Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 71

Each permutation in permutation group PSL2 consist of fixed points and cycles of equal lengths. Prove or disprove it.

For the standard permutation representation of the finite projective special linear group $text{PSL}_2$, I have noticed the fact that every permutation contains the cycles of one length, except for...

Asked on 11/24/2021 by Slepecky Mamut

1 answer

Question about the definition of tensor product of homomorphisms

I am working on an exercise about tensor products. We introduced them as the quotient space given by the following definition:For two Abelian groups $A$ and $B$ we...

Asked on 11/24/2021 by Zest

1 answer

Probability of gaining a game series

Let's say I have a team, and we are playing a game against another team, where our probability of winning each game is $p$. We get the offer to...

Asked on 11/24/2021 by Silkking

0 answer

Prove that $xg(x)<int_{0}^xg(x)dx$

Let $f(x)$ satisfy the differential equation$$frac{d(f(x))}{dx}+f(x)=g(x)$$ where $f(x)$ and $g(x)$ are continuous functions. Also it is known that $f(x)$ is a decreasing function of ...

Asked on 11/24/2021

1 answer

Integration on the punctured plane

Let $M = mathbb{R}^2backslash{0}$,$$ alpha = frac{xcdot dy-ycdot dx}{x^2+y^2}$$and $mathcal{C} = {(f(e^{itheta})costheta,f(e^{itheta})sintheta);thetainmathbb{S}^1}$, where $f:mathbb{S}^1to (0,1)$ is smooth. Let $j:mathcal {C}to M$ be...

Asked on 11/24/2021 by MathNewbie

1 answer

Show that if the matrix of $T$ with respect to all bases of $V$ is same, then $T = alpha I$ where $T$ is a linear operator on $V$

Now the only hint I could derive from the question that we might have to use eigenvalues as $Tx = lambda x$ for $T = lambda I$. I...

Asked on 11/24/2021

4 answer

Is $(B_t,B_t)$ a Brownian motion on the line ${(x,x)mid xinmathbb R}$?

I saw today that $(B_t^1,B_t^2)$ is a brownian motion on $mathbb R^2$ iff $B_t^i$ a independent Brownian motion on $mathbb R$. So, if for example, ...

Asked on 11/21/2021

1 answer

What is the kernel of $h$ where $h:S_3 to mathbb{R}^*$

$S_3$ is the permutation group on 3 symbols and $mathbb{R}^*$ denotes the multiplicative group of non zero real numbers under multiplication. $h: S_3 to mathbb{R}^* $is given...

Asked on 11/21/2021 by user686123

2 answer

Critical Points of $dy/dx=0.2x^2left(1-x/3right)$

I am trying to determine the critical points of the ODE $$frac{dy}{dx}=0.2x^2left(1-frac{x}{3}right).$$ Setting the right-hand-side to zero gives two solutions, namely $x=0$ and $x=3$. I was wondering...

Asked on 11/21/2021

2 answer

What's the difference between a Proof System and a Theory?

I found this question Is the axiom of induction required for proving the first Gödel's incompleteness theorem? I am apparently under the (wrong) impression that a theory and a...

Asked on 11/21/2021 by Threnody

1 answer

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