darklight03/StackMIAsub huggingface dataset:
I am learning the theory of large deviations. In so many results in the theory and from the very beginning in each book about this subject one starts by introducing a family of probability measures satisfying some properties and defined on some (Polish) space. I do not understand why one needs in some important context and any context of the theory of large deviations to introduce a sequence or family of probability measures. Can somebody explain and provide some example of why one needs many, i.e. a sequence, measures ? Many thanks.
In the ideal quantum information version of metrology, a maximally entangled state is viewed as the best resource for quantum metrology. The optimal phase uncertainty of the NOON state reaches to the Heisenberg limit. Later we have seen that for same average particle number, an entangled coherent state (ECS) outperforms the phase enhancement achieved by NOON states for small number of photons. Can we say that ECS violates the standard Heisenberg limit? If Heisenberg limit is standard then hoe coherent states give better phase measurement?
I can get a bit overwhelmed trying to find which frac or h symbol corresponds to the output of a complex expression. An easy way is to copy paste into lyx and edit there as you can edit the output directly by clicking on the right symbol but that can cause context switches and might lead to using the mouse which might break the flow and slow down the writing process.
Imagine that a person is walking with a constant velocity along the horizontal plane and turns the fan on the filing into a circular motion. Then, after sometime the fan will achieve a constant velocity, Then derive a relation to know the relative velocity of the fan with respect to that person! Say the radius of the fan is r, the acceleration is a, and the constant velocity achieved by the fan is v in time t.
I know partial derivatives should be used to solve this, but I'm wondering is there any to find the plane using the vector method of getting the Normal vector and a point on the plane. In this case, we already have a point, we just need to somehow find the Normal vector. Also, is there any connection between Normal vectors and partial derivatives in this case of finding equations for tangent planes?
In the communication network given below, link failures are independent, and each link has a probability of failure p. (consider the physical situation). A can communicate with B as long as they are connected by at least one path which contains only in-service links. Given that exactly five links have failed, determine the probability that A can still communicate with B. Given that exactly five links have failed, determine the probability that either g or h (but not both) is still operating properly. Given that a, d, and h have failed (and no other information), determine the probability that A can communicate with B.
Title says it all really. As is commonly known, the trace of the density matrix must be one and the trace over the density matrix times an operator is the expectation value of that operator. If you instead add up ALL the entries of the matrix (perhaps times some function related to the row/column indices) does this represent something OR does it equal some numerical value? Does it have some numerical relationship to the trace (strictly greater, or smaller, etc.?)
I would like to know the structure of the sentence and also meaning. Is the vision subject? What in the sentence is what? The vision to do today what is needed for tomorrow. Can I understand.. like this? the vision we do today is what we need for tomorrow. The sentence was part of a speech as follow. Reject pessimism and fatalism. Refuse limits on our spirations. To do that, we need to have the imagination and confidence to do things differently and better. The vision to do today what is needed for tomorrow.
Correct me if i am wrong but all circuits must follow the law of conservation of energy. And the energy is supplied by the action of source to create a potential difference by moving charges against electric field In a battery the energy of chemical reactions that create potential difference is equal to the energy used so the spin of an electric generator must have enough energy to equal it's usage in multiple homes. So all of heat energy that get's used in multiple homes and rotating fans they all get singled out by a spinning conductor in a magnetic field? Ik this might be stupid but to me it seems sorta impossible
Since the only thing a computer can do is modify its machine state, and you can always change from one state into another state (there exists such a program) and so each program is invertible; and if all the programs are deterministic, then associativity also makes sense. Two programs are considered equivalent iff they do the same thing to the machine's state, given any starting state. So do I have the title right or not?
I found one passage that I really cannot understand the grammar structure. The below is the problematic sentence. The crates feature voids, allowing large volumes of water sufficient surface area to seep back into the ground. - Source I think this sentence should be; The crates feature voids with sufficient surface are, allowing large volumes of water to seep back into the ground. I want ask why you can bring the words "sufficient surface area" suddenly between "water" and "to". Could someone explain this grammar structure ?
I was going through the energy/mass equation and it is said that both of the said quantities are interconvertible. That made me think that if we try putting actual values into the equation, the interconversion is actually very large; speed of light itself is a large constant, and the product of its square and mass of a said object would be large. Putting our energy consumption into consideration then, why do we have energy problems in the world? Relative to our world's energy consumption, we should have infinite amount of energy for the world. Why is it that we still struggle with energy problems all over the world?
A high voltage wire can either have an large excess of electrons (net negative charge density), or a large defect of electrons (net positive charge density). The voltage difference between the wire and the human can be positive or negative. Are both cases equally dangerous? Is there a difference between electric shock from a positive wire and from a negative wire? (In one case electrons will rush into my body, in the other electrons will rush out of my body)
Suppose I have an equipotential surface S. Thus the electric field at each point on said surface is direction normal to the surface. Will the magnitude of this electric field be constant for all points on this surface? (This reasoning comes from the feeling that if the electric field strength were to differ, a closed loop path along such field lines may have work done by electric force as non zero) I may be wrong, so this is just a small thought. Thank you.
Was is generally accepted as singular - 'a dog was in the garden', were, plural - 'some dogs were in the garden. So why is 'You was in the garden' so wrong, (you were in the garden) but have to be 'you were in the garden, singular and plural? It seems to be restricted to only the noun 'you', which could be singular or plural - and in a lot of cases, that fact remains hidden.
In Quantum Mechanics conservation laws are fundamental, I was thinking about spin altering models of interaction such as the Ising Model and realized that it isn't at all clear how angular momentum conservation occurs in such a situation. If there is spin flipping occurring where does the contrary compensating angular momentum go as to have global angular momentum conservation? The interaction fields absorb this angular momentum?
During JJ thomson experiment and similiar other experiments,they found that cathode rays were deflecting from its direction under magnetic fields and electric field,also the gold leaf attached to co-axial cylinders led to conclusion that the cathode rays are negatively charged,but later,By Putting a paddle wheel or fan in path of cathode,the wheel turned and moved,the fan also moved,This led them to conclusion that they must have mass,but is this the only criteria required for an unknown object to have mass,that they can perform mechanical work?The scientists at that time concluded that they have mass,and then went on to calcultate charge to mass ratio of it,assuming rays has mass?Can't any other particle now known do work as well as have no mass?
Are there any experiments done to verify the absence of forces caused by complex structural organisations in systems? Afaik, experiments in QM and Standard model QFT talk about the validity of the interactions in individual particles that are not in any complex sturctures. Experiments in Condensed matter physics involve configurations with some structure. In these cases, there is no requirement of downward causation. Are there any experiments in more complex organizations which rule out downward causation? Is it even practically possible at our current experimental strength?
When the size of the observable universe was small as a proton what was the physical content of it? Was there a limit of particles in such a tiny volume with enormous high density and energy? Can we find more than one proton inside such a volume, can we assume that because an electron, a quark, or a photon are point particles there was no maximum limit for the number of say electrons instide a volume the size of a proton?
For example does a virtual electron have the same characteristic intrinsic values like mass, charge, magnetic moment etc. as a normal stable electron? Or can these range wildly and not having specific values for the case of the virtual particles and if yes don't you think that the term for example "virtual electron" is kinda of misleading? How can for example a virtual particle ten times the mass of its normal stable counterpart be the same particle? Wouldn't it be a less specific but nevertheless more correct description of these particles be the term virtual fermions in general or virtual bosons or virtual pairs without labeling them with a specific normal particle's name of the Standard Model of particles?
While calculating electric flux through an uncharged ring kept near a charge, we tend to draw a spherical Gaussian surface that covers the ring by edges but while using the gauss law, we tend to take the entire circular region of ring as area bounded by it(just like we do for circular disk). However, the ring has electric field passing through it only in the ridges.So why are we taking the entire circular region in case of ring where in the middle there is actually no area?
I decided to use the Maple software to help me solve dynamic optimization problems, and I found this final solution for T. (example in the picture). example What does the LambertW mean for the solution T? Can I get rid of this expression to express T in simple terms? Does theLambertW (including the expression inside it) have a solution or an equivalent expression? If this is the final form, I assume I can no longer proceed with symbolic/analytical solution, and I must move to computation?
i just started my study in organic semiconductor. I realized to increase conductivity, polarons are formed in the polymer backbone. From what i read due to localised energy state level by polaron that can exist in the band gap, the band gap is narrowed. My question is if why is can polaron exist in band gap while electron can't though they are both almost identical. Also, do the formation polaron exist as somewhat of a 'bridge' to narrow the gap between conduction band and valence band? Helps or guides are really appreciated.
The soundness of FOL is proved in meta-language(natural language) by proving every deduce rule is correct, so we feel peaceful using those rules to deduce. But the process of proving every deduce rule is correct also uses deduce rules in natural language. For example, proving the correctness of PC(Proof by Case) also uses PC in natural language, so we assume the PC rule exists and assume PC is correct in natural language. Do we need to construct another meta-language for the natural language to prove those assumptions like we are doing for FOL? Otherwise, how can we feel peaceful using those rules when deducing in FOL? Furthermore, is it possible to construct such a meta-language for an unrestricted language such as the natural language?
At one time or another, you've probably inquired about something (perhaps online) and been met with the curt or critical response. It's meant to showcase their cleverness. It's more of a concealed boast than it is a help. Is there a word or phrase which calls out is the disingenuousness of the help, since it's not that at all? This word or phrase characterizes the response and not the person or the behavior.
recently I was solving questions on uncertainty principle but never came across questions involving system of particles like combination of electron and alpha particle. I wanted to understand how to deal system of particles while solving uncertainty principle questions. My initial thought was to calculate total uncertainty in momentum of the system and then using the conservation of momentum, divide this uncertainty in momentum by the respective masses of electron and alpha particle to obtain their respective uncertainty in velocity. Is this approach right?
Hi there my question is pretty much in the title. I have to create tables which are longer than one page. The caption needs to be above the table, it would also be a great extra option if i could rotate the text inside the cell and i would need an automatically adjustable cell width just like tabularX does. Do you have any recommendations? Thank you
I've been reading that expectation values of an observable is all what we can get and are the key quantities of the theory, but performing the same experiment many times would generate a distribution probability for the possible values of the observable, which is better than only expectation values. So why do we claim that 'all we can get is expectation values'? Also, why cannot we model these uncertainties in the a priori knowledge of a measurement using random variables and probability language? Is it really necessary to go through this whole formalism?
How the word livid came (according to Merriam-Webster) to have three different meanings (in addition to the default, 'furious', one)? As I see, it could mean blue-and-black pallid reddish. I mean, I know that all meanings are accepted, but is that so? If I say to someone My car is livid. won't they have any predisposition to favour one of the meanings? At least based on your experience, which option is the first you think of?
I know that the search for Higgs would be quite pointless if there was no estimation of its mass. Namely the perturbative violation of unitatity, gave us an upper bound on its mass.Unitarity Constraints on Heavy Higgs Bosons I wonder if there are enough parameters in the Standard Model of particle physics, such that it introduces sharp bounds on SUSY parameters that cannot escape experiments? Is there in general any model independent prediction made by SUSY or it can always be rescued by means of introducing new fields and couplings phenomenologically?
He brought some food to eat on the road. He found some beer to drink in the fridge. Is it only reality and sanity that keep us from taking the beer example to mean he would be squashed in the fridge like a contortionist, sipping a beer? Or do the verbs license, or if that is too strong, erect interpretive guide-rails for, adjunct phrases? Is meaning accruing as we parse, eliminating certain possibilities and bringing others to the fore? What is the real-time elimination of improbable meanings called in the linguistic literature?
People say my idols are Messi and Ronaldo(no hate) but I dont know why I am attracted to Physics and Math.It always amazes me, this is just a dumb question which i suppose is gonna be closed by midnight today but can someone teach me physics? I would love to and also do questions he/she gives me, it will be like a free trial for me as a student and you as a teacher. Once again, even though this is closed, just know that I love you guys and you are what I aspire to be one day.
Latex IEEE format color problem As you can see the text after the figure until the end of the paper became light blue. But, it supposed to be black. I don't know what happened! I utilized both 'color' and 'xcolor' package in my paper. When I remove the highlighted text inside the paper, the problem is solved. But, I think it is the figure problem in ieee latex format that cause the change of the text after it
In accelerated pure rolling ,as we know velocity of the bottom most point is zero with respect to ground but what makes it to have zero tangential acceleration. If tangential acceleration is to be zero at that point ,it must have net force zero in horizontal direction.The ground applies friction on bottom most point, which in turn applies some internal force on oher points in the body(due to rigidity of body) causing the whole body to get angular acceleration ,the other points applies the same reaction force on the bottom most point .We don't know the magnitude of internal forces. So on what basis we say that these forces cancel each other to make the tangential acceleration or horizontal acceleration of the point zero?
I want to write the i and j as one "ij", as can be seen in the Dutch language, in my LaTeX document, but can't figure out how to do it, even with ChatGPT! If someone knows more, please hit me up! It could be the case that this is just not possible as it is not that frequently used, especially not when actually typing it. If so, please let me know too. Thank you.
I'm using xindy to create indeces. However, the default sort order is not sensible for uppercase and lowercase. Is there a way to create a .xdy file so that the uppercases are sorted in front of lowercases. Here is an example: A Abel....... Alex....... aboutism... account.... axis....... B Bible...... basics..... bigger..... I think the issue is, by default, uppercase letters are mapped to lowercase letters, thus cannot be distinguished former and sorted according to that. I wonder if anyone can help me create a .xdy that sorts alphabet case-sensitively.
I read this thread of articles by Casher(quite marginal in terms of citation) where they show in certain realistic models SUSY is broken by non-perturbative effects. Explicit breaking of supersymmetry by non-perturbative effects The SUSY currents turn out anomalous. Now I want to add a twist: Does the anomaly survive even by addition of extra dimensions? If so, is the number of such dimensions the same as critical superstring theory? Or Super gravity?
Construct a triangle ABC when angle A, length of angle bisector from A and circumradius are given. Since angle A and circumradius are given, we can find out the length of BC. I can elaborate on the same further if you're interested... This seems like a simple problem but I can't get it. Thank you! In a circle with a radius equal to circumradius, an angle equal to angle A constructed from any point will intersect the circle at two points, the distance between which will remain constant and equal, in fact, to side BC. This is how we can get length of side BC given angle opposite it and the circumradius.
Hopefully my question is not out of order in this site. I am trying to weigh an object that is too wide/long for my weight scale. If just put it on top of it it tips over. So my solution is to place my hand on the 'short side' to prevent it from tipping over. Assuming I am not pushing (just holding my hand as an 'stopper'), does that change the weight the weight scale measures? why/why not?. I guess if I push the measured weight would increase (not sure either). details: I am trying to weigh a planter to know if it is safe to put in the balcony.
The statement of class existence theorem includes "F be a formula that quantifies only over sets" then there exists a class A such that it contains only sets and a set x is in A iff F(x) is true. I am curious to see an example which breakz this requirement and have a quantifier over classes, and what kind of paradox it causes. I mean the requirement for the class A to contain only sets pretty much covers Russell's paradox of not belonging to itself. But why for quantifiers should be over sets only? What formula F will cause problems?
If the circulation is negative and flux is clearly not zero then will the flux also be negative? If a curve C and its vector field are going in opposite directions (meaning C is going clockwise and the vector field is going counterclockwise), then circulation will be negative. If the vector field is pointing outwards from the curve meaning it is leaving the curve then will the flux remain positive?
If I penetrate water's surface with needle (using hand) then Cohesive forces> Adhesive forces and water molecules climb up the needle (exactly like capillary action) and needle behaves hydrophilically and when I make it rest like mosquito's legs on water, it floats (mosquitos actually float on water due to surface tension and hydrophobic nature of legs), the needle behaves hydrophobically and Cohesive forces> Adhesive forces in this case. So, my questions is, Is hydrophobic and hydrophilic nature orientation and position dependent (like whether needle is in bulk after penetrating "skin" of water or at surface like mosquito's leg)?
In PWT, the wave function depends on the positions of all the particles. Therefore the velocity of a given particle depends of the positions of the other, it's why the theory is non local. In the model why there is a single wave for all the particle and not a wave for each particle? So that the velocity of a given particle does not depend on the other.
I want to know like for continuity of a function at a given point we can check the limit of the function at that point and the value of the function at that point but how to verify if a function is uniformly continuous or not over a given interval and all kind of interval that is for open , closed and semi open or closed interval
This figure is taken from Wolfram MathWorld. The site classified the third region as not simply connected, and I get it, but it isn't also multiply connected, since multiply connected means that I can connect any two points in the region with a curve that lies entirely in the region. However, it is clear that I cant connect one point in the upper subregion with another one in the down subregion with a curve that lies totally in the region, correct? Note A multiply connected region is a connected region but not simply.
the decision partition problem is Np-complete.Now I would like to proof that if a polynomial Algorithm exists for the decision Problem than another polynomial algorithm would exist too, that would give two sets A and B that fulfill the decision Problem.Clearly this problem is Np hard .I would like a hint or something to help me to approach this problem because I am lost.How can I use the decision partition problem to output the sets A and B
Air can hold water in proportion to partial pressure of water vapor. This is affected by temperature. But is the water capacity of air also affected by ambient pressure? I did find some answers that water holding capacity of air decreases with increasing pressure. Quora link, UCAR link But I was unable to find any equations that would tell me exactly how much it changes. In this case we talk only about change in pressure. So temperature and volume would stay the same. I will be glad for any sources that can answer me this relationship.
I have a man-in-the-street question that was probably "predetermined". If everything around us is co-interacting particles whose source is some infinite small point that started their expansion into nothing due to the Big Bang, how come those particles have any interactions? They should become further with every second, just as grenade fragments that can only meet each other after the explosion only if there are some external preexisting obstacles on their way that cause their bounce.