Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 139

Connection between max and min of symmetric random variables

I bumped into a problem and I wonder if the following statement is true: Let $X_1, X_2, ..., X_n$ be symmetric random variables (possibly dependent) centered around zero (i.e....

Asked on 01/25/2021 by losleon

1 answer

How to prove that there is not a monomorphism from Klein 4-group to $Z_6$(or a epimorphism from $Z_6$ to $V_4$)?

How to prove that there is not a monomorphism from Klein 4-group to $Z_6$(or a epimorphism from $Z_6$ to $V_4$) ? I know that:If ...

Asked on 01/25/2021 by Tota

1 answer

Homomorphisms between fields are injective.

How would I prove this? I know that I must show $f(a)=f(b) Rightarrow a = b$ I also know I must use the definition of homomorphism, ie: $f(a+b)=f(a)+f(b)$...

Asked on 01/25/2021

4 answer

We have an integer n. We have n boxes where each box contains a non-negative amount of balls. Find all the permutations which satisfy some criteria

Let $n$ be a positive integer. We have $n$ boxes where each box contains a non-negative number of pebbles. In each move we are allowed to take two...

Asked on 01/25/2021 by Michael Blane

1 answer

Approximation of the sum of a series $S(t)=-frac{2}{pi t} cos(frac{pi t}{2}) sum_{m odd}^{infty}frac{m^2alpha_m}{t^2-m^2}$ as $tto +infty$

The function S(t) has the following infinite series form: begin{align}S(t) &=frac 2pi int_0^{pi/2} dx sin(tx){sum_{m odd}^{infty} alpha_m cos[m(frac pi2-x)]}\&=-frac{2}{pi t} cos(frac{pi t}{2}) sum_{m odd}^{infty}frac{m^2alpha_m}{t^2-m^2} \end{align} Where...

Asked on 01/25/2021 by Yolbarsop

0 answer

Homogenous space of elliptic curve E/$Bbb Q$

Does a homogenous space for an elliptic curve E/$Bbb Q$ always have a $Bbb Q _p$ rational point for every prime $p$? And why? I know that...

Asked on 01/25/2021 by bellow

1 answer

On the functional square root of $x^2+1$

There are some math quizzes like:find a function $phi:mathbb{R}rightarrowmathbb{R}$such that $phi(phi(x)) = f(x) equiv x^2 + 1.$If such $phi$ exists (it does in this example), $phi$ can be viewed...

Asked on 01/25/2021 by user1551

9 answer

Is there a simple way to find all the solutions of $x_1 + x_2 + dots + x_k + dots + x_K = N$ when $x_k$s and $N$ are all non-negative integers?

Suppose I want to find all the possible solutions for the equation below. $$x_1 + x_2 + dots + x_k + dots + x_K = N$$ where $$x_k...

Asked on 01/25/2021 by Cardinal

2 answer

Minimizing the Schatten 1-norm over symmetric matrices.

Let $X$ be an $n times n$ Hermitian matrix, it follows that we can write $X=A+iB$ where $A$ is symmetric and $B$ is skew-symmetric. Let $S$ be the set of...

Asked on 01/25/2021 by gene

2 answer

The frontier of a set

I'm trying to prove that a certain set is dense in a metric space.I have a metric space X, an open subspace $Ysubset X$ (same metric) and an...

Asked on 01/25/2021 by Gal Ben Ayun

1 answer

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