darklight03/StackMIAsub huggingface dataset:
I'm a beginner in the subject & my question can be meaningless, so I'm sorry from start if that's the case. I just don't understand why all of the image f(L) can be a sublattice of L' when f is a homomorphism from L to L'. I learned that all subsets of a lattice don't have to be a sublattice at all. If I don't understand wrong, it's not about the elements of the lattices actually but about the operator differences between them. So why there is not a possibility of a non-inherited operator of f(L), or a non-sublattice lattice of the L' as f(L)?
Like the multiple pronunciations of "ough" or different spellings for the same sounds in English I've read come from mixing different dialects into one language. Whereas with French, they imposed on centralized set of rules. Or in Spanish, there are multiple languages/dialects in Spain (though I think at least Franco did try to impose Castellano for all). And other countries have their own histories of language homo/heterogeneity routes taken. What made English turn out the way it did, as opposed to others? In other words, did England ever try to impose one set of rules on how to say written letter combinations (e.g. 'ough'), like other languages have done, one way or another?
Suppose a square table. You are shooting from a corner. A ball ends its path upon landing in a corner. At what angles can you shoot a ball from your corner such that the ball will never come back to your corner? Edit: seemingly my question would be how can you prove that if the trajectory is periodic, how can you prove that it will encounter another "corner" point before it returns to itself?
I have a matrix, if I apply inverse function from existing softwares, I get an inverse matrix for every non singular matrix. I would like to know if there is a measure that tells that how close the approximation to check weather to consider the inverse matrix not. In my application, there is a possibility to discard an inverse matrix that's not well approximated. I am looking for few hints, keywords to look for or an advice in calculating the measure. I really appreciate any kind of help.
I know that particles don't go from one end to the other, they just vibrate and transfer sound energy to next particle. How do they return to equilibrium again? Do they return just after collision with next particle in the medium or do they return as a consequence of reflecting off objects like a slinky? And if they return after reaching objects and reflecting back, is that how we hear our own sound. What will happen if you levitate in the atmosphere arbitrarily at one place (assumption), will you be able to hear your sound provided there are no objects around?
Is it important to understand the concept of a universal 'now', to explain that time is a local phenomenon, and the rate of time varies throughout the universe, always dependent on the local distribution of mass, and within passing particles dependent on their relative velocity? I currently think that there is a universal now, but each point in space 'thinks' that it is a different age. I understand that photons don't age (relative to us) because of their relative speed, and they see their entire path since they were formed, (perhaps in a primordial star) as all squished into a single instant, including my retina as I see it.
Couldn't we just assume that waves have mass and momentum and can become localized? Dirac Deltas can be given a rigorous mathematical foundation but physicist do not use the Gelfand triple. Why not just assume that electrons, photons, etc., have the same dimension as space? I know string theory does this but are there reformulations of QFT that use this idea that together with the insight that renormalization has a connection with scale invariance gets rid of all the problems that plague QFT? It just seems to me that the concept of a particle is a very unphysical idea.
This is the answer. My question is why the integral of E is not zero if there is positive charge on the inner surface when the field lines end on the shell. And why the integral of E is zero when all charges is negative on the inner surface, the field lines also ends on the shell. What is the difference between these two situations?
Molecules in solids get polarized and the resulting dipoles align with the external bias field. Can this be done with lightweight spheres that are oppositely charge on their surfaces? Like surfaces that are contact electrified. If a powder made of such oppositely charged fused spheres is placed in a bias field, will each individual particle (two oppositely charged fused spheres) align themselves? If clumping becomes an issue, I guess we could vibrate them lightly while in the bias field.
How do they calculate the line of sight of a galaxy or binary star system from an observer's point of view. the velocity of a star in a binary star system depends on the line of sight so how do they measure that crucial parameter with precise values? but in case of unresolvable binary star system like spectrometric and astrometric binaries how do they take the (sin i) parameter
I know this may sound very weird, but I'm curious on what makes the water be like water? Like why, when we get into a pool, we are like in a "lower gravity" pull? All our movements are slowed down in water in comparison to air? I very much know it is a strange question, but I've really never thought of it this way, I've always assumed water is like that, but never actually started to think why we move like that underwater. I'm guessing, it has to do with the properties of the water, but if someone can shed some more light on this, I'd appreciate it?
Apparently, the special relativity theory is based on analyzing the motion of a point particle with relative speed near the speed of light. However, if I apply and combine this theory with a collection of particles with Newton's third law acting, is it correct to analyze the mass as a whole, whose dynamics equation is still modeled by F(net)=dmv/dt, where F(net) is the sum of all forces experienced by sub-particles within the system, and that m is modeled by Is this correct? If so, please provide reasonable reasons.
Suppose a bunch of micron sized particles are charged positively on one half of their surface, and negative on the other. If they are arranged randomly, I understand they will have high entropy, as the system is in disorder. If under the influence of an electric field, we shake these particles such that they align themselves (they will, right?), the dipoles are now in the state of least energy and the system is more ordered, so I understand the entropy must have decreased? Yes, not the total entropy, just the particles themselves. Is my understanding correct, and if yes, will this bring a decrease in temperature of the particles? Before: After applying electric field and shaking:
The white line is a flexible conducting foil suspended on the metal wire. I think the external DC circuit will induce a charge on the flexible part and the other charges move to ground. The charged flexible part will incline towards the oppositely charged electrode from the AC circuit and once the voltage reaches peak, the air breaks down and the charge is transferred. When the current switches, the flexible part moves towards the other electrode and a spark transfers the charge in the same direction as before. Am I hideously mistaken?
In Arabic, this idiom is used to refer to the fact that when your survival, basic, or primitive needs are not met, you can't think of arts, music, your ambitions, or luxury. e.g. A: "Why is he not planning with us for the vacation? It will be a once in a life time tour around the world!" - "He has a trial next month and could lose half of his savings to his wife, a hungry man can't enjoy the sunset" In the example, the primitive need for the feeling of safety blocks the way of planning for luxarious vacation.
I am doing competetive programming task called "Ptaszki" Its easy dfs with some observations. But i came across the following problem: I have two sequances of size n and m respectively and i want to count the number of ways to insert x different elements into this sequances You can choose for every element to which sequance it will go. You can also insert every element to the start or the end of the sequance. I dont have any idea how to solve it. Could you please help me?
I see some textbooks showing how Hubbard model with Mean field approximation can explain ferromagnetism of band electrons(stoner theory), but intuitively I can't understand why an on-site Hubbard repulsion term (rather than say Heisenberg term which correlate neighboring sites) can lead to a long-range ferromagnetic correlation. Although hubbard U seems to prefer non-zero spin at a certain site, whether one site's spin is up or down will not have any influence on another site's spin direction, so by what means are different sites correlated?
Now (hypothesis) -- And the Physics of Time In this page the author talks about (find in page) (in the context of LIGO Observatories-->) "In their most powerful event, reported just this past February, the combination of two massive black holes should, according to general relativity theory, have resulted in a massive amount of new space in the vicinity of the final star" Please explain my question. I don't get this!!!
I came across this sentence: But I craved it so hard at the time, didn't I just? The author appears to be a native speaker. The part that confuses me is the "just" at the end of the question. Is it meant to lessen the guilt of "craving it"? If so, can question tags be ended with other words than "just" to slightly alter the meaning of the question?
Dark matter is believed to be a substance of unknown origin with mass that is distributed in space. Can the same observed effects be explained by an intrinsic curvature of regions of space without presence of any mass energy in them? Say during big ban the space got randomly curved such that there are areas with curvature that is just the property of space, like valleys and hills in a landscape. If so, it might be that there are no dark matter particles or any baryonic matter to explain visible effects.
What is the correct way to describe people inheriting a castle? (American and British English) Castle heirs or Heirs of the castle or Heirs to the castle It's just a phrase I've heard, but I've seen it written in various ways and I want to know which is the correct way. "heirs to the kingdom, heirs to the castle, heirs to blah blah". Sometimes they put, example, "heirs of the crown" or "crown heirs".
I have three doubts regarding the magnetic field due to the charge:- Is a magnetic field generated when a charged particle moves with constant velocity or it only generated when the charge particle is accelerated or both? Why and how does movement of charge result in the creation of a magnetic field around the particle? We also know that motion is relative so if we observe in frame of moving charged particle then its magnetic field should not be there, then what we do in this case? Note (related to third question): as we use pseudo force in non-inertial frame then what do we use in this case?
I was studying various cryptographic encryption schemes and why modular arithmetic is being used so much while encrypting messages. Why don't we use simple multiplication with a large known prime with the message, as factorizing large numbers takes exponential time complexity, so it would be hard for an intruder to decrypt the message? So, simply using an encryption scheme that multiplies a large prime on the message to be encrypted is also hard to decrypt for an intruder without knowledge of the prime number multiplied. Why was there a need felt for modular arithmetic-based encryption schemes? wanted just a motivation why we should study modular arithmetic...
Can modular exponentiation be used to shuffle a list? I have noticed that modular exponentiation sometimes repeats every number only once, and therefore works like a shuffle mechanism for a list. I do not exactly know within what constraints it does this. I am interested in modular exponentiation for shuffling lists to reduce the computation needed to know the new position of any given object (that each object can know its new position, without knowing the position of every other object or the list as a whole).
A transgender colleague requires being referred to as "they" and not "he /she" In what number do I use verbs with this pronoun when it refers to a single person: they is/ are(?) a transgender ? Anther example: When a person is elected the chair of the committee, they give(s?) an inaugural speech. I know I could say "he or she" gives, but this sounds to me too formal or too long. With a transgender, this option does not work; So, back to the transgender example: Do(es ?) they require being referred to as "they" ?
Here contains a template for a thesis. In style_sheets there's a template.tex file. The template works by editing that file and compiling. When one does so there is an appendix A and appendix B at the end of the pdf. I have used this write my thesis, but still am not able to remove appendix A and B. Erasing the appendix code in template.tex makes it where the file won't compile. How can I remove the appendix chapters?
The above is one of the four two-dimensional lattice systems. See this article for some info. The parallelogram is the primitive unit cell, because it can be translated in order to recreate the entire lattice. So, what is the hexagon then? The conventional unit cell, whatever that means? Is it shown because the symmetry operations that can be performed spans a greater part of the lattice than that which is provided by the primitive unit cell?
In very long wires, such as hundreds of kilometers, when we flip a switch and turn on the electricity, does the magnetic field (that iron filings organize around) start to form in one direction and then move through the conductor to the other end? Such that iron filings around the whole wire, would start to react to the magnetic field at different times, with delay the further from the start we get? If yes, does the magnetic field forming propagate in the opposite direction to conventional current, the direction that the electrons travel in?
Assuming that light travels as photons that can interfere with themselves while also only being detected as specific localized points, the results of the Elitzur-Vaidman quantum bomb tester experiment demonstrate that the interference of a photon can be affected without the photon itself being absorbed/affected by the object which affects the photon's interference. Does this mean that events that could have happened but did not ("counterfactual"), e.g. the photon being absorbed by the "bomb", are what determine what actually is observed, e.g. the photon being detected at Ddark? If so, how can this occur -- is the explanation for this, for now, strictly dependent on interpretation?
In the above question , there will be induction of charge on inner sphere , hence on its surface there must be non zero value of electric potential . But in the solution , the electric potential on the surface of inner sphere has been taken as zero. Inner sphere is connected to earth does it mean that electric potential on its surface is zero despite of charge on the sphere ? Does it mean that any conductor even if it has charge is connected to earth will have zero electric potential? I can't digest this , pls provide some useful insights
Suppose event H is a subset of G, where everything in the event H is contained in G but not vise-versa, the probability that H occurs is r and the probability G occurs is s, what's the probability that either G or H will occur, but not both occurring? The probability that G will occur but H will not occur is (s-r). The probability that H will occur while G not occurring is zero.
I am curious to know if the relatively newly developed melanin-based semiconductor materials made with polydopachrome have been able to create films or crystals which visually reflect blue, purple or green hues (translated in to nm). If so, was the form of synthesized polydopachrome utilized in creating those outcomes more resembling that found in in the plant/fungi or more represententative of those found in the animal/insect kingdoms? If blues, greens and purple light reflecting melanin based semiconductors exist, are the structures associated with concentrated or unusual copper bonds? Zinc? Manganese?
Considering the probabilistic relationship between the momentum and position of an electron, are the pictures that show the interaction between electrons and positrons an accurate description of particle motion? We often see visuals that represent the probabilistic nature of particles as probability clouds. How can this converge to well-defined paths? (I never studied this subject, this is just knowledge from general physics books and videos.)
By this I mean say you had and entire galaxy to work with, and you could measure the exact wavelengths of the waves you send out and record it. You would shoot this light beam across the galaxy and measure the exact wavelength of the light you are transmitting, and receiving. Could you compare the difference in the wavelengths between the same light and calculate the one way speed of light from it?
Since value of electric field decreases as we go from surface to the centre for a solid insulating uniformly charged sphere then why does the potential increases as we go from surface to the centre?According to me we will need to do less work against weak electric field therefore the potential will be less as we go inside the sphere from the surface since electric field is decreasing as we go from the surface to the centre.
i think the title speaks for itself, since the defining trait for NP class is that - they are the set of decision problems verifiable in polynomial time by a deterministic Turing machine. thus it shouldn't matter if the algorithm computing the function belongs to any particular class - exp or factorial, even non-PR , as long as they are computable, but i am unable to find any specific example. if there aren't any known such algorithms or problems, can it be proven that they atleast should exist ?
Just as underwhelm/overwhelm exist without any usage of 'whelmed' (generally speaking) I'm wondering if there's any adverb ending in -ly without an adjectival counterpart (or that has dropped out of usage). For example where 'he walked XYZly' is recognisable, correct, or common for this or some other time period; whilst 'his walk was XYZ' is not. NB: I've found no other answers for this question elsewhere, and search engines usually lead to explanations of 'flat adverbs' not ending in -ly which is not what I'm asking.
I can't make out clearly what could be defined as a "topic element". In "A Communicative Grammar of English", Geoffrey Leech has written: Fronting is often accompanied by inversion; that is, not only the topic element, but the verb phrase, or part of it, is moved before the subject. Accompanied by this diagram: Now, "x" in the above diagram is stated to be "the topic element". However, from what I've learned, the topic is usually either "given info" or used to link statements. Moreover, they are usually subjects. Yet here "down" and "never" are considered to be "the topic element"? I'm truly desperate for an answer here.
Reflective is obvious, but what about the other properties? It's weird when we check the symmetric property of the identity relation. The symmetric property happens when (in a matrix representation) the upper triangle and the lower triangle that exists in a matrix that's divided by the matrix's diagonal get mirrored. Also, you can make a graph representation of the relation and see that it's just loops. So is it symmetric or not? (also, check out if it's antisymmetric or not because I think the matrix representation shows that it's antisymmetric)
"Underpinned by left-wing perspective,the defence gains in significance,based as it is on the development of critical art of inheritance,of combing past and present and establishing links to shape a better world." In this sentence how the word "based" is used as i have read based on but here is nothing such.please reply correct should have been "Underpinned by a progressive left-wing perspective, the defense gains in significance, as it is based on the development of critical art of inheritance, combing past and present and establishing links to shape a better world.". so how it is used?
How rare or how common are the analytic (differentiable infinitly many times) functions in real applied math? Is it like a "this almost never happens" or is it "most of the time you can approximate a physics experiment with analitic functions (and if you failed, you are bad at math)"? I ask because there are so many nice properties of analytic functions in complex analysis. But are they relevant? Seems like "differentiable forever" is too strong of a limitation.
So - I know that when we observe galaxies, we are observing their past. And that if the same past-them were to be looking at us, they would see our past. But when we look at their past - that is a moment in time that would, to them, be the present. So, what I cannot find an answer to (possibly because I don't know how best to search for it) is: does it then make sense to say that it is possible that a galaxy that is future to us, could be observing our present - but as past to them? (if that is so then that opens up a whole can of worms that all time is occurring at all times, yes?)
Hypothetically speaking if you had a satellite going near the speed of light in a straight line towards an exoplanet light years away and that satellite had a telescope pointed at the surface of an exoplanet. What could a year long journey look like, while traveling near the speed of light, through the lens of that telescope that what light years away pointed directly at the surface of the exoplanet? would the telescope capture the planet in fast forward as the light information would be entering the telescope faster? Would it be slower as time dilates for exoplanet because it not moving the sleed of light?
I have to prove that if the dimension of vector spaces V and W is the same then T: V->W is injective if it is surjective. My idea is as such: know that all elements in W have corresponding element in V (surjective) Know that all elements in V correspond to some element in W (map) I want to use that I know that V and W must be over the same field (by homogeneity) and generalize that since the dimension is the same then the number of elements must be the same, thus proving injection. Is this valid?
one day I kept my phone in my pant pocket, I haven't opened it for a long time. My phone is covered with a plastic case. So why the phone is getting wet when I observed it after some time even though plastics are non conductive towards heat. When I kept my phone in pant pocket without the case then no wet has been observed by me on the phone Whether it is due to heat of the phone or the sweat of mine due to the heat released by the phone or the heat is mainly due to heat from the screen of the phone (as some background apps were running at the time) which is open and it is not close by any non-conductive material
The normal force may be unevenly distributed on the surface of contact between two bodies. I had a discussion with my friend but was unable to prove whether this assertion is true or false under two RIGID bodies. I know it is a unreal question. Therefore, I am seeking a mathematical solution to this question. (If this question is independent from classical mechanics, how to prove?)
In India, most educated People say that " my exams have been preponed" As an English teacher I know that Americans say moved up and Britishers say that advanced in the context. One of the best English professors I know in India says that prepone is the right word in the context.Even some native speakers said that the word prepone could be accepted. I would like to know the opinion of the experts in the group.