snippet stringlengths 143 5.54k | label int64 0 1 |
|---|---|
G is a given sphere in the space. For any line e that has no common point with G, define the line f as the conjugate of e with respect to G if f joins the points of tangency on the two planes tangent to G passing through e. Show that two lines of the space passing G are skew if and only if their conjugates with respect... | 1 |
Let's says there is a fundamental particle: That is so massive that it is a black hole by itself (Compton wavelength < Schwarzschild radius) That carries a conserved quantum number (e.g. charge of an exotic interaction) which no lighter particle carries Would it be able to emit Hawking radiation? If not, does it contra... | 1 |
I am a programmer and I am doing a camera simulation, I am stuck in a matter of how to know where arrives every ray of light after traveling through the lens and being refracted. Every point of the object gives an infinite number of rays, but in my simulation I will take five random rays to trace from every point from ... | 1 |
I'm going to start a degree course in physics next year. So far in high school I covered some physics without calculus. I know that I will start everything from the beginning at university, but I would like to prepare in some ways. Then the question is: what should I do? Should I revise what I studied? Should I go head... | 1 |
There are so many books teaching how to take derivative and integration of a function. I think I'm good enough (enough for me lol) in those parts, my problem is that I can't start solving a question and even don't know where to start (finding or making the correct function or equation, kind of calculus applications in ... | 1 |
This question is quite specific but I am not sure which verb tense I should use when committing/checking in code. If I fix a bug and checking in the code, should I write: Fixes bug on feature A Fixed bug on feature A I always use past tense because the bug was fixed before I check in but it looks a bit strange when I l... | 1 |
I'm writing a short bio of my character who has made a contract with a demon and is now required to do her bidding. He's not necessarily a slave, he still has the freedom to do whatever he likes, I guess it's kind of like a DnD warlock-patron type of relationship where she occasionally has tasks for him to do and he's ... | 0 |
Is there a standard, formal or defacto, for what exactly a TeX distribution is and what programs/features need to be supported to be a TeX distribution? I feel like this question has had to have been asked before, and while my searching turned up a number of similar questions none got at the heart of what I was after. ... | 0 |
I'm feeling kind of stumped on this, even though I think I know the answer. If I had written this sentence, I would just rephrase it to avoid the issue, but I came across it and found myself wondering. The sentence: "All that stuff like cars and planes is releasing carbon dioxide." At first glance, it seemed wrong and ... | 0 |
My question: What is Happening During Particle Collisions if Particle Location is Defined by a Wave Function? From my understanding, we can define particle location by a probabilistic wave function from Schrodinger's equation. So the particle doesn't exist in one exact spot naturally. So what actually happens then when... | 0 |
I would like to buy a book to study multivariable calculus. Currently, the texts I have in mind are: Vector Calculus, Linear Algebra, and Differential Forms A Unified Approach by Hubbard & Hubbard Multivariable Calculus with Applications by Lax & Terrell Functions of Several Real Variables by Moskowitz & Paliogiannis I... | 0 |
I always assumed that the word censorious meant someone or something that is given to censorship. Like if you say that a community, an organization, or a person is overly-censorious, that means they frequently or unnecessarily censor content. But I just looked up the word in my favorite dictionary and found that censor... | 0 |
Everything I can find says that time dilation approaches infinity at the event horizon of a black hole. Black holes evaporate over a finite amount of time. Wouldn't this imply that somebody falling into a black hole would eventually just see the event horizon shrink away from them as fast as they fall into it. This see... | 0 |
In the Wikipedia page for the Ising Model it is written without citations: One of Democritus' arguments in support of atomism was that atoms naturally explain the sharp phase boundaries observed in materials[citation needed], as when ice melts to water or water turns to steam. My question is: Is this statement historic... | 0 |
I am working on TeXmaker and all of the sudden this message popped up (this problem occured after closing and re-opening the program and the code is correct, there i no error inside of it). I tried to run the same code on TeXstudio but it gave me the same problem. I tried to search everywhere in the internet to see if ... | 0 |
I am learning about EM waves and am getting confused. Here is a picture from an intro. textbook I am using. Looking at this, it is clear that both E and B are perpendicular to the direction of motion, and all is fine. However, let's say the wave was propagating at an angle theta to the z axis. In this case, you can sti... | 0 |
Most explanations of the integer quantum Hall effect start out in the grand canonical ensemble, where the plateaus arise when the chemical potential (or equivalently the Fermi energy) is in the gaps between the Landau levels. However, they then usually continue with a statement that working at fixed chemical potential ... | 0 |
In set theory, the notions of set and membership are considered primitive. We only specify some of the properties that we think our primitive notions have using the axioms. Usually, the very first axiom of set theory is the axiom of extensionality which specifies that two sets are equal if and only if they have the sam... | 0 |
I have been searching for an automatic method (a computer program) to evaluate any first-order logic (FOL) formula given some knowledge base. The most common approach to do this is to use PROLOG. The issue with PROLOG is that it employs a subset of FOL which, for example, restricts the use of quantifiers. When searchin... | 0 |
To "empathize" with someone means to "understand and share the feelings of another" (Oxford dictionary). In science fiction, an "empath" is "a person with the paranormal ability to perceive the mental or emotional state of another individual." (Oxford dictionary) Is there a word to describe the "opposite" (behaviour in... | 0 |
The second law of thermodynamics states that the entropy of the universe increases over time and this has lead to theories like the heat death of the universe and the big rip. What this means in effect is that all matter and energy has an expiration date, beyond which it gets divided accross infinite space and this is ... | 0 |
The other day I wasn't feeling so well so I visited a doctor. He recommended that I take a break and get intravenous therapy so I did. I laid on a bed and the nurse inserted a needle into my left arm which was connected to the pack of liquid containing vitamins. I soon fell asleep. More than half an hour later I woke u... | 0 |
Many elementary explanations of the Einstein-Lorentz transformation derive it using Einstein's special relativity postulates, combined with some thought experiments considering light sources and observers. However, I have read that these thought experiments often do not hold when subject to rigorous mathematical scruti... | 0 |
I have two rectangles of different sizes side by side. I want to scale them both (each maintaining their original aspect ratio) so they each end up with the same height and together equal a specified, fixed width. I would like to find a formula that will work no matter what the sizes of the rectangles are (some may be ... | 0 |
I'm reading Carroll's GR book. I'm able to follow it for the most part, but a couple of paragraphs are a bit hard to decipher: According to the WEP, the gravitational mass of the hydrogen atom is therefore less than the sum of the masses of its constituents; the gravitational field couples to electromagnetism (which ho... | 0 |
As we know, the recent Nobel prize was awarded for the creation of attosecond light pulses. I read this excellent answer, describing both how the pulses are created and what applications they have. I understand how the pulses are created by the addition of waves with harmonic frequencies in a classical sense. However, ... | 0 |
First, let me acknowledge there are numerous posts on this question already. The most pertinent to my specific question is probably this one. To restate the problem: "A family has two children. Find the probability that both children are girls, given that at least one of the two is a girl who was born in winter." The s... | 0 |
There are various threads on this site explaining the mathematical details of how, in QFT, position operators are non-relativistic. I can follow some of the math, while some of it goes over my head. But even with the parts of the math I can follow, I have a hard time relating it to anything conceptual -- that is, all t... | 0 |
I've read several threads over the past several days talking about how photons don't have wavefunctions in the same way as massive particles do because they don't have non-relativistic limits. If I understood correctly, that's because the usual position operator introduced in introductory QM courses really only applies... | 0 |
As a caveat, i am not a mathematician but rather a programmer with an amateur interest in patterns, fractals, sequences, data science. That said, i have been following recent developments in aperiodic tiling with interest. I've had an idea for an application for it, but I don't know enough in the field of mathematics t... | 0 |
Consider a sample of an ideal gas kept in a pouch of some volume. This pouch is then kept in a bigger container of volume V. As soon as we open the pouch then the gas will expand irreversibly in the container. Also consider that this expansion is adiabatic in nature and no energy flows in or out of the container. If we... | 0 |
I would like to know if there are any books on combinatorics and number theory that follow an axiomatic approach akin to that of Sierpinski's General Topology. I have found some books for both subjects that might follow this axiomatic approach but they aren't explicit about it. The books I am referring to are: Aigner's... | 0 |
This is probably a really common word and I'm having a moment, but it occurred to me the other day that I can't think of the verb that describes the action of sweeping a knife across a pat of butter, which has the effect of scraping butter from the pat onto the knife. It's kind of the opposite of "spreading"; i.e., the... | 0 |
Suppose two particles A and B collide. Consider the position vs time plot of the trajectories of A and B, shown in green and red in the following diagram. The two trajectories "meet" at coordinates (x', t') indicating collision, although according to the Pauli exclusion principle, two particles cannot be at the same po... | 0 |
I do understand that we can't experimentally verify anything we imagine about the interior of a black hole. If we were to apply what we know about the physics of the observable universe and assume that those laws remain valid on the other side of an event horizon, then are the following assumptions at least plausible? ... | 0 |
I've encountered a few possible definitions of a "connected ring" and am having some confusion relating them. The first one is defined for any commutative ring: A commutative connected ring has a spectrum which is connected in the Zariski topology. But there is also the concept of a topological ring, where the ring its... | 0 |
I understand that the state space representation is mathematically equivalent to the transfer function representation for linear systems, and that it allows us to solve the corresponding DE by finding the eigenvalues of a matrix. However, for nonlinear systems, the transfer function can only represent a linear approxim... | 0 |
In my school, I learned that when two blocks are placed on the ground with one block above the other, if a force is applied to the lower block, two opposing forces of friction act on it: one from the ground and the other from the upper block's surface. Consequently, according to Newton's third law, the upper block expe... | 0 |
In analyzing Compton scattering we consider the conservation of both energy and momentum. However, in analyzing the photoelectric effect only the conservation of energy is taken into account. In fact, if the momentum of the photon is taken into account there seems to be a violation of the law of conservation of momentu... | 0 |
I'm not sure if this is an appropriate question for here, so fair enough if it gets closed/down-voted. I'm self-studying mathematics, did basic real analysis (Riemann, not Lebesgue integraton) and complex analysis, and I'd like to move on to functional analysis shortly. I have two books: Muscat's Functional Analysis (U... | 0 |
I was playing with numbers in my middle school math club and found a beautiful pattern. I presented my idea in front of my club mates. The teacher was impressed with my result and suggested I write a short manuscript and have it published somewhere. I thought it was a great idea so I agreed. It took over six months to ... | 0 |
I encountered several times a certain type of sentences (in colloquial contexts) which were clearly grammatically incorrect but seems to be widely spread and, as a non-native English speaker, I would have liked to have more information about that. It is about the conjugation of the modal verb to be. I have heard many t... | 0 |
Imagine an air hockey table where there is a puck P and a rectangular slab S. Both are free to move as there is zero friction. The slab is at rest in the middle of the table. The puck is moving towards the slab and collides with it in an elastic collision. The puck is not spinning before the collision. As this is a clo... | 0 |
I do not feel comfortable with such constructs that contain "one's work ...ing" as the following: "University of British Columbia marine biologist Amanda Vincent has won the prestigious Indianapolis Prize for her work protecting seahorses." "Learn more about her work protecting the rights of women and girls." No matter... | 0 |
I know that we can consider an object as point object, if its size is negligible as compared to distance traveled by it in reasonable amount of time. But in my book Ncert there is questions which asks to determine which of the following are point objects: (a) a railway carriage moving without jerks between two stations... | 0 |
If we place a conductor between the plates of a capacitor, the conductor reaches an electrostatic equilibrium with the surrounding electric field. At this equilibrium state, the charges within the conductor have redistributed such that the electric field inside the conductor is nullified. Now, what happens if we separa... | 0 |
I am working on an English-language online resource. It seems an obvious good idea to allow users to choose a version in British English or American English spelling. However, I've noticed that spell-checkers also provide options such as Canadian English, Australian English, South-African English, Jamaican English, Hon... | 0 |
Physicist Grigory Volovik has put forward some ideas about the universe undergoing a topological phase transition (especially in the early stages of the universe). He published a book called "The Universe in a Helium Droplet" where he explained his ideas. You can find a brief discussion about it here. In one discussion... | 0 |
There are examples in physics in which a simple law results from an immeasurably more complicated set of underlying interactions. Consider Hooke's law, for instance: there is a very simple equation that relates the extension of a spring to the force required to extend it further, yet the underlying physics when conside... | 0 |
Gravitational waves carry energy. The sticky bead argument shows that this energy can be extracted: https://en.wikipedia.org/wiki/Sticky_bead_argument But Lee Smolin points out that "In principle, nothing can screen out the force of gravity or stop the propagation of gravitational waves, so nothing can be perfectly iso... | 0 |
I read this from Div, Grad, Curl and All That: The second reason for introducing the electrostatic field is more basic. It turns out that all classical electromagnetic theory can be codified in terms of four equations, called Maxwell's equations, which relate fields (electric and magnetic) to each other and to the char... | 0 |
I am currently writing the conclusions of my bachelor's thesis on convergence spaces and there are a couple of points I would like to make, but lack the proper references to cite in order to do so. The first point I would like to make is that one of the starting points of General Topology was trying to axiomatize the n... | 0 |
Crossposted on MathOverflow I am an undergraduate mathematics student with a keen interest in pursuing research in the formalization of natural languages (from a more mathematical-logical approach), yet there aren't many resources that provide an overview of this very technical field. I wish to be able to provide mysel... | 0 |
It seems that there are many terms in linear algebra that have multiple names. For example, unitary and orthogonal both refer to the same general idea, a Hermitian is essentially a self-adjoint matrix, invertible and nonsingular, and there are definitely more that I can't think of off the top of my head. I've noticed t... | 0 |
I'm a current MA student doing research in formal semantics, which is an application of, among other things, logic and model theory to the study of the semantics of natural languages. I'd like to build up a stronger foundation in formal logic before tackling other topics / projects. I love the interplay between logic, ... | 0 |
I have a conceptual question about graphs which I couldn't find the answer to. I am calculating some node centralities and using them as features for a machine learning problem. I am using Networkx python library. I noticed that for the degree centrality the library does the weighting of the values by the highest possi... | 0 |
I'm currently writing my master thesis on "Differentiable Stacks". I'm really fascinated by the idea of generalizing manifolds to include also orbifolds/leaf spaces of foliations/moduli spaces... I formally understand the construction of differentiable stacks as stacks on the category of smooth manifolds possessing a r... | 0 |
According the classical physics, the electron should radiate energy and fall to the nucleus in a short period of time. However, this was not the case. Hence, Bohr proposed his theory, suggesting that electrons existed in specific orbits, where they did not radiate energy. These orbits had quantised or discrete energies... | 0 |
There was an open dump yard a few miles away from where I used to live for an internship. It was not noticeable during the daytime, but once the sun sets, the dump yard reminded us of its presence through its stinking odor. The smell came every evening and left the following day as if on a schedule, and my colleagues s... | 0 |
We know that Carleman's condition is a sufficient condition for the determinacy of Hamburger moment problem and the Stieltje's moment problem. The first one look at measures on the real line, and the second one look at measures on the positive side of the real line. There is a third problem called Hausdorff moment prob... | 0 |
I am simulating a simple Lennard-Jones fluid confined between two fixed walls and I am analyzing the autocorrelation function of the velocity along the direction of the confinement (normal to the walls). I observe an exponential like decay which is in line with the rough expectation, but in addition I observe periodic ... | 0 |
"Weed" (the annoying plant you don't want in your garden) and "weed" (the psychoactive drug) are treated differently grammatically. Just some example sentences "There are weeds in my garden" vs "There is weed in my garden" "There is a weed growing in this pot" vs "There is weed growing in this pot" "How many weeds are ... | 0 |
I just thought of this question, and a quick wiki search did not turn up anything. So, here is the question: Rel is the category whose objects are sets, and whose morphisms are binary relations. Is there a way to differentiate between morphisms that are functions and morphisms that aren't using purely category theoreti... | 0 |
I'm currently working on a variant of a non-convex low-rank matrix completion algorithm, whereby we take a uniform sample of entries in a (symmetric) matrix and look to complete said matrix. For various reasons, we're interested in trying to reduce the bandwidth of our matrix initialization for our algorithm, and our f... | 0 |
In some linguistics papers that I have been reading, it has been argued that a false sentence has the same semantic status as a noun phrase that fails to refer. A classic example of an English noun phrase that fails to refer would be the present King of France, if uttered today. This is because, of course, France has n... | 0 |
It's commonly stated in the literature that the free distance of a convolutional code is the minimum Hamming distance between the all-zero path and any other (non-all-zero) path in the trellis originating in the zero state and ending in the zero state. (The free distance of a code is defined as the minimum Hamming dist... | 0 |
I have a setup consisting of two lidar sensors with a known extrinsic calibration. Both lidars have messages with the same timestamps (no timedelay between them). My goal is to estimate odometry using the data from these lidars. To achieve this, I have performed a scan-matching algorithm (ICP) and obtained transformati... | 0 |
I'd like track my LaTeX projects using git, especially when collaborating with other authors. I'd also like to track my texmf directory in a separate git repository. My desire is to add my texmf repository as a git submodule to each LaTeX project. However, I can't figure out how to tell latexmk (really, pdflatex) to se... | 0 |
I have a relatively strong background in the theory of numerical analysis of partial differential equations (PDEs) and functional analysis, particularly applied to the numerical analysis of PDEs using the finite element method. I'm also very interested in graph theory. I was wondering if there are any theories or resea... | 0 |
In Borevich & Shafarevich's Number Theory, the authors define integral equivalence of quadratic forms as follows: Two forms of the same degree with rational coefficients are called integrally equivalent if each can be obtained from the other by a linear change of variables with rational integer coefficients. They furth... | 0 |
Here is the sentence in dispute: In humans, the femoral angle shows no correlation with femoral length. The question: why would 'femoral angle' receive a definite article, but not 'femoral length'? I feel like it does, but my co-author says no. I can't really justify it, but I feel like 'angle' somehow needs the articl... | 0 |
In Reed-Solomon codes, the symbols of a code word contains multiple bits. Since the error correction and detection happens at the symbol level, it doesn't matter how many errors there are within the same symbol, it only counts as a single symbol error. Because of this, Reed Solomon codes are considered to be a great ca... | 0 |
I'm a graduate aerospace engineering who's really interested in the topic of numerical methods and in particular for structure preserving schemes. Hopefully at September I will start a phd in this subject, as a consequence of my work of thesis. However, I do feel my mathematical background is kinda poor, coming from an... | 0 |
I was going through the derivation of a mathematical equation for the upthrust exerted on a body which is given in my book. It says that the downward pressure exerted on the upper surface is less than the upward pressure on the lower surface. Thus, there is a net pressure acting in the upward direction and therefore, a... | 0 |
While I was reading the book "In Search of Schrodinger's Cat" I found an interesting excerpt on how Max Planck used Boltzmann's statistical equations to solve the Blackbody radiation problem. The book mentions that there will be very few electric oscillators at very high energy end and at the lower end, electric oscill... | 0 |
I was reading a Mathematics books and it gave the axiomatic definition of a function as being a mapping from a set called "The domaine of the function" to another set called "The codomaine of the function", and at first I thought the codomaine is the image of the domaine by the function (i.e. the set that contains and ... | 0 |
I have a hard time understanding GR. I understand a lot (from a math point) about (pseudo)Riemannian manifolds, and I also learned about Einstein's elevator thought experiment. So let me elaborate: From a physics point of view, you can take the elevator and derive that light has to bend, also that there has to be gravi... | 0 |
I'm trying to create a transition effect in a situation when a character suddenly finds himself falling, and his last word, which ends in '-y', is transitioning into an unintelligible scream. However, English is not my native language, and when I've tried to write it as 'Maryeeee!!' it was criticized as awkward and wei... | 0 |
I'm working on a problem where I need to convert an undirected and unweighted graph with cycles into a tree while preserving the edge information (all the edges from the graph are preserved in the resulting tree). For the resulting tree, the height and nodes duplication should be minimized. Nodes duplication can happen... | 0 |
I am beginning to learn chemistry/physics, and I have recently read about JJ Thompson's experiment which led to the discovery of the electron. In every source that I've read, the writers note that Thompson used an anode and a cathode to conduct electricity. In addition, the magnet supposedly had N/S ends. I did not kno... | 0 |
My understanding of a simple k-vector is that it is the wedge product of k vectors. Also, two simple k-vectors are the same, when their magnitude, attitude and orientation match. Now my question is, could I just define a simple k-vector in this way? Meaning "a simple k-vector is an equivalence class of ordered k-tuple ... | 0 |
So I am writing a program that works with regular polygons, and in part of that I need to represent circles that are inscribed and/or circumscribed upon the polygon. As this is programming, I need to refer to the relationship between the polygon and these circles. I have searched all around, but all of the places I hav... | 0 |
I can imagine a relatively simple experimental setup whose resulting data could easily be compared with theoretical predictions: Send two identical atomic clocks into orbit and settle them at rest relative to each other. Then synchronize them. Then use thrusters attached to one clock to oscillate it, causing it to expe... | 0 |
As I understand, for elevation mapping using InSAR, one typically requires an out-of-plane baseline to create the required phase difference between images to detect objects at height. This usually requires either multiple satellites flying in formation or waiting for a repeat pass of a single satellite. This paper, A N... | 0 |
I would like to ask your opinion on the point that looks simple. Consider the group of orthogonal matrices of order n over the field R of reals, equipped with the topology induced by the Euclidean norm of matrices. Let g be one of such matrix and denote by X the topological closure of the cyclic group generated by g. M... | 0 |
Perhaps another way to put it is, what exactly does it mean to quantize the EM field and why is it necessary? What mathematical properties does the quantized version of the field have that the classical version doesn't and vice versa? For context, I was reading a thread about where specifically classical E&M fails and ... | 0 |
I am new in Linear Algebra and I have encountered the concept of Solutions of linear equations. According to the textbook I use, a solution of a linear equation is a vector whose components satisfy the equation. However, I am puzzled by the choice of "vectors" specifically. Why is it not defined as a point whose coordi... | 0 |
I have been reading the Loop Antenna section of Antenna Theory by Constantine Balanis and trying to understand how exactly a ferrite core improves the performance of a small loop antenna. Balanis writes, The radiation resistance, and in turn the antenna efficiency, can be raised by increasing the circumference of the l... | 0 |
I've been really stumped on this particular concept. In Case A, when a bar magnet is brought towards a copper coil around a soft iron core, in accordance with Faraday's Law of Electromagnetic Induction, the the pole facing the magnet acquires a North Polarity while the opposing pole acquires a South Polarity. Now by Le... | 0 |
Is it correct to say that, in English, when you use the Present Simple tense in the Interrogative Negative form you are either implying the negative or just confirming the affirmative (depending on the order of "Do", "subject" and "not"), but no other possibility? Like in the scene of The Lord Of the Ring - The Return ... | 0 |
Have studied traditional point-set topology, but find there's a fairly large gap between the preparation typical point-set courses give you, and the level assumed in algebraic topology texts. Looking for a good introductory book on topology that uses more categorical / modern language - something that would segue smoot... | 0 |
I'm studying nonlinear control systems, especially the Pontryagin's minimum principle and its applications. Throughout my studies, the authors have always defined the control systems with state variables and output variables. However, in this article Optimal Control of an SIR Model with Delay in State and Control Varia... | 0 |
This might be a stupid question, but, why is it that gamma rays are able to penetrate almost any barrier without question? We know that gamma rays are simply high frequency waves with massive amounts of energy. However, what processes can enable it to go through layers of bonded atoms of metals and just about anything ... | 0 |
I am studying interacting QFT in the context of quantum fields in curved backgrounds, and I am getting some confussion about the concept of particles. To study some gravitational phenomena involving particles (e.g. Unruh effect, Hawking radiation, etc.), it is typically sufficient to deal with free fields, which are ex... | 0 |
I'm working on a set of beamer class slides in TeXstudio. Usually upon compile, the preview slide visible on the right will be at the position of the cursor - instead, for me, it consistently jumps two slides behind. This is reflected in the behaviour of the preview when I enable the "scrolling follows cursor" option -... | 0 |
I noticed that in several 'throwing' sports like the javelin throw and the shot put there have been a few cases where competitors tried to introduce a technique where they throw the projectile further by rotating their entire body (these techniques were then banned for safety reasons). As an example, there is the cartw... | 0 |
I am wondering if the esteemed members of this forum can help me with these questions, which have bothered me for a long time and are what have brought me to this forum. One thing I struggle to understand and work with is the use of the "editorial we." I am a copyeditor and proofreader, and I have a client who consiste... | 0 |
In a textbook for thermodynamics, it considers a situation where work is done to a system by an irreversible work source through a thermally insulating piston, and it states "any irreversible work source can be simulated by a reversible work source". It briefly explains the reason; what the work source does is simply t... | 0 |
As per my understanding: Multiple fermions cannot have the same quantum state (as per Pauli exclusion principle) Multiple fermions can occupy the same physical space as long as they have different quantum states (or numbers or properties such as spin) If both these statements are true then, part of the second statement... | 0 |
According to wikipedia, the aurora borealis is primarily caused by charged particles from the solar wind being redirected to the poles by earth's magnetic field and slamming into the nitrogen and oxygen atoms in the upper atmosphere. This slamming gives the electrons in those oxygen and nitrogen atoms enough energy to ... | 0 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.