text stringlengths 256 16.4k |
|---|
Search
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 ... |
Search
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 ... |
Search
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 ... |
I think there are two legitimate sources of complaint. For the first, I will give you the anti-poem that I wrote in complaint against both economists and poets. A poem, of course, packs meaning and emotion into pregnant words and phrases. An anti-poem removes all feeling and sterilizes the words so that they are clear.... |
Definition:Continuous Real Function/Left-Continuous/Point Definition
Let $f: A \to \R$ be a real function.
Let $x_0 \in A$. $\displaystyle \lim_{\substack{x \mathop \to x_0^- \\ x_0 \mathop \in A}} f \left({x}\right) = f \left({x_0}\right)$
where $\displaystyle \lim_{x \mathop \to x_0^-}$ is a limit from the left.
Furt... |
We have now seen some of the most generally useful methods for discovering antiderivatives, and there are others. Unfortunately, some functions have no simple antiderivatives; in such cases if the value of a definite integral is needed it will have to be approximated. We will see two methods that work reasonably well a... |
In electrodynamics, for a line segment of length 2L with a uniform line charge $\lambda$, the electric field at a distance z above the midpoint of this straight line segment is
$E\left(\vec{r}\right)=\frac{1}{4 \pi \varepsilon_{0}}\frac{2 \lambda L}{z\sqrt{z^{2}+L^{2}}}\hat{z}$
For a field point z > > L:
We may 'transl... |
This is related to another question I just asked where I learned that the equation of motion of a harmonic oscillator is expressed as:
$$\ddot{x}+kx=0$$
What little physics I grasp centers on geodesics as derived from the principle of stationary action and the Euler-Lagrange equations. I have therefore become accustome... |
Omega, $\omega$
The smallest infinite ordinal, often denoted $\omega$ (omega), has the order type of the natural numbers. As a von Neumann ordinal, $\omega$ is in fact equal to the set of natural numbers. Since $\omega$ is infinite, it is not equinumerous with any smaller ordinal, and so it is an initial ordinal, that ... |
In this section, we show that the proof of Theorem 7 in [2] is wrong. Following [2], we define 1-liv\(_2\) to denote the family of languages \(B_n\) restricted to words of length 2. Let us first restate the theorem.
Theorem 7 (Bianchi et al. [2] ). Consider propositional variables r( a) (\(\lnot r(a)\), resp.) with the... |
Two players A and B each has a fair coin and they start to toss simultaneously (counted as one round). They toss in $n$ ($\ge 1$) rounds and stop because they have accumulated the same number of heads (could be 0, the case that both of them did not get any head) for the first time. What is the distribution of $n$ and i... |
As mentioned in the comments, Binet's formula,
$$F_n=\frac1{\sqrt{5}}(\phi^n-(-\phi)^{-n})$$
where $\phi=\frac12(1+\sqrt 5)$ is the golden ratio, is a closed-form expression for the Fibonacci numbers. See this related question for a few proofs.
As for counting how many Fibonacci numbers are there that are less than or ... |
Does this inequality always hold : $$\frac{1}{6} \pi ^2 \prod _{i=1}^x \frac{\left(p_i\right){}^2-1}{\left(p_i\right){}^2}\leq \frac{1}{p_x}+1 $$
such that $p_i$ is the $i$-th prime number
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.Sign up to join this ... |
Solving a differential equation generally goes something like this:
One is given a set of initial conditions. There is a large freedom of choice in doing so. For example, in Quantum Mechanics any normalizable $\psi(x,0)$ will do The differential equation then determines how the state evolves, giving $\psi(x,t)$ for all... |
Recently Makoto Kikuchi (Kobe University) asked me the following interesting question, which arises very naturally if one should adopt a mereological perspective in the foundations of mathematics, placing a focus on the parthood relation rather than the element-of relation. In set theory, this perspective would lead on... |
I'm trying to derive the Chernoff bound $\mathrm{erfc}(x) \le \exp(-x^2)$, by first showing:
$$\mathrm{erfc}(x) = \frac{2}{\pi}\int_{0}^{\frac{\pi}{2}}\exp\left(-\frac{x^2}{\cos^2\theta}\right)d\theta$$
This equality should be derived by considering 2 independent, standard gaussian random variables $x_1, x_2$ and the r... |
Euclidean Geometry • Equitable Distributing • Linear Programming • Set Theory • Nonstandard Analysis • Advice • Topology • Number Theory • Computation of Time (Previous | Next)
In the following section, the Set Theory is presupposed.
Definition: A family of sets \(\mathbb{Y} \subseteq \mathcal{P}(X)\) is called
topolog... |
Prove that: $$6 \not\left|\ \left\lfloor\frac 1 {(\sqrt[3]{28} - 3)^{n}}\right\rfloor \ (n \in Z^+)\right.$$ ($\lfloor x\rfloor$ = largest integer not exceeding $x$)
I am very bad as English and number theory, please help me
Mathematics Stack Exchange is a question and answer site for people studying math at any level ... |
Inspired by Joshua Grochow and Iddo Tzameret's answers in a post on http://cstheory.stackexchange.com , I would like to get more references on possible connections between complexity theory and set ...
In this post, when I talk about bounded arithmetic theories,I mean the theories of arithmetic according to "Logical Fo... |
ISSN:
1534-0392
eISSN:
1553-5258
All Issues
Communications on Pure & Applied Analysis
March 2002 , Volume 1 , Issue 1
Select all articles
Export/Reference:
Abstract:
An efficient adaptive moving mesh method for investigation of the semi-classical limit of the focusing nonlinear schrödinger equation is presented. The me... |
I'm asking about the answer here:
I didn't understand the best answer here
Choose edge $e \in T_1 \mathop{\Delta} T_2$ with $w(e) = \min W$, that is $e$ is an edge that occurs in only one of the trees and has minimum disagreeing weight. Such an edge, that is in particular $e \in T_1 \mathop{\Delta} T_2$, always exists:... |
An anisotropic harmonic oscillator in three dimensions is given by the potential:
$$V(X,Y,Z)=\frac{1}{2}m\omega^2\bigg[\bigg(1+\frac{2\lambda}{3}\bigg)(X^2+Y^2)+\bigg(1-\frac{4\lambda}{3}Z^2\bigg)\bigg].$$
The energy eigenvalues of the stationary states are:
$$E_{n_x,n_y,n_z}=(n_x+n_y+1)\hbar\omega\sqrt{1+\frac{2\lambd... |
V. Gitman, J. D. Hamkins, and A. Karagila, “Kelley-Morse set theory does not prove the class Fodor theorem.” (manuscript under review)
@ARTICLE{GitmanHamkinsKaragila:KM-set-theory-does-not-prove-the-class-Fodor-theorem, author = {Victoria Gitman and Joel David Hamkins and Asaf Karagila}, title = {Kelley-Morse set theor... |
You have the concept slightly wrong.
This part is mostly correct:
In Reinforcement learning a random-initialized network will first "play"/"do" a sequence of moves in an environment. (In this case a Game). After that, it will receive a reward r.
Technically neural networks are not required in RL, and it is really worth... |
Parentheses and brackets are very common in mathematical formulas. You can easily control the size and style of brackets in LaTeX; this article explains how.
Contents
Here's how to type some common math braces and parentheses in LaTeX:
Type LaTeX markup Renders as Parentheses; round brackets
(x+y)
\((x+y)\) Brackets; s... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
The axioms of Kripke-Platek set theory
Kripke-Platek set theory ($\text{KP}$) is a collection of axioms that is considerably weaker than ZFC. The formal language used to express each axiom is first-order with equality ($=$) together with one binary relation symbol, $\in$, intended to denote set membership.
$L_\alpha$ i... |
I'm trying to solve a problem but I suspect my solution is incorrect. I'm hoping someone can verify and perhaps give me an idea about how to solve it correctly.
We have three fair coins and each is tossed until the first head appears on each coin. (So once one head appears on one of the three coins, we stop tossing tha... |
I need to prove the fact that a quantum channel (a superoperator) cannot increase the Holevo information of an ensemble $\epsilon = \{\rho_x, p_x\}$. Mathematically expressed I need to prove
$$\begin{align} \chi(\$(\epsilon)) \leq \chi(\epsilon) \end{align} \tag{1}\label{1}$$
where $\$$ represents a quantum channel (a ... |
I'm dealing with a CGARCH-M model that the long and short-run volatility components have different effects on returns. Here are its mean and variance equations:
Mean equation:
$$ y_t = \alpha + \beta x_t + \gamma_1 \sqrt{\sigma_{t}^2-q_{t}}+\gamma_2 \sqrt{q_{t}} +\varepsilon_{t} $$
Variance equation:
$$ \sigma_{t}^2 = ... |
What are the integrals of motion of a system with the following Lagrangian?
$$L=a\dot{\phi_1}^2+b\dot{\phi_2}^2+c\cos(\phi_1-\phi_2)$$?
where $a,b,c$ are constants, $\phi_1,\phi_2$ are angles and $\dot{\phi_i}$ represents differentiation wrt time.
I believe the Hamiltonian is conserved, but are there any more?
Perhaps ... |
Let $A = C^\infty(S^1)$ be the ring of smooth functions on the circle (if you prefer, you can see it as the ring of smooth $2\pi$-periodic functions $\mathbb R \to \mathbb R$).
First, $A$ isn't Noetherian : the ideal $I_{\mathscr V(0)}$ of functions vanishing on a neighbourhood of $0$ isn't finitely generated.
But the ... |
I have following problem: I have a sorted sequence of $N$ integers (assume they are monotonically increasing). I want to check whether there is any subsequence of length $\ge N/4$, such that consecutive elements of the subsequence all differ by the same value.
For example, in the sequence [3,4,5,8,12] there are two suc... |
Let $G$ be an Abelian group. And let H={$g\in G |\mathrm{order}(g) < \infty$}
I need to prove that H is a normal subgroup in G.
I know that if i prove it's a subgroup, it will be normal as well, since G is Abelian. But i wonder about it being a subgroup.
I know this has to work: $$\forall h_1, h_2\in H,\hspace{1cm}h_1*... |
Can you please help me find this integral?
$$\int \sin(\ln(x)) dx$$
Give me a clue or show step by step solutions please.
Thank you very much.
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 ... |
I liked @ttnphns's suggestion (that he made in the comments above) so much, that could not resist from trying it out.
As @ttnphns said, LDA is equivalent to canonical correlation analysis (CCA) between your multivariate data and the set of dummy variables coding class labels. In case of only two groups, there is only o... |
The inhomogeneous PME in several space dimensions. Existence and uniqueness of finite energy solutions
1.
Departamento de Matemática Aplicada, E.T.S.I. de Caminos, Canales y Puertos, Universidad Politécnica de Madrid. 28040 Madrid, Spain
2.
Departamento de Matemáticas, Universidad Autónoma de Madrid, Cantoblanco, 28049... |
It looks like you are on the wrong track.
While it is trivially true that $(L_1^*L_2^*)^{(0)} = \lambda = (L_1\cup L_2)^{(0)}$ where $\lambda$ is the language consisting of the empty word, it is more often than not that $(L_1^*L_2^*)^{(1)}\neq (L_1\cup L_2)^{(1)}$. For example, if either $L_1$ or $L_2$ has a non-empty ... |
I'm interested in numerical analysis but I don't have experience on it. I was wondering how one can solve integral equations numerically like $\int_0^x e^{t^3}dt=4$? I was thinking whether there is some numerical differential equation solution method faster that finding some range $a\leq x\leq b$ and then splitting tha... |
I've seen Baire category theorem used to prove existence of objects with certain properties. But it seems there is another class of interesting applications of Baire category theorem that I have yet to see.
First I found this MathOverflow problem:
Let $f$ be an infinitely differentiable function on $[0,1]$ and suppose ... |
Search
Now showing items 1-10 of 53
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... |
Search
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 ... |
Search
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 ... |
The change of Gibbs energy at constant temperature and species numbers, $\Delta G$, is given by an integral $\int_{p_1}^{p_2}V\,{\mathrm d}p$. For the ideal gas law $$p\,V=n\,RT,$$ this comes down to $$\int_{p_1}^{p_2}\frac{1}{p}\,{\mathrm d}p=\ln\frac{p_2}{p_1}.$$ That logarithm is at fault for a lot of the formulas i... |
Cardinal characteristics of the continuum The subject known as cardinal characteristics of the continuum explores the rich territory---sometimes hidden from view, depending on the set-theoretic background---between the countably infinite cardinal $\aleph_0$ and the uncountable cardinality of the continuum. The subject ... |
Given initial values $d[0]$ and $k[0]$, I would like to solve for the initial rate of change, $\dot d[0]$, and compare this value against some data.
I have the following profit function, which I would like to maximize:
$$\pi=\int^T_0 e^{-pt}(-50 (d - .1)^2 (d - .95) (d - .7) - 4 (.3 - k)^2 + 2 d k - \dot d^2-\dot k^2) ... |
I came across the following YouTube video by Numberphile today:
It is about multiplicative persistence which means roughly the following. We take an integer and multiply the digits together to get a new number. This will be done in a loop until we get a single digit number. Example: 3279->378->168->48->32->6. The persi... |
> Input
> Input
>> 1²
>> (3]
>> 1%L
>> L=2
>> Each 5 4
>> Each 6 7
>> L⋅R
>> Each 9 4 8
> {0}
>> {10}
>> 12∖11
>> Output 13
Try it online!
Returns a set of all possible solutions, and the empty set (i.e. \$\emptyset\$) when no solution exists.
How it works
Unsurprisingly, it works almost identically to most other answe... |
Let $R$ be the ring of all functions $f : \Bbb{R}\longrightarrow \Bbb{R}$ which are continuous outside $(-1,1)$ and let $S$ be the ring of all functions $f : \Bbb{R}\longrightarrow \Bbb{R}$ which are continuous outside a bounded open interval containing zero (depended on $f$). Is it true that $R \cong S$?
They are not ... |
I began with problem which looked simple in the beginning but became increasingly complex as I dug deeper.
Main questions: Find the number of solutions $s(n)$ of the equation$$n = \frac{k_1}{1} + \frac{k_2}{2} + \ldots + \frac{k_n}{n}$$where $k_i \ge 0$ is a non-negative integer. This is my main questions. After tying ... |
Thanks but ERF or ERFC that doesn't replicate =NORM.DIST(1,0,1,TRUE) = 0.84134475 - unless I'm missing something here.
you are missing something.
The error function and cumulative normal distribution differ by several factors in their definitions and have different limits of integration
(1+erf(1/sqrt(2.)))/2;=0.8413447... |
This question is inspired partly by this question Any reference on Brownian Motion continuity. In this post, the author asked if the following three axioms can define a Brownian motion without assuming the continuity axiom
"
4.$W(t)$ is continuous with probability one. i.e. $\lim _{h\rightarrow 0}P(|W(t+h)-W(t)|>\epsil... |
Intersection with Complement is Empty iff Subset
Jump to navigation Jump to search
Theorem $S \subseteq T \iff S \cap \map \complement T = \O$
where:
$S \subseteq T$ denotes that $S$ is a subset of $T$ $S \cap T$ denotes the intersection of $S$ and $T$ $\O$ denotes the empty set $\complement$ denotes set complement. $S... |
Contents
Integral expression can be added using the
\int_{lower}^{upper}
command.
Note, that integral expression may seems a little different in
inline and display math mode - in inline mode the integral symbol and the limits are compressed.
LaTeX code Output
Integral $\int_{a}^{b} x^2 dx$ inside text
$$\int_{a}^{b} x^... |
Answer
Period$=\frac{\pi}{5}$ seconds Frequency=$\frac{5}{\pi}$ cycles per second
Work Step by Step
The period can be found by first comparing the equation $s(t)=-4\cos 10 t$ to $s(t)=a\cos w t$ to find $w$ which is the angular velocity. By comparing the two equations, we find that $w=10$. Next, we find the period usin... |
Since the statement in question is an “if and only if” we need to prove both directions. That is, we need to show$$mn=1 \text{ for some integers $m,n$ implies } m=n=1 \text{ or }m=n=-1$$and $$m=n=1 \text{ or } m=n=-1 \text{ implies } mn=1.$$
To prove that $A$ implies $B$ we assume that $A$ is true and deduce that $B$ m... |
(Note: This post is more technical than most stuff I write here. The intended audience here is not the general public, or even the general educated public: it’s students of geometry, broadly understood. In any case, if you don’t know what a differential form is, you’re probably not going to get much out of this.)
I’d l... |
Contents Homework 5, ECE438, Fall 2011, Prof. Boutin Question 1
Diagram of "decimation by two" FFT computing N-pt DFT. N=8 in this question.
where $ W_N^k = e^{-j2\pi k/N} $
Recall the definition of DFT:
$ X[k]=\sum_{n=0}^{N-1} x[n]e^{-j2\pi k/N},\ k=0,...,N-1 $.
For each k, we need N times complex multiplications and ... |
The concepts of on-policy vs off-policy and online vs offline are separate, but do interact to make certain combinations more feasible. When looking at this, it is worth also considering the difference between
prediction and control in Reinforcement Learning (RL). Online vs Offline
These concepts are not specific to RL... |
The situation with solids is considerably more complicated, with different speeds in different directions, in different kinds of geometries, and differences between transverse and longitudinal waves. Nevertheless, the speed of sound in solids is larger than in liquids and definitely larger than in gases. Young's Modulu... |
Answer
$s(1.466)\approx2$ This means that after $t=1.466$ seconds, the weight is about 2 inches above the equilibrium position.
Work Step by Step
We calculate $s(1.466)$ by substituting $t=1.466$ into the equation and solving: $s(t)=-4\cos 10t$ $s(1.466)=-4\cos (10\times1.466)$ $s(1.466)=-4\cos (14.66)$ $s(1.466)=-4(-0... |
An ideal diatomic gas undergoes an elliptic cyclic process characterized by the following points in a $PV$ diagram:
$$(3/2P_1, V1)$$ $$(2P_1, (V1+V2)/2)$$ $$(3/2P_1, V2)$$ $$(P_1, (V1+V2)/2)$$
A rough sketch:
This system is used as a heat engine (converting the added heat into mechanical work).
Evaluate the efficiency ... |
As I understand it a perfect electrical conductor (PEC) will expel all electric fields and time-varying magnetic fields. For this post I'm assuming low enough frequencies as to ignore displacement current and wave phenomenon. As a result the boundary conditions for the magnetic field become:
$$\hat n \times (H_1 - H_2)... |
ISSN:
1930-5311
eISSN:
1930-532X
All Issues
Journal of Modern Dynamics
January 2008 , Volume 2 , Issue 1
The editors of the Journal of Modern Dynamics are happy to dedicate this issue to Gregory Margulis, who, over the last four decades, has influenced dynamical systems as deeply as few others have, and who has blazed ... |
Producing Reports With knitr Overview Teaching:60 min Exercises:15 min Questions
How can I integrate software and reports?
Objectives
Understand the value of writing reproducible reports
Learn how to recognise and compile the basic components of an R Markdown file
Become familiar with R code chunks, and understand thei... |
I have a question about solving equations with trigonometric functions. To my understanding, one can use inverse functions like this:
$$\sin \theta = a, \quad \arcsin a = \theta$$
But I do not know how to solve something with more than one function, like this one:
$$xy\sin \theta = zxy\cos \theta $$
I was able to simpl... |
First: The paper references [37] for Levy's Lemma, but you will find no mention of "Levy's Lemma" in [37]. You will find it called "Levy's Inequality", which is called Levy's Lemma in this, which is not cited in the paper you mention.
Second: There is an easy proof that this claim is false for VQE. In quantum chemistry... |
Answer
The central angle is $32.2^{\circ}$
Work Step by Step
Let $\theta$ be the angle in radians. Let $r$ be the radius. We can use the arc length $d$ to make an expression for the radius $r$: $d = \theta ~r$ $r = \frac{d}{\theta}$ Let $A$ be the area of the sector. Then the ratio of the angle $\theta$ to $2\pi$ is eq... |
@user193319 I believe the natural extension to multigraphs is just ensuring that $\#(u,v) = \#(\sigma(u),\sigma(v))$ where $\# : V \times V \rightarrow \mathbb{N}$ counts the number of edges between $u$ and $v$ (which would be zero).
I have this exercise: Consider the ring $R$ of polynomials in $n$ variables with integ... |
For any integers $a,b,c\ge 0$,one has the well known identity or Dixon's Theorem:$$\sum_{k\in\mathbb{Z}} (-1)^k\left(\begin{array}{c}a+b\\a+k\end{array}\right)\left(\begin{array}{c}b+c\\b+k\end{array}\right)\left(\begin{array}{c}c+a\\c+k\end{array}\right)\ =\ \frac{(a+b+c)!}{a!\ b!\ c!}\ .$$There are tons of proofs in ... |
I could need some advice on extensions of the CIR model.
The standard CIR reads
$dr(t)=\kappa(\theta-r(t))dt + \sigma \sqrt{r(t)} dW(t)$.
A possible extension, if we would like the short-rate to also include negative values, could be a displaced version, so that $r(t)+\alpha$, where $\alpha>0$, follows a CIR model.
Fur... |
First of all, you should specify whether you want all components or the most significant ones?
Denote your matrix $A \in \mathbb{R}^{N \times M}$ with $N$ being number of samples and $M$ dimensionality.
In case you want all components the classical way to go is to compute covariance matrix $C \in \mathbb{R}^{M\times M}... |
Answer
The area of the region that is cleaned is $75.4~in^2$
Work Step by Step
We can convert the angle to radians: $\theta = (95^{\circ})(\frac{\pi~rad}{180^{\circ}}) = 1.658~rad$ We can find the total area covered by the 10-inch arm. Let $A$ be the total area of the sector. Then the ratio of the angle $\theta$ to $2\... |
Topological Methods in Nonlinear Analysis Topol. Methods Nonlinear Anal. Volume 47, Number 1 (2016), 43-54. On the asymptotic relation of topological amenable group actions Abstract
For a topological action $\Phi$ of a countable amenable orderablegroup $G$ on a compact metric space we introduce a concept of theasymptot... |
为了更好的帮助您理解掌握查询词或其译词在地道英语中的实际用法，我们为您准备了出自英文原文的大量英语例句，供您参考。
If is a ?2-grading of a simple Lie algebra, we explicitly describe a-module Spin0 () such that the exterior algebra of is the tensor square of this module times some power of 2.
The operation adj on matrices arises from the (n - 1)st exterior power functor on mo... |
After a while since my last post, I have finally come back to getting some things written! Been really involved with work and other important things for myself, but I recently got most of these things out of the way so it is time to get back to the blogging grind! WOOT! Introduction
In the world of calculus, a fundamen... |
Basic Order Theory We will denote an arbitrary ordering relation by $R$. We will establish some preliminary definitions: An ordering $R$ is reflexiveif and only if $xRx$, for all $x$ in the domain of $R$. An ordering $R$ is irreflexiveif and only if $\neg xRx$. An ordering $R$ is transitiveif and only if $xRy$ and $yRz... |
I was able to solve this using trig instead of vector math. Here's how it looks as a triangle.
Notice that since this is meant for a computer coordinate system, the \$y+\$ axis is down. Also the angles are as such: \$x+ = 0°\$, \$y+ = 90°\$, \$y- = -90°\$, and \$x- = ±180°\$
Additionally, we know that line B's angle is... |
I have data tracking about 25,000 individuals as each one moves through a Markov chain.
I want to know the
shape of the relationship between a continuous 'covariate' (my independent variable of interest) and the transition intensities between the different states. The shape is really important for my question.
To find ... |
Subset Relation on Power Set is Partial Ordering Theorem
Let $S$ be a set.
Let $\powerset S$ be the power set of $S$.
Then $\struct {\powerset S, \subseteq}$ is an ordered set.
Proof
Then $\exists a, b \in S$ such that $a \ne b$.
Then $\set a \in \powerset S$ and $\set b \in \powerset S$.
However, $\set a \nsubseteq \s... |
Contents
Now that we studied a couple of techniques to create a Bézier patch, a problem remains. We need to shade this patch. Generating the position of the points is something we can already do but for shading, but we also need a normal. How can we generate a normal at the position of each vertex of the grid? We can e... |
Search
Now showing items 1-6 of 6
Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
In the previous sections, the density was assumed to be constant. For non constant density the derivations aren't ``clean'' but are similar. Consider straight/flat body that is under liquid with a varying density. If density can be represented by average density, the force that is acting on the body is \[F_{total} = \i... |
Let $f$ be an entire function and $B$ be a bounded open set in $\mathbb {C} $. Prove that boundary of image of $B$ under $f$ is contained in image of boundary of $B$. Does the same result is true for unbounded open set in $\mathbb C.$
If $f$ is constant it is clear. Assume it is non-constant.
Then by the open mapping t... |
In a triange $ABC$, points $D$ and $E$ are taken on side $BC$ such that $BD=DE=EC$. If $\angle ADE=\angle AED=\phi$, how can we prove that
$$\frac{6\tan\phi}{\tan^2\phi-9}=\tan A$$
The key here is recognizing the identity we wish to prove. Note that
$$\tan{A} = -\frac{\frac{2}{3} \tan{\phi}}{1-(\frac13 \tan{\phi})^2}$$... |
为了更好的帮助您理解掌握查询词或其译词在地道英语中的实际用法，我们为您准备了出自英文原文的大量英语例句，供您参考。
As a corollary we obtain that the moduli space of rank 3 and degree 0 bundles on a smooth projective curve of genusg is C-M.
Lower degree bounds for modular invariants and a question of I.
In particular, we prove an integral formula for the degree of an ample di... |
The key idea is that the sampling distribution of the median is simple to express in terms of the distribution function but more complicated to express in terms of the median value. Once we understand how the distribution function can re-express values as probabilities and back again, it is easy to derive the
exact sam... |
Second-Order Systems, Part I: Boing!!
Spring-mass-damper systems are fairly common; you’ve seen these before, whether you realize it or not. One household example of these is the spring doorstop (BOING!!):
(For what it’s worth: the spring doorstop appears to have been invented by Frank H. Chase during World War I.)
The... |
Kolmogorov axioms
There are a few ways to axiomatize the subject of probability. This is one way of doing it:
$$P(E) \in \mathbb, P(E) \ge 0$$ $$P(\Omega) = 1$$ $$P\left(\bigcup_{i=1}^nE_i\right) = \sum_{i=1}^nE_n \text{ , where all sets $E_i$ are mutually exclusive}$$
Consequences
For this second problem, let's start ... |
We hope you’ve seen it many times. It’s on the covers of our books. It’s on our business cards and stationery. It’s even on a “sponsor a highway” sign on Route 9 in Natick,Massachusetts. But, do you really know what the logo is?
I’m talking about the L-shaped membrane.We’ve used various pictures of it ever since The Ma... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
July 2009 , Volume 23 , Issue 3
Select all articles
Export/Reference:
Abstract:
We consider the impact of noise on the stability and propagation of fronts in an excitable media with a piece-wise smooth, discontinuous ignition proces... |
A sample of $\pu{1.42 g}$ of helium and an unweighted quantity of oxygen gas are mixed in a flask at room temperature. The partial pressure of helium in the flask is $\pu{42.5 torr}$, and partial pressure of oxygen gas is $\pu{158 torr}$. What is the mass of the oxygen in the container?
As volume is not stated, I assum... |
The answer is
no, there are transcendental numbers $\theta$ which aren't rational multiples of $\pi$ such that $\tan(\theta)$ is algebraic. Indeed, since $\tan$ is onto $\mathbb R$, there exists a value of $\theta$ for which $\tan(\theta)=\sqrt{2}$. On one hand, by Lindemann-Weierstrass theorem, $\theta$ has to be tran... |
I am interested in understanding how and whether the transformation properties of a (classical or quantum) field under rotations or boosts relate in a simple way to the directional dependence of the radiation from an oscillating dipole.
For example, the EM field from an oscillating electric dipole $\mathbf{d}(t) = q x(... |
I am trying to understand the Feynman path integral by reading the book from Leon Takhtajan.
In one of the examples, there is a full explanation of the calculation of the propagator
$$K(\mathbf{q'},t';\mathbf{q},t) = \frac{1}{(2\pi\hbar)^n} \int_{\mathbb{R}^n} e^{\frac{i}{\hbar}(\mathbf{p}(\mathbf{q'}-\mathbf{q})-\frac... |
Second-order set theories In construction.
$\text{ZFC}$, the usual first-order axiomatic set theory, can only manipulate sets, and cannot formalize the notion of a proper class (e.g. the class of all sets, $V$), so when one needs to manipulate proper class objects, it is tempting to switch to a second-order logic form ... |
The well-ordered replacement axiom is the scheme asserting that if $I$ is well-ordered and every $i\in I$ has unique $y_i$ satisfying a property $\phi(i,y_i)$, then $\{y_i\mid i\in I\}$ is a set. In other words, the image of a well-ordered set under a first-order definable class function is a set.
Alfredo had introduce... |
This could relate to different applications, but my application of interest is in similarity-search systems based on high-dimensional feature vectors. In these systems, since search based on Euclidean distance is costly, the vectors are encoded as binary vectors. Then the search is done based on Hamming distance comput... |
I often encounter the integrals in the following form:
$\int_0^\infty{\rm Bessel}(ax)\cdot{\rm Bessel}(bx)\cdot f(cx)dx$,
where Bessel can be $J$, $N$, $H^{(1)}$, $H^{(2)}$, $I$, or $K$; and $f(x)$ can be $\sin(x)$, $e^x$, etc. For example,
$\int_0^\infty K_\nu(ax)I_\nu(bx)\cos(cx)dx=\frac{1}{2\sqrt{ab}}Q_{\nu-1/2}(\fr... |
The answer is
There is one valid solution which is $S=4, I=2, N=7, U=8, E=1, V=5, L=9$
Formatting as above
427
* 27 --------- 2989 854 --------- 11529
Proof
First we note that $N \times N \equiv L (\bmod 10)$ so immediately we cannot have $N=0,1,5,6$ as then $L=N$ which is not permitted. Also important is $I \times N \... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.