darklight03/StackMIAsub huggingface dataset:
I am making a academic presentation. I want to put the reference in the block. But I want to put the reference number directly after word "Theorem". so I tried The reference showed up right in the block which is really terrible. It seems that the block affects the footcite. How do I solve it?
I want to find a formula for the nth dose derivative of the function I have tried to use the first line as my start point but am getting confused. I want a set of coordinates that can depict the local maximum of the nth value. the equations above are surge functions.
While obviously not optimal, I've usually found that such an "algorithm" is pretty close to the true shortest possible path, and is obviously runnable in polynomial time, with an O equal to your sorting algorithm
I am using a document class report and I need the first page after the title page to have some text on it (it is my layperson summary) and after that the abstract and the main part of the file. Is there a way to do it? I am inputting both that piece of text and the abstract from separate .tex files.
My professor explained me in the best manner possible about the electric potential energy and why it is NOT defined for a single charge, BUT my question is as Electric potential is just electric potential energy with one charge being a unit positive charge, therefore is electric potential also defined for a system of charges?
when I worked with idea of something being homogeneous. I always felt I reverse engineering what we are doing in linear algebra to find the eigenvectors and eigenvalues. could someone explain it simply
I am reading the synctex source code, now I found he comment mentioned two type of coordinates, page coordinates and TeX coordinates. anyone know about the two type of coordinate system? The docs only mention that page coordinate The origin is at the top left corner of the page.
Inside negatively charged ball there is constant electric potential. If electron will be placed inside ball with constants potential will it give mass from electric potential as same as higgs field give mass?
I'm trying to determine electric motor power sizing with requirements given for covering a particular distance within a certain time. The knowns are the vehicle mass, the allotted time, the target distance to cover, and the vehicles initial velocity. The result would be used as the absolute minimum possible motor output power rating that would satisfy the requirement.
Do Solar Eruption occupy more than one rotational layers? Is it possible to confirm this just for most outer layers? Does the number of layers occupied by those eruptions when they happen tell us anything about the relationship between Gravity and Entropy? #Update This is how i imagine Sun's Differential Rotation Each speed on the image has a different value
So it just hit me, "When is just before"? Cos just before could be a second ago or half a second ago or a tenth of a second ago and so on. So when? And do the final velocity formulas put this into consideration?
if we are able to create plasma in isolated environment possessing temperature much more than temperature of sun then why are we not able to create something that can go to the sun?
It is always confusing to me what to call the network with which we make phone calls. If mobile network regards to accessing internet with cellular data, then what network it is called to make phone calls?
Just curious how these two magnets are spatially related to? And in case there is no any special preferred particular orientation, what is anyway their spatial orientation relation (relative angles)? Possible varying with seasons or year cycles. There must be a record of these measurements? I cannot find anything about this on the internet?
In mathematics different integer also that mean different rule to for divisibility of integer, But this is not flexible way to learn divisibility of Integer then Is there another way, maybe some kind of formula to learn it? And also if there is, please provide the source, I would really appreciate it
I understand the kernel is the map of everything to zero, but does that mean that the only way for a kernel who is just made up of the zero from the previous area is for the range to equal the codomain.
When I was under the shower I experienced when I look quickly at a single line of water falling from one pore (from top to the bottom) it looks "drop drop" instead of continuous. Why is it like that?
Pretty coincidental that time happens to be like the three spatial dimensions.. or is it? Time is one dimensional with past and future, similar to left and right, up and down, back and forward of the other dimensions.
We are currently using the term circularizing (I made it up) as the technique of using artificial intelligence to check something, have devs check what artificial intelligence suggestions, which allow artificial intelligence to spit out new data, that devs have to check, and on and on. Is there a word to describe this process or can I just use what I made up?
If we change slits' width in ydse, what changes will be seen in the fringe pattern and it's density I found a source from a book saying but how could the pattern gets less sharp on increasing the width, if we increase the width less waves will be diffracted thus more sharp please someone help me with question
What maths notation to give to the set of elements composing leaves of a tree structure? Suppose the tree T is n-ary, I want to notate the set {n / n in Leaves(T) } How to do that?
If gamma ray burst contain energy equivalent to the mass of the sun, then it would be bent by its own gravity and refocus periodically, right? It could possibly go on forever without dispersion, enabling it to travel across the universe?
In LMFDB, equation of some curves are given however there are also those are not. My question is "Is it possible to find explicit equation of curves by using its generating vector?" I add link for you to see example. The curve that we have its generating vector
We know in pure translation force distributed evenly in each particle on rigid body, so in effect every particle of body moves with same velocity or acceleration in pure translation. What happened in pure rotation, how force is distributed in pure rotation particle by particle to moves a body in pure rotation?
The question is as simple as that. This is the kind of thing I want to achieve: The idea is to make a symbol used for divided differences. It needs to be a true delta letter rather than a triangle, but actually it is not that easy.
the graph of the function[The graph of the functionthe graph of the first derivative of the functionThe attached graph shows the existence of turning point but the first derivative of the graphed function is never zero anywhere within the domain of the function. What does this mean?
In general spectral analysis, we have examples of unbounded from below hamiltonians with discrete spectrum. Is it okay to say that they have no sense in physical context, because for me it looks like particle can emmit infinite energy in some weird sense.
I want to mark a fraction, which I shorten, with an arc. Haver anybody an idea how to start? I wish that it looks like the text in the picture. Is there a way to do it?
i Know elementary and their applications and there is a theorem: "The inverse operation (function) of an elementary row operation exists and is a elementary row operation of the same type." i want to know the proof of this theorem! thanks :)
I am looking to study more about electron impact ionization. I noticed that this topic or anything collision-related, is not present in Chen in detail. Is there another resource that I can use to understand this better?
suppose we have a circle to which we make a target and rotate it without breaking the basic definition of a tangent how many tangents are drawn as rectangles strips i have tried with integrals but I really want to know the answer to this question
I searched on the Internet for the answer and found none. How can one find it? Also, I write "SLITEX" because methinks every letter of the name is, even if small, raised or lowered, the capital one but feel free to groundedly correct.
If still charges in a wire loop do not respond to a(or have their own) magnetic field, then how is current is generated by changing a magnetic field? And why only a changing magnetic field? What actually happens at the atomic level?
Though both of these terms come from other languages, they are both said in English, depending on where one is. One (ay wey as a more English form) can mean holy crap!, and the other can mean something similar. Maybe it can be due to a related background?
I have not got any solution after a few try. In latex, how we can comment out a single word from a line. I mean for example Hello %this is so on it comments out this and the rest of the line as well. Is there any way to comment out only this part, not the rest of the line ?
When an ideal gas is compressed isobarically the given energy by the external source is let out as heat alongwith some more heat that comes from the decreement of internal energy. My question is why doesnt the energy given by the external source increases the internal energy and some lets out some heat?? Maybe I am missing something conceptually about so please help.
While proving associative property of vector addition graphically, everything else appears symmetric except the fact that vector a do not have a derived line as part of the final graph. Is it due to a being considered base?
Let the Zhegalkin polynomial for function consist of those and only those monomials that are not included in the polynomial for function . How different can the functions and be? (Write the maximum and minimum number of sets on which they different for each ).
i used to substitute a value into the actual book prescribed answer and the into the answer i got to see if the equations yield the same answer. i now want to confirm if the method i am using is legitimate. this is my solution to the question this is the book solution
This question looks like me value theorem by canceling of a way to apply it in the problem quite yet. An image I messed around with the given equation and tried to set it equal to the second derivative but it I came up with nothing. I'm suspecting that my method to solve this problem is incorrect.
I asked a question a while a go what is a bound state and the question was closed because there is a similar question. Now since best description we have to describe nature in quantum field theory How we define bound states in quantum field theory?
have you ever encountered works on set partition in which the principle of inclusion exclusion is used in the case of a single parameter and reused in the generalized case (with several parameters) ?
Does there exist such a notation? It looks similar to old factorial notation, but its in upper right corner rather than lower left. I need it as math environment or with some simple code so as to achieve: These are made in ms word.
If particles are excitations of fields: how does the field record the spin of a particular particle? There is no space to record the spin states of two particles, of opposite spin, in the field.
I what taught that my last name which starts the Mc that the c should be above the symbol =, does anyone know what this means? I can not really type it out on a key board but if you write it out with a pencil you can see the M "lower case c with = under it".
I have the following in my notes: I dont understand the statement 'simple model fails' Is the graph shown supposed to be theoretical model or is that the experimental data. This are equation derived before the graph:
I feel that the reason to define thing like current density is that we want to use the directional nature of the current like a vector quantity and since electric current is not a vector so we define something which has same direction as current but a vector? is is true?
my sir told me that he will get a shock, but why not bird then he replied bird has legs acting as insulators i am in confusion what is the right explanation to this
I make reference at this question: Package pgfkeys: I do not know the key '/tcb/O' and I am going to ignore it and to accepted answer. If the text of question and or of the answer span on the next page, like here: the left arrow dont span on the next page (with both tcoloboxes breckables). Can we solve this problem?
I was at a complexity optimization class and they said all constant sheaves are a twist of a perverse sheaf; is it specifically in complexity optimization or is it true for all constant sheaves?!
I'm using the Overleaf documentation to produce a bibliography with in-text citations, using bibLaTeX (compiler is XeLaTeX, document class is article). I've tried all of the citation styles on the overleaf webpage, and none produce superscript in-text citations (i.e. numbers as superscripts). The closest I can get is numbers in square parentheses. Is there no citation style that has superscript numbers? Or does this indicate that something else is going wrong?
I have seen that the notion of affine scheme is a generalization of the notion of affine varieties where the coordinate ring is replaced by any commutative unit ring, and the variety with the Zariski topology is replaced by any topological space. Does this mean that every affine variety is an affine scheme? I think that if we have an affine variety X and we construct its structure sheaf then the affine variety is a locally ringed space but how we conclude that it is isomorphic to a spectrum of a ring? Or there is another proof of this statement?
Is there any expression in English that refers to the situation when someone who is just an acquaintance (not a close friend) happens to be present around you at a social gathering (be it at a house party, a club ...), and you are debating whether to show them that you have seen them out of being shy or to avoid an awkward greeting? I'm seeking anything that fits the bill, whether it's a single word, or a phrase.
A directed graph G=(V,E) is given and I am asked to prove if there is a tree of shortest path of this graph that cannot be returned using BFS. Meaning to say if it is true or not that for every tree of shortest path a BFS can return it. I thought that the answer is true, for every tree of shortest path there is a way of arranging the adjacency lists of G such that a BFS can return this tree, but I cannot find a mathematical way of proving it. Or maybe it is false, meaning there is a counter example of a tree of shortest path that cannot be returned by BFS but I can't find this example either. I would appreciate some help, thanks!
Airplanes traveling at supersonic speeds produce sonic booms because the pressure waves they create converge to produce an extra high intensity wave. But what about planes traveling at slower speeds? These create pressure waves too (although they do not converge). Are these pressure waves the sound you hear from an ordinary plane in the sky? I always thought the sound of an aircraft came from its engine noise.
Chess is an incredibly intricate game, offering an immense number of moves and combinations. Due to this complexity, determining the precise count of legal chess games poses a significant challenge. As of my knowledge, the total number of possible legal chess games remains unknown due to the vast array of potential moves and positions that can emerge during gameplay. However, I've been pondering an intriguing question: Can we establish whether the total number of legal chess games is odd or even? It's a captivating puzzle that has captured my attention. I've given it considerable thought, but I must admit that I'm still uncertain about the parity of the total number of games. Can anyone direct me how to approach this?
The Hills mechanism postulates that when a stellar binary system is perturbed by a supermassive black hole (SMBH), the tidal forces at play result in the capture of one star while simultaneously ejecting the other. My question is as follows: Why does one star become captured while the other is ejected? Is it not possible for the SMBH to capture both stars and maintain the binary system within its orbit, or alternatively, eject the entire binary system?
A graph is homogeneous when every isomorphism between two finite induced subgraphs can be extended to an automorphism of the whole graph. I was reading Diestel's graph theory where he describes the following graph and says its clearly homogeneous. It's not immediately apparent to me why. If I have an isomorphism between two finite induced subgraphs, and map every other vertex outside the subgraphs to itself, does it become an automorphism of the entire graph? But wouldn't that make almost anything homogeneous? What is special about this one?
Most eye floaters are caused by age-related changes that occur as the jelly-like substance (vitreous) inside your eyes liquifies and contracts. Scattered clumps of collagen fibers form within the vitreous and can cast tiny shadows on your retina. The shadows you see are called floaters. If you look in a mirror while getting floaters would you see an image of the floaters in the mirror? Since they are basically shadows on the retina, I think we should theoretically be able to see an image but practically not because the shadow image would be very small.
I have been trying to find the proof of the derangement theorem, and have checked out some materials on them (since its proof has not been taught to us). But I have not been able to understand much of it. So, I was thinking, is the inclusion-exclusion principle used? Since the expression seems somewhat familiar. If not, then could someone please explain the proof in a slightly simplified manner?
I am trying to understand what fugacity really is. I asked a related question on chemistry stack exchange but am not satisfied with the answer. In many books, such as Physical Chemistry by Engel and Reid, Physical chemistry bh Castellan, etc. fugacity is called as effective pressure. My questions are a)What does the word 'effective' is trying to say? and b) If we already have various equation of states that have already accounted for intermolecular forces, then why is there a need for fugacity? I'm sorry if this is a stupid question but english is not my first language and maybe I am not interpreting fugacity correctly. So any help is appreciated!
Objects appear in different colours because they absorb some colours (wavelengths) and reflect or transmit other colours. The colours we see are the wavelengths that are reflected or transmitted. As far as I understand, when an atom absorbs a photon, one of its electrons gets excited (and unstable). So it drops back to ground state, emitting that energy in the form of photons of a specific colour. This means that we should find objects to be in certain colours, but, for example, hydrogen gas is colourless. How is this possible? Shouldn't Hydrogen gas have a specific colour related to its emission spectra? I was reading an article on this topic today (https://www.khanacademy.org/science/chemistry/electronic-structure-of-atoms/bohr-model-hydrogen/a/spectroscopy-interaction-of-light-and-matter), and this came into my mind. Can anyone please help in clearing my understanding?
What I mean is how the shape of an object affects it's physical properties. I've been studying Marine Biology and there's constant talk of how a fish's shape determines how well it can swim but no explanation of why, say, "Stream lining" reduces water resistance outside of it "just making sense" and I'd like something more in-depth. Similar phenomena would be: How a blade's shape determines how it cuts, Why certain shapes are more structurally sound, What determines a shape's aerodynamics. Is there a field of research dealing with this? It's been driving me mad.
An excerpt from my grammar lesson: In a formal context, 'due' should always be treated as an adjective, and 'due to' must therefore follow or refer back to a noun, as in: his success was due to hard work. In this case, how is 'hard work' considered a noun? In a prior lesson, a noun was defined as a word that names a person, place or thing. by this definition, isn't 'hard work' more appropriate to be a verb? Am I missing something?
I recently engaged in a lively debate with a friend about whether the term "hot dog" qualifies as a misnomer. My argument stemmed from the fact that a hot dog doesn't actually contain dog meat. Instead, it's typically made from beef, pork, or a combination of meats. My friend argues that the term "hot dog" supposedly originates from a playful association with the dachshund sausage, given its resemblance to the dog breed and therefore, it shouldn't qualify as a misnomer. While this may be true due to the term's roots in historical references, it still inaccurately portrays the contents of this food today with the lack of any canine involvement.
The connection between Markov processes and Potential Theory is well known, as is conformal invariance of Brownian motion which allows probabilistic proofs of statements in Complex Analysis, like Picard's theorem. What are some results in these areas (Potential Theory, Complex Analysis, maybe Complex or Differential Geometry) that admit probabilistic proofs, and possibly for which no other proof is known? To what extent are probabilistic methods in these areas actually crucial in proving new theory and to what extent are they more of an interpretation of facts that are already known? It would be great if there were some survey about this. Thanks in advance for your answers.
My friend is working on a snow gun, which involves using compressed air to blow apart water coming out of a pressure washer. I read that you can cool air by compressing it, which makes it hot, then letting the compressed air lose energy by cooling to room temperature. I was going to use the ideal gas law to find the change in temperature when compressed/decompressed, and Newton's law of cooling to find the time it'd take to cool down. However, I don't think the ideal gas law can be used in this case. What equations are appropriate to find the temperature of a gas before and after it is compressed?
Suppose we have two entangled particles, A and B. If we measure particle A and then subsequently entangle particle B with a third particle, C, would the state of particle A influence the combined states of particles B and C? Specifically, would there be any correlation between the combined spins of B and C and the measured spin of A? Have there been any experiments conducted to explore or validate this scenario?
"We understand that a set is a collection of objects, but not every collection qualifies as a set, as exemplified by the collection of all sets (consider Russell's Paradox). To define the collection of all sets, we employ the term 'proper class.' Now, I would like to confirm if my understanding here is accurate: A class is a collection of objects, and these objects can be sets. Classes are categorized into two groups, namely small classes, known as sets, and large classes, referred to as proper classes. Is this correct?"
I am studying a rotating cylinder model in general relativity. The interior metric is given, but I am trying to express the exterior metric. It has to be practical and describe spacetime around a rotating cylinder. So far I have considered the Kerr metric, of course, the Janice-Newman-Winicour metric, and the Tomimatsu-Sato metric. For the Kerr metric, I am struggling to express it in cylindrical coordinates. Doing so will make it easier to match it to the interior metric. Any suggestions or inputs would be appreciated, thanks.
As a high school student, I'm curious whether everything emits thermal radiation, including monatomic gases and substances composed of a single type of atom and no molecules. Can these objects emit radiation in all wavelengths, and if so, how is it possible in the absence of molecules?Is it necessary for an object to be a blackbody in order to emit thermal radiation across all wavelengths?