Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 28

Prove that there exists $T in mathcal{L}(V, W)$ such that $operatorname{null}(T) = U$ if and only if $dim (U) ge dim (V) - dim (W)$

Suppose that $V$, and $W$ are finite dimensional vector spaces and that $U$ is a subspace of $V$. Prove that there exists $T in mathcal{L}(V,...

Asked on 12/21/2021

3 answer

Does a sequence of $d$-SOS polynomials converge to a polynomial that is also $d$-SOS?

Let $mathbb{R}[X]_{leq 2d}$ denote the real vector space of polynomials of degree at most $2d$ in the coordinate ring $mathbb{R}[X]$ of variety $X$.Definition: A polynomial...

Asked on 12/21/2021 by Tio Miserias

0 answer

A term for multiples made by using an odd/even factor

(I bet you will send me to english.stackexchange.com and they will send me back here) I will use an example - I have two lists of integers:list A: 0,...

Asked on 12/21/2021

1 answer

Solving 4 simultaneous homogeneous equations

$frac{-hbar^2}{2m}(a^2b_0-4ab_1+6b_2)-Ze^2b_1-Eb_0 = 0$$frac{-hbar^2}{2m}(a^2b_1-6ab_2)-Ze^2b_2-Eb_1= 0$$frac{-hbar^2}{2m}(-2ab_0+2b_1)-Ze^2b_0 = 0$$frac{-hbar^2}{2m}(a^2b_2)-Eb_2 = 0$here I need to find the values of $a,b_0,b_1,b_2$E = $-displaystylefrac{Z^2e^2}{18a_0}$$a_0 = displaystylefrac{hbar^2}{me^2}$...

Asked on 12/21/2021

1 answer

Application of Game Theory in time-varying networks.

I am a complete newbie to game theory. But I need to analyze the applicability of game theory to my work.Considering a dynamic time-varying network where every user has...

Asked on 12/21/2021

0 answer

What conditions on the coefficient category allow one to check isomorphisms for sheaves on stalks?

Let $mathscr{C}$ be a category which admits small limits and small filtered colimits.For a topological space $X$,one can define $operatorname{Sh}(X;mathscr{C})$ to be the subcategory of...

Asked on 12/21/2021 by Chris Kuo

0 answer

How to find the dominant eigenvalue of a Next generation matrix

I have been working with a compartmental model and I am now trying to compute the basic reproduction number. To do this I must find the spectral radius (dominant eigenvalue)...

Asked on 12/21/2021

1 answer

Question on the Definition of Automorphism

So I am missing something very basic here, but here it goes. As a consequence of the definition of a homomorphism we must have that $f(e) = e'$. Consider...

Asked on 12/21/2021 by James Eade

1 answer

Closed-form expression for $sum_{n = 0}^{infty}(frac{(ln(4n+3))^k}{4n+3}-frac{(ln(4n+5))^k}{4n+5}),$ where $k$ is a positive integer

I recently came across this infinite series:$$sum_{n = 0}^{infty}left(frac{(ln(4n+3))^2}{4n+3}-frac{(ln(4n+5))^2}{4n+5}right)$$Is it possible to express the series in closed-form? If so, how should I go about it?More generally, how...

Asked on 12/21/2021

0 answer

The cardinality of the intersection of a subgroup and its conjugate

Let $G$ be a finite group and $A$ be a subgroup of $G$. Suppose $A^x$ and $A^y$ are two conjugates of $A$ such that...

Asked on 12/21/2021 by user792898

2 answer

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