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Let $\Omega \subset \mathbb R^d$ an open set and $u,v\in W^{1,p}(\Omega )\cap L^\infty (\Omega )$. Prove that $uv\in W^{1,p}(\Omega )$ and $$\partial _i(uv)=u\partial _iv+v\partial _iu.$$
I in fact don't really understand why we want $u,v\in L^\infty (\Omega )$. But here is the proof :
Let $K\subset \subset \Omega $ an... |
I found this question here but it does not fully answer my question. The answer there was that "composite bosons can occupy the same state when the state is spatially delocalized on a scale larger than the scale of the wavefunction of the fermions inside".
Let's say we do a BEC with bosonic atoms (for example in a harm... |
Difference between revisions of "User talk:WikiSysop"
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==Test external Link 29th January 2015==
==Test external Link 29th January 2015==
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[http://
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[http://.de]
==Test Copy&Paste HTML==
==Test Copy&Paste HTML==
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In particle physics, scalar potentials have to be bounded from below in order for the physics to make sense. The precise expressions of checking lower bound of scalar potentials are essential, which is an analytical expression of checking copositivity and positive definiteness of tensors given by such scalar potentials... |
I am having some troubles with a question regarding a joint distribution with several normal distributions.
The question is put up like this:
$X_1 , X_2$ are two normal distributions with the distribution $N(0,I_1) $. $Z_1 = \frac{X_1 +X_2}{2}, Z_2 = \frac{X_1 -X_2}{2}, Z_1 = \frac{X_2 -X_1}{2}$.
Find the joint distrib... |
Institute of Mathematical Statistics Lecture Notes - Monograph Series Escape of mass in zero-range processes with random rates Abstract
We consider zero-range processes in $\Z^d$ with site dependent jump rates. The rate for a particle jump from site $x$ to $y$ in $\Z^d$ is given by $\lambda_x g(k) p(y-x)$, where $p(\cd... |
How to treat $\epsilon$ and '\$' in top-down parser using predict table?
The construction of the predict table
Given a product $X \rightarrow w$, row $X$ and column $t$
-Mark $X \rightarrow w$ for each $t \in FIRST(w)$ -If $NULLABLE(w)$, then mark $X \rightarrow w$ for each $t \in FOLLOW(w)$ as well
says to create colu... |
This document is part of the “DrBats” project whose goal is to implement exploratory statistical analysis on large sets of data with uncertainty. The idea is to visualize the results of the analysis in a way that explicitely illustrates the uncertainty in the data.
The “DrBats” project applies a Bayesian Latent Factor ... |
I'm trying to find all conformal automorphisms of the upper half plane $\{\Im[z] \gt 0\}$, known to be $f(z) = \frac{az + b}{cz + d}$ where $a, b, c, d$ are real and $ad - bc \gt 0$.
The main work is to show that automorphisms are rational functions with real coefficients. The thing I'm having trouble with is steps (1.... |
Am I doing this right? I split the problem up into the cases of 2 same, 3 same, 4 same, but I feel like something special has to be done for 2 of the same, because what if there are 2 pairs (like two 3's and two 4's)?
This is what I have:
For 2 of the same: $5\times 5\times 6\times {4\choose 2}=900$
For 3 of the same: ... |
I came across the following problems on null sequences during the course of my self-study of real analysis.
Let $x_n = \sqrt{n+1}- \sqrt{n}$. Is $(x_n)$ a null sequence?
Consider $y_n = \sqrt{n+1}+ \sqrt{n}$. Then $x_{n}y_{n} = 1$ for all $n$. So either $(x_n)$ or $(y_n)$ is not a null sequence. It seems $(y_n)$ is not... |
This is the fifth post in a series on bubbles in the U.S. Equity Market. The first part can be found here.
Overview
In Part 2, we discussed the test developed by Phillips et al. to detect bubbles. As I mentioned in that post, the ADF test is basically looking for extreme return persistence. This gave me an idea - in th... |
I'm wondering if someone can provide a clarification between 2 seemingly opposing definitions from reputable sources on dynamical systems!
My Russian textbook, "Dynamical Systems I: Ordinary Differential Equations and Smooth Dynamical Systems" by Anosov, Arnol'd, Aronson, et al., says the following to determine whether... |
I want to calculate the total electrostatic energy of the Cavendish Experiment (two concentric spheres of radii $R_{1,2}$ which are connected, outer one gets charged, then removed, then after removing the outer sphere and measuring the charge of the inner one, it's zero).
The formula for this is:
$E_{tot} = \frac{1}{2}... |
Expected Discounted Utility
Expected discounted utility is one of the most common ways to represent preferences over risky consumption plans. Consider an agent, sitting at time , who will receive a consumption stream until :\begin{equation}U_t(c)= E_t \left[ \sum \limits_{s=t}^T \beta^{s-t}u_s(c_s)\right]\end{equation}... |
Yes, the question you meant to ask is true, although (as pointed out already) it is not quite correct as stated. To keep things clear, I will start by restating your question in a more precise form.
Let $n> 1$ be an integer and let $a_1,\ldots,a_n$ be positive real numbers, all between $0$ and $1$. Prove that$$\frac{\s... |
How would I solve the following.
An algorithm that is $O(n^2)$ takes 10 seconds to execute on a particular computer when n=100, how long would you expect to take it when n=500?
Can anyone help me answer dis.
Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of com... |
I'm learning about
Measure Theory and need some help with this problem:
Let $0 < \alpha < 1$. We construct a set $C_\alpha$ (Cantor type) as follows: In the first step we remove from the interval $[0, 1]$ a "middle" open interval of length $(1 - \alpha)3^{-1}$. In the nth step we remove $2^{n-1}$ open intervals of leng... |
If I understood well Riemann-Lesbegue lemma it says that the Fourier transform $\hat{f}(\xi)$ of a function $f(x)$, $x\in\mathbb{R}$ decays to zero with $\xi\to\infty$. Furthermore the more $f$ has continuous derivative the faster its Fourier transform goes to zero. In particular a discontinuous e.g. $f(x)=\text{Heavis... |
Let's say I have a noncyclic multiplicative group $G_m = \{j < m, \gcd(j,m) = 1\}$, with multiplication $\bmod m$. This has order $\varphi(m)$, and suppose I can determine its factorization.
Now suppose I have some prime $p_1 \in G_m$ which has order $n_1$ such that $n_1 < \varphi(m)$ (since $G_m$ is noncyclic) and $n_... |
Answer
See the answer below.
Work Step by Step
$0\leq\ell\leq n-1$ $\begin{smallmatrix} &n &\ell & Valid\ ?\\ \hline\\ 3p&3&1&\surd\\ 4s&4&0&\surd\\ 2f&2&3&\times\\ 1p&1&2&\times \end{smallmatrix}$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll ha... |
I found an unclear step for me in Zorich, Mathematical Analysis I, sec. 5.5, pag. 270. We are trying to find all $z \in\mathbb{C}$ for which the series:
$$c_0+c_1(z-z_0)+c_2(z-z_0)^2+...$$
converges. To do this, we try to understand when it converges absolutely, applying the Cauchy criterion to the series:
$$|c_0|+|c_1... |
Difference between revisions of "Applied/ACMS/absS18"
(→ACMS Abstracts: Spring 2018)
(→ACMS Abstracts: Spring 2018)
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The numerical simulation of single particle scattering of electromagnetic energy plays a fundamental role in remote sensing studies of the atmosphere and oceans, and in efforts to model ... |
Suppose that there is some natural number $a$ and $b$. Now we perform $c = a^2 + b^2$. This time, c is even.
Will this $c$ only have one possible pair of $a$ and $b$?
edit: what happens if c is odd number?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals i... |
There are a thousand apps for organising your life, calendars, todo lists, note trackers, but the big kahuna, the true Swiss army knife is org-mode. Out of the box, org-mode understands LaTeX and code snippets, todo lists and bookmarks, projects and agendas. Best of all, it comes with a powerful text editor, Emacs! Thi... |
for
disjointsets $(A_n)_{n \in \mathbb{N}}$
$P(\cup_n A_n) = \sum_n P(A_n)$
Is that really disjoint rather than pairwise disjoint?
If we have events $A, B, C$ s.t.
$A \cap B = \emptyset$
$A \cap C = \emptyset$
$B \cap C \neq \emptyset$
$P(B \cap C) > 0$,
then A, B and C are disjoint but not pairwise disjoint...I think?... |
I have a question refer to The first theorem of the isomorphisms. The theorem states that if we have a $$\dot G \cong \frac{G}{\ker(\varphi)}$$ where the co-domain $\dot G$ will be isomorphic to the quotient group $G$ by the $\ker(\varphi)$ and $\frac{G}{\ker(\varphi)}$ from my understanding contains all equivalence cl... |
Kaj Hansen
As an undergraduate, I studied mathematics at the University of Georgia. In early 2014, I put together a short series of expository videos on Ramsey theory that can be viewed here (produced and published by my good friend Eddie Beck).
I'm active primarily in the point-set topology and various abstract algebr... |
When i asked this question, the teacher thought i was questioning the concept of integrals, whereas I do nearly fully understand integrals, just not how it is used to find area under a curve.
Note sure what you are asking. There could be 2 interpretations to this question:
How to use integration to find area under a cu... |
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Now showing items 1-10 of 19
J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
Probability Seminar Spring 2019 Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. We usually end for questions at 3:15 PM.
If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu
January 31, Oanh Nguyen, Princeton
Title:... |
System of generalized mixed nonlinear ordered variational inclusions
Department of Mathematics, Jazan University, Jazan, 45142, KSA
In this paper, we consider a system of generalized mixed nonlinear ordered variational inclusions in partially ordered Banach spaces and suggest an algorithm for a solution of the consider... |
A subset $A$ of a topological space $(X,\tau)$ is said to be
denseif $\overline A=X$. Prove that if for each open set $O\neq\varnothing$ we have $A\cap O\neq\varnothing$, then $A$ is dense in $X$.
Could you please check if the following is right? Thanks!
A characterization of $\overline A$ is $$\overline A=\bigcap_{\al... |
It should be little surprise that this can be attacked via contour integration. As always, the challenge is to find the contour and the function to integrate over that contour. At the risk of presenting a
deus ex machina, I am simply going to present these and demonstrate how they provide what we need.
Consider the fol... |
Can biological enzymes catalyze thermodynamically unfavorable reactions? I read that an enzyme lowers the activation energy of a reaction by offering an alternative reaction pathway with a lower activation energy, however the ΔG of the reaction is unchanged. If enzymes
can do this, then how exactly does this work?
Can ... |
A minimum, if boring example is that of two uncoupled 1D linear ODE (with incommensurate constants) on a torus, such as can be found in Hasselblatt & Katok:
$$\left\{\begin{aligned}\dot x &= \omega_1\\\dot y &= \omega_2,\end{aligned}\right. \tag{4.2.3}$$
whose trivial solution is
$$\left\{\begin{aligned}x &= x_0 + \ome... |
Osmotic pressure Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane. [1] It is also defined as the measure of the tendency of a solution to take in water by osmosis.
The phenomenon of osmotic pressure arises from the tende... |
What does it mean for the ratio of the lengths of the sides of a rectangle to be
rational, say $\frac{5}{3}$? It means that if the long side of the rectangle is divided into five equal parts, and if one counts out three of those parts, then the length of the resulting line segment equals the length of the short side of... |
Suppose I want to estimate the following VAR(1) model: $$ Y_t = \mu + \Phi Y_{t-1} + \varepsilon_t $$ where $Y_t=(y_{1t}, y_{2t},…,y_{kt})'$, $\mu=(\mu_1,…,\mu_{k})’$ and $\Phi$ a matrix of coefficients. I’m interested in obtaining the coefficients in $\Phi$ such that the resulting vector of predicted values $\hat{Y}_t... |
One excellent resource is to try Kaggle and to examine some of the competitions, some of which are specifically on the application of machine learning to credit scoring.https://www.kaggle.com/c/GiveMeSomeCreditYou wil see that the winning solution is made public, including source code and output.https://github.com/IdoZ... |
Which is the best way to put function plots into a LaTeX document?
To extend the answer from Mica,
pgfplots can do calculations in TeX:
\documentclass{standalone}\usepackage{pgfplots}\begin{document}\begin{tikzpicture} \begin{axis}[ xlabel=$x$, ylabel={$f(x) = x^2 - x +4$} ] \addplot {x^2 - x +4}; \end{axis}\end{tikzpi... |
I guess I can't avoid the temptation. Try:
simulate this circuit – Schematic created using CircuitLab
In both examples above, you want to use an ultra low current supply, rail-to-rail i/o opamp, with low offset voltage and current. I think the LT1494 may be at least interesting here. The opamp needs to be in control wi... |
Let $A=\mathbb K[X_1,\ldots,X_n]$ be a polynomial ring over some field $\mathbb K$. Let $\mathfrak p\subseteq A$ be a prime ideal. Let $Z(\mathfrak p)=\{ \mathfrak m\subset A\text{ maximal}\mid \mathfrak p\subseteq\mathfrak m\}$ be the set of maximal ideals of $A$ that lie over $\mathfrak p$. My intuition says that $$ ... |
Please tell me where I've gone wrong (if I did in fact make a mistake). I'm pricing a long forward on a stock. The usual setup applies:
This has payoff $S(T) - K$ at time $T$. We are at $t$ now. $S(T) = S(t)e^{(r-\frac12 \sigma^2)(T-t)+\sigma(W(T)-W(t))}$. $W(t)$ is a Wiener process. $K \in \mathbb{R}_+$. $Q$ is the ri... |
Related Topics: More Lessons on Vectors
In these lessons, we will learn how to determine if the given vectors are parallel.
A vector is a quantity that has both magnitude and direction.
What are Parallel Vectors?
Vectors are parallel if they have the same direction.
Both components of one vector must be in the same rat... |
ok, suppose we have the set $U_1=[a,\frac{a+b}{2}) \cup (\frac{a+2}{2},b]$ where $a,b$ are rational. It is easy to see that there exists a countable cover which consists of intervals that converges towards, a,b and $\frac{a+b}{2}$. Therefore $U_1$ is not compact. Now we can construct $U_2$ by taking the midpoint of eac... |
Let $R$ be a commutative ring with unit element. Suppose that it only has a finite number of ideals. Show that it is a field
My reasoning is as follows:
Let $a \in R-\{0\}$. Since $R$ is a commutative ring, it can be shown that $Ra$ is an ideal of $R$. It follows that $Ra^n$ is also an ideal of $R$, for every $n \in \m... |
How many kids?
This is the toughest factor to find. While Santa isn't specific to a single religion, traditions differ in various parts of the world, and belief rates in Santa Claus are not tracked by the WHO, looking at Christians seemed to be a reasonable, if imperfect, start. According to 2010 estimates, there are 2... |
NTS ABSTRACT
Return to NTS Fall 2015
Contents Sep 03
Kiran Kedlaya On the algebraicity of (generalized) power series
A remarkable theorem of Christol from 1979 gives a criterion for detecting whether a power series over a finite field of characteristic p represents an algebraic function: this happens if and only if the... |
Here $\mathbb N = \{2,3,4,\dots\}$ with the binary operation of addition.
If $m \in \mathbb N$ we denote by $G_{\mathbb N} (m)$ the semigroup generated by $m$.
Definition: A number $p$ is said to be prime if for all $m \lt p$, $\;p \notin G_{\mathbb N} (m) $.
We denote the set of non-empty finite subsets of $\mathbb N$... |
I'm having a little difficulty understanding the definition of monoidal category. I intuitively understand what the axioms are expressing, but I'm having a bit of difficulty knowing which functors the natural isomorphisms are actually relating. My weak understanding of the situation is that $\alpha$ is a natural isomor... |
Mathematical symbols are used to perform various operations. The symbols make it easier to refer the maths quantities and help in easy denotation. It is interesting to note that the whole of maths is completely based on numbers and symbols. The math symbols not only refer to different quantities but also represent the ... |
$$ \lim_{(x,y)\to (0,0)} \frac {x^3y^2}{x^4+y^6} $$ Does this limit exist?
I've tried substituting y=x^0.5 and y=x^(2/3) which both goes to 0.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to ... |
Solve the following PDE, $$ u_t(x,t)=ku_{xx}(x,t)-bu(x,t)$$ where $b>0$, with boundary conditions $$u(0,t)=u(c,t)=0 $$
My attempt
Assume $u(x,t)=X(x)T(t)$ and plugging into the diffirential equation,
$$X(x)T'(t)=kX''(x)T(t)-bX(x)T(t)$$
$$\dfrac{T'(t)}{T(t)}=k\dfrac{X''(x)}{X(x)}-b=-\lambda$$
Then solving $X(x)$ gives t... |
Let $G$ be a finite group with $|G|>2$. Prove that Aut($G$) contains at least two elements.
We know that Aut($G$) contains the identity function $f: G \to G: x \mapsto x$.
If $G$ is non-abelian, look at $g : G \to G: x \mapsto gxg^{-1}$, for $g\neq e$. This is an inner automorphism unequal to the identity function, so ... |
We will establish the identity by counting the elements of the same set two different ways.
Begin by considering the trinomial coefficient for ($m$, $n$ - $m$, $k$); i.e., the coefficient of the $a$
m$b$ n-m$c$ k term in the expansion of ($a$ + $b$ + $c$) n+k.This coefficient can be calculated by counting the number of... |
Definition:Standard Representation of Simple Function
Jump to navigation Jump to search
Definition
Let $\left({X, \Sigma}\right)$ be a measurable space.
Let $f: X \to \R$ be a simple function.
A standard representation of $f$ consists of: a finite sequence $a_1, \ldots, a_n$ of real numbers a partition $E_0, E_1, \ldot... |
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Now showing items 1-10 of 27
Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
Here are some crazy ideas, with absolutely no guarantee that they'll find a good solution -- but ideas you could try.
One possible heuristic approach might be to use quadratic programming combined with randomized rounding and some more heuristics.
In particular, introduce variables $x_i$ (for $i=1,2,120$); the idea is ... |
(For easier discussion, I suggest you to read the introduction of Schroder's equation and the section on 'Conjugacy' of iterated function, in case you are not familiar with these topics.)
Let $f(x)=\frac12\arctan x$, and $f_n(x)$ be the $n$th iteration of $f$.
Let us reduce functional iteration to multiplication: if we... |
Hello, I don't know if this is a good place for exposing my problem but I'll try...
I have a gauge theory with action:
$S=\int\;dt L=\int d^4 x \;\epsilon^{\mu\nu\rho\sigma} B_{\mu\nu\;IJ} F_{\mu\nu}^{\;\;IJ} $
Where $B$ is an antisymmetric tensor of rank two and $F$ is the curvature of a connection $A$ i.e: $F=dA+A\we... |
The existence of the exponential on $\mathbb{C}$ has a very basic, yet very strong consequence : $(\mathbb{C}^*,\cdot)$ is a quotient of $(\mathbb{C},+)$. This question is concerned with fields $K$ such that $K^*$ is a quotient of $K$ ; that is, with the existence of a
surjective group morphism $K\to K^*$. I will refer... |
Some explanations first
The substitution in the question introduces the reduced wave function $u(r)$ by solving the original radial equation in polar coordinates,
$$-\frac{1}{2}\left(R''(r)+\frac {1}{r}R'(r)\right) - \frac{1}{r}R(r) + \frac {m^2}{2r^2}R(r) = E R(r)$$
using the
ansatz
$$R(r)\equiv \frac{1}{\sqrt{r}}u(r)... |
Alles, B. and D'Elia, M. and Giacomo, A. Di (2005)
Analyticity in theta on the lattice and the large volume limit of the topological susceptibility. Physical review. D, Particles, fields, gravitation, and cosmology, 71 . 034503. ISSN 1550-7998 Abstract
Non-analyticity of QCD with a \theta term at \theta=0 may signal a ... |
The Reynolds number, with $\rho$ the density, $u$ the velocity magnitude, $\mu$ the viscosity and $L$ some characteristic length scale (e.g. channel height or pipe diameter) is given by$$\text{Re}=\frac{\rho~u~L}{\mu}.$$This is a dimensionless relation of the ratio of inertial forces ($\rho u u$) to viscous forces ($\m... |
What causes it and how does it occur? If you do post some mathematics, please explain what each term means too please.
Quantum fluctuations are a popular buzzword for the statistical triviality that the variance (the spread of values) of a random variable A (in context of quantum physics, this could be the position of ... |
First let us fix the terminology.
The space (1) is known in General Topology as the Golomb space. More precisely, the
Golomb space $\mathbb G$ is the set $\mathbb N$ of positive integers, endowed with the topology generated by the base consisting of arithmetic progressions $a+b\mathbb N_0$ where $a,b$ are relatively pr... |
Boundedness and a priori estimates of solutions to elliptic systems with Dirichlet-Neumann boundary conditions
1.
Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 84173 Bratislava, Slovak Republic
2.
Institute of Applied Mathematics and Statistics, Comenius University, Mlynská dolina, 84248 Bratislav... |
I figured I'd answer a self-contained post here for anyone that's interested. This will be using the notation described here.
Introduction
The idea behind backpropagation is to have a set of "training examples" that we use to train our network. Each of these has a known answer, so we can plug them into the neural netwo... |
ok, suppose we have the set $U_1=[a,\frac{a+b}{2}) \cup (\frac{a+2}{2},b]$ where $a,b$ are rational. It is easy to see that there exists a countable cover which consists of intervals that converges towards, a,b and $\frac{a+b}{2}$. Therefore $U_1$ is not compact. Now we can construct $U_2$ by taking the midpoint of eac... |
ä is in the extended latin block and n is in the basic latin block so there is a transition there, but you would have hoped \setTransitionsForLatin would have not inserted any code at that point as both those blocks are listed as part of the latin block, but apparently not.... — David Carlisle12 secs ago
@egreg you are... |
this might be a stupid question, but I wanted to know that if a,b,c are positive reals and $$ab+bc+ca\geq 3$$ Can we say that $$3 \sqrt[3]{(abc)^2} \geq 3$$ By applying am-gm? I'm confused about whether we can do this or not. I'd really appreciate it if someone could explain.
I believe we cannot arrive at this conclusi... |
Given real vectors $d = (d_1, \ldots, d_n)$ and $\lambda = (\lambda_1, \ldots, \lambda_n)$, where I will assume that their coefficients are arranged in non-increasing order, the Schur-Horn theorem says that there exists a Hermitian matrix with the diagonal given by $d$ and spectrum given by $\lambda$ if and only if $d ... |
Consider a single particle (a single qubit if you will) in some arbitrary state $|\psi\rangle$ and an eigenvector $|\lambda\rangle$ corresponding to the eigenvalue $\lambda.$ Consider the time evolution of this system in some infinitesimal time $\epsilon$ to be given by a unitary operator U: $|\psi(\epsilon)\rangle = U... |
The soft-photon theorem is the following statement due to Weinberg:
Consider an amplitude ${\cal M}$ involving some incoming and some outgoing particles. Now, consider the same amplitude with an additional soft-photon ($\omega_{\text{photon}} \to 0$) coupled to one of the particles. Call this amplitude ${\cal M}'$. The... |
AI News, Sequence Classification with LSTM Recurrent Neural Networks in Python with Keras On Tuesday, March 6, 2018 By Read More Sequence Classification with LSTM Recurrent Neural Networks in Python with Keras
Sequence classification is a predictive modeling problem where you have some sequence of inputs over space or ... |
Hyperbolic tangent function \({\rm tanh}\) is often used to generate the stretched structured grid.
In this blog post, I will introduce some examples I have found in the references.
Example #1 [1]
\begin{equation}y_j = \frac{1}{\alpha}{\rm tanh} \left[\xi_j {\rm tanh}^{-1}\left(\alpha\right)\right] + 1\;\;\;\left( j = ... |
Construct a hyperbolic triangle from $A$, $B$, and the center of the unit circle, $C$. Let $a$ be the length of $BC$, $b$ the length of $AC$, and $c$ the length of $AB$. Let $\alpha$, and $\gamma$ be the values of $\angle CAB$ and $\angle ACB$, respectively.
The value of $c$ is given as distance $d$:$$c = d$$
The value... |
ok, suppose we have the set $U_1=[a,\frac{a+b}{2}) \cup (\frac{a+2}{2},b]$ where $a,b$ are rational. It is easy to see that there exists a countable cover which consists of intervals that converges towards, a,b and $\frac{a+b}{2}$. Therefore $U_1$ is not compact. Now we can construct $U_2$ by taking the midpoint of eac... |
I have been trying to find the gaussian curvature of a pseudo sphere. I assumed the parametrization: X(u,v) = (cos(u)*sech(v), sin(u)*sech(v), u - tanh(u)). I know that it's a surface of revolution obtained by the tractrix. I could find it calculating the coefficients of the first and second form. But I observed that i... |
How can I show this is the case?
Since you have full specification of the sampling distribution of your observations, you can get the explicit form of the log-likelihood. Treating $\sigma$ as fixed and removing additive constants we have:
$$\ell_\mathbf{x}(\theta) = -\frac{1}{2 \sigma^2} \sum_{i=1}^n (x_i - \theta)^2 \... |
In my class it was said that
"A tangent vector $X \in T_p(\mathbb{R}^n)$ acts on a one-form to give a real number"
and
"A one-form acts on a tangent vector to give a real number"
Now the 'tangent space' $T_p(\mathbb{R}^n)$ is a $n$-dimensional vector space and the elements of $T_p(\mathbb{R}^n)$ which we call tangent v... |
You are correct that with a greedy target policy $\pi$, $\pi(s_t, a_t)$ always equals either $1$ or $0$. This does not mean the algorithm cannot learn though. It only means that the algorithm can only learn from the sequence of steps up until an action was taken that the target policy (which can be greedy) would never ... |
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Now showing items 1-1 of 1
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Yes, if $X$ is smooth and $\bar X\cap \mathbb P^{n-1}$ is smooth
in the scheme theoretic sense, then $\bar X$ is indeed smooth. In other words if $s\in \bar X$ is singular, so is $s\in \bar X\cap H $ for any hyperplane $s\in H\subset \mathbb P^{n}$ .
Beware however that you have to take scheme-theoretic intersections.
... |
Here is one proof.
Lemma. Let $X$ be a cell complex, $G$ a finite group and $G\times X\to X$ is an action. Then for every field $F$ of characteristic zero,$$H^*(X/G; F)\cong H^*(X;F)^{G},$$ where the right hand-side is the ring of invariants under the $G$-action on $H^*(X)$.
This lemma is an application of the "transfe... |
Consider the parameter integral
$$I(a)=\int_0^1\frac{\log(a+t^2)}{1+t^2}\mathrm dt\tag1$$
Where $\log$ denotes the natural logarithm and $a\in\mathbb{C}$. I am struggling to evaluate this integral in a closed-form. I am not even sure whether there is such an expression.
However, first of all lets just concentrate on so... |
Let $\mathcal{N}$ and $\mathcal{M}$ be algebras of sets on $S$ and $T$ respectively. Let $\mathcal{N}\times\mathcal{M}$ the algebra generated by the rectangles in $S\times T$ (i,e the sets with the form $A\times B$ where $A\in\mathcal{N}$ and $B\in\mathcal{M}$). We denote by $\mathcal{N}\triangle\mathcal{M}$ to the $\s... |
You might consider 241162 and 102575. This is actually a history of science question, on a half-century old landmark in the intellectual history of 20th century physics, whose importance cannot be overstated. Perhaps it belongs to another site.
For a quartic potential, following Schwinger, the
σ mass may be sent to inf... |
I apolgize for contributing yet another question asking about an application of CS. Here it is:
Suppose $p_1, \dots ,p_n$ and $a_1,...,a_n$ are real numbers such that $p_i \geq 0$, $a_i \geq 0$ for all $i$, and $p_1 + \dots + p_n = 1$. Then $$(p_1a_1+ \dots + p_na_n)\left(\frac{p_1}{a_1}+ \dots + \frac{p_n}{a_n}\right)... |
I want to find sum of the first $n^{th}$ term of this sqequence . $$2,5,13,35,97,275,793,...\\s_n=2+5+13+35+97+...$$
What is the closed form formula for $s_n$?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to si... |
Lasted edited by Andrew Munsey, updated on June 15, 2016 at 2:10 am.
Amplitude modulation (AM) is a technique used in electronics, most commonly for transmission via a
There was an error working with the wiki: Code[23] wirelessly.
Amplitude modulation works by varying the strength of the transmitted signal in relation ... |
I have reduced my solution of a 1D heat equation boundary value problem to the following:
$$W(z, t) = \sum_{n=1}^\infty b_n \sin(\lambda_n z) e^{-\lambda_n^2 \alpha t}$$
To get the coefficients $b_n$, I apply the initial condition that: $W(z, 0) = T_0$, which gives the Fourier Sine Series:
$$\sum_{n=1}^\infty b_n \sin(... |
We are interested in estimating Conditional Quantile Treatment Effects on the Treated (QTT) with two periods of panel data (or repeated cross sections) under a Difference in Differences Assumption. These are defined by
\[ CQTT_x(\tau) = F^{-1}_{Y_{1t}|X=x,D=1}(\tau) - F^{-1}_{Y_{0t}|X=x,D=1}(\tau) \]
for \(\tau \in (0,... |
Can the Ricci curvature tensor be obtained by a 'double contraction' of the Riemann curvature tensor? For example
$R_{\mu\nu}=g^{\sigma\rho}R_{\sigma\mu\rho\nu}$.
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up.Sign up to ... |
Differences
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Both sides previous revision Previous revision rational_numbers [2016/04/23 13:49]
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Could somebody explain to me where these two formulas come from as applications of the binomial theorem? $$\sum_{k=0}^n {n \choose k}(-1)^kk^r=0$$ for non-negative integers $r\lt n$. And $$\sum_{k=0}^n {n \choose k}(-1)^kk^n=(-1)^nn!$$
They don’t come from the binomial theorem: they come from the inclusion-exclusion pr... |
Let $f\in \mathcal R[0,1]$ , and $g:\mathbb R \to \mathbb R $ is continuous and periodic with period $1$ . Then is it true that
$\lim_{n \to \infty}\int_0 ^1 f(x)g(nx)dx=\Big(\int_0^1f(x)dx\Big)\Big(\int_0^1 g(x)dx\Big)$ ?
Mathematics Stack Exchange is a question and answer site for people studying math at any level an... |
I started to study about Metric space at uni and am confused with the definitions open and closed set. It seems to me that being an open set always satisfies the definition of a closed set.
closed as unclear what you're asking by Parcly Taxel, Namaste, Jack, TheSimpliFire, Saad Feb 25 '18 at 9:37
Please clarify your sp... |
In chemistry, the
mass fraction w_i is the ratio of one substance with mass m_i to the mass of the total mixture m_{tot}, defined as [1] w_i = \frac {m_i}{m_{tot}}
The sum of all the mass fractions is equal to 1:
\sum_{i=1}^{N} m_i = m_{tot} ; \sum_{i=1}^{N} w_i = 1
Mass fraction can also be expressed, with a denominat... |
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