darklight03/StackMIAsub huggingface dataset:
In finite-dimensions, the complexification of a real vector space is easily shown to be isomorphic to the original real space by using a proof which involves explicit use of a finite basis. Does the result also hold for infinite-dimensional spaces?
Someone has just messaged me saying as a professional business owner I should know the difference and that my sentence is wrong! I am not sure! Especially as I am from Yorkshire and we all know we speak differently up here! So why wasn't you good enough? Or So why weren't you good enough?
I have an ionic liquid solution phase and an organic phase. They are immiscible. When I place a small piece of nylon fibre in the liquid it always goes to the liquid/liquid interface instead of staying in the aqueous/organic bulk phase. What is the phenomena behind this, and to understand this, what are the concepts I have to search for?
I found in this site that if we use a set of colored lights we'll have colored shadows. But why is that? As far as I know a shadow is where there is no light. So why isn't the shadow that is produced by colored lights just black like a normal shadow that is produced by white light?
If an electrically conductive material has lots of protons, then how will it conduct electrons even though they should be getting attracted? Do the electrons somehow get pulled in the direction of the conductor?
Is it possible to have two table of contents in beamer which contain the contents of two different sections, e.g. the main part and the appendix part. One table of content only includes sections from the main part, and the latter one which is shown after the main part only shows the appendix sections?
given a parallelogram, show that the area of the parallelogram follows the relationship of two adjacent sides times sin of the angle between them. I tried dividing the Parallelogram into two congruent triangles, then finding out if I could get a relationship using the law of sines since I am stuck on how to integrate sin of the diagonal into the relationship.
I am studying mathematics at the undergraduate level and I am interested in the world of mathematical logic. I would like to know the opinion about which books or texts are recommended for an introduction to the subject and then a deepening? I am grateful to all those people who give me their opinion or recommendation of texts or notes, on mathematical logic.
I know how to find the quadratic residues and I know how to determine the quadratic nonresidues by simply taking the complement of the positive integers lower than p against the known residues; is that the only way to find nonresidues? It feels like there should be a method that's more direct.
Given an arbitrary set of Christoffel symbols for a spacetime. How does one identify the Euler, Coriolis force, centrifugal force and linear fictitious force? I suspect it should be possible to do it both from the metric and Christoffel symbols?
Does anyone know of any free and relatively easy-to-use math apps like Geogebra that can be programmed (or were explicitly designed) to draw the geodesic between any two selected points on a saddle surface like the one below? Thanks in advance.
I am interested in reference material for Physical Applications of Stochastic Processes. The playlist does have an associated book, but it is a litte dense, and the derivations are mostly left to the exercises. Is there any book/site that covers the same material (a different perspective), or even one on general stochastic processes.
I want to typeset a truth table where the truth values of a complex formula are aligned with the corresponding connectives as shown in the attachment. Would someone know a solution? Thanks in advance!
A TLDR summary is used to shorten a long detailed article. However, what if you have written a brief and concise summary, but would like to add further non-essential background details at the end?
In @UmbertoP's response to the question, "Partition of real numbers into dense subsets of positive measure," the answer is understandable to a advanced undergraduate; however, I have inadequate knowledge of measure and set theory. I tried to create a more explicit example here but it's too complicated. Question: Is there a more explicit version of Umberto P's answer that's understandable to an average undergraduate?
On the web, I have not found much concerning the argument which is convincing to me. I have then worked out a proof of Fatou's Lemma assuming convergence in measure. I ask you if it sounds fine. Thank you so much.
I know what real projective line is. But what is a formal definition of a projective line? Unfortunately there is nothing on Wikipedia about it. They are always talking about projective line as a part of projective plane. How would one describe projective line without any underlying space? Thanks.
I know latex, but new in xslt (learning now), I need to convert the tex to xml file through XSLT (one of my friend suggest, but i failed to convert). Please suggest or give example to convert the files.
Looking at the P-H diagram, the working fluid pressure drops when it goes through the expansion valve. Temperature drops at constant enthalpy due to Joule-Thompson effect. Therefore the system must be pushing the working fluid to lower pressures when there is not enough refrigerant, but why would it do that? Is the suction pump working harder?
what is the nature of force on electron in atom .Is it coulombic or electromagnetic force? As electron is in random motion so we cannot take it as electrostatic force. Please clear my confusion.
I am writing this document for HR at work and wish to outline what our staff should do to get reimbursed. The sentence should be something along the lines of... All incurred expenses/expenses incurred should be claimed within three months of their taking place. Is there a rule?
When light is refracted through little drops of water the rainbow is formed behind the water molecules. When light is refracted through a glass prism the rainbow is formed inside the prism. Then why when the light is refracted through a bubble the rainbow is formed on the surface of the bubble?
I can find some properties and characterizations of path algebras and its elements in representation theory books but I want some references that study and treat path algebras as invertible elements, idempotents, ideals, etc... without focusing on representation theory. Best regards.
I wonder about the possible influences of the continuum hypothesis or its negation on quantum theory. Could we think about a physical system for which Hilbert space would have dimension cardinality (cardinality of orthonormal basis set) between integers and reals (thus in favour of continuum hypothesis negation)? J.
I know the effect would be incredibly small if there is one. If I were to point a laser pointer at the moon and a gravitational wave were to pass by perpendicularly to the laser would it shift the point on the moon momentarily as the wave passed?
It is well-known that the Laplace-Beltrami operator for a Riemannian manifold takes a relatively simple form with the harmonic coordinates. This operator should be obtained as a product of Dirac operators. So, my question is: What should the form be for this Dirac operator? Does some literature exist about?
This has always bugged me. The energy levels are discrete, so an electron is said to only absorb photons with EXACTLY the energy of the jump between levels. Otherwise, the photon passes straight through right? But isn't photon energy on a continuous spectrum such that the energy match would have to be infinitely precise? How is that possible?
To what extent is the Ising model for the ferromagnetic transition experimentally relevant for real ferromagnets ? For example if one quantitatively compares the magnetization versus temprature data rescaled by the critical points, do the data match with Ising scaling ? Any hints to compilations of data or comparisons would be appreciated.
For example, the paper I am reading states that the current was "periodically interrupted without changing polarity" to "demonstrate that the peaking behavior is not due to a capacitive effect." They observe a standard voltage trace. What does "capacitive effect" mean in this context?
Is Anti de Sitter spacetime repulsive because of its negative scalar curvature? Will a fluid flowing radially inward experience an opposition that has a radially outward component? And how can one quantify this "opposition"?
It is known that it is impossible to have a non-singular vector potential for the monopole magnetic field. How about the monopole harmonics? Could the wave functions be made single-valued and finite on the sphere?
I have seen several suggestions on ways to indicate a person's middle name was preferred over their first name: Firstname "Middlename" Surname Firstname Middlename "Middlename" Surname Firstname Middlename Surname, aka Middlename Is there any consensus on the best approach in an obituary?
In wikipedia page of tensor product, there is a tensor product of mixed type tensors: I wonder exactly how the map works (it takes in ... and spits out ...). Can someone help me to find an explicit form of this map? I met this problem when looking at second covariant derivative of tensor fields. Thanks.
Consider an electron that is launched towards an atomic nucleus. As the electron gets closer to the nucleus, the electric potential energy between these particles changes, it decreases. According to energy conservation what follows is an increase of energy outside of this electron-nucleus system. Is it now correct to say that the emitted bremsstrahlung x-rays provide this increase in energy?
I am a maths hobbyist, and now I study books on differentiable manifolds and their geometry (tensors, connections). My question is : what is the use (or examples) of the linear connections ? Or later, the Levi-Civita connection, in Riemannian Geometry ? What calculus we can do with them ? Thank you very much !
I'm new to latex and this is my first time using it to write my report. I want to style my Table of contents and list of figure like the following images- table of contents- list of figures- I have no idea where to start and how to format toc and tof like this. I would greatly appreciate your guidance and expertise.
In atomic collisions,does the neutron fuse with the proton of hydrogen and release a photon which is absorbed by the electron which then gets excited to higher energy state? Or do the neutron and proton stay in contact like a deuterium nucleus without any release of photon. In the latter case how is the lost kinetic energy of the neutron absorbed by the electron?
Is it even possible to calculate a particle number of some field in lattice field theory? After all, it's implemented in the formalism of imaginary time path integrals, here's no such concepts as particle number operator, creation and annihilation operators. After searching the internet i didn't find anything useful. I'm interested in bosonic fields.
I am looking for an appropriate word for parking a car at the Workshop, for repair in the coming days. The word deposit gives an impression of a financial transaction. I put/deposited/parked my car in the workshop for repair. What can be the most appropriate word in this context?
It is commonly explained that semiconductors like silicon, germanium, GaAs... are opaque because all of the visible wavelengths are above the band gap so they get absorbed. However silicon and germanium have indirect bandgaps and require a phonon interaction which should be rare. Why are they not transparent to the human eye?
This appears in an Olympiad handout by Kevin Zhou. However I don't get where this result came at all. How would you prove it? I also don't see in what situations the right side of the expression can be more useful than the left side.
The image of things falling into a Black Hole stays frozen on the event horizon forever. So how is it that we don't see the image of a dying star where a Black Hole formed? We see the black, with an accretion disk.
It is well known that there are algorithms developed for asymmetric encryption that take advantage of the fact that the product of two prime numbers cannot be factored in polynomial time. Usually, prime numbers are not used in symmetric encryption. Do you know of any algorithm where prime numbers are used at any stage of symmetric encryption?
Is Shockley-Read-Hall recombination synonymous with all phonon-assisted nonradiative processes? In organic molecules, "internal conversion" is used to describe non-radiative decay from excited states. It seems like nonradiative recombination can take many forms (including Auger Recombination, recombination at defects and recombination at surfaces). Looking for clarification.
What ratio of final to initial mass of a rocket to achieves the highest energy efficiency - the highest ratio of final mass kinetic energy to chemical energy expended? And more generally the relation of efficiency to mass ratio. This is a bit hypothetical because we are not usually interested in efficiency in this sense, but the answer is curious none the less.
Bands and solo singers have discographies, (film) actors have filmographies, and so forth. Is there a similar term for television? I've come across "televisiography", but the article's author compared its usage to cinematography and not filmography.
As we all know that in a pn junction depletion layer is formed and due to immobile charges electric field is directed from n side to p side but why does this electric field acts as a barrier for diffusion rather than an enhancer for diffusion of charge carriers?
I keep coming across "quotes" on the internet that say things like "psychology says, if a person blah blah" I'm wondering what the term would be when someone 'mislabels' a field of study (psychology in this case) as a person, as if a field of knowledge is someone talking, I don't know how else to put this. Thanks for any help!
Are there actual equations for the Parton Distribution Functions for quarks and gluons? I've been looking high and low for theory-based papers about this and it seems like a wild goose chase at this point. If the answer to that question is no, are there any theoretical results that can be used to compare to experimental results? Hope to hear an answer soon.
I'm working on a class file in Overleaf, and would like to be able to have the editing tab for the class file and the main file open at the same time, rather than needing to repeatedly switch between them. Is there a way to do this?
I'm not sure how can the following formula be derived. Please explain step by step with reasons: Present value of constant cashflow at fixed rate: Future value of constant cashflow at fixed rate:
Are the most fundamental particles, e.g., bosons, fermions, etc., capable of further subdivision? Are they at their most fundamental? Or do we consider them so because we're just not capable of going any further? theoretically, couldn't any fundamental particle always have some smaller component on which it depends?
Recently, I got an internship as a Content Writer, and they issue a report for the work done using Grammarly for further corrections before finalizing. I have noticed that a lot of the suggested changes by Grammarly were of usage of passive voice. How do I avoid this to begin with and why is considered wrong?
"This is because of abrupt discontinuity of fields" I have read this or similar sentences in many papers. I am bit puzzled. How and under what conditions electric field can be discontinous? In my opinion this is unphysical, field lines start at one charge and end at opposite charge. Then how can fields be discontinous midway?
I found a tutorial on converting a PDF to SVG, but this method seems to only work on local devices. I wonder if it is possible to output images from LaTeX using online compilers like Overleaf.
According to the Wikipedia page here, a real, unsymmetric tridiagonal matrix can be brought to symmetric form by a similarity transform. Does anyone know if a generalization of the formula given there exists for unsymmetric tridiagonal matrices which are complex and Hermitian, and; contain nonzero elements in their upper-right and lower left corners (i.e. which are subject to periodic boundary conditions) Thank you!
If a spaceship approaches a rapidly spinning planet, would the planet's inhabitants , the inhabitants of the planet where the spaceship came from , and the spaceship's occupants observe time dilation between all each other due to their relative motion?
I plotted some simulated stellar emission spectrums from PHOENIX which also each came with their respective effective temperatures. With the effective temperatures, I used Wien's law to estimate the peaking wavelength of the spectrums. Why does Wien's law seem to underestimate the peak wavelength? Also, why is the error increasing with lower effective temperatures of the star that emits the spectrum?
I used Google Scholar to export the citations in Latex but they are not written in a correct and homogeneous form for all the references. How can I use Mendeley to reorganize my references already made by Google Scholar? I don't want to do this work manually because I have a lot of references.
I am working on a heavily mathematically project about plasma. In particular, I want to find references that treat the problem from microscopic models that include relativistic and magnetic effects (Coulomb forces, QFT, etc) and obtain kinetic models (BBGKY, Landau equation, Maxwells equation, etc). What are some state of the art papers/references?
Why doesn't the Hafele-Keating experiment settle the twin paradox? It is my understanding that clocks were used, and that the shifts matched the calculations. Doesn't this settle the twin paradox if we replace humans with clocks, implying that the travelling twin is the one who age less?
Given an undirected graph, denote N as the number of vertices and E as the number of edges in the Graph. The Graph consists of k connected components where k <= N. Assuming each connected component is complete, What is the minimum number of edges in G (as a function of N and k)?
"The phone is ringing" refers to an incoming call, so saying that is misleading when you've gotten a text/notification. Is there a different word to use in that sentence ("The phone is _______") to mean "the phone is making the sound of receiving text/notification"?
About a hundred people had already gathered, a guard rail the only thing separating them from the crater's edge. Is it not more proper to say "About a hundred people had already gathered, a guard rail was the only thing separating them from the crater's edge."? It naturally sounds more clear in my opinion when was is used.
Just realized the Japanese word Kawaii is pronounced Ka-wa-ii (three syllables). With that in mind those two last "i" in Hawaii look suspicious now. Shouldn't they be pronounced separate, making up a third syllable? Otherwise, what's the purpose of the double "i"?
Thinking of compound words or phrases where the order of the words can be swapped around and still make sense: Examples: Lighthouse - House Light Birdhouse - House BirdRacetrack - Track Race So far that's all I've been able to discover. Is there a word for this reversibility phenomenon?
In the formula of the law, we have to find the cross product of the distance(r) and the infinitely small part of the conductor dl. My doubt is why are these both considered as vectors ? Aren't they measurements of lengths ? I'm unable to relate vectors with this concept, kindly help me out :)
I need to plot this algebraic curve in tikz but I don't understand how to deal with these curves in tikz since it's not a function. Desmos tells that it should look something like this I only need a curve without axis or whatever and only in tikz.
I used the program R to calculate the values of the maximums and the points where the new function starts, however, I don't know how to use these points to graph the function I'm looking for. Image of the results I got from R
I came across (a pretty sad) poem by Meggie Royer. She writes: I stood by as strangers stroked her muzzle and she wilted beneath their touch like she did once for mine. For context: she writes about her dog here. I interpret 'wilting' as something positive in this case. Can someone shed some light on this for me?
I have recently been looking at random variables and did come upon the below matrix (in image form because it is too large to copy): I have been attempting to find the inverse of this matrix, and have only been able to find decimal approximations. Does anyone know of any software or site that could compute the exact inverse?
Can the word provenance be used in reference to a person, or should it only be used for objects? For example, would it be improper to ask someone for their provenance? Longman, and AHD, for instance, only mention it being used for 'things' / 'objects'.
I'm trying to trace back the etymology of 'palatable', but what I'm really looking for is the process of semantic expression over time. When did the word begin to be used to speak of things unrelated to food? I will be grateful for any leads, resources, or information.
I am wondering where can I find examples of explicit calculation of Bala-Carter correspondence for algebraic groups of classical types of small ranks. Would you please give me some clues? Thank you very much!
Consider the following (mock) sentence: We use a class of methods in which fruit (here: bananas) are combined with vegetables (here: pumpkins). An editor has proposed instead: We use a class of methods in which fruit (i.e., bananas) are combined with vegetables (i.e., pumpkins). The meaning strikes me as different however. Question: Are both sentences correct? Do they differ in their meaning?
When using the changes package, it highlights the changed text and adds a superscript denoting the author id. Is it possible to suppress this superscript? I use different colors for different authors. PS: This is a follow-up question to this question, but is also a stand-alone question.
Suppose a plane mirror is half-submerged in another medium (say water) and light rays are incident obliquely on mirror at the interface separating two media. My questions - (a)- Will reflected rays suffer refraction ? (b)- What angle will the reflected rays make with normal after reflection? Will angle of reflection be same as angle of incidence (as given by law of reflection) ?
So imagine you have a bottle of water or any type of liquid (like a bottle of milk that has just been opened)that is completely full or even three quarter of it is full,why does the water or milk come out of the bottle in waves when you pour it in a glass?
Can someone please show me the formalisms of the energy and the momentum conservation in the curved space-time for electromagnetic? I know it's going to be two equations. but I couldn't find them anywhere and I couldn't calculate them.
When resolving vectors into their horizontal and vertical components, why must the individual vectors form a closed triangle? I don't understand why vectors must form a closed triangle when one vector is the sum of the other two. Why is this true, and how do prove this?
I've seen in many places, including Weibel's excellent book, that the category of short exact sequences (in an abelian category) has kernels and cokernels, although it is not abelian. However, I cannot find any analogous information about the category of long exact sequences, so: Are there kernels and cokernels in this category? In other words, is it pre-abelian? Thank you!
I was reading this thread Exterior power of a tensor product and I found that the result cited in first answer is very useful to me, but I couldn't prove it myself and what's said there is not enough for me. Can you give me a good reference?
I was playing around with Desmos today and came up with this formula for finding global minima: It works by descending until it finds a negative value. The same method could work with multiple variables using nested products. Would that be a computationally feasible method to use in machine learning?