darklight03/StackMIAsub huggingface dataset:
I have a question about the potential and wave functions of discrete energy levels of quantum point contacts. Assuming one has a rectengular potential well: Can the potential of the QPC be assumed to be infinite or is it finite and the charge carriers also have a probability of being outside the potential well? Is it also necessary for the wave functions to drop to zero at the edges so that the quantized conductance can be observed?
On looking upon the process of penetration of radiation. I came upon this: "If the particle has enough energy, it can deposit its energy to break the molecular bonds displacing the electrons, hence it can penetrate the object. So, if the same thing is done in a large scale with higher concentration of radioactive particle hitting an object per unit area, would it be possible to break nearly every single molecular bonds, and resulting into the object breaking apart in dust?
I'd just like to enquire on how this sort of chapter style is done. I am aware it is some permutation of the memoir class with hansen style chapter headings, however the number seems to be in sans-serif, the text in CMU serif, and the document to be in a different font to what I typically find on hansen templates. If anyone could replicate this for me, it would be greatly appreciated.
Is the wire in the figure below homotopic to a wire between the two points that just go straight above the pipe? My knowledge of topology is very basic, and it seems to me that the pipe can be seen as some kind of hole, so the wire seems to really be impossible to untie. However, there is a youtube video that seems to untie it. Is it a trick or is my intuition wrong, and if so is it easy and evident to tell why they are homotopic without having to watch the video? Or something else that I am misunderstanding? enter image description here
In the Wikipedia entry associated with the Kahn-Kalai conjecture, there is the following assertion This conjecture concerns the general problem of estimating when phase transitions occur in systems. As this entry notes, the conjecture (technically "theorem", as is recently proved) is in the field of graph theory and statistical mechanics I am particularly interested in the consequences of this conjecture in view of statistical mechanics and (even if possible) its implications and applications to formation of complex networks in engineering fields. The main article, as far as I can see, heavily focuses on graph-theoretic facets of the conjecture. So, is there any applied exposition of this conjecture?
For example: Should the free market then only capture that which is beyond necessity? I'm not sure if "then" is accomplishing anything, or if it is even correct in this sentence. Perhaps it should be written more like Should the free market only capture that which is beyond necessity? But this sentence doesn't sound like it is referencing any contextual information. Perhaps this Then should the free market only capture that which is beyond necessity?
So some authors consider (sigma additive) signed measures on algebras (that are closed only under finite unions) instead of on sigma algebras. This happens for instance when considering the subset of finitely additive signed measures that are sigma additive. So my questions is what can I do with these a sigma additive measure on an algebra? I.e., do the usual convergence theorems hold? What kind of restrictions arise?
When firing single photons and letting and interference pattern occur. If you were to draw a straight line from one of the slits to a particular interference gap on the screen, and continued this line through the screen, when you moved the screen to different distances from the slits, would an interference gap be present along the lines trajectory at all screen distances? Or would the interference alternative between gap/no gap along the lines trajectory at different screen distances?
I'm using the FrontiersinHavard Latex class provided by the author guidelines of the Frontiers Media. Strangely enough, even though their guidelines specifically state table captions should be placed above the table, the class forces the captions under the tables. There is also little to no documentation on that document class itself. Are there any options to disable this behavior when declaring the document class, or does one need some other workaround to override the document class?
When water molecule is cooled, it is well known that it expands: That's the reason the rocks in the desert explode in the cold of the night: the rocks have water inside that expands with cold and breaks the rock. Other molecules compress when cooled. Could this effect (expansion/contraction when heated) be used to moved an electron as a POC of doing work? For example, water is a polar molecule, so it's mere expansion/contraction seems to point that it can move electrons. Given there are random temperature fluctuations everywhere, it seems possible to use these micro contractions/expansions. Does this break any known rules? If we manage to use a diode equivalent, it would move electrons in only one direction.
We consider an electron "Bob" trying to escape from a metal surface as shown (blue circles represent electrons, red circles represent ions). I know that Bob can't leave the metal surface is because the attraction due to the ions is greater than the repulsion due to the electrons below. My question is: why F(attraction, by ions near the surface) is greater than F(repulse, by electrons)? Thank you!
Suppose I have N unique objects, where N is known, but I have a subsample of only M of them in a bag, where M is unknown. I draw X from the bag with replacement (where X is known) and observe A unique objects (where A is known). If I next draw Y from the bag with replacement (where Y is known) what is the distribution for B, where B is the number of unique objects I will observe?
In one of our class discussions about the origins of the word Bank (Money), a guy guessed that maybe it comes from the Bank (the land alongside a river) since the sand gets deposited there, as an equivalent to Bank being a money depositing place. It felt right, except Bank comes from Banque, a Latin word for table, as that's how the financial transactions used to happen, over a table. Now, what I want to know is could it be that Bank and Bank are related? One coming from the other? If so, which one came first?
Is there any difference between an axiom and a postulate? I would say that while an axiom is any proposition fixed as true without premises in a theory, a postulate is (also according with its etymology postulatum = something that is requested) something that is necessary to assume to make a theory fit (also in a consequential way) with some kind of experimental measurement. Is there any convention about it?
Although inertial forces are just our mathematical creation to help apply Newton's law even in non-inertial frames, can we assume or is it (mathematical proof) that inertial forces also create its field. I think it does so, because when we say that we cannot distinguish between gravity and accelerated motion, we assume them to be same. Is it just as assumption or a correct assumption?
Im currently a math masters student. Im doing good and i obtain good grades. Im interested to pursue PHD. At a masters level course i have never been able to solve all exercises which a lecturer has given. This really bothers me and i feel like i need to solve every single exercise problem easily if i want to pursue PHD since these problems in most cases have known solution, hence how i should be able to do research in mathematics if im not able to solve these known problem? My way of thinking might be too black and white in this sense. So my question: people who have completed a phd or a fellow masters student; were you able to solve every single exercise at classes?
I know that if a wire is carrying current, the force is F= iBl sinc But what if the wire does not have current, and rather the magnetic field around it varies. Will there still be a force? If so, what will be it's magnitude. You may consider magnetic field direction as required to get a value of force if possible. Note: This is not repeated question. Other similar questions are regarding wires carrying current. Mine is for wires with no current.
Why are terrestrial planets like the Earth so much smaller in size than the gas giants? Why can't they be the larger ones? Why are there no stars made up of something solid(/rocky)?(To generate energy, it could maybe use fission in place of fusion)But anyways, Is it because that would violate some laws of physics or mathematics or is it just the way the universe formed? If it is due to the former then what fundamental laws does it break?
Is there a general book of mathematics which starts from first order logic, treats set theory (in ZF setting) in which first order logic is used, then abstract algebra (in which set theory is heavily used), topology (at least point set topology) and finally mathematical analysis (in which all the previous concepts are used). In all these parts most important results should be covered. In this way one can study mathematical analysis having solid foundations of mathematics? Am I dreaming or a book of this kind exists?
I know from calculus that Riemann Integrals are Riemann sums. We use such integrals to calculate areas under curves. But why does adding an infinite amount of small terms give a finite result for non divergent curves? I know the obvious answer would be to just look at the graph of the function and we can see there is a finite area. But I keep thinking of the Harmonic series and how adding an infinite amount of smaller and smaller terms has as a result infinity. How can we be sure the small terms if the Riemann sum also don't add up to infinity?
I have read yesterday the following statement: An initial object when it exists is the colimit of the empty diagram. A terminal object when it exists is the limit of the empty diagram. And I found some justification of the second statement here: What means an empty diagram? but still the justification is not very clear to me, I am wondering if someone can explain this to me in a simpler way please?
Using a magnifying lens with the sun as the source, one can focus the light in a single point. Is it possible to use just lenses, or any number of transparent materials of any particular shapes, to focus sunlight into a line and not just a point, and turning it into what I think is called a "focused beam of light"? Is it possible to do with just transparent materials?
In a recent chat conversation, I asked someone quite high up in my global organization but not belonging to my regional org setup - "Shall I send an email copying my supervisor", and he replied in the chat window with a "I am good". What does it mean? I wanted an opportunity to introduce my supervisor to him through email, but what should I make of his response? Is he asking me to send the email (OR) is he asking me not to send the email?
According to several dictionaries I have, "validate" is a transitive verb. But both Grammarly and ChatGPT judge the following (imperative) sentence as correct: Ensure feature quality by validating with the UI team before release. I would use: Ensure feature quality by validating it with the UI team before release. Is the sentence without it correct? If yes, is it because the verb can be intransitive or because of something else? Edit: corrected them to it.
It is well known that the electric field by a ring on a point charge can be easily calculated by integrating the each infinitesimal electric field by each infinitesimal charge. However if one were to attempt to calculate the contrary, that is, electric field exerted by a point charge on a ring, how can one integrate each infinitesimal electric field by the point charge on the ring, since unlike the former, the electric field in the latter case is not generated by an infinitesimal charge, rather by a well defined, let's consider, Q charge?
After learning about progressive waves, I struggle to understand what physically causes particles to move up and down in such a wave. What mechanism is actually transferring energy as these particles move up and down? Only longitudinal waves seem intuitive to me. Furthermore, consider water waves. Do we still consider this transverse, even though the particles move in circles rather than up and down. What causes this movement? Is it true water can only be transversal due to the attraction and interactions between water molecules?
In all the textbooks that I've seen complex numbers were presented as a given (from history - Cardano's formula etc.). Fundamental theorem of algebra, Frobenius theorem and others use complex numbers as some answer. But is there a way to deduce complex numbers constructively from some (algebraic) reasons without any knowledge about its existence? I'm looking for questions where the only best answer would be complex numbers. Something like "what is algebraic closure of the field of real numbers?", but without any a priory reference to complex numbers. Maybe someone can tell me where I can read about this?
I'm currently learning Latex and using Overleaf plus documentation. Sometimes I want to quickly see what other options a package has to offer. Since Overleaf shows a PDF preview, I would like to know if there is a way to quickly list that package's options. Basically what I'm looking for is a page like TeX_primitives_listed_by_TeX_engine that shows each primitive but with a link that explains watch each one does. Like the docs for any programming language, for example.
Imagine if you have a molecule with a large size, e.g. proteins. Anything that rotates experiences pseudoforces if my understanding is correct (e.g. coriolis, centrifugal etc). Since every molecule rotates, does this have any effect on these molecules that we could measure? Or properties that arise because of these pseudoforces? My guess would be more smeared out electron clouds, or weaker covalent bonds or something. Or a clustering of more heavy atoms in the centre point since farther from the centre would mean weaker bonds. My guess could also be that the effect is so small that it is negligble. Probably only really big molecules that spin very fast could have an effect (if any).
I hope I can ask this question here. I have downloaded Asymptote from windows-binaries and want to run an asy-program that contains the row (it has worked a long time ago) import gsl; But that seems not to be included in the distribution. The manual says something about If asymptote is compiled with... you have access to the gsl-library. Obviously the version I downloaded from the webpage is not compiled with gsl. How do I find a version that is, och how do I add it to the version I have? -anders
I'd like to achieve the following using Latex: I'm open to still-better ways of formatting such block matrices. But the above is what I'm thinking towards, right now. I'll be doing a lot of these and I'd like to beautify the stuff I've been posting before. Especially since directed graphs, column and row spaces, the left and right nullspaces, modified network analysis, and the Schur complement method can figure prominently in analysis. I'm not very familiar with using tikz packages. But I'll learn more, if needed. The following is an example of the above that I do not want to produce: It's sad-looking and I'm hoping for something significantly better, more in the direction of the first image above.
We know that inside solenoid the magnetic field are same at all point's and are parallel to each other My question is why they are parallel as my teacher explained it as solenoid is set of multiple circular loops and one face coil form North pole while other will form South pole and magnetic field lines from both poles will join in parallel I think this explanation is not correct Any response would be appreciated
A long rectangular cardboard thrown in air starts spinning automatically on its way down. Few observations in this experiment: Long rectangular cardboard pieces spin well Doesn't work well with square / circular pieces Long ellipsoid pieces seems to spins the most Also note the spin axis on the way down. Even if you give a little torque to it spin it vertically upwards, eventually on way down the spin stabilizes so the body starts spinning around the horizontal axis This doesn't work with paper / foam as they start floating. Higher density materials like iron / glass of the same size/shape also don't spin A small demonstration can be seen in this video. Can someone explain the exact physics/aerodynamics behind this?
In a system, the total energy is composed of Electronic >> Vibrational > Rotational >> Translational. As far as I understand, temperature is only related to the average kinetic energy, which includes Vibrational, Rotational, and Translational components and not electronic energy (excitement states)?? If theoretically, so much energy is added to the system that initially, the temperature increases due to these first three degrees of freedom, but then more and more electronic excited states are populated because the molecules kinetic energy provides enough that electronic excitation occurs, which, of course, takes up that kinetic energy, wouldn't this lead to brief drops in temperature with energy input?
I wonder about the Hmiltonian form fo the Potts model and would like to know about its matrix form using the generalized Pauli matrix. I believe it might be possible in a smiliar way applied to the Ising model, as you can see in the website below: How can I explicitly express the Ising Hamiltonian in matrix form? I'm not sure if it's just changing the Pauli matrix into generalized form from the Ising model.
I try to apply the replica trick in a two-dimensional gravitational model. I interesting for the case where the semiclassical geometry is an evaporating black hole. These geometries have no time-reflection symmetry. In many related articles they say that the geometries must have time-reflection symmetry, but I can't find why. It seems to me that the method can generalize to geometries with no time-reflection symmetry.
I am organizing an algorithmic lecture at my university, which is more theoretical. Regarding Landau-notation and runtime analysis, using algorithms that implement mathematical formulas is great. In my opinion, it helps the students see the connection. Of course, I also want some difficult exercises, and I am searching for mathematical functions that have a very algorithimal touch, if you know what I mean. Because it is hard to describe, here are two examples of such functions: nth prime number and nth Dedekind number. Can you provide me with similar formulas?
Force acting on person when jumping from boat is denoted by red colour and force acting on boat is denoted by yellow colour. I have not included the buoyant force and boat weight force on the boat. Coming back to my question:- The force applied by the person on the boat(F)can I Say it friction force which moves the boat in backwards direction and in reaction force acts on person feet can also be called friction force?? Or it some other kind of force like muscular force which moves the boat in backwards and person in forward??
The force repulsing two protons never goes away, meaning that there is a constant force pushing the protons apart forever. Firstly, where are these protons getting the energy to constant apply this force, and where is the nucleus getting the energy to continue to hold them together? Is it the binding energy? If so does it eventually run out of energy to hold them together?
I'm writing an academic article title, and, for matter of capitalizations, I would like to know: if "-based" is appended to a word, is "-based" treated as another word and should be written with capitalized "B", or is "-based" treated like a suffix that became one with the word, and thus is written with a non-capitalized "b"? Title example: "Computer-Based Strategies For Asking About Title Capitalization On Stack Exchange"; "Computer-based Strategies For Asking About Title Capitalization On Stack Exchange".
I need a reference for this elementary result which I assume to be true and known. Adding a citation in the paper I'm writing (even to a problem in a textbook) would be faster and more elegant than adding the proof itself (which may elude my decaying brain): Given a finite set S of real closed intervals, if each pair of intervals has an overlap (intersection) of length at least k, then the intersection of all the intervals in S has length at least k. Thanks.
Which could exhume a response like, "Lul, nice term for this type of pun subgenre." A pun is the humorous use of a word or phrase so as to emphasize or suggest its different meanings or applications, or the use of words that are alike or nearly alike in sound but different in meaning; a play on words. But I'm not sure of this type of subgenre. Edit: If it's not a pun (the jury seems out on whether it counts, I didn't think it was myself until I saw it included any play on words), an answer on what type of joke it is would then suffice.
How do we define radius in quantum mechanics. A particle has wave-particle duality, so do we define the radius as Compton wavelength or Bohr radius or some sort of superposition of both? I don't think that either of it works, because of the Heisenberg uncertainity principle, the Bohr radius would vary because the electron shell is probabilistic and requires a wave function. Also we have defined classical electron radius, but as the name says it is classical rather than quantum mechanical. I was curious about this because as I was estimating the Kugilblitz Swarzchild Radius that is required to produce a Micro Kugilblitz with LHC at it's maximum energy, I got the result but I was unable to find the particle at the same or below size Thanks!
I've been having a little bit of a debate with one of my friends about the correct use of a word. I hope the native English speakers can help me put an end to this :) I know the word "bold" is mostly used as in brave and courageous, but is it right to use it as prominent, too? This aspect of this issue seems bolder than the rest. Can it be used like this or is it meaningless?
I have seen in this link that there is a way to calculate the rolled material length and the number of turns based on: the material thickness inner diameter of the roll external diameter of the roll Is there a way to calculate the length of a material roll (in my case fabric) without knowing its thickness but with knowing its number of turns? So calculate the length by knowing: the number of roll turns inner diameter of the roll external diameter of the roll
"Norton's Dome is a thought experiment that exhibits a non-deterministic system within the bounds of Newtonian mechanics. " A ball rolled to the top can reach it in finite time with zero energy at the end, which means if you time reverse it the ball appears to star moving for no reason. By don't use just use an inverted cone with a point at the top? Whouldn't this be much simpler?
We see only stars whose light is not older than the age of universe. This is understood. If a star is too far away that currently we don't see it then possibly we will see it later, then the age of the universe will grow. What I don't understand is how a star that we see now can move away out of visible universe in future.
I have created some otf files of fonts for symbols and I'd like to write a package from them and then upload it to CTAN. But I have no experience in writing a package. So is there any reference to write a package from otf files? Please give some advice on the references which should be very basic. Specifically, with otf files of some fonts for symbols in hand, how to write a package like MnSymbol?