text stringlengths 256 16.4k |
|---|
Recently I am reading the book
The Ricci Flow: techniques and applications: Part I: geometric aspects by Bennett Chow et al.. Here I have encountered a result (Proposition 1.13) due to Hamilton which states that "Any expanding or steady Ricci soliton $(g,X)$ on a closed manifold $M^n$ is Einstein. Any shrinking Ricci s... |
Probably an application of Glivenko-Cantelli's theorem as I suggested in the comments will work.
Assume that the $\xi_t$ are defined on a probability space $(\Omega,\mathcal F,\mu)$. We can assume that $G$ is the cumulative distribution function of a real valued random variable. Let $(\eta_t,t\in\Bbb Z)$ be a collectio... |
As far as I know, the first Diophantine problem (over a number field) that was solved using Spec and other tools of algebraic geometry was the following result (proved by Mazur and Tate in a paper from
Inventiones in the early 1970s):
If $E$ is an elliptic curve over $\mathbb Q$, then $E$ has no rational point of order... |
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 1-9 of 9
Measurement of $J/\psi$ production as a function of event multiplicity in pp collisions at $\sqrt{s} = 13\,\mathrm{TeV}$ with ALICE
(Elsevier, 2017-11)
The availability at the LHC of the largest collision energy in pp collisions allows a significant advance in the measurement of $J/\ps... |
Alan Jeffrey tweeted the following in reply to the previous post:
@jeremysiek wouldn't it be easier to change the defn of application to be ⟦MN⟧σ = { W | T ∈ ⟦M⟧σ, V ∈ ⟦N⟧σ, (V′,W) ∈ T, V′ ⊆ V }?
The idea is that, for higher order functions, if the function \(M\)is expecting to ask all the questions in the table \(V'\)... |
I need help finding the formula for this summation notation: $$\sum_{k=1}^n{k^{2k} }$$ or $$1^2 + 2^4 +3^6 +.....+n^{2n} $$
And preferably not involving calculus.
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... |
Let $p$ be a prime number.
1) What is the degree over $\Bbb Q_p$ of 'the' algebraic closure $\overline{\Bbb Q_p}$ of $\Bbb Q_p$ ? 2) What is the order (the cardinality) of the absolute Galois group $G$ of $\Bbb Q_p$ ? 3) What is the degree over $\overline{\Bbb Q_p}$ of the completion $\Bbb C_p$ of $\overline{\Bbb Q_p}$... |
Assume that the uniformly distributed bound surface and bound volume current, $\vec{K}_{b}$,$\vec{J}_{b}$ respectively, are in the azimuthal direction $\phi$ within an infinitely long solenoid with a current passing through the wounded coils centered on the z-axis.
Clearly, the magnetic field field has no z and $\phi$ ... |
Cryptology ePrint Archive: Report 2002/031 A Parallelizable Design Principle for Cryptographic Hash Functions Palash Sarkar and Paul J. Schellenberg Abstract: We describe a parallel design principle for hash functions. Given a secure hash
function $h:\{0,1\}^n\rightarrow \{0,1\}^m$ with $n\geq 2m$, and a binary tree of... |
There is a "high temperature" limit, it is actually the same point. 5K is hotter than 1K, and 1000K is hotter than both. The temperature $\pm \infty$ is actually the same temperature, and for negative temperatures you get hotter the closer you get to zero (from below).
Most systems cannot reach negative temperatures, b... |
February 3rd, 2019, 04:04 AM
# 1
Newbie
Joined: Feb 2019
From: Uppsala
Posts: 1
Thanks: 0
Solve x^120 + x^3 + 2x^2 + x +3 ≡ 0 (mod 7)
Hi,
I'm having trouble with this one:
x^120 + x^3 + 2x^2 + x +3 ≡ 0 (mod 7)
What is x?
February 3rd, 2019, 05:19 AM
# 2
Senior Member
Joined: Aug 2017
From: United Kingdom
Posts: 313
Tha... |
Above-Average Smoothing of Impulsive Noise
In this blog I show a neat noise reduction scheme that has the high-frequency noise reduction behavior of a traditional moving average process but with much better impulsive-noise suppression.
In practice we may be required to make precise measurements in the presence of highl... |
This question concerns a system of equations that arise in the study of one-soliton solutions to the Davey-Stewartson equation.
In what follows, $f(z)$ denotes a function which depends smoothly (but not necessarily analytically!) on $z=x+iy$. Thus $f:\mathbb{C} \rightarrow \mathbb{R}$ or equivalently $f:\mathbb{R}^2 \r... |
Jean Duchon
Retired from CNRS, Institut Fourier (Grenoble).
Postal address: 297 Grande Rue, 38160 Saint-Antoine, France.
My professional email address is no longer active. My new email (not to be spread, please) is through gmail dot com, it is my name dot my wife's name (mesdag).
Saint-Antoine l'Abbaye (Isère), France
... |
There is also one question directly relating to this question, that is, how to define the sum of uncountably many numbers (not necessarily positive numbers). The difficulty lies in the fact that there could not be any order of this summation, since there are uncountably many of terms. So, when we talk about the sum of ... |
Question:
If two identical masses are attached to two walls facing each other and the two masses themselves are connected by a third spring (all springs have same initial length and spring constant k). Now we apply two driving forces to these two masses respectively: one on the left with $F_dcos{2\omega t}$ and the one... |
I'm trying to read through and understand this proof from Rudin, but am a bit confused at just a few steps. I'm going to try to replicate the proof and pause at those particular steps.
Theorem. Suppose $S$ is an ordered set with the least-upper-bound property, $B \subset S$, $B$ is not empty, and $B$ is bounded below. ... |
To understand what is going on lets examine your initial plot. We assign it to the variable
g:
g = Show[
Plot[1/2 x + 1/2, {x, -6, 7}],
ListPlot[{{4, -2.5}, {2, 1.5}}, Joined -> True, PlotMarkers -> Automatic]
]
g // ImageDimensions
{360, 224}
The figure's aspect ratio is therefore:
#2/#1 & @@ ImageDimensions[g] // N
0... |
Your score is simply the sum of difficulties of your solved problems. Solving the same problem twice does not give any extra points. Note that Kattis' difficulty estimates vary over time, and that this can cause your score to go up or down without you doing anything.
Scores are only updated every few minutes – your sco... |
We define the thermal density operator as
$$\tau(\beta) = \frac{e^{-\beta H}}{\mathrm{Tr}(e^{-\beta H})}$$
where $H$ is the systems Hamiltonian. The thermal state is characterized by the fact that it maximizes the entropy for a given, fixed energy.
Now when we consider the second law of thermodynamics which states that... |
Colloquia/Fall18 Contents 1 Mathematics Colloquium 1.1 Spring 2018 1.2 Spring Abstracts 1.2.1 January 29 Li Chao (Columbia) 1.2.2 February 2 Thomas Fai (Harvard) 1.2.3 February 5 Alex Lubotzky (Hebrew University) 1.2.4 February 6 Alex Lubotzky (Hebrew University) 1.2.5 February 9 Wes Pegden (CMU) 1.2.6 March 2 Aaron Be... |
How many digits are there in the number $200^{2010}$? I have tried to re-write it as $(2\cdot 100)^{2010} = (2\cdot 10^2)^{2010} = 2^{2010} \cdot 10^{4020} = 1024^{201} \cdot 10^{4020} = 1.024^{201} \cdot 10^{4623}$. But how do I write $1.024^{201}$ as a power of base 10? I would like to solve the problem without logar... |
If you could travel to the center of the Earth (or any planet), would you be weightless there?
Correct. If you split the earth up into spherical shells, then the gravity from the shells "above" you cancels out, and you only feel the shells "below" you. When you are in the middle there is nothing "below" you.
{I am usin... |
I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal operator. I understand from the Wikipedia article that requiring that energy stay positive forces $T$ to be represented by an an... |
Let's assume that the vapor pressure of both components can be modeled with the Antoine equation. This gives us a convenient way to address the question algebraically. The vapor pressure of most chemicals is excellently modeled by the correct Antoine equation for that chemical. The equation is:$$\log_{10}{p} = A-\frac{... |
Possible Duplicate: Why can ALL quadratic equations be solved by the quadratic formula?
How to derive this: $x = \frac{-b + {\sqrt{b^2 + 4ac}}}{2a}$
From this:
$ax^2 + bx + c = 0$
I know this may be a little elementary :)
Mathematics Stack Exchange is a question and answer site for people studying math at any level and... |
@egreg It does this "I just need to make use of the standard hyphenation function of LaTeX, except "behind the scenes", without actually typesetting anything." (if not typesetting includes typesetting in a hidden box) it doesn't address the use case that he said he wanted that for
@JosephWright ah yes, unlike the hyphe... |
You want a table that models "stacked" probabilities.
For example, if the chance of any individual attempt's success is 40%, your table might look like this:
\begin{array}{cc}n\text{ to success} & \text{d}100\text{ roll}\\ \hline1 & 01-40\\2 & 41-64\\3 & 65-78\\4 & 79-87\\5 & 88-92\\6 & 93-95\\7 & 96-97\\8 & 98\\9 & 99... |
Coefficients of Cascaded Discrete-Time Systems
In this article, we’ll show how to compute the coefficients that result when you cascade discrete-time systems. With the coefficients in hand, it’s then easy to compute the time or frequency response. The computation presented here can also be used to find coefficients of ... |
I know the answer to the above question, but I have a question on some of the reasoning.
The way I know how to solve it is $$\lim_{x \rightarrow 0}f(x) = \lim_{x \rightarrow 0}\left(f(x)\cdot \frac{x^2}{x^2}\right) = \lim_{x \rightarrow 0}\left(\frac{f(x)}{x^2}\cdot x^2\right) = \left(\lim_{x \rightarrow 0}\frac{f(x)}{... |
I have the feeling, that this is a superbly stupid question. And I also have the feeling that it is quite possible, that my answer will be wrong.
First of all the parts-per-notation should be avoided as it is not compliant with SI and highly ambiguous. Secondly, it generally may only refer to a unitless number - a mola... |
In Poincare Gauge Theories spin connections take the role of the Levi-Civitta connection of GR for defining covariant derivatives. The GR can be formulated as a Poincare Gauge Theory which is called the Teleparallel equivalent of GR. In this theory the spin connection is decomposed into a flat spin connection $A_{ab\mu... |
Linear models describe a continuous response variable as a function of one or more predictor variables. They can help you understand and predict the behavior of complex systems or analyze experimental, financial, and biological data.
Linear regression is a statistical method used to create a linear model. The model des... |
Some existence results for dynamical systems on non-complete Riemannian manifolds
DOI: http://dx.doi.org/10.12775/TMNA.1999.008
Abstract
Let $\mathcal M^*$ be a non-complete Riemannian manifold with bound-ed topological
boundary and $V: \mathcal M \to \mathbb R$ a $C^2$ potential function subquadratic at infinity. In t... |
I would proceed as follows:\begin{align*}x_t &= x_{t-\delta t} + \alpha (\beta - x_{t-\delta t}) \delta t + \sigma x_{t-\delta t}^\gamma (w_t - w_{t-\delta t}),\\x_t &= \max (x_t, \ 0),\end{align*}where $w_t - w_{t-\delta t}$ is a normal random variable with mean $0$ and variance $\delta t$, which can be obtained by an... |
ISSN:
1531-3492
eISSN:
1553-524X
All Issues
Discrete & Continuous Dynamical Systems - B
June 2014 , Volume 19 , Issue 4
Select all articles
Export/Reference:
Abstract:
RS feedback models have been successful in explaining the observed phenomenon of clustering in autonomous oscillation in yeast, but current models do no... |
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 ... |
Trigonometry Complex Numbers Geometric Series Integrals of Complex Functions and Integration by parts
A series of the form $a b^k, a b^{k+1}, \ldots, a b^{l}$, where $a$ and $b$ can be any {\em complex} number is called a geometric series with $l-k+1$ terms. For example, $1,\frac{1}{2},\frac{1}{4},\ldots$ is an infinit... |
Distribution of charge
within the region where the field is located, is obviously uniquely defined, because it's just
$$\rho=\epsilon_0\nabla \vec{E}$$
However, if you cut out a region of space, and want to predict the contents of this region based only on the field outside, you can't do it in a unique way.
The reason ... |
Infinite product of complex numbers Set
context $(z_i)$ … Sequence($\mathbb C$) definition $\prod_{i=1}^\infty z_i\equiv \mathrm{lim}_{n\to\infty}\prod_{i=1}^n z_i$ Discussion todo: Interestingly, I think I see the nLab doesn't want to allow e.g. $\prod_{n=1}^\infty (17-n)$ to be zero. (Reference below)
I recon infinit... |
What your book states is not generally true. Two counter-examples:
Ammonia ($\ce{NH3}$) will liquefy at room temperature and a pressure of approximately $\pu{10bar}$. (
CRC Handbook of Chemistry and Physics 44th ed; information as cited on Wikipedia’s data page).
Butane ($\ce{C4H10}$) will liquefy at room temperature a... |
This question already has an answer here:
I have to show that for any $b >1$, we have $$ b^n > n$$ for all $n$ sufficiently large, using only very basic analysis (no calculus). My attempt is as follows.
We know that $b^{n+1} - b^n = b^n(b-1)$. For $n$ sufficiently large, say $$n \geq N = \left\lceil \frac{\ln(2/(b-1))}... |
I am writing this answer to try and learn something about the various scattering processes for myself, so hopefully another more detailed and more sophisticated answer will also be posted, that both I (and the OP, of course!) can learn from.
Bhabha scattering is the electron-positron scattering interaction involving an... |
I am thinking about the deletion error correcting codes for quantum information.
In classical information theory, there exist some deletion error correcting codes. An easy example is the following situation:
Alice prepares a set $\{ 00,11 \}$ and sends an element of the set to Bob. Here Bob knows the set. One deletion ... |
I've read that any real skew-symmetric matrix $A$, where $A^T = -A$, can be brought into block diagonal form
$ A = Q \, \Sigma \, Q^T = \left( \begin{array}{ccccl} \vec{q}_1 & \vec{q}_2 & \vec{q}_3 & \vec{q}_4 & \dots \end{array} \right) \, \left( \begin{array}{ccccl} 0 & \lambda_1 & 0 & 0 & \dots \\ -\lambda_1 & 0 & 0... |
Let $\mu_4 = E(X-\mu)^4$. Then, the formula for the SE of $s^2$ is:
$$se(s^2) = \sqrt{ \frac{1}{n}\left(\mu_4 -\frac{n-3}{n-1} \sigma^4\right)}$$This is an exact formula, valid for any sample size and distribution, and is proved on page 438, of Rao, 1973, assuming that the $\mu_4$ is finite. The formula you gave in you... |
What if we make a tunnel through the earth and drop a ball or any other body into it? How would the gravity behave on the ball, and , will the ball pop-up on the other side? If yes, then how much time will it take? A question, which is usually asked in competitive exams and for general interest.
This article is a descr... |
We present state sums for quantum link invariants arising from the representation theory of U_q(\mathfrak{gl}_{N|M}). We investigate the case of the N-th exterior power of the standard...
Pages
We provide a finite dimensional categorification of the symmetric evaluation of \mathfrak{sl}_N-webs using foam technology. As... |
I'm working on an exercise from functional analysis.
Let $E$ be a vector space and $\|\cdot\|_1$ and $\|\cdot\|_2$ be two complete norms on $E$. Now suppose that $E$ satisfies the following property:
$\bullet$ if $(x_n)$ is a sequence in $E$ and $x,y\in E$ such that $\|x_n-x\|_1\to 0$ and $\|x_n-y\|_2\to 0$, then $x=y$... |
How can I get the closed-form of the above expression.I tried to find it but I can't do.
Let $x=\tan(\pi/9)$.
First, $$\tan 3a=\frac{\tan a+\tan 2a}{1-\tan a\tan 2a}=\frac{\tan a+\frac{2\tan a}{1-\tan^2 a}}{1-\frac{2\tan^2 a}{1-\tan^2a}}=\frac{3\tan a-\tan^3a}{1-3\tan^2a}$$
Since $\tan(\pi/3)=\sqrt 3$ you have
$$\sqrt ... |
Last Updated: May 4, 2019
Several methods have been developed in order to save computational time and cost for unsteady flow computations compared to LES.
Keywords Detached-Eddy Simulation (DES), Scale Adaptive Simulation (SAS), Grey area problem Detached Eddy Simulation (DES) Detached-Eddy Simulation (DES) is a hybrid... |
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 ... |
This blog discusses a problematic situation that can arise when we try to implement certain digital filters. Occasionally in the literature of DSP we encounter impractical digital IIR filter block diagrams, and by impractical I mean block diagrams that cannot be implemented. This blog gives examples of impractical digi... |
Tex2im tex2im is a simple tool that converts LaTeX formulas into high resolution pixmap graphics for inclusion in text processors or presentations. With tex2im you can write files containing only the formula in latex mathmode and transform them to many different graphic formats.
latex2html can do something similar, but... |
My question refers to differential equations in Sobolev spaces. It is as follows:
Let $\Omega \subset \mathbb{R}^n$ be a bounded open set. Let $a: H_0^1(\Omega) \times H_0^1(\Omega) \rightarrow \mathbb{R}$ be a bilinear symmetric form, such that:
(continuity in $H^1$) $\forall u,v \in H^1(\Omega) \; \; \; a(u,v) \leq c... |
I'm considering a symmetry transformation on a Lagrangian
$$ \delta A = \int L(q +\delta q, \dot{q} + \delta \dot{q} , \ddot{q} + \delta \ddot{q}) dt $$
the general variation takes the form
$$ \delta A = \int \frac{ \partial L}{\partial q} \delta q + \frac{\partial L}{\partial \dot{q}} \delta \dot{q} + \frac{\partial L... |
User:Nikita2 Pages of which I am contributing and watching
Analytic function | Cauchy criterion | Cauchy integral | Condition number | Continuous function | D'Alembert criterion (convergence of series) | Dedekind criterion (convergence of series) | Derivative | Dini theorem | Dirichlet-function | Ermakov convergence cr... |
Let $X$ be an abelian variety.
In "Mumford, Abelian Varieties" the Riemann-Roch Theorem has the following form:
For all line bundles $\mathcal{L}$ on $X$, if $\mathcal{L}\cong\mathcal{O}_X(D)$, we have $\chi(\mathcal{L})=\frac{(D^g)}{g!}$, $\chi(\mathcal{L})^2=\deg\phi_\mathcal{L}$, where $(D^g)$ is the $g$-fold self-i... |
What are some alternative ways to represent the golden ratio? I already know the relatively boring ones compared to the complex ones as well as:
$\displaystyle \frac{1+\sqrt 5}{2},$ $\displaystyle \frac{1}{1+\frac{1}{1+\frac{1}{1+}} \dots},$ $\displaystyle \phi + 1 = \phi ^{-1},$
and also the multiplier of consecutive ... |
This answer focuses on identifying families of solutions to the problem described in the question.
I've made two provisional conjectures in order to make progress with the problem:
The result can be stated for three $2n$-gons rather than two $n$-gons and one $2n$-gon.
Solutions have mirror symmetry. Or equivalently, in... |
Unlike usual spin the isospin is an
internal degree of freedom, the particle type that doesn't have any relation to spacetime. The similarity between ordinary spin and isospin originates from the $2\times 2$ unitary matrices group $SU(2)$ being an universal covering of the 3d rotation group $SO(3)$. That means that the... |
Talk:Absolute continuity
Could I suggest using $\lambda$ rather than $\mathcal L$ for Lebesgue measure since
it is very commonly used, almost standard it would be consistent with the notation for a general measure, $\mu$ calligraphic is being used already for $\sigma$-algebras
--Jjg 12:57, 30 July 2012 (CEST)
Between m... |
I have this assignement for my discreet math course, and I would like a opinion on my answer:
Let $a = p_1^{e_1} + p_2^{e_2} + ... + p_s^{e_s}$ and $b = q_1^{f_1} + q_2^{f_2} + ... + q_t^{f_t}$ be positive integers expressed as sum of powers of prime numbers. In $\Bbb N$ , let these two binary relations be defined:
$$a... |
Does the following integral converge?
$$\int_1^\infty \sin^2 (x^2) \, dx$$
I tried $$\int_1^\infty \sin^2(x^2) \, dx=\int_1^\infty \frac{1-\cos(2x^2)}{2} \, dx = \frac{\sqrt{2}}{4} \int_1^\infty\frac{1-\cos(u)}{2\sqrt{u}} \, du$$
The idea is that, I want to compare the original integral to a divergent $p$-integral. But... |
Given that $\textbf{F} = \langle z,x,y \rangle$,
The plane $ z=2x+2y-1$ and the paraboloid $ z= x^2 +y^2$ intersect in a closed curve.
I'm trying to use stokes theorem to find the line integral.
Attempt:
We know that Stokes Theorem is given by: $\iint_S (\nabla \times \textbf{F}) \cdot \textbf{N}\: d\textbf{S} $
$\nabl... |
I've had to rewrite the question as i made agrievious errors in the first go-round.
Given a (pseudo)Riemannian metric g, we can identify its components with the symmetric product of gamma matrices:
$$\gamma^{\mu}\gamma^{\nu}+\gamma^{\nu}\gamma^{\mu}=2g^{\mu\nu}I$$
The gammas act as basis vectors and their products and ... |
While I’ve been quite happy with the performance of my Predictaball football rating system, one thing that that’s bothered me since its inception last summer is the reliance on hard-coded parameters.
Similar to many other football rating methods, it’s an adaptation of the Elo system that was designed for Chess matches ... |
Title Minimization of functionals of the gradient by Baire's theorem Publication Type Journal Article Year of Publication 2000 Authors Zagatti, S Journal SIAM J. Control Optim. 38 (2000) 384-399 Abstract
We give sufficient conditions for the existence of solutions of the minimum problem $$ {\mathcal{P}}_{u_0}: \qquad \... |
Search
Now showing items 1-1 of 1
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Hedonic Evaluation Approach
The
hedonic approach to economic assessment can be used for evaluating the economic value of environmental goods such as noise, air or water quality, landscape and similar goods.
The
hedonic approach is based on the assumption that goods can be considered aggregates of different attributes, ... |
We consider implicit signatures over finite semigroups determined by sets of
pseudonatural numbers. We prove that, under relatively simple hypotheses on a
pseudovariety V of semigroups, the finitely generated free algebra for the
largest such signature is closed under taking factors within the free pro-V
semigroup on t... |
Probability Seminar Spring 2019 Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. We usually end for questions at 3:15 PM.
If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu
January 31, Oanh Nguyen, Princeton
Title:... |
There is no way to calculate the Starting Current or Locked Rotor Current (LRA) without more information!
Single-phase or three-phase? NEMA Motor Design B, C or D?
What does academic education's sake mean? A voltage of 15V with a power of 132kW is meaningless for an induction motor. You just can't make up numbers. You ... |
Separable Differential Equations: Exponential Decay
When I was in high school, my chemistry teacher presented me with a radioactive decay problem, and a formula that read:
$$Q=Q_{0} * e^{-r t}$$
Where \(Q\) represented the current amount of radioactive material, \(Q_0\) represented the starting amount of material, and ... |
What questions led to the invention of complex differentiation/integration? How were their definitions agreed upon?
Real differentiation/integration has an obvious meaning. To extend calculus to the complex numbers, why would this be done, is it even meaningful to call it 'differentiation'/'integration'?
What questions... |
Can the centralizer of Inn(G) in Aut(G), where G is preferably any non-abelian finite one, equal to Inn(G) itself? Clearly, such centralizer contains all $f$ in Aut(G) where $f(g)g^{-1}$ are in Z(G).
To summarize (thanks to Steve D. for the article pointer):
If $G$ is a group, an automorphism $\sigma\in\mathrm{Aut}(G)$... |
Let $$U_1 = \left\{ \left( \begin{array}{cc} x_1\\ x_2\\ x_3\\ x_4\\ \end{array} \right) \in \mathbb{R} :-x_1-x_2+x_3=0 \right\}$$
$$U_2 = span \left( \left( \begin{array}{cc} -1 \\ 1 \\ 1 \\ 2 \\ \end{array} \right), \left( \begin{array}{cc} 2 \\ -1 \\ -1 \\ 2 \\ \end{array} \right) \right) $$
, find the bases for $U_... |
The primal assignment problem that I have is:
$\begin{align} & \max \sum\limits_{i=i}^N\sum\limits_{j=1}^N c_{ij}x_{ij} \\ &\text{subject to} \\ &\sum_{i=1}^N x_{ij} = 1,~~j=1,\dots,N \\ &\sum_{j=1}^N x_{ij} = 1, ~~i=1,\dots,N \\ &x_{i,j} ~\in \{ 0,1 \} \end{align} $
and I would like to obtain its dual, which should be... |
Given a large sparse matrix $\Sigma$, I want to find a (block) diagonal matrix $\Omega$ which approximates $\Sigma^{-1}$.
In this specific problem, we know that $\Sigma$ is a block tridiagonal matrix. The blocks are of size $3 \times 3$. The blocks on the diagonal of $\Sigma$ stem from covariance matrices, i.e. they ar... |
Let us call any commutative semigroup $(S, +)$ strongly homogeneous if it satisfies the following three properties:
P-1. Every endomorphism on $S$ is a bijection.
P-2. Any two endomorphisms on $S$ commute.
P-3. For every $x, y \in S$ there exist one and only one endomorphism $\psi$ on $S$ such that $\psi(x) = y$.
Is th... |
Can anyone please help me to prove $ X=M$ using the following set of the equation(first-order logic)in Isabelle/HOL?
$ N>=M$
$ \forall n. 0\leq n<N \rightarrow n<M$
$ X=N$
where $ N, M, X$ are integers constant. $ n$ integer variable.
Can anyone please help me to prove $ X=M$ using the following set of the equation(fir... |
As I said in the comments I think is fine the way you did it. I would suggest you to use "congruent to" instead of "equal to" as in my comment from the beginning, or add it at the end of the conversions you did as a last step.
Said that, maybe your question is more related with this point:
how you could make a solution... |
We have to point out some simple remark of capital importance. First of all, the lagrangian
is not defined as $L = T - V$. This turns out to be true only on a riemannian manifold; the fact this is almost always true in classical mechanics is an "accident" due to the postulates of classical (non relativistic) mechanics.... |
In Introduction to Algorithms (CLRS) 3rd Edition, page 299, the section attempts to prove:
The expected height of a randomly built binary search tree on $ n$ distinct keys is $ O(\lg n)$ .
We define “randomly built binary search tree on $ n$ keys” as:
a binary search tree that arises from inserting the keys in random o... |
The covariance of two random variables $X$ and $Y$ is defined by: $$\mathrm{Cov}(X,Y）= \operatorname{E}(X-\operatorname{E}(X))(Y-\operatorname{E}(Y))=\operatorname{E}(XY)-\operatorname{E}(X)\operatorname{E}(Y)$$
Another related definition is correlation coefficient $$\rho(X,Y) = \frac{\mathrm{Cov}(X,Y)}{\sqrt{\mathrm{V... |
Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision classical_phase_density [2015/08/18 20:27]
nikolaj
classical_phase_density [2015/08/18 20:29] (current)
nikolaj
Line 25: Line 25: ^ $ \frac{\mathrm d}{\mathrm dt}{\hat\rho}(\pi(t),t)=0 $ ^ ^ $ \fr... |
With careful use of the
\phantom family of commands, you can get proper alignment inside and outside of the
cases (i.e., the second portion of your equation) as well:
This is a general solution that I often use and will work across different environment as well. We fix a size for portions of the equations, and use
\mak... |
NULL CONTROLLABILITY OF DEGENERATE NONAUTONOMOUS PARABOLIC EQUATIONS DOI Number First page Last page Abstract
$$
u_{t}-M(t)(a(x)u_{x})_{x}=h\chi_{\omega},\qquad (x,t)\in Q=(0,1)\times(0,T),$$ where $\omega=(x_{1},x_{2})$ is a
small nonempty open subset in $(0,1)$, $h\in L^{2}(\omega\times(0,T))$, the diffusion coeffici... |
X
Search Filters
Format
Subjects
Library Location
Language
Publication Date
Click on a bar to filter by decade
Slide to change publication date range
Physical Review Letters, ISSN 0031-9007, 11/2017, Volume 119, Issue 19, pp. 191802 - 191802
We report the first evidence for isospin violation in B -> K*gamma and the fir... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
Here's a common definition of a function (for example, Wiki follows this definition):
A
relationbetween sets $A$ and $B$ is any subset $R \subseteq A \times B$. We say that this relation is a functionif it satisfies the property $$ (a,b_1) \in R \text{ and }(a,b_2) \in R \implies b_1 = b_2 $$
This definition of a funct... |
Definition:Greatest Common Divisor/Integral Domain Definition
Let $a, b \in D: a \ne 0 \lor b \ne 0$.
Let $d \divides a$ denote that $d$ is a divisor of $a$.
Let $d \in D$ have the following properties: $(1): \quad d \divides a \land d \divides b$ $(2): \quad c \divides a \land c \divides b \implies c \divides d$
Then ... |
Version 17 (modified by 7 months ago) (diff), 'perturbative' and 'real' particles; the perturbative weight 'perturbative' and 'real' particles
(following text is taken - slightly modified - from: O.Buss, PhD thesis, pdf, Appendix B.1)
Reactions which are so violent that they disassemble the whole target nucleus can be ... |
it is gained by: start with a torus — a shape like the surface of a doughnut — and remove a slice. Attach two interlocking smaller tori, one on each side of the gap left by the slice, and repeat the process, slicing each torus and inserting an interlocking pair of smaller tori that you will subsequently slice and inser... |
In this vignette, we illustrate on a synthetic dataset how to perform post-selection inference (PSI) for a set of kernels using our R package
kernelPSI (Slim et al. 2019). The kernels are selected in a forward fashion according to quadratic kernel association scores, leading to the modeling of the selection event as a ... |
tl;dr: I've found a fatal gap in this proof that I've been unable to close. I'll leave this answer up in case either: a) I figure out how to fix it or b) it inspires someone else to figure out how to fix it.
Let $G = (X \cup Y, E)$ be a bipartite graph without a perfect matching. We'll say that a subset $S$ is
deficien... |
This Integral came up while attempting another question:
$$f(y)=\int_{0}^{\frac{\pi}{2}} \ln(y^2 \cos^2x+ \sin^2x) .dx$$
The suggested solution was as follows: $$f'(y) = 2y \int_{0}^{\pi/2}\frac{cos^{2}x}{sin^{2}x + y^{2}cos^{2}x}dx$$ $$= 2y \int_{0}^{\pi/2}\frac{dx}{tan^{2}x + y^{2}}$$ $$= 2y \int_{0}^{\pi/2}\frac{sec... |
What you're looking for is a cross spectral analysis. These notes show how it works for a bivariate case, but it's easy to apply this to multivariate series.
You start with multivariate time series:$x_t=(x_{1t},\dots,x_{nt})$. You define the matrix of autocovariate functions
$\Gamma(j)=\gamma_{mk}(j)\equiv cov(x_{mt},x... |
Let $n\in \mathbb N$ and $\{x_n\}$ is a monotone sequence. Prove that: $$ \{y_n\} = {1\over x_1 + x_2 + \dots + x_n} $$ is also a monotone sequence.
Given $\{x_n\}$ is monotone then by definition: $$ \forall n\in\mathbb N:x_n \le x_{n+1} \tag1 $$ or: $$ \forall n\in\mathbb N:x_n \ge x_{n+1} \tag2 $$ Let's prove for $(1... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.