomial edge ideals. Do you have a gentle introductory reference to this topic suitable for undergraduates? We can assume that the students are comfortable with basic algebraic objects such as rings and ideals, as well as what graphs are and some of their basic theory.
I'm not sure if there's a better way to say this: It would have been better if my brother had died rather than struck a bargain in the red desert. Am I using that right? Ugh! Help me please. This is the first line of my story and my critique group is arguing about which sentence is correct.
I learnt that an optic fibre uses the concept of total internal reflection (TIR) to transmit data at high speed, but why do they not use just simple mirrors instead of using refractive medium and making a light incident at an angle more than the critical angle, so that total internal reflection can occur?
I am currently studying intro to analytical number theory by Tom Apostol. It is a very def-thm-proof kind of textbook, and even after taking notes of definitions and theorems, i still struggle with exercises. Can someone please suggest a method for me to get more out of the book? Also, does anyone have lecture notes that can be paired with the book?
I would like to learn what prerequisites are needed in order to be able to work on a postgraduate thesis on the topic: Invariant Einstein metrics on compact simple Lie groups and Stiefel manifolds. I have noted Lie groups, differentiable manifolds, general theory of relativity, and tensor analysis.
Assuming that a sinusoidal wave with an amplitude a million times bigger than the diameter of a black hole enters a black hole, what happens to those parts of the amplitude that are not inside the black hole? The other question I have is, "Does the black hole change the amplitude of a frequency that enters it?"
Sorry everyone. I do not really know if this belongs here, but I can't find a solution by myself, since I have no idea of what could be happening here! I have the fonts installed, but TexStudio says they are missing! How could I start solving this problem?
According to wikipedia: https://en.wikipedia.org/wiki/Affinity_laws, when shaft speed is constant, the pressure is proportional to square of impeller diameter. I am wondering why this is true. Surely, for larger diameter, more air is pumped, so we need a stronger force. But why pressure also need to increase?
Do we know absolutely nothing about what might be the state of matter-energy inside the black hole? Are there existing theories or research that explore the possibility of a metastable vacuum inside black holes?
Say I have a bunch of colors in math mode. How do I remove all of these colors (reset to default or black) efficiently? (If the colors are in text i.e. not math mode, I can just do this: Select text > Text Style > Color > Default > Apply. But when the colors are in math mode, this doesn't work.) Related
In programming it is rather the norm than the exception to have functions whose input are different data types. For example a function who produces a substring of a given string would have the following signature in Java: public static String substring(String s, int n) {..} Are there examples of such functions in Mathematics and what is their application?
According to my understanding we get a lot of energy during nuclear reaction because mass transforms to energy. According to picture below total mass remains the same after reaction. Is the picture wrong?
Minimal sufficient statistics are supposed to have the lowest dimension among all sufficient statistics. Then, is any sufficient statistic having the same dimension (as the mss) a minimal sufficient statistic? If the answer is no, is there any simple counterexample?
Consider these four situations: a tennis ball falling on a wooden floor a tomato falling on a wooden floor a book falling on a wooden floor a tennis ball falling on a soft mattress Why only in the first situation the object bounces?
It seems that paths of the Brownian motion are always continuous (please correct me if i am wrong). Levy process is the generalization of Brownian motion by allowing for jumps at random times. So why always people talk (e.g. using Donsker's theorem) about the relation between random walk and Brownian motion (and not between Levy process and random walk)?
Is there a word (or maybe a metaphor) to cover the idea of religion, mysticism, occult, and philosophy all together? In other words, how would you name a bookshelf with books and other texts by or about the following authors? Thomas Aquinas George Gurdjieff Aleister Crowley Aristotle
Let's say a box is moving to the right and friction is slowing it down. The friction force vector pointing to the left and the object moving to the right, should the vector be drawn on the left side of the object like this: : Or on the right side of the object like this:
Is there a specific name for the following graph? "Acyclic tree" is not unique and "one-dimensional lattice" doesn't sound quite right. Saying "line graph" is, in my opinion, ambiguous. The reason I ask this is because I need to reference this graph without the use of this picture, or any pictures for that matter.
In quantum field theory, consider acting on the vacuum with a local unitary operator that belongs to the local operator algebra associated with a region. In such a way, can we obtain a state that is orthogonal to the vacuum? i.e., Can the one-point function of a local unitary be zero? If so, any examples?
The Hauptvermutung (ie. the question in the title) is known to be false for PL manifolds and topological manifolds, but I can't find a result for smooth manifolds (with boundary), though I recall reading it is true. If not, is something close to this true?
I am trying to self-study probabilistic measure theory after completing my undergrad degree, and I am curious if there are more interesting applications of measure theory aside from Lebesgue integration ? It seems like (correct me if I am wrong here) measure on its own is a rich field before delving in integration of measurable functions.
If someone says something such as, "I don't know what else to do," it kind of implies a request for some suggestions. In the case the person doesn't actually want ideas for what to do, would this be considered a rhetorical statment?
As far as I know, the magnetic properties of a bar magnet is due to the alignment of electronic spins of all the atoms. According to the uncertainty principle the electronic spin is randomly up or down. So, why a bar magnet has certain poles while it may be expected its poles interchange? I appreciate any help about my misunderstanding.
In Latin, it simply means "an amount", which can be of anything and of any size. In modern English, especially in physics, it means the smallest amount physically possible, i.e. a physically indivisible amount of something, especially pertaining to energy.
I would like to justify text in lstlisting. If the line gets too long, there doesn't seem to be any way to automatically add a new line. Is there a way to justify text?
In the sentence below, 'do' refers to 'sense the environment' ,which is evident. But can 'do' refer to only a verb 'sense'? Share what you think about this, and please explain why it is or isn't okay. It is lazy and dangerous for the ecologist to assume that all other organisms sense the environment in the way we do.
I have a question about the use of "as well as" and "as did". Which would fit better in the following sentence? When the earthquake began, at least fifteen men and women fell to the ground, as did many children playing in the park that day. I appreciate any assistance you can provide.
How can Dirac neutrinos exist if neutrinos have no charge? As far as I'm aware, the antiparticle of a particle is its charge conjugate while all of its other characteristics remain same. How then can a neutrino be distinct from an antineutrino?
I've stumpled upon a peculiar usage of the Past Perfect Tense. At the end of the WWII, the Cold War had begun. The world would lay divided between two superpowers. This context seems suitable rather for the Past Simple Tense. I would be thankful for any hints as to why this tense was used. Have a good day, Damian
What are some famous open problems and conjectures in Lie symmetry theory? Is there some kind of list of these problems available or possibly a historical survey of the development of theory of symmetry groups?
What's the phase difference between A and B on the following diagram. Where it is a standing wave. This question doesn't even make sense to me as from watching animations of standing waves, points A and B cannot even appear at the same time. We cannot have two minimums next to each other. So what is it asking?
If i were to make an observation of the orbital motion of the planet Mercury from an inertial frame of reference, would I observe the precession of Mercury's perihelion? or would I observe it moving in the way predicted by Newton's mechanics? And if I will observe the precession of Mercury's perihelion, would my frame of reference still qualifies as being inertial?
I learnt that a point source produces spherical wavefronts and i know the reasoning behind that too and while studying the concept again a question popped in my mind, that "Are those spherical wavefronts equidistant ?", most online sources don't have an answer. A clear explanation for the question would be greatly appreciated.
Is there a list giving an estimate of the abundance of every element of the periodic table in the Earth's Core - possibly differentiating by inner core and outer core? I am specifically interested in estimates for extremely rare trace elements.
A steady state is Nash if it is strict and pure. And there can be multiple steady states, but not all of them satisfy the conditions of a Nash Equilibrium. Is this right?
in textbooks I find only results about the weak convergence of univariate stochastic processes. I am looking for a reference text which treats also the convergence of multivariate (vector) stochastic processes. Any hints? Thanks. Ciao Karl
I like to use the cochineal font for my document, however for this font I understand there are no corresponding mathematical fonts. So I am asking if anyone knows of any font similar to cochineal that also supports math fonts or a math font similar to cochineal fonts. I am using the KOMAscript class for the document. Thanks for all.
How do I get LyX to show the reference in full (without the "..." ellipsis)? Example: Below, I want LyX to show me "Ref: VeryLongLabelNameABC" instead of "Ref: VeryLongLabelNameA..." (which in this case is actually even longer and takes up more space)?
Electric potential is the amount of Work required to move a unit positive charge from infinity to a region of an electric field. Why do we need a positive charge for that? Can't we use negative charge?