darklight03/StackMIAsub huggingface dataset:
I am trying to figure out how to solve the questions above for the given PDF but im not sure how to do the steps. I'm not looking for answers here as I want to know how to do it, just looking for the equations and steps for each part. I know the standard deviation is the square root of the variance correct?
An essential part of a guitar is its hollow body. Without it, the strings wouldn't be very loud; as far as I know, the purpose of the body is to set up some sort of resonance and make the sound louder. How does this work? How can an isolated system amplify sound? Where is the energy coming from?
For programming purpose, I'd like to compare the entropy of two Poisson distributions to the entropy of a single Skellam distribution. The entropy of a Poisson distribution is given in this wiki article. What is the entropy of a Skellam distribution?
I am writing a sentence like so: "I bought the Dell laptop because not only did I find the price appealing but I also liked the the fact that the laptop had an integrated webcam." Is my use of ".. not only .. but also ..." appropriate? Is there a better way to phrase such a sentence?
I know that 'Jutland', a part of Denmark, comes from the Danish 'Jylland', which describes the same region. But was that name just invented at random, or does it come from the verb 'jut', as the land juts out into the ocean?
I have read that accelerating or oscillating electron emits photons. But why and how does it so? And why only photons? There are other bosons like gluons, W and Z bosons, so why does electron emit only photons? And what is the mechanism ?
When we write a business email and want some information from the mail recipient, then which is the most professional way to ask for information? Does using "please" in a sentence make it look bad?
I recently went through some important numbers like the Stirling and Bell number for calculation of partitions /equivalence relations. I was wondering if someone can help me get a list of important numbers and their applications in Combinatorics ; like Catalan , Fibonacci , Stirling etc.???
For example, the word "jihad." Translated, the word means "struggle" or "strive" and I am sure there are others. The word "jihad," is just taking the pronunciation of the word in the native tongue, and spelling it phonetically in English. Is there a specific word for that?
Why do some pressure cookers initially leak steam from the sides and after a while settle down and don't leak? Is it a positive feedback mechanism from the building steam which makes the sealing tighter and vice versa?
I have a distance matrix M and have used multidimensional scaling and it gives me some eigenvalues. How should I interpret such eigenvalues? Do they show some sort of variability or what? More practically, I really cannot understand the real meaning of eigenvalue. For example I can understand |M|, but I have no sense about the eigenvalue.
I heard that If we travel for long distances in the direction of the rotation of the earth, we can gain some extra hours in the journey. Is it true? What if we travel in the opposite direction?
The multline environment does exactly what I want in splitting a long formula between lines by utilizing the horizontal space to the fullest. (I don't want the alignment features of the align environment.) The problem is, I want to vertically center the equation number, as opposed to making it appear on the second line (as it does by default). How do I do this?
Is it possible to create a head-mounted optical device that allows the user to see the wind, by means of thermal imaging / infrared detection, variations in the light's refractive index, or something similar?
I wanted to ask about the exact meaning of pathology. Is it just for disease or can we use it for other things? I mean, for example, if I want to talk about the determination of harms in culture or technology, can I use the term "technology pathology" or "culture pathology"?
I am writing a paper on a dystopia and how the leader came to be. I need a term to describe how he wasn't elected into power but he just assumed the role of instigator and no one questioned him.
Caroline wondered whether there were coffee shops and restaurants in other galaxies. She imagined them installed on floating asteroids, or in the rest area of cosmic highways. Since the universe was so infinitely large, how couldn't there be at least one or two? Is installed a good term to use in this case? If not, are there other better options?
Why in adiabatic compression and expansion small volumetric change occurs while in isothermic compression or expansion very small pressure is applied and volume changes very significantly i am referring to PV diagram of Carnot engine?
This question is about font in Tex. I want to make my Tex output have the font as in this book https://www.math.wisc.edu/~boston/ddt.pdf but I do not know how. I have no idea where to begin. I appreciate your help!
Both the Laplace transform and the Fourier transform in some sense decode the "spectrum" of a function. The Laplace transform gives a power-series decomposition whereas the Fourier transform gives a harmonic (or loop-based) decomposition. Are there deep connections between these two transforms? The formulaic connection is clear, but is there something deeper? (Maybe the answer will involve spectral theory?)
How does our sun create positrons? And does the sun emit said positrons after their creation? I read that the sun creates positrons at it's center but I couldn't find how they form. Is it a byproduct of fusion or does it occur as our sun stars to die?
I read that the following is ungrammatical: Because of the accident, he arrived at the dock an hour late. As such, he missed the boat and forfeited his deposit. Why? What is the correct usage of as such?
Refraction: light changes direction of propagation when entering a material with a different refractive index. Does the direction of propagation of light change sharply and almost instantaneously (as shown in the diagram) or smoothly?
I'm not a native English speaker, but sometimes I get the feeling that the pronunciation of English words is random. Why is "Yosemite" is pronounced as "Yoh-Sem-Ee-Tee" and written as "Yosemite" and not as "Yosemitee"?
It is well known that any conformal mapping of the unit disk onto itself extends to the unit cirle. However, is there an homeomorphism of the unit disk onto itself which does not extend to a continuous function on the closed unit disk? If yes, can you give an explicit one? Thank you, Malik
If I issued a payment to a company, and I wanted them to notify me when receiving the payment, could I say 'please acknowledge the payment when receiving it?' Is the word 'acknowledge' alright to be used here?
Which of the following, if any, is correct? You answered the same questions as me. You answered the same questions as I did. You answered the same questions as I have. How can you tell? I tried Googling it, but I only get Breaking Bad references. I also saw this, but I don't know how it would apply in this context.
I have this fragment: ... the experience and knowledge gained will be helpful in my career as a neuropathologist. Is the "as" here okay? It somehow does not sound right to me. Obviously I want to say that it will be helpful to me, during my career in neuropathology.
Here are a few attributes that a text may have: "name", "length", "quality", etc. What's the name of the text attribute that refers to the text itself? Would that be the text's "content", the text's "body" or something else?
Is there a way to convince LaTeX to automatically add tildes in front of one- and two-letter words, numbers and such simple things (in normal mode, not in math mode)? I know there are preprocessors for that, but manually launching them is tedious. What's the best way to achieve it automatically?
I came across this sentence as I was reading a book: My clothes disintegrated, victims of the sea. I think saying: My clothes, victims of the sea, disintegrated. would be correct. Which one is the right one?
When an object is heated a lot and then brutally cooled down or vice-versa, it can crack or even break spectacularly. What happens inside that makes it do that? Is it only because the hot core swells when the cold surface shrinks, which causes internal stresses? Bonus: Are certain materials more sensitive to thermal shocks (high CTE?)?
I am working on a project involving the motion of rigid body. From the literatures, I found two main tools, namely the dual-quaternions and screw theory. May I ask what are the major differences between them? It is appreciated that if some documents can be suggested for beginners.
I'm using the memoir class, and would like new chapters to begin on the left-hand page, unless the chapters in question are only one page long. Neither openleft nor openany give this behavior. I am not opposed to using another class, or using sections instead of chapters, if I can get this behavior by doing so.
What is the third order term in the Taylor Series Expansion? I know it will just be third order partial derivatives but I want to know how is it expressed in a compact Matrix notation. For instance Jacobian for first order, Hessian for second order partial derivatives. In other words, what is the third order term in the equation below? Thanks for your help!
I used "It's not fair", but someone told me "fair" is the "F" word, and they don't like it in their house. Should I avoid using it? ps: sorry if my question offended someone, I didn't mean to it.
I need a prove that pumping lemma can't be used to prove regular language. Pumping lemma is only used for proving non-regular language, but I need to show that how it can't be used to prove regular languages?
Are there any interesting theorems outside of set theory that use ordinals in their proofs? The only example I know of is Goodstein's theorem, and I haven't been able to find anything else. In other (more vague) words, what is the use of ordinals? (Other than Goodstein.) Theorems that use the word "ordinals" in their statement don't count; Goodstein is a good example.
I remember there is a theorem that states that if you have more polynomials than the number of variables, there must be an algebraic relation between them, but I forget what the theorem is called. (I'd also appreciate if I could be directed to a proof of it.) Thanks.
Are the finite dimensional comodules the compact objects in the category of comodules over a Hopf algebra? If yes, is there a reference? If no, which are the compact objects? Here by compact I mean that the Hom functor from the compact object preserves filtered colimits. Thank you!
I have to build a simple electromotor in the following way: I attach a permanent magnet to a battery, connect some metal supports to the terminals of the battery, and place a coil of wire on the supports, suspended above the magnet. My question is, will it still work just as well (or at all) if the wire is insulated? Thanks!
I tend to think of data structures of type Structure.Field.Subfield as analogous to file directories. I.e that Structure is a folder and Field is a folder inside the folder.. etc. Is this a good way to think about it?
I'm having a brain cramp: if cookies should be avoided, and carrots are preferable instead, is it correct to say: Avoid cookies in favor of carrots. or if not, what's the correct way to phrase?
I understand the mathematical definition of Uniform Continuity. But I was wondering that if there is a intuitive explanation for this concept similar to Continuity where we sometimes say that if I draw the graph of a continuous function I do not need to lift the chalk from the board.
For the sake of argument, assume the LHC was able to accelerate / focus / collide neutron beams, with the same energy levels it runs at for p-p collision. Would the collisions produce any major differences vs the p-p collisions?
Is there a simple, elegant solution to add footnotes in a table (tabular)? Preferably, the solution can also support the cleveref package. EDIT: My intended effect is that, the footnotes should be displayed at the bottom of the page, just as regular footnotes are. However, I've checked out ctable package but found no such feature. Am I missing something?
We are given the lengths of all sides of a polygon. We need to determine if the given polygon is convex or concave. How can this be done? What is the propery applied to determine this?
I'm starting to read Baby Rudin (Principles of mathematical analysis) now and I wonder whether you know of any companions to it. Another supplementary book would do too. I tried Silvia's notes, but I found them a bit too "logical" so to say. Are they good? What else do you recommend?
I've exhausted the usual High School curriculum for Mathematics and i need some recommendations. I want to start a serious course in Mathematics at a local college, but that's simply too long to wait, i'd like to get started now. So right now i'm just looking for some fantastic books and some fantastic tips, any recommendations are appreciated.
Consider the following examples: "And it is a bottle, too." "And it is a bottle too." Is there a semantic difference between these two sentences? Or do they mean the same thing, with or without the comma before "too"? If not, what is the correct usage of the comma in context of "too"?
I have learned that the classical measurement of the speed of light with a rotating mirror does not work with a laser (as opposed to, say, a mercury-vapor lamp). Can you tell me if and how coherency of light is necessary/contraindicated for the success of this experiment?
If we consider a balloon full of air submerged in water then we all know that it will rise rapidly. I am having trouble understanding this at the level of individual molecules of air and water. What is a molecular/microscopic explanation for this phenomenon?
Is it correct to use "But" at the start of a sentence like this? You can afford it. But think twice before buying it. Won't using "But" instead of "However" mark me as a non-native speaker?
I have read that the electric energy flows from the battery into the circuit through electric field created outside the wires into the light bulb (or any other resistor). I have also read that the friction caused in the movement of electrons cause light bulb to heat up. So which is the correct explanation?
I am preparing my CV with moderncv and chose the casual style. Now, I would like to omit the icons for phone, email etc. How do I do this? Thank you very much in advance!
I am trying to understand a statement of a problem. Wondering how can a striaght lines in three different planes meeting at one point. Does not it imply that all the three planes are also intersecting at some line?. Can three lines in parallel planes meet at some point?.
I am compiling my document in Persian using XeLaTeX, but the references are all in English and I'm appending them using BibTeX. At the end of the document, the references are all unknown characters, how could I handle this problem?
I want to simulate an impact between two bodies according to gravity, and eventually considering other forces to stick matter together. I'd like to use python to do this, but I am open to alternatives. What kind of tools or libraries can I use to perform this task ?
The nebulae we see in the night sky are forming new stars. The stars are eating up the nebulae and there is no obvious process in which those nebulae are being created to compensate for that. Shouldn't the universe have run out of those nebulae a long time ago?
Often when I want to say that something became clear, I may instead say that the thing "became lucid" or that the thing is "becoming lucid" is there a single word that I can substitute for this?
Consider the following excerpt of the Liouville's theorem proof taken from "Arnold - mathematical methods of classical mechanics": In changing the variables in the integral, I don't understand why there is not the absolute value of the Jacobian determinant. Why the determinant of the Jacobian of the flow is positive?
If one pays for transportation of oneself a fare has been paid. What is paid if the transportation is of a non-person object (a parcel, a letter, a vegetable, a box of rocks)?
Why do people use "skies" instead of "sky" (when, indeed, we only have one sky)? Reach for the sky/skies! and I'm glad to finally see some blue skies. I'm glad to finally see a blue sky.
So, I came to naming a variable in my PHP today. The variable was to contain information about the state of a switch, E.g - on and off. However, I couldn't, for the life of me, think of what to name it. I ended up settling for State. But for arguments sake, what other words could I have substituted for State?
According to the Oxford English Dictionary, a diatribe is defined as a forceful and bitter verbal attack against someone or something. I had previously understood it to mean something more along the lines of drawn out, longer than it needs to be, impassioned persuasion. For example, in a friendly letter, My [diatribe] begins here. Any alternatives?
I'm gluing the edges of a square together with the caveat that there's a "fold" down the middle. I think this produces sort of a sphere with four "pinches". I'm wondering if my intuition is correct and if someone could provide a more rigorous foundation for what I'm trying to do and elaborate on the nature of the singularities.
There are n studio apartments in a building. Some of the apartments are connected with each other by direct phone line. Prove that it is possible to assign to each apartment a female or a male in such way that each person has direct connection with at least as many people of the opposite sex as he/she has with people the same sex.
So the sentience is "It's hard to find a good path to taking this mission on", I wonder why it is "to taking it on" not "to take it on", is "taking" using as a gerund? Can I say "It's hard to find a good path to take this mission on"? What's the difference?
I really like the nLab and its collaborative style of writing. Are there any other websites which follow the same philosophy, but on different topics, or with different points of view? For example, is there one more on the metric aspects of Riemannian Geometry, Geometric Analysis, Harmonic Analysis and the like?
Intuitively to me it seems likes increasing compression ratio would require more work to compress the gasses before ignition, so you'd just end up getting back what you put in - like a spring. What am I missing?
If yes, why don't they fill up with water, and can you breathe the air there? Like, it's not exactly atmosphere there, but an underwater cave with higher ceiling. P.S. Possible that it has a different name than air pocket, but due to my limited knowledge of English, I have no idea. Thanks in advance!
Possible Duplicate: Calculating prime numbers The question is in the title. Is there a number that is divisible only by numbers greater than its square root? If not, why? I need this because it can speed up a calculation algorithm significantly if the answer is no.
We often use "cool water". But can we use "cool water" or "cold water"? Which is correct? Examples: I drink cool water only. People always like cool water. In the above examples, instead of the word cool, can we use cold?
If you want to fly a spaceship with human passengers as close to the Sun as possible, then what effects would the spaceship have to be designed to counteract in order to keep the passengers alive and how close to the Sun could you get before there would be no way to counteract the effects ?
There is a book titled Running for Mortals. I didn't recognize word mortal. Then I looked up it and get the meaning as below. mortal N - A human being I wonder, is mortal widely used as human being or it is used only for special areas like sports, medical, etc?
What is an uncommon synonym for the noun "motion" (movement)? I'm looking for cool sounding words like "twitter" that are synonyms or somehow relate to motion, the noun that means movement. Example: "I bought a motion detector to alert my household of criminals."
There are many documentaries, forums, blogs and more dedicated to Dark Matter. I have been frantically searching for an answer to my question however none of my sources have clarity to the matter of hand. I would really love a clear explanation to: What exactly is Dark Matter? Please help me to have a clear understanding.
I was wondering what happens to the electron after it leaves it's valence shell and strikes a stable valence shell; in an insulating material? I realize that the energy from the strike, is absorbed by the atom that was struck and that these electrons do not 'break free'...so what happens to the electron that struck them?
I hold him in high regard. The court holds him responsible/liable. She held it dear. We hold these truths to be self evident. This construction only seems to work with certain adjectives. Are these examples all set phrases or can it be used freely? Can I say "I hold that crazy" and make sense?
I have a question like how can we mathematically prove that for a general matrix Conjugate Gradient method will always converge within n steps in exact arithmetic ? where n is the size of the matrix.
I'm writing a presentation using the Singapore theme. The dots in the navigation bar are appearing vertically (one below the other) rather than horizontally. This is consuming a lot of space of my frames and is even not looking good presentation wise. I have seen presentations using this theme where the dots appear horizontally. How can I do this?
I have a maximum number of pixels that I can process in my app at one time. The user must be able to open any image and if it's bigger than the maximum number of pixels it should be scaled down to fit the maximum resolution size. Keeping the rectangle ratio. How can I calculate the new rectangle?
I can't find the precise definition of what is the orientation of a GaAs lattice. Being the superposition of two fcc lattices (one of Ga, the other of As), I would think that it is the direction of the closest Ga atom to any As atom of the structure. Is it right?
I am writing a chapter in a book and I want to say that "I believe that this researcher is right ....", in a more formal way. Can I say "The present author believes ....."
In statistics one often hears the phrases "log likelihood" and "log error". Why is it natural to consider the logarithm of these guys? My wild guess is that the Gaussian is a pretty "normal" distribution, and it's natural to take the log of such a thing. But this is pretty sketchy. A pointer to a reference would be great.
I wrote "How is conditions being unfair not an issue?" instead of "How are conditions being unfair not an issue?" as I believe the subject of the sentence is 'conditions being unfair' rather than 'conditions'. However, I'm not quite sure. Which is it?
So I understand that the an inner product space basically uses pythagorean theorem because it is similar to a distance formula. I'm still having trouble with this proof. I am a bit confused about where to start. It could be notation that is throwing me off, so any breakdown would be great.
I always find it very difficult to understand the notion of chemical potential physically/intuitively unlike pressure and temperature in statistical mechanics. Can some one suggest some nice references or briefly discuss about it intuitively. Actually I came across it again in the context of AdS/CFT. It will be really helpful if it is discussed in holographic context.
There's a Polaroid photo in the album, and I want to ask the owner about the person in it. Can I ask him: "Who's that man in the snapshot (shot)?, or I should ask "Who's that man in the picture (photo)?" Thanks in advance, Victor.
Is there a name for this manner of purposely speaking in double negatives, e.g. I wouldn't say no to a cup of tea! I've noticed it as a habit of some people, perhaps often going along with a particular type of sense of humour and British understatement.
in a company bylaws document, I'm trying to describe situations in which a the term of a company director can be ended. These include death, as well as "going insane" or "losing his mind" - but I'm looking for a more "PC" or "legalese" way of saying this. Any ideas?