text stringlengths 256 16.4k |
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Approach
My question asks whether or not the elapsed proper time between meetings is always less for A than it is for B, for every possible radius of A's orbit.
One way to answer this would be to calculate the ratio of the two elapsed proper times as in reference [1] cited by user m4r35n357, but my question is less dem... |
Crossing Bridge in Crowds Problem
Solution
If there is nobody on the bridge at noon, no one has entered it in the five-minute interval before noon. Since there are $144$ intervals of $5$ minutes in $12$ hours, the probability that an individual enters the bridge in a specific one is $\displaystyle\frac{1}{144}.$ The pr... |
If I take a series RLC circuit connected to a battery, the impedance is minimized when $\omega = \frac{1}{\sqrt{LC}}$.
I also know that the series RLC circuit is analogous to a damped driven harmonic oscillator. However, the resonant frequency of a damped driven harmonic oscillator is reduced due to the damping. It is ... |
Let $(a_n)$ be any sequence and $(b_n)=n(a_n-a_{n+1})$.
Prove that if $\sum a_n$ and $\sum b_n$ converges then $\lim_{n\to \infty}na_n=0$ and $\sum a_n= \sum b_n$.
The second part, assuming the first part, I've shown. I'm having trouble showing $\lim_{n\to \infty}na_n=0$. I know that $\lim a_n=0$ and $\lim n(a_n-a_{n+1... |
This is a question in the theory of random dynamical systems.
Let $(X,d)$ be a compact metric space, let $(I,\mathcal{I},\nu)$ be a probability space, and let $(f_\alpha)_{\alpha \in I}$ be an $I$-indexed family of continuous functions $f_\alpha:X \to X$ such that the map $(\alpha,x) \mapsto f_\alpha(x)$ is jointly mea... |
Welcome to TeX SE!
The key issue is that
ebgaramond-maths issues the following
\DeclareSymbolFont{letters} {OML} {EBGaramond-Maths} {m} {it}
This overwrites the existing
letters font. This enables all of the characters which the font does provide and which are used in the
OML encoding. However, it does this by telling ... |
Wavepackets in inhomogeneous periodic media: effective particle-field dynamics and Berry curvature
Date2017-04-23
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Abstract
We consider a model of an electron in a crystal moving under the influence of an external electric field: Schr\"{o}dinger's equation w... |
I refer to hand-waving a lot in this post. That is not to say that it was in appropriate. Feynman pretty much said at the outset that his treatment of thermal physics was going to be less than rigorous.
I've been rereading Feynman's Lectures on thermal physics with the intent of summarizing the material. I have not bee... |
Answer
$39.7mg \space C_{21}H_{26}N_{2}S_{2}$ for one tablet
Work Step by Step
Let's use the entire 12 tablet data and divide by the answer by 12 to get the initial tablet thioridazine content We are given $.301g$ BaSO$_{4}$ so we need to work backwards in the way the reaction occurred because we started with Thioridaz... |
Package
GLMMadaptive provides a suit of functions for fitting and post-processing mixed effects models for grouped/clustered outcomes which have a distribution other than a normal distribution. In particular, let \(y_i\) denote a vector of grouped/clustered outcome for the \(i\)-th sample unit (\(i = 1, \ldots, n\)). T... |
Some readers may be familiar with Bob Palais’ article “π Is Wrong”. Within it Palais argues that π is the wrong choice of circle constant. This quote, from the author’s website, summarizes his main argument:
As noted in the last page of the pdf, I suggest calling the alternate constant 2 π=6.283… `1 turn’, so that 90 d... |
June 19th, 2018, 07:45 AM
# 3
Math Team
Joined: Jan 2015
From: Alabama
Posts: 3,264
Thanks: 902
I had not seen the term "pseudo-quadratic equation" before but it appears to be what I have seen called "an equation of quadratic type". That is any equation that can be made into a quadratic by a substitution. For example, ... |
Blackbody radiation is a cornerstone in the study of quantum mechanics.This experiment is what led to the discovery of a field that would revolutionize physics and chemistry. Quantum mechanics gives a more complete understanding of the fundamental mechanisms at the sub-atomic level.
Introduction
The work done at the tu... |
№ 8
All Issues Volume 60, № 8, 2008
Ukr. Mat. Zh. - 2008. - 60, № 8. - pp. 1011–1026
We prove a Hadamard-type theorem which connects the generalized order of growth $\rho^*_f(\alpha, \beta)$ of entire transcendental function $f$ with coefficients of its expansion into the Faber series. The theorem is an original extens... |
Article
Keywords: general connection; classical linear connection; bundle functor; natural operator
Summary: Let $G$ be a bundle functor of order $(r,s,q)$, $s\geq r\leq q$, on the category $\Cal F\Cal M_{m,n}$ of $(m,n)$-dimensional fibered manifolds and local fibered diffeomorphisms. Given a general connection $\Gamm... |
Let $X \in \mathbb{R}^{a \times b}$ and
$$\|X\|_2 = \sigma_{\max}(X) = \sqrt{\lambda_{\max} \left( X^T X \right)}$$
How can I compute $\nabla_X \|AX\|_2$, where $A \in \mathbb{R}^{c \times a}$ is some known matrix?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and profes... |
Quote:
Originally Posted by
yaser
Correct. The solution was also given in slide 11 of Lecture 12 (regularization).
yes my point was how do you solve this numerically - given that people will already have a good least squares code ( doing SVD on Z to avoid numerical ill conditioning), there is no need to implement (poor... |
Under the CEV model the stock price has the following dynamics:
$dS_t=\mu S_tdt+\sigma S_t^\gamma dW_t$, where $\sigma\geq0, $ $\gamma\geq0$.
According to Wikipedia, if $\gamma <1$ the volatility of the stock increases as the price falls.
But why is this true? Shouldn't be the exponent negative in order to have an inve... |
CryptoDB Paper: New (and Old) Proof Systems for Lattice Problems
Authors: Navid Alamati Chris Peikert Noah Stephens-Davidowitz Download: DOI: 10.1007/978-3-319-76581-5_21 Search ePrint Search Google Conference: PKC 2018 Abstract: We continue the study of statistical zero-knowledge (SZK) proofs, both interactive and non... |
Loaded Dice Problem
Solution 1
Let $p_i$ be the probability of $i,$ $i=1,\ldots,6,$ coming up for the first die and $q_i$ for the second. Assuming all the sums come up with the same probability, the latter equals $\displaystyle \frac{1}{11}.$ Then $p_{\small{1}}q_{\small{1}}$ is the probability of the sum being $2$ suc... |
Here is a geometric explanation. See if it makes sense to you.
$(X,Y)$ is a uniform random point in the square $[0,1] \times [0,1]$.
But what is $(W,Z) \equiv (\min(X,Y), \max(X,Y))$?
Imagine folding the square along the $y=x$ line, aka $+45°$ line, folding the lower triangle onto the upper triangle. Then $(W,Z)$ is wh... |
I'm currently trying to import a set of data from a file (comma or tabbed delimited, doesn't matter) for creating a table. Below is an example of this data (DH parameters in case you're curious):
Link \alpha a \theta d0 0 0 0 01 \frac{\pi}{2} 0 \theta_{1} 3402 \frac{-\pi}{2} 0 \theta_{2} 03 \frac{-\pi}{2} 0 \theta_{3} ... |
Good morning fellow mathematicians! Today we are going to discuss an integration method, which I find to be pretty helpful and applicable in many situations. After deriving the formula we are interested in, I'm going to provide you with an example, where this very method might come in handy.
Let us consider the followi... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
This question is an offshoot of this earlier MSE post.
Citing Banks, et. al.: "Let us call an integer $n$ a
Descartes number if $n$ is odd, and if $n = km$ for two integers $k, m > 1$ such that $\sigma(k)(m + 1) = 2n.$"
From the same paper, we have the divisibility constraints $$2k - \sigma(k) \mid k$$ and $$2k - \sigm... |
Theory Seminar: Function-Inversion Problem: Barriers and Opportunities דובר: דימה קוגן (אונ' סטנפורד) תאריך: יום רביעי, 2.1.2019, 12:30 מקום: טאוב 201
n the function-inversion problem, an algorithm gets black-box access to a
function $f:[N] \to [N]$ and takes as input a point $y \in [N]$, along with
$S$ bits of auxilia... |
Bernoulli Distribution Introduction
The Bernoulli distribution is our first attempt to connect data to mathematical statistics. We will learn that mathematical statistics has a deep theory about what exactly produces data. As with much of mathematics, statistics theorizes that functions are the culprits behind data.
To... |
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:2531-2550, 2019.
Abstract
In this work we provide an estimator for the covariance matrix of a heavy-tailed multivariate distribution. We prove that the proposed estimator $\widehat{\mathbf{S}}$ admits an \textit{affine-invariant} bound of the form ... |
dpsmith December 3rd, 2017 07:50 AM
Normal Subgroups of p-groups
Let G be a p-group and N ≠ (1) be a normal subgroup of G. Then N and Z(G) have a nontrivial intersection. Is this an induction problem?
johng40 December 3rd, 2017 04:04 PM
Since you mention induction, I assume that G is finite; aside: I realized I don't k... |
Mitchell Feigenbaum obituary in the
New York Times
"Mitchell J. Feigenbaum, a pioneer in the field of mathematical physics known as chaos, died on June 30 in Manhattan. He was 74." So starts Feigenbaum's obituary in the
Times, July 18, 2019. The reporter is Kenneth Chang, who surveys Feigenbaum's career (at his death h... |
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:1158-1160, 2019.
Abstract
We study the logistic bandit, in which rewards are binary with success probability $\exp(\beta a^\top \theta) / (1 + \exp(\beta a^\top \theta))$ and actions $a$ and coefficients $\theta$ are within the $d$-dimensional unit... |
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2017, Universitario. Storia dell'arte, ISBN 9788859617211, Volume 3, 230 pages
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2008, Testi e studi, ISBN 9788859604082, Volume 22, 130
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2006, Testi e studi, ISBN... |
Applied/ACMS/absS18 Contents 1 ACMS Abstracts: Spring 2018 1.1 Thomas Fai (Harvard) 1.2 Michael Herty (RWTH-Aachen) 1.3 Lee Panetta (Texas A&M) 1.4 Francois Monard (UC Santa Cruz) 1.5 Haizhao Yang (National University of Singapore) 1.6 Eric Keaveny (Imperial College London) 1.7 Anne Gelb (Dartmouth) 1.8 Molei Tao (Geor... |
Edit: After thinking about it some more I came up with something much simpler than the phase-locked loop.
The problem you are having is because you are filtering with a boxcar. The boxcar filter has a lot of ripples in the frequency domain, so if you choose the wrong width you don't get good attenuation of your approxi... |
April 21st, 2015, 04:15 PM
# 1
Newbie
Joined: Apr 2015
From: Switzerland
Posts: 1
Thanks: 0
$\int\limits_{\gamma} \frac{z}{(z-1)(z-2)}$, $\gamma(\theta) = re^{i\theta}$
$\int\limits_{\gamma} \frac{z}{(z-1)(z-2)}$, $\gamma(\theta) = re^{i\theta}$, $2 < r < \infty$
For $0 < r < 2$, we can use Cauchy's integral formula an... |
The Fibonacci sequence reappears a bit later in Dan Brown’s book ‘The Da Vinci Code’ where it is used to login to the bank account of Jacques Sauniere at the fictitious Parisian branch of the Depository Bank of Zurich.
Last time we saw that the Hankel matrix of the Fibonacci series $F=(1,1,2,3,5,\dots)$ is invertible o... |
Doing this with angles, as Jyrki suggested, is cumbersome and difficult to generalize to different dimensions. Here is an answer that's essentially a generalization of WimC's, which also fixes an error in his answer. In the end, I show
why this works, since the proof is simple and nice. The algorithm
Given a distance m... |
$\ A = \begin{bmatrix} 3 & 0 & 0 \\ 0 & a & a-2 \\ 0 & -2 & 0 \end{bmatrix} \\ a \in \mathbb R$
I need to find for which $\ a$ values $\ A $ will
not be diagonalizable $\ A $
I was thinking trying the elimination way so finding values which $\ A $ can be diagonalize first.
so the characteristic polynomial of $\ A $ is ... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
Learning Objective
Draw a Lewis electron dot diagram for an atom or a monatomic ion.
In almost all cases, chemical bonds are formed by interactions of valence electrons in atoms. To facilitate our understanding of how valence electrons interact, a simple way of representing those valence electrons would be useful.
A
Le... |
Currently, I'm trying to implement a Finite Difference (FD) method in Matlab for my thesis (Quantitative Finance). I implemented the FD method for Black-Scholes already and got correct results. However, I want to extend it to work for the SABR volatility model. Although some information on this model can be found on th... |
In order to begin to make a connection between the microscopic and macroscopic worlds, we need to better understand the microscopic world and the laws that govern it. We will begin placing Newton's laws of motion in a formal framework which will be heavily used in our study of classical statistical mechanics.
First, we... |
Three Complex Numbers Satisfy Fermat's Identity For Prime Powers Problem
Solution 1
Not that $x^6=y^6=2^6=z^6.$ Also, $x+y=2=z$ and $\displaystyle \frac{1}{x}+\frac{1}{y}=\frac{1}{2}=\frac{1}{z}.$
Now, all prime numbers are in the form $p=6m\pm 1.$ Assume $p=6m+1.$ Then
$\begin{align} x^{p}+y^{p}&=x\cdot x^{6m}+y\cdot ... |
Let $p(x)=x^4+ax^3+bx^2+cx+d$ where a,b,c,d are constants. If $p(1)=10$, $p(2)=20$, $p(3)=30$, compute $\frac {p(12)+p(-8)}{10}$. I have tried so far. \begin{align} a+b+c+d=&9\\8a+4b+2c+d=&4\\27a+9b+3c+d=&-51 \end{align} Manipulating these, I got $6a+b=-25$. Now, $$\frac {p(12)+p(-8)}{10}=\frac{24832+1216a+208b+4c+2d}{... |
The simplest antenna is a short (total length $l$ much smaller than one wavelength $\lambda$) dipole antenna, which is shown above as two colinear conductors (e.g., wires or conducting rods). Since they are driven at the small gap between them by a current source (a transmitter), the current in the bottom conductor is ... |
There is these notes about Gaussian Quadrature and I am trying to understand what does the sentence "is exact for all polynomials of degree up to $2n+1$" actually mean.
Gaussian Quadrature - General $n$:
Given an interval $[a,b]$ and a natural number $n$, we want to find constants $A_i$ and $x_i\in[a,b]$ such that the ... |
Problem:
Let $M$ be a Riemannian manifold. Consider the function $f: M \rightarrow \mathbb{R}$ where $f(x)=\text{dist}_M^2(p,x)$, and $p \in M$ is fixed. Show that $\text{grad}(f)=-2\exp^{-1}_x(p)$ as vectors in $T_xM$. (Assuming that $\exp^{-1}$ exists and is smooth etc.)
My attempt at a proof:
We must show that $\lan... |
I want to find Euler-Lagrange equation for the following:
$$J(u) = \int \left( \frac{\psi(x) u + \dot{u}}{\psi(x)u - \dot{u}} \right)dx, \text{where} \ \psi(x) \ \text{is an explicit function of} \ x.$$
First, I have made the following substitution:
$$y = \frac{\dot{u}}{u} \implies \int \left( \frac{\psi(x) u + \dot{u}... |
I will start with examples in order to more easily explain what I'm after.
The first example shows how I would like four equations arranged. The vertical alignment of the equal signs in each row is perfect, of course, because each is a single line in an align structure. But, not all four equations can be numbered. The ... |
This is related to the question Hall-Littlewood functions and functions on the nilpotent cone, and arises in the construction of Coulomb branches of gauge theories. The motivation is explained at the bottom.
Let us prepare some notation. Let $\lambda$ be a dominant coweight of $GL(N)$, i.e., tuples of (not necessarily ... |
The
beta of a plasma, symbolized by β, is the ratio of the plasma pressure ( p = n k B T) to the magnetic pressure ( p mag = B²/2 μ 0). The term is commonly used in studies of the Sun and Earth's magnetic field, and in the field of fusion power designs.
In the fusion power field, plasma is often confined using large su... |
It’s been a while, so let’s include a recap : a (transitive) permutation representation of the modular group $\Gamma = PSL_2(\mathbb{Z}) $ is determined by the conjugacy class of a cofinite subgroup $\Lambda \subset \Gamma $, or equivalently, to a dessin d’enfant. We have introduced a
quiver (aka an oriented graph) whi... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
Two Equilateral Triangles on Sides of a Square Problem
Solution 1
Consider the counterclockwise rotation $r$ around $C$ through $60^{\circ}.$ $r(E)=D,$ $r(F)=B,$ and let $r(A)=A'.$ Then $\Delta AA'C$ is equilateral. In particular, $AA'=CA'.$ It follows that $AA'CD$ is a kite so that $A'D$ is the perpendicular bisector ... |
Square is a regular quadrilateral. All the four sides and angles of a square are equal. The four angles are 90 degrees each, that is, right angles. A square may also be considered as a special case of rectangle wherein the two adjacent sides are of equal length.
In this section, we will learn about the square formulas ... |
Notation Hiding constants
Unless explicitly stated otherwise, \(O(\cdot)\)-notation hides absolute multiplicative constants. Concretely, every occurrence of \(O(x)\) is a placeholder for some function \(f(x)\) that satisfies \(\forall x\in \R.\, \abs{f(x)}\le C\abs{x}\) for some absolute constant \(C>0\). Similarly, \(... |
Large time behavior of ODE type solutions to nonlinear diffusion equations
1.
Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan
2.
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
$ \begin{equation} \left\{ \begin{array}{ll} \partial... |
Consider the simple integral:
\[ I = \lim_{\lambda\rightarrow\infty}\int_{-\infty}^{\infty}dx\;e^{-\lambda f(x)} \]
Assume \(f (x) \) has a global minimum at \(\underline {x = x_0} \), such that \(f' (x_0) = 0 \). If this minimum is well separated from other minima of \(f (x) \) and the value of \(f (x) \) at the globa... |
In 1923, Louis de Broglie, a French physicist, proposed a hypothesis to explain the theory of the atomic structure.By using a series of substitution de Broglie hypothesizes particles to hold properties of waves. Within a few years, de Broglie's hypothesis was tested by scientists shooting electrons and rays of lights t... |
Answer
325
Work Step by Step
Applying the proper formula, we find: $$\sum _{k=1}^nk=\frac{1}{2}n\left(n+1\right) \\ \frac{1}{2}\cdot \:25\left(25+1\right) \\ 325$$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have
24 hours to send in a draft. An... |
Abstract
Let $(\sigma_{1}, \ldots, \sigma_d)$ be a finite sequence of independent random permutations, chosen uniformly either among all permutations or among all matchings on $n$ points. We show that, in probability, as $n\to\infty$, these permutations viewed as operators on the $n-1$ dimensional vector space $\{(x_1,... |
I have generalized gamma distribution with the following equation:
$$ f(x) = \frac{\lambda^{a\tau}\tau x^{a\tau - 1}}{\Gamma(a)}e^ {{(x\lambda)}^\tau} $$
and log-likelihood function
$$ l(a, \lambda, \tau) = a \tau n \log{\lambda} + n \log{\tau} - n \log{\Gamma(a)} + (a \tau - 1) \displaystyle\sum_{i=1}^{n} \log{x_i} - ... |
Definition:Cotangent Contents Definition
In the above right triangle, we are concerned about the angle $\theta$.
The
cotangent of $\angle \theta$ is defined as being $\dfrac {\text{Adjacent}} {\text{Opposite}}$.
Let a tangent line be drawn to touch $C$ at $A = \left({0, 1}\right)$.
Then the cotangent of $\theta$ is def... |
Chapter Review Exercises True or False? Justify your answer with a proof or a counterexample.
1) The rectangular coordinates of the point \(\displaystyle (4,\frac{5π}{6})\) are \(\displaystyle (2\sqrt{3},−2).\)
2) The equations \(\displaystyle x=cosh(3t), y=2sinh(3t)\) represent a hyperbola.
Solution: True.
3) The arc ... |
Export file: Format RIS(for EndNote,Reference Manager,ProCite) BibTex Text Content Citation Only Citation and Abstract
Some results on ordinary words of standard Reed-Solomon codes
1 Mathematical College, Sichuan University, Chengdu 610064, P. R. China;
2 Department of Mathematics, Sichuan Tourism University, Chengdu 6... |
Ordinary Differential Equations (ODEs) describe the rate of change of dependent variables with respect to a single independent variable and are used in many fields to model behavior of the system. There are many good
C libraries available to solve (i.e., integrate systems of ODEs) and SUNDIALS available from the Lawren... |
Definition:Linearly Dependent/Set Definition Let $\struct {G, +_G, \circ}_R$ be a unitary $R$-module. Let $S \subseteq G$.
That is, such that:
$\displaystyle \exists \set {\lambda_k: 1 \le k \le n} \subseteq R: \sum_{k \mathop = 1}^n \lambda_k \circ a_k = e$
where $a_1, a_2, \ldots, a_n$ are distinct elements of $S$, a... |
Quasi-categories (or $\infty$-categories, as they are often called) are a very convenient setting for doing abstract homotopy theory. One of their amazing features is the following: Given a diagram of quasi-categories, we can form its homotopy limit, yielding a quasi-category again. For example, the inverse (homotopy) ... |
Periodic solutions of some classes of continuous second-order differential equations
1.
Departament de Matemátiques, Universitat Autónoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
2.
Department of Mathematics, Laboratory LMA, University of Annaba, Elhadjar, 23 Annaba, Algeria
We study the periodic sol... |
HALP: High-Accuracy Low-Precision Training by Chris De Sa, Megan Leszczynski, Jian Zhang, Alana Marzoev, Chris Aberger, Kunle Olukotun, and Chris Ré Using fewer bits of precision to train machine learning models limits training accuracy—or does it? This post describes cases in which we can get high-accuracy solutions u... |
Let $k$ be an algebraically closed field, and $f_0,\dots,f_m \in k[x_0,\dots,x_n]$ be homogeneous polynomials of the same degree. Denote by $I\subset k[x_0,\dots,x_m]$ the kernel of the homomorphism sending $x_i$ to $f_i$. Do we have the following statement?
For any $\xi\in k^{m+1}$, $\xi$ is a common zero of $I$ if an... |
Created in the early 17th century, the gas laws have been around to assist scientists in finding volumes, amount, pressures and temperature when coming to matters of gas. The gas laws consist of three primary laws: Charles' Law, Boyle's Law and Avogadro's Law (all of which will later combine into the General Gas Equati... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
This isn't an answer to conjecture 1, just an elaboration of things others mentioned.
There is every reason to think that the answer to conjecture 1 is yes and even that for fixed $m \gt 1$ we have that for each odd integer $x \geq 3$ there are infinitely many $n$ with $p_{n+m}-p_n-p_m=x.$ We don't know that there is e... |
The monstrous moonshine picture is the subgraph of Conway’s big picture consisting of all lattices needed to describe the 171 moonshine groups.
It consists of:
– exactly 218 vertices (that is, lattices), out of which
– 97 are number-lattices (that is of the form $M$ with $M$ a positive integer), and
– 121 are proper nu... |
Monotonicity and symmetry of solutions to fractional Laplacian equation
School of Mathematical Sciences, Shanghai Jiaotong University, Shanghai 200240, China
$0 < \alpha < 2$
$\Omega$
$\mathbb R^{n}$
$\begin{equation}\left\{\begin{array}{ll}(-\Delta)^{\alpha/2} u(x)=f(x,u,\nabla{u}),~u(x)>0,&\qquad x\in{\Omega}, \\u(x)... |
Ltoh is a customizable LaTeX to HTML converter. It handles text,tables, and hypertext links.
ltoh is a large Perl script, and hence is(almost completely) platform independent.
ltoh is customizable in thatyou can specify how to translate a given LaTeX2
ltoh will give a friendlywarning.
See the
ltoh web page for document... |
Once we have a one-to-one function, we can evaluate its inverse at specific inverse function inputs or construct a complete representation of the inverse function in many cases.
Inverting Tabular Functions
Suppose we want to find the inverse of a function represented in table form. Remember that the domain of a functio... |
As Paul Garrett intimates in his answer, the notion of cuspform is fundamental, but can be subtle in its meaning and implications. Here are a few different points of view that might help:
From the point of view of someone interested in the relationship between modular forms and algebraic number theory, Hecke eigenforms... |
In examples/large_deformation/hyperelastic.py a rotation by displacements is applied. By using a similar function the vectors defining the force couples could be defined for dw_surface_ltr (IMHO). Does it make sense?r.----- Reply message -----From: "Andre Smit" <freev...(a)gmail.com>To: <sfepy...(a)googlegroups.com>Sub... |
I have a question. First, I know that convergence in measure of a sequence of functions $f_n$ is different than convergence a.e., wich means there are sequences that converge in measure but not a.e. but this excercise got me in doubt if there is some kind of duality between convergence in measure and convergence a.e.
E... |
After the answers by joshphysics and user37496, it seems to me that a last remark remains.
The quantum relevance of the universal covering Lie group in my opinion is (also) due to a fundamental theorem by Nelson. That theorem relates
Lie algebras of symmetric operators with unitary representations of a certain Lie grou... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
The thermal de Broglie wavelength is roughly the average de Broglie wavelength of the gas particles in an ideal gas at the specified temperature. It is defined as
\[\Lambda= \sqrt{\frac{h^2}{2\pi mk_BT}}\]
where
his the Planck constant mis the mass \(k_B\) is the Boltzmann constant Tis the temperature. References ↑ Lou... |
We say that $\Omega$ is a star-shaped domain (with respect to the origin) of $\mathbb R ^n$ if :
$$\Omega = \{x\in \mathbb R ^n : \left \| x \right \| < g(\frac{x}{\left \| x \right \|})\}\; \text{and}\;\; \partial \Omega = \{x\in \mathbb R ^n : \left \| x \right \| = g(\frac{x}{\left \| x \right \|})\} $$ with $g$ is ... |
Or: “How photons and electrons say hello”
Low energy — Photoelectric effect This is the first one you learn: a photon knocks an electron out of its atomic orbit. It is most likely to occur at low energies… as you move up in energy it becomes more likely that the photon will be scattered rather than absorbed. Medium ene... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
In the book
The Geometry of Domains in Spaces by Krantz and Parks, the authors proved the weak $(1,1)$-type estimate of the maximal function $M_\mu f$, where $\mu$ is a Radon measure, using their version of the Besicovitch covering theorem.
Let $d$ be a positive integer. Then there exists a constant $C=C(d)$ such that ... |
Larmor's formula$$P = {2 q^2 \dot{v}^2 \over 3 c^3}$$ states thatelectromagnetic radiation with power $P$ is produced by accelerating(or decelerating; hence the German name bremsstrahlungmeaning "brakingradiation") an electrical charge $q$. Charges can be accelerated byelectrostatic ormagnetic forces, gravitational acc... |
All lattices in the moonshine picture are
number-like, that is of the form $M \frac{g}{h}$ with $M$ a positive integer and $0 \leq g < h$ with $(g,h)=1$.To understand the action of the Bost-Connes algebra on the Big Picture it is sometimes better to view the lattice $M \frac{g}{h}$ as a primitive $h$-th root of unity, ... |
The way the Taylor polynomials of a function of one variable progressively converge to the graph of the function like
y = cos x is really quite impressive and is inherently interesting. We can extend this topic into three dimensions using CalcPlot3D.
As an exercise, I require my students to generate the linear and quad... |
Abstract
We give infinite series of groups $\Gamma$ and of compact complex surfaces of general type $S$ with fundamental group $\Gamma$ such that
1) Any surface $S’$ with the same Euler number as $S$, and fundamental group $\Gamma$, is diffeomorphic to $S$. 2) The moduli space of $S$ consists of exactly two connected c... |
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn" entsteht erst dadurch, dass wir sie beobachten.'Google Translate says this means something ...
@EmilioPisanty Tough call. ... |
Definition:Symmetric Difference/Definition 2 Definition
The
symmetric difference between two sets $S$ and $T$ is written $S * T$ and is defined as: $S * T = \paren {S \cup T} \setminus \paren {S \cap T}$
where:
There is no standard symbol for symmetric difference. The one used here, and in general on $\mathsf{Pr} \inft... |
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Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
I have a short question, related to the ongoing search of mathematics instructors for counter-examples to common undergraduate mistakes.
The classical example of a function that is differentiable everywhere but has discontinuous derivative is\begin{equation} f(x)=\left\{ \begin{array}{cc} x^2\sin(1/x) &(x\neq0), \\ 0 &... |
Can someone please verify my answers to the following questions?
Answer true or false to the following questions:
Two elements of a group in the same conjugacy class must have the same order
A group of order 24 can have 5 conjugacy distinct classes of cardinalities 1, 4,4,6, and 12 respectively.
The group $S_3$ has thr... |
Because the operators \(x\) and \(p\) are not compatible, \([\hat{X},\hat{P}]\neq 0\), there is
no measurement that can precisely determine both \(x\) and \(p\) simultaneously. Hence, there must be an uncertainty relation between them that specifies how uncertain we are about one quantity given a definite precision in ... |
April 27th, 2016, 01:56 PM
# 1
Newbie
Joined: Apr 2016
From: massachusetts
Posts: 7
Thanks: 1
Drawing a card probability
This is just something I became curious about, not homework or anything, but I don't understand the result I'm getting.
My attempt at a problem statement:
A contestant is presented with a game where ... |
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