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Minimal sufficient statistics are supposed to have the lowest dimension among all sufficient statistics. Then, is any sufficient statistic having the same dimension (as the mss) a minimal sufficient statistic? If the answer is no, is there any simple counterexample? | 0 |
Consider these four situations: a tennis ball falling on a wooden floor a tomato falling on a wooden floor a book falling on a wooden floor a tennis ball falling on a soft mattress Why only in the first situation the object bounces? | 0 |
It seems that paths of the Brownian motion are always continuous (please correct me if i am wrong). Levy process is the generalization of Brownian motion by allowing for jumps at random times. So why always people talk (e.g. using Donsker's theorem) about the relation between random walk and Brownian motion (and not between Levy process and random walk)? | 0 |
Is there a word (or maybe a metaphor) to cover the idea of religion, mysticism, occult, and philosophy all together? In other words, how would you name a bookshelf with books and other texts by or about the following authors? Thomas Aquinas George Gurdjieff Aleister Crowley Aristotle | 0 |
Let's say a box is moving to the right and friction is slowing it down. The friction force vector pointing to the left and the object moving to the right, should the vector be drawn on the left side of the object like this: : Or on the right side of the object like this: | 0 |
Is there a specific name for the following graph? "Acyclic tree" is not unique and "one-dimensional lattice" doesn't sound quite right. Saying "line graph" is, in my opinion, ambiguous. The reason I ask this is because I need to reference this graph without the use of this picture, or any pictures for that matter. | 0 |
In quantum field theory, consider acting on the vacuum with a local unitary operator that belongs to the local operator algebra associated with a region. In such a way, can we obtain a state that is orthogonal to the vacuum? i.e., Can the one-point function of a local unitary be zero? If so, any examples? | 0 |
The Hauptvermutung (ie. the question in the title) is known to be false for PL manifolds and topological manifolds, but I can't find a result for smooth manifolds (with boundary), though I recall reading it is true. If not, is something close to this true? | 0 |
I am trying to self-study probabilistic measure theory after completing my undergrad degree, and I am curious if there are more interesting applications of measure theory aside from Lebesgue integration ? It seems like (correct me if I am wrong here) measure on its own is a rich field before delving in integration of measurable functions. | 0 |
If someone says something such as, "I don't know what else to do," it kind of implies a request for some suggestions. In the case the person doesn't actually want ideas for what to do, would this be considered a rhetorical statment? | 0 |
As far as I know, the magnetic properties of a bar magnet is due to the alignment of electronic spins of all the atoms. According to the uncertainty principle the electronic spin is randomly up or down. So, why a bar magnet has certain poles while it may be expected its poles interchange? I appreciate any help about my misunderstanding. | 0 |
In Latin, it simply means "an amount", which can be of anything and of any size. In modern English, especially in physics, it means the smallest amount physically possible, i.e. a physically indivisible amount of something, especially pertaining to energy. | 0 |
I would like to justify text in lstlisting. If the line gets too long, there doesn't seem to be any way to automatically add a new line. Is there a way to justify text? | 0 |
In the sentence below, 'do' refers to 'sense the environment' ,which is evident. But can 'do' refer to only a verb 'sense'? Share what you think about this, and please explain why it is or isn't okay. It is lazy and dangerous for the ecologist to assume that all other organisms sense the environment in the way we do. | 0 |
I have a question about the use of "as well as" and "as did". Which would fit better in the following sentence? When the earthquake began, at least fifteen men and women fell to the ground, as did many children playing in the park that day. I appreciate any assistance you can provide. | 0 |
How can Dirac neutrinos exist if neutrinos have no charge? As far as I'm aware, the antiparticle of a particle is its charge conjugate while all of its other characteristics remain same. How then can a neutrino be distinct from an antineutrino? | 0 |
I've stumpled upon a peculiar usage of the Past Perfect Tense. At the end of the WWII, the Cold War had begun. The world would lay divided between two superpowers. This context seems suitable rather for the Past Simple Tense. I would be thankful for any hints as to why this tense was used. Have a good day, Damian | 0 |
What are some famous open problems and conjectures in Lie symmetry theory? Is there some kind of list of these problems available or possibly a historical survey of the development of theory of symmetry groups? | 0 |
What's the phase difference between A and B on the following diagram. Where it is a standing wave. This question doesn't even make sense to me as from watching animations of standing waves, points A and B cannot even appear at the same time. We cannot have two minimums next to each other. So what is it asking? | 0 |
If i were to make an observation of the orbital motion of the planet Mercury from an inertial frame of reference, would I observe the precession of Mercury's perihelion? or would I observe it moving in the way predicted by Newton's mechanics? And if I will observe the precession of Mercury's perihelion, would my frame of reference still qualifies as being inertial? | 0 |
I learnt that a point source produces spherical wavefronts and i know the reasoning behind that too and while studying the concept again a question popped in my mind, that "Are those spherical wavefronts equidistant ?", most online sources don't have an answer. A clear explanation for the question would be greatly appreciated. | 0 |
Is there a list giving an estimate of the abundance of every element of the periodic table in the Earth's Core - possibly differentiating by inner core and outer core? I am specifically interested in estimates for extremely rare trace elements. | 0 |
A steady state is Nash if it is strict and pure. And there can be multiple steady states, but not all of them satisfy the conditions of a Nash Equilibrium. Is this right? | 0 |
in textbooks I find only results about the weak convergence of univariate stochastic processes. I am looking for a reference text which treats also the convergence of multivariate (vector) stochastic processes. Any hints? Thanks. Ciao Karl | 0 |
I like to use the cochineal font for my document, however for this font I understand there are no corresponding mathematical fonts. So I am asking if anyone knows of any font similar to cochineal that also supports math fonts or a math font similar to cochineal fonts. I am using the KOMAscript class for the document. Thanks for all. | 0 |
How do I get LyX to show the reference in full (without the "..." ellipsis)? Example: Below, I want LyX to show me "Ref: VeryLongLabelNameABC" instead of "Ref: VeryLongLabelNameA..." (which in this case is actually even longer and takes up more space)? | 0 |
Electric potential is the amount of Work required to move a unit positive charge from infinity to a region of an electric field. Why do we need a positive charge for that? Can't we use negative charge? | 0 |
I couldn't find this sort of question anywhere, but this is similar to possession, like when you say "Amanda's book" instead of "the book of Amanda," but those two have slightly different meanings. What's it called when you make the noun go after the word "of" and it describes the first noun? | 0 |
I've come across a question that asks what the subatomic particles are. The answer being the proton, neutron and electron. However, from my understanding subatomic particles also include quarks etc. So what do main subatomic particles even mean? Could someone please provide a cited definition for subatomic particles? | 0 |
It is possible to create fire by friction. For example - by striking a stone with another stone or by striking a matchstick on a rough surface. My question is: Can we say that, where there is fire there must be some kind friction in the fuel , at atomic or molecular level? | 0 |
In the above question , one way of approach is definitely multiplying the matrices and comparing the respective elements then solving the equations. But I am not able to figure out a more efficient solution? | 0 |
We can't use computers for factorising the number, as it's from a math contest where no computers are allowed. So I need to find a way with some manipulations. I can't find a way to approach it. | 0 |
My question is the following. It is known that any Von Neumann algebra can be uniquely decomposed as integral over algebra factors. It is also know that any mixed state can be uniquely expressed as sum of irreducible states. There is any connection between these two decompositions? Maybe by using the GNS theorem? | 0 |
I don't know much about logic, but similar to how certain theorems "require" their proofs to use the axiom of choice, are there theorems which "require" induction? Is there a way to detect them? Thanks! | 0 |
By using the kernel of both transformations, we can easily check that they're not injective functions (due to the fact that kernel does not only contain the zero vector by seeing both operators as linear transformations) So, what am I interpreting wrong? I'm a bit confused on this. Thanks in advance for the help! | 0 |
The Rindler coordinates are calculated in an inertial rest frame, from which the worldlines of accelerating observers are determined. How does this coordinate space look like in the frame of an accelerating observer? I was able to find a YT video where the lecturer shows the image below, but I was not able to find more information regarding it. | 0 |
I want to make a cv. I Found this this (Simple CV) template I want to use but i can't change the language to Greek. I tried using the command usepackage[ ]{babel} but didn't work can someone help ? | 0 |
If I am standing still, and a car is driving away from me at a constant speed. What would the relativistic effects be? Would it appear to move slower as it got farther away? With each second would I be seeing farther back in time when compared to the cars current location? | 0 |
I'm reading some Shakespeare and noticing past tense verbs are written as deceiv'd and search'd etc rather than the modern deceived and searched. When did the shift take place in English to the modern way of writing it? Do we know how it happened? | 0 |
This is a screenshot of a page of a textbook I am writing. The image is a jpg file that was inserted using the environment wrapfigure of the package wrapfig. How can I force the paragraph starting with "Una rappresentazione grafica ..." to be typeset at the normal page width? | 0 |
I.e. compute the Euclidean path integrals of QED/the statistical field theory of electrodynamics? I have never seen anyone discuss this anywhere and I am wondering why? What if there is just an electromagnetic field at some temperature where we don't need quantum effects? That can happen right? | 0 |
We know that a real sequence which is increasing and bounded above converges to its supremum. Is this possible for a non - increasing sequence as well? State that sequence. I am not able to think of a suitable example for this. Please help me. | 0 |
I would like to know; if it is possible to force magnet wedges (as seen in picture) together to form a "Uni-Pole Radial Ring Magnet?" Also, if it is possible to force smaller "Uni-Pole Radial Ring Magnets" (like the one shown below) together to form a larger one? The magnets are neodymium. | 0 |
When I read Mathematical Typography, I noticed that the prototype font presented (the predecessor of the Computer Modern font family) had different numbers (bottom). My question is, are there any versions of the font available anywhere that still has this number style? | 0 |
Many results about single-sorted FOL generalize to the multi-sorted setting (see here). Are there aspects that do not generalize or are importantly different when working in a multi-sorted setting? I am starting to work in the multi-sorted setting and am wondering if there is anything to look out for if one is used to working in the single-sorted setting. | 0 |
If it can be shown that a given NP-complete problem such as Clique cannot be reduced to a given P-complete problem, such as Horn-SAT, then we can conclude that P does not equal NP? | 0 |
How do you visualize an electro-magnetic wave? If there is a very narrow beam (like the one produced by may be a maser?) confined within a few centimeters (in its wave-front) with amplitude say x, what does that mean in terms of its spatial presence? | 0 |
Just out of pure curiosity, are there any examples of the consequences of accepting (or accepting its negation) the continuum hypothesis outside set theory? I know for Zorn's lemma, which is equivalent to AC, there are many applications in algebra, analysis, and topology, but I did not really find many for the continuum hypothesis beyond pure set theory. | 0 |
I'm wondering if there are number systems with bases other than integers? For example, with a fractional, imaginary, irrational, transcendental basis, or with the basis "infinity"? If there are, then how is the translation made in and between them? | 0 |
The potential difference across the terminals of a battery with resistance is equal to the emf when there is no current.But when there is a current there the potential difference decreases or increases depending on the direction of the current.How does this change in voltage occur.Does the charge density at the plates of the battery change? Or, something else happens? | 0 |
I am working on a thesis and I am using Euler's criterion. I am interested in it's origin, so the first publication of it by Euler. I found some references, though I did not find the original work of Euler. It's not linked in mathscinet, either. Does anybody know where I can see the first usage? | 0 |
I've written a .sty file, named creator.sty. When I was using TexLive, there is a folder where all .sty files are stored. I'm now changing to Tectonic, and I cannot find such a folder, and I don't want to put creator.sty into every project I develop. Is their any way to install a custom package by Tectonic? | 0 |
Recently I came across this question, where the top voted answer claimed that all homogeneous equation represent a set of straiight lines passing through origin. I was wondering if this was true generally, and if so, how can we prove this? | 0 |
Judging by the wiki page I get the feeling that this type of heat pump would not function if it's radiator were hotter than the heat source, but I can't quite put into words why and I feel like there might be something that I'm misunderstanding. Edit: Here is the link to the wikipedia page on it: https://en.wikipedia.org/wiki/Absorption_refrigerator | 0 |
I was studying vectors and came up with this question Show that the line joining the midpoints of two non parallel sides of a trapezium is parallel to the parallel sides and is equal to half of their sum. Is this anyhow mid point theorem for trapezium or is it applicable here? | 0 |
Are "the roof of the building" and "a house of stone" grammatically different prepositional phrase constructions? Or are they both understood to be possessives with the latter not in the usual sense of ownership/possession but something that "belongs" to a particular class or category? | 0 |
Whenever I slightly touch the touchpad on my Mac Texmaker chooses to "unfocus" the cursor so I cannot write. Then I need to click the text window again to keep writing. I have tried to find out how to stop this from happening, but I can not find the place to fix this in the options. Any help is greatly appreciated. | 0 |
Does the fractional quantum Hall effect always occur when the integer quantum Hall effect occurs? In other words, is there an example of a material where the IQHE can be measured without the "noise" of the FQHE, allowing us to see the idealized IQHE as shown here? | 0 |
Given N nodes I randomly pick a permutation of the nodes and use this permutation to define an assignment: I associate one and only one node to each node. This procedure naturally defines a graph made of loops (auto loops are allowed). I was wondering what's the average number of loops in such a graph | 0 |
I am able to add the figure in a lyx document, by using float and insert graphics. But when I view in the pdf, I don't see the figure in the inserted location. Instead I see the location of the file inside a blank box. See below. I want to know why this is the case and any suggestions on how to fix it | 0 |
I'm surprised that I can't find any research on this topic. Maybe it's too obvious? Kinoshita proved that contractible continuum do not have FPP, but his example is not locally connected. Maybe if we add this to the conditions it will have FPP? UPD: Continuum as a nonempty compact connected metric space | 0 |
I am studying the Koopman operator and its spectrum. Koopman spectrum is a new topic for me and It is hard to understand what kind of dynamical system shows the point spectrum and what does not. what are the dynamical systems with point Koopman spectrum? does a dissipative system or more specifically the damped pendulum show the point Koopman spectrum? | 0 |
How is there so much pressure at the bottom of the ocean and therefore a greater force transmitted by collision, even though the temperature remains constant ? Shouldn't greater pressure and therefore greater molecular acceleration create a higher temperature ? | 0 |
For the hydrogen atom, a simple separation of variables give the energy eigenvalue of the Schrodinger operator for one electron in a spherical potential. It is well known that there are no such explicit solutions for the helium atom. However, is there a rigorous mathematical proof that the helium atom's Hamiltonian operator indeed has discretized eigenvalues? | 0 |
I've been trying to learn how to graph some miscellaneous functions and I came across this. I put it in Desmos and this is what I ended up with. Can you let me know how did the graph get its shape? And how can one graph such type of functions on their own? | 0 |
Consider a damped sinusoid. It has a obvious absolute maxima, but it also has an infinite number of critical points. Is there a general solution to finding an absolute extrema given a function that has an infinite number of critical points? | 0 |
I was reading multivariable calculus , where there were a few topological definitions on things like open ball, limit points, boundaries etc.i came across the statement "a limit point of a set need not belong to the set". Why is this true? can someone give a visual and mathematical proof of this. | 0 |
I was doing my car license's questions, and it came up this question, why would the stoppage distance (the distance which the car stops after breaking) increase if you add more weight on top of the motorcycle? I thought it would decrease, since the friction force depends on the normal force which increases after adding weight to it, isn't it? | 0 |
Can photons form black holes the same way as other matter? If there happens to be enough of them concentrated in an area of space so that enough energy exists within a radius to form an event horizon, will an actual inescapable black hole then come into existence? | 0 |
While working with the Huygens-Fresnel integral, I learned about the Rayleigh integral again, and I can't tell where they apply and whether they can be replaced equivalently. Also, in terms of structured light in a focusing system, which is better to use. Of course, I'd love to get some references! | 0 |
I have made predictions for the amount of conversions of a particular website. After predicting the amount for every day. I looked for ways to get a prediction interval for every day. The residuals are plotted as follows: Residuals From my knowledge this is not normally distributed. I am curious if there is a way to get prediction intervals. | 0 |
Which of the two books do you recommend? I have been studying mathematics for three semesters and would like to improve my skills in demonstrating and understanding proofs more easily. I am open to other book suggestions. | 0 |
As is known, non-zero infinitesimals exist. It can be proved. In the book "A Primer of Infinitesimal Analysis" John Bell introduced infinitesimals that indistinguishable from zero. He did it implicitly. How did he know that such infinitesimals exist? He didn't prove it. How to prove it? Thanks. | 0 |
Has every infinite simple group a faithful irreducible representation? This question solves the finite case. However, the proof requires a non-trivial linear representation of a finite group. I want to know if the conclusion is true for an infinite simple group. If it is not, can you give me a counterexample? | 0 |
Is there a popular English expression equivalent to this Russian proverb? It translates to: Water wears away a stone. And has the meaning that, step by step, eventually we (it) will get there (reach the goal, etc.). It can also be used to mean that harm or something undesirable can be inflicted over time. | 0 |
When deriving the expression of momentum expectation value one gets to what's shown in the picture. However, every text I've seen so far simply neglect the first term inside the integral. I would comprehend if there were linear factors of the wave function itself, since it goes to zero. However this is not the case and I don't get why this term's cancelled. | 0 |
I use a random number generator to generate normally distributed numbers. The problem is negative numbers are unphysical in that particular simulation. So I use "if/else" to discard them. My question is: What is the resulting distribution? It's obviously not Gaussian any more since it is cut on the left. | 0 |
I have just started studying about affine schemes and I am searching for books about Spec as a functor from the category CRings to the category AffineSchemes can you suggest me some? Also I am searching about the geometric results of this equivalence of categories, any ideas? | 0 |
a newbie here. For my thesis I needed to replicate this graph: I think it needs to be done in TikZ. It would be extremely helpful if I get an ipnut from the experts here. Thanks a bunch in advance. | 0 |
I'm studying probability theory, and I have a question. From the definition of a random experiment, we don't know the outcome of an experiment, but we can calculate and get outcomes. How? If an event is random, how do we know its random variables and its outcomes? Which definition or axioms allow us to know outcomes? | 0 |
In dynamical systems, what is the distinction between a homoclinic orbit and a limit cycle? It seems to me like a homoclinic orbit is effectively just a limit cycle with a particular fixed point along the way, but in both cases can't we describe the object as an attractor (or source, depending on stability) curve in phase space, periodically traversed? | 0 |
It is well known that If in a triangle a median has the measure half the length of the side it is drawn, then the triangle is a right triangle. Is there any trigonometric proof of the above statement? | 0 |
I know that perhaps some will answer with "the double slit experiment" but what is it that makes the double slit experiment something probabilistic? I cannot understand this and please I ask you to explain this as if I were a child | 0 |
I would like the first line of footnotes to be indented, like below. It seems the easier approach is to override the template using YAML at the top of my input document, but I don't know what to insert in the YAML. | 0 |
Today, l learned a new word 'supine'. It has multiple meanings, but I am asking about the opposite of the following meaning: Lying on the back facing upwards. In other words, what is the suitable word to describe the following: Lying on the stomach facing downwards | 0 |
Is proving mathematical theorems one kind of computing? I read somewhere in a book that proofs are one kind of computation. I am not talking about formal proofs, I am talking about the informal natural language arguments that mathematicians use in their daily work. | 0 |
I have a GitHub link and I want to use it as a reference. How can I put it in a .bib file and then cite it? I am using bibtex. An example GitHub link I want to reference: https://github.com/LLNL/zfp | 0 |
I am a first year student. I am trying to find a precise definition of cardinal numbers. I am unable to find it anywhere. I am fine with finite cardinalities. I also know that different sets have different sizes. But how to have a precise definition of a cardinal number ? | 0 |
This might be a random question, but I've always wondered, can the principle of induction be used not only for proving sum formulas, but something else? Is there anything else we can use it for? | 0 |
The script fancy-preview is obsolete and no longer works in the recent TeXLive versions (see, for example, this question). According to the author of fancy-preview, there are some better options, but he never mentions what the option is. Since his words are not very convincing, do we have any alternative for fancy-preview? | 0 |
I am interested in writing a chess book in LaTeX. Are there any existing LaTeX templates for writing Chess books in overleaf? Also, is there any streamlined way to use Chessbase directly for writing a chess book, whether it is in LaTeX or not. | 0 |
Can anyone recommend a nuclear physics textbook which is focused on theory rather than engineering and comes with full solutions to all the problems provided in a separate solutions manual. I MUST have a full solution manual. It may be an introductory text or advanced. Either way I can use it. My query is very specific and there is no duplicate question. | 0 |
To my knowledge the "white-sky albedo" is the surface albedo corresponding to diffuse illumination while "black-sky albedo" corresponds to the direct illumination. I am confused with the term "Lambertian albedo" used in some radiative transfer models (e.g libRadtran). Is it the same with the "white-sky albedo"? If not, what is their difference? | 0 |
I think the body should not move since maximum static friction is greater than the applied force but my book says that it will roll. Also I have read that static friction is independent of the area of contact. Please tell me where am I going wrong? | 0 |
As I know Newton physics is used for most engineering, aerospace, mechanical, naval etc. Where we must use Theory of Special Relativity and Theory of General Relativity to get correct results, only for astronomy, big distances/objects etc? | 0 |
I can understand the logic behind spin-stabilizing bullets, which travel only a few hundred meters on fairly flat trajectories. But I cannot understand the logic for artillery. Won't spinning shells remain the same orientation throughout the trajectory, causing them to belly flop on the target? | 0 |
Can I use when as a replacement for how often? Is it common to use when to ask about the frequency of an action? ex: Question: When do you do the dishes? Answer: Sometimes I do the dishes. | 0 |
In the case of a free particle, if you have perfect knowledge of its momentum, the uncertainty in its position becomes infinitely large. Does this imply that there is a finite probability of finding the free particle anywhere in the entire universe? | 0 |
As I do exercises in my physics book, there are a lot of questions that ask me to list the brightness of rays (reflected and refracted) in ascending order. A very difficult one is shown below. Can anyone explain why the answer is D? And also how I can do similar questions? Thanks! | 0 |
Heisenberg's uncertainty principle states that we can't mutually determine both the trajectory and momentum of a subatomic particle. According to Einstein, If we take two particles with different masses,join them and let them spring apart. Their velocities and positions will be related , so can we calculate both velocity and position? IS the Heisenberg's Uncertainty principle disproved? | 0 |
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