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When do boundedness wrt metric and wrt order agree?

In Wikipedia: A subset $S$ of $\mathbb{R}^n$ is bounded with respect to the Euclidean distance if and only if it bounded as subset of $\mathbb{R}^n$ with the product order. More generally, I ...
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How to calculate the gradient of matrix equation

Short question: How do I calculate the gradient of the $MSE(a, b)$ equation below? Longer explanation: This problem arises, while I'm following a derivation of a term for an optimal beamvector $a$ in ...
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Density Question - Statistics

A point is picked randomly in space. Its three coordinates $X$, $Y$, and $Z$ are independent standard normal variables. Let $R = \sqrt{X^2+Y^2+Z^2}$ be the distance from the point from the origin. ...
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splitting arrays in matlab

Greetings All I'm trying to 1)split an array into multiple parts 2)export each part to separate wave files 3)re-import wav files and join them together to make sure the array data that was split ...
367 views

Finitely generated free group is a cogroup object in the category of groups

I am trying to show that every finitely generated free group is a cogroup object in the category of groups. (Note I believe that this is also true for non-finite free groups, but that is probably much ...
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Prove that $a$ is quadratic residue modulo every prime if and only if $a$ is perfect square [duplicate]

Possible Duplicate: Proving that an integer is the $n$ th power Prove that $a$ is quadratic residue modulo every prime if and only if $a$ is perfect square My attempt was, Since $a$ is ...
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How to determine the degree of a polynomial?

If $$g(x) = x^4 + x^3$$ From my understanding, the degree of the above polynomial i.e. $g(x)$ is 4. However, for this polynomial, $$f(x) = (x-1)(x-2) \cdots (x-p+1)$$ What degree does $f(x)$ have? ...
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Assume that $\phi:\mathbb{R}^n\rightarrow \mathbb{R}^n$ is a smooth vector field, and assume that we can find vectors $y_k,x_k$ ($k$ positive integer) such that $(\phi(x_k)-\phi(y_k),x_k-y_k)\geq k \... 1answer 3k views Trajectory of a projectile meets a moving object (2D) First of all, I asked this question on Stackoverflow, but I realize this is a better place to ask the question. So i moved it here. I've looked for quite some time now to find a nice math solution ... 2answers 347 views Concerning the definition of effective quotient orbifold I've been trying to figure out orbifolds, and in all of the sources I seem to be confused with the orbifold structure on quotient orbifolds. A quotient orbifold is defined as follows. Let$M$be a ... 1answer 88 views an estimate for derivative let$F$a closed convex subset of$\mathbb{R}^n$, let$x,y\in F$and assume that for any$s\in[0,1]$we have$f(s):=\mid sx+(1-s)y-z\mid\geq \mid y-z\mid$why is it true that$\frac{\partial}{\...
Given $T\circ S=\emptyset$ and $R$ nonempty, would $$(T \circ S) \circ R$$ be anything other than the empty set? I'm also curious the other way around. I think that it would be just empty.
Is the Galois group of an irreducible separable polynomial of degree $n$ isomorphic to a group on exactly $n$ letters? Is that enough to prove that a degree $n$ polynomials has $n$ roots. What I mean ...