Artificial intelligent assistant

perturbed

answer Answers

ProphetesAI is thinking...

MindMap

Sources

1
perturbed
perturbed, ppl. a. (pəˈtɜːbd, poet. -bɪd) [f. perturb v. + -ed1.] 1. Disquieted, agitated, restless; confused, deranged.1512 Helyas in Thoms Prose Rom. (1828) III. 45 Matabrune was ful sorye and perturbed of these tidings. 1602 Shakes. Ham. i. v. 183 Rest, rest, perturbed Spirit. 1656 tr. Hobbes' El... Oxford English Dictionary
prophetes.ai 0.0 3.0 0.0
2
Perturbed Attention Guidance
Perturbed Attention Guidance is a simple modification to the sampling process to enhance your Stable Diffusion images. stable-diffusion-art.com
stable-diffusion-art.com 0.0 1.5 0.0
3
Perturbed angular correlation
The perturbed γ-γ angular correlation, PAC for short or PAC-Spectroscopy, is a method of nuclear solid-state physics with which magnetic and electric fields Today only the time-differential perturbed angular correlation (TDPAC) is used. wikipedia.org
en.wikipedia.org 0.0 0.90000004 0.0
4
Passerby perturbed after stumbling upon scene left behind ...
14 hours ago — A Reddit user shared the adverse aftermath of a public celebration. ... Down may receive a commission on sign-ups ... DOWN COMPANY. All Rights ...
www.thecooldown.com 0.0 0.6 0.0
5
Perturbed differential equation Given a differential equation $y'(t)=f(t,y(t))$, where f satisfies the condition $(u-v)(f(t,u)-f(t,v))\le0$ for all $u$ and $v$. Suppose $W$ satisfies a perturbed differential equation ...
$$\begin{align} (U-W)(U'-W')&=(U-W)\bigl((f(y,U)-f(t,W)-r(t)\bigr)\\\ &=(U-W)(f(y,U)-f(t,W))-(U-W)\,r(t)\\\ &\le-(U-W)\,r(t) \end{align}$$ From here $$ |U'-W'|\le r(t) $$ and $$\begin{align} |U(t)-W(t)|&\le|U(0)-W(0)|+\int_0^t|U'(s)-W'(s)|\,ds\\\ &\le|U(0)-W(0)|+\int_0^t|r(s)|\,ds. \end{align}$$
prophetes.ai 0.0 0.6 0.0
6
Convexity of "perturbed" convex function Suppose $x\in\mathbb{R}^n$ and that we have the following "perturbed" quadratic form: $$Q(x) = x^\intercal A x + x^\intercal B + x^\intercal F(x)$$ where $A\in\mathbb{R}^{n\t...
No, simply let $F(x) = -2Ax$ when $||2Ax||\leq \gamma$ (and 0 otherwise) and you will always have a negative definite quadratic locally somewhere.
prophetes.ai 0.0 0.3 0.0
7
Relation between perturbed matrix and condition number of the matrix If A is non‐singular but the perturbed matrix (A+δA) is singular, then show that $$∥A∥/∥δA∥≤y $$ Where y is condition number of the matrix A. Tried...
If $A+E$ is singular, $(A+E)x=0$ for some $x\neq 0$, so $$ x=-A^{-1}Ex\implies\|x\|\leq\|A^{-1}\|\|E\|\|x\|\implies 1\leq\|A^{-1}\|\|E\| \implies\frac{\|A\|}{\|E\|}\leq\|A^{-1}\|\|A\|. $$
prophetes.ai 0.0 0.3 0.0
8
Exp. Stability of perturbed system with temporally vanishing perturbation I have a perturbation problem for which I can't find a fitting theorem in Khalil's Nonlinear Systems. Maybe someone can point me in the right d...
Ok, it is not true. Consider $\dot x = -x +e^{-3t}$. The solution is $x=c_1e^{-t}-0.5e^{-3t}$ with $c_1=x_0+0.5$. So $\|x\|$ has a part that is independent from $x_0$, which means that for arbitrarily small $\|x_0\|$, the exponential stability condition breaks.
prophetes.ai 0.0 0.3 0.0
9
Find perturbed eigenvalues, eigenvectors by perturbation methods Suppose we know $A_0v_0^k = \lambda_0^k v_0^k$, we can find the following perturbed eigenvalues and eigenvectors $$(A_0+\epsilon A_1)v(\epsilon) = \lamb...
As your matrix is singular in $\epsilon$, it is not too far-fetched to suspect that its eigenvalues will be singular, too. This is supported by the relation between the trace and determinant of a matrix and its eigenvalues, see e.g. here#Eigenvalue_relationships). So (ignoring the fact that for a $2...
prophetes.ai 0.0 0.3 0.0
10
(PDF) Numerical Solution of Singularly Perturbed Delay Reaction ...
「澳洲」澳洲国立大学 麦考瑞大学 卧龙岗大学 拉筹伯大学 新南威尔士大学 堪培拉大学 塔斯玛尼亚大学 莫道克大学 艾迪斯科文大学 西澳大学 科廷大学 圣母大学 新南威尔士州 悉尼科技大学 查理斯特大学 悉尼大学 南十字星大学 西悉尼大学 纽卡斯尔大学 ...
www.academia.edu 0.0 0.3 0.0
11
Effect of perturbation on Perron eigenvalues Let the entries of a $n \times n$ non-negative matrix be perturbed by a small amount so that the new matrix remains non-negative. I am interested in knowing how the Perron ...
I don't have a good reference on perturbations of PF eigenvalues but it is fairly simple to make examples. For $\epsilon\geq 0$: $$ M_\epsilon = \left( \begin{matrix} 1 & 1 & 0 \\\ 0 & 1 & 1\\\ \epsilon & 0 & 1\end{matrix}\right) $$ has char pol $p(\lambda)=(\lambda-1)^3-\epsilon\ $ so the leading e...
prophetes.ai 0.0 0.0 0.0
12
Multiplicities of the eigenvalues of a perturbed matrix Suppose $S$ is a symmetric and positive definite matrix in $\mathcal{R}^{n\times n}$. Suppose that $D$ is a diagonal matrix with diagonal $[1,a^{-1},\cdots,a^{-n...
No. Consider, e.g. the case $0<a<1$ and $S=D^{-1}$. I don't know what can be said about the multiplicities of the eigenvalues of $DS$ in general, but we do know that all eigenvalues of $DS$ are positive, as $DS$ is similar to $D^{1/2}SD^{1/2}$, which is positive definite.
prophetes.ai 0.0 0.0 0.0
13
Finding approximate eigenvalues of perturbed matrix Assume I have some constant matrix $A$ to which I add a perturbation, resulting in $M(\epsilon )=A+\epsilon B$ the perturbed matrix ($B$ is constant as well), and th...
There is a proof that shows that if the matrix $A$ is perturbed by a symmetric matrix $E$, then its eigenvalues do not move by more the $||E||$. There are other useful results, like the Bauer-Fike theorem and related results that can help you determine other results for bounds on perturbed eigenvalues
prophetes.ai 0.0 0.0 0.0
14
Approximating the inverse of a perturbed matrix Consider a matrix $A$ which we subject to a small perturbation $\partial A$. If $\partial A$ is small, then we have $(A + \partial A)^{-1} \approx A^{-1} - A^{-1} \parti...
The usual argument is that, if you perturb $A$ by a small $X$ and get $(A+X)^{-1}=A^{-1}+Y+O(\|X\|^2)$, where $Y$ is the first-order (i.e. linear) change in $A^{-1}$, then by comparing the first-order terms on both sides of $\left(A^{-1}+Y+O\left(\|X\|^2\right)\right)(A+X)=I$, you get $YA+A^{-1}X=0$...
prophetes.ai 0.0 0.0 0.0
15
A max-min inequality for a rank-1 perturbed symmetric matrix Can someone explain why the underlined inequality is true? Thank you for your time. ![enter image description here](
I just realized that this is just a consequence of the Courant-Fischer theorem for symmetric matrices which states that $\substack{\text{max}\\\\\text{dim}(L)=k}\substack{\text{min}\\\x\in L\\\x\neq0}\dfrac{x^\text{T}Ax}{x^\text{T}x}=\lambda_k(A)$ with the eigenvalues ordered as $\lambda_1(A)\geq\la...
prophetes.ai 0.0 0.0 0.0