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upsilon

upsilon (juːpˈsaɪlən, ˈʊpsɪlɒn) [a. Gr. ὖ ψιλόν ‘slender u’, the adj. having reference to its later sound (y).] 1. The Greek letter υ, υ (originally V, Y) representing the vowel u (see U, V, and Y). Also attrib., = having the form of this letter.1642 Howell For. Trav. xi. (Arb.) 56 In some places of... Oxford English Dictionary

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Upsilon

Usage In particle physics the capital Greek letter ϒ denotes an Upsilon particle. Coptic Ua Latin Upsilon Mathematical Upsilon These characters are used only as mathematical symbols. wikipedia.org

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Show that is $\upsilon$ is an eigenvector of the matrices A and AB (assume invertibility) Show that is $\upsilon$ is an eigenvector of the matrices A and AB with corresponding eigenvalues $\lambda \neq 0$, $\mu$ resp...

Your reasoning is right, since you seem to assume invertibility of $A$. Without invertibility of $A$, the statement is wrong: Take $$ A=\pmatrix{1&0\\\0&0}, \ B = \pmatrix{0&0\\\1&0}, \ v = \pmatrix{1\\\0}, $$ then $Av = v$, $AB=0$, but $v$ is not an eigenvector of $B$.

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when was upsilon founded

Upsilon Pi Epsilon was founded on January 10, 1967 at Texas A&M University and has chartered over 270 chapters at college campuses around the world.

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Solve $f'' - \frac{iw}{\upsilon}f=0$ We are given $u=u(y,t)$ and $$\frac{\partial u }{\partial t}= \upsilon \frac{\partial ^2 u }{\partial y^2}$$where $\upsilon$ is the viscosity. Look for solutions of the form $u=Re\...

$$\frac{d^2 f}{dy^2} - \frac{iw}{\upsilon}f=0$$ Looking for solutions on the form $e^{ay}$ requires : $$\frac{d^2 e^{ay}}{dy^2} - \frac{iw}{\upsilon}e^ {ay}=0 \quad\to\quad a^2-\frac{iw}{\upsilon}=0 \quad\to\quad a=\pm\sqrt{\frac{w}{\upsilon}}\:i^{1/2}$$ $i=e^{i\frac{\pi}{2}}\quad\to\quad i^{1/2}=\left

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If $u_n \rightharpoonup u\,$ in $\,L^2(\Omega)\,$ and $\,u_n^2 \rightharpoonup \upsilon$ in $L^1(\Omega),\,$ then is $\upsilon=u^2$? If $u_n \rightharpoonup u$ in $L^2(\Omega)$ and $u_n^2 \rightharpoonup \upsilon$ in ...

The answer is: _Not in general._ For example, $\Omega=(0,2\pi)$, $u_n(x)=\sin nx$. Then $u_n\rightharpoonup 0$, since $$ \int_0^{2\pi} f(x)\,\sin nx\,dx\to 0=u, $$ for all $f\in L^2[0,2\pi]$. Meanwhile $$ v_n(x)=u_n^2(x)=\sin^2 nx=\frac{1}{2}-\frac{\cos (2nx)}{2}\rightharpoonup \frac{1}{2}=v, $$ and...

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Question about Radon Nikodym If $\mu$ is absolutely continuous with respect to $\upsilon$, then a theorem is $\frac{d|\mu|}{d\upsilon}=\left|\frac{d\mu}{d\upsilon}\right|$. Let's say that $\lambda$ is the Lebesgue mea...

The mistake is $\mu(A)=|\int_Ah\,d\lambda |$. You need to go back to the definition of $|\nu |$. It is not defined by $|\nu|(A)=|\nu(A)|$. Rather, $|\nu |$ is defined as $\nu^++\nu^-$, where $\nu^+(A)=\nu(A\cap P)$ and $\nu^-(A)=-\nu(A\cap N)$, where $(P,N)$ is the Hahn decomposition of $\nu$.

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Radiative Decays of the Upsilon(1S) to a Pair of Charged Hadrons

Using data obtained with the CLEO~III detector, running at the Cornell Electron Storage Ring (CESR), we report on a new study of exclusive radiative Upsilon(1S) decays into the final states gamma pi^+ pi^-, gamma K^+ K^-, and gamma p pbar..

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Show that $\Omega \setminus N_A \ni x \mapsto 1_A(x) \cdot \int\limits_{\Upsilon} k(x,t)f(t)d\nu(t)$ is measurable Assume $(\Omega,\mathcal{A},\mu)$ and $(\Upsilon,\mathcal{B},\nu)$ are measure spaces with $\sigma$-fi...

$\int\limits_{\Omega\times\Upsilon} 1_A(x) k(x,t)f(t) d(\mu\times\nu)(x,t)=\int\limits_{\Omega}1_A(x) \int\limits_{\Upsilon} k(x,t)f(t) d\nu(t) d\mu(x) $\Omega \times \Upsilon \ni(x,t) \mapsto 1_A(x) k(x,t)f(t)$ And since the first integral is finite $g$ as the inner integrand of the right hand side is

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怎样简易的理解科氏加速度？教材推导太难理解了？

设小球的径向运动方向转过一个微小角度d\theta 径向速度由\upsilon _{1} 变为\upsilon _{2} ，径向速度的变化量为d\upsilon ，如下图所示。而径向速度大小不变，即 \upsilon _{1} =\upsilon _{2} 由于d\theta 是一个无限小量，故按求弧长方法来求径向速度\upsilon 的改变量，即 d\upsilon =\upsilon _{1}d\theta =\upsilon _{2}d\theta=\upsilon zhihu

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What does the notation mean? Given a measure space $(\Omega,\mathcal{F},\upsilon)$ and a $p>0$. What does the following mean? $$ \|f\|_p=(\upsilon|f|^p)^{1/p}$$

I think they're trying to say: $$ \|f\|_p=\left(\int_\Omega \vert f\vert^p dv\right)^{1/p} $$ One way to justify their shorthand is that integration is like "measuring" the function, so $v\vert f\vert^p$ could be thought of as shorthand for $\int_\Omega\vert f\vert^pdv$.

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Sigma Finite Measure restricted to a small sigma-algebra is still sigma finite? Let $(X,M,\upsilon)$ be a $\sigma$-finite measure, $N$ a sub-$\sigma$-algebra of $M$, then $\upsilon|_N$ is $\sigma$-finite measure in $(...

No, consider $X=\mathbb{N}$ and $M$ is the collection of all the subsets of $\mathbb{N}$ and $v$ is usual counting measure. Now let $N=\\{\emptyset,\mathbb{N}\\}$ and you see the statement is false.

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Coordinate-free differentiation techniques in Riemannian geometry I encountered the following identities while reading this article on global calculus (p. 10): $$ d(\|df\|^2)=2\mathop{\iota_{\mathop{\mathrm{grad}} f}...

By simply using the definition. The first thing to remember is that the covariant derivative commutes with metric and inverse metric. The second thing to remember is that the covariant and exterior derivatives agree when acting on a scalar function. So, $$ d(\|df\|^2) = \nabla(\|df\|^2) = \nabla g^{...

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Show that the determinant of jordan normal form wtih spatial weight matrix by its eigenvalues I try to figure out the proof of determinant of matrix by eigen decomposition, $$det(I_n-\lambda W)=det(QQ^{-1}(I_n-\lambda...

So we know (given) that there is a $Q$ such that $QWQ^{-1}$ is triangular. The first step is to introduce $Q$ $$\det(I - \lambda W) = \det( Q^{-1}Q(I-\lambda W))$$ Second let's use the property $\det(AB) = \det(BA)$ where $A = Q^{-1}$ and $B = Q(I-\lambda W)$ hence $$\det(I - \lambda W) = \det(Q(I-\...

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Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$. Let $f$ be an entire function that satisfies $|f(z)| \leq 1 + |z|$ for all $z\in \mathbb{C}$. Show that $f(z) = az +b$ for fi...

Here's the big missing idea: if a function's second derivative is identically zero, then the function is at most a linear polynomial. So you should show that the right hand side is zero when $n = 2$.

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upsilon

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upsilon

Upsilon

Show that is $\upsilon$ is an eigenvector of the matrices A and AB (assume invertibility) Show that is $\upsilon$ is an eigenvector of the matrices A and AB with corresponding eigenvalues $\lambda \neq 0$, $\mu$ resp...

when was upsilon founded

Solve $f'' - \frac{iw}{\upsilon}f=0$ We are given $u=u(y,t)$ and $$\frac{\partial u }{\partial t}= \upsilon \frac{\partial ^2 u }{\partial y^2}$$where $\upsilon$ is the viscosity. Look for solutions of the form $u=Re\...

If $u_n \rightharpoonup u\,$ in $\,L^2(\Omega)\,$ and $\,u_n^2 \rightharpoonup \upsilon$ in $L^1(\Omega),\,$ then is $\upsilon=u^2$? If $u_n \rightharpoonup u$ in $L^2(\Omega)$ and $u_n^2 \rightharpoonup \upsilon$ in ...

Question about Radon Nikodym If $\mu$ is absolutely continuous with respect to $\upsilon$, then a theorem is $\frac{d|\mu|}{d\upsilon}=\left|\frac{d\mu}{d\upsilon}\right|$. Let's say that $\lambda$ is the Lebesgue mea...

Radiative Decays of the Upsilon(1S) to a Pair of Charged Hadrons

Show that $\Omega \setminus N_A \ni x \mapsto 1_A(x) \cdot \int\limits_{\Upsilon} k(x,t)f(t)d\nu(t)$ is measurable Assume $(\Omega,\mathcal{A},\mu)$ and $(\Upsilon,\mathcal{B},\nu)$ are measure spaces with $\sigma$-fi...

怎样简易的理解科氏加速度？教材推导太难理解了？

What does the notation mean? Given a measure space $(\Omega,\mathcal{F},\upsilon)$ and a $p>0$. What does the following mean? $$ \|f\|_p=(\upsilon|f|^p)^{1/p}$$

Sigma Finite Measure restricted to a small sigma-algebra is still sigma finite? Let $(X,M,\upsilon)$ be a $\sigma$-finite measure, $N$ a sub-$\sigma$-algebra of $M$, then $\upsilon|_N$ is $\sigma$-finite measure in $(...

Coordinate-free differentiation techniques in Riemannian geometry I encountered the following identities while reading this article on global calculus (p. 10): $$ d(\|df\|^2)=2\mathop{\iota_{\mathop{\mathrm{grad}} f}...

Show that the determinant of jordan normal form wtih spatial weight matrix by its eigenvalues I try to figure out the proof of determinant of matrix by eigen decomposition, $$det(I_n-\lambda W)=det(QQ^{-1}(I_n-\lambda...

Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$. Let $f$ be an entire function that satisfies $|f(z)| \leq 1 + |z|$ for all $z\in \mathbb{C}$. Show that $f(z) = az +b$ for fi...