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So I work a lot with ergodic theorems but it is a bit confusing.We have a probability space $(Omega,mathcal{F},P}$ and a measure preserving mapping $T:OmegarightarrowOmega$.We say...
Asked on 02/16/2021 by Eduard
1 answerHow to prove that $x(t) = cos{(frac{pi}{8}cdot t^2)}$ aperiodic? My process was as follows: $x(t+T)= cos{(frac{pi(t+T)^2}{8})}$. So, $T^2 + 2tT -16=0$ which seems periodic to me... Can...
Asked on 02/16/2021 by YK1
2 answerI'm trying to compute a most general unifier. There are many rules and I'm confused by them. So here is the example: {P(z,g(c)),P(g(x),z),P(z,z),P(g(y),g(c))} - x, y and z are...
Asked on 02/16/2021 by Milano
1 answerHow to check if a number can be represented as the sum of two consecutive perfect cubes. for eg N = 35 can be represented as the sum of two...
Asked on 02/16/2021 by sqrt
2 answerHow to compute $mathbb{P}(B(tau)leq a)$, where $tau$ ~ Exp(λ), which is independent of $B(t),tgeq 0.$ here is my computation:$ mathbb{P}left(Bleft(tauright)le aright)=mathbb{E}left[mathbb{E}left[1_{left{ Bleft(tauright)le aright} }|tauright]right]=int_{0}^{infty}lambda...
Asked on 02/15/2021 by Wheea
1 answerEvaluate following definite integral:$$int_1^2 frac{(1+ln x)^5}{x}dx$$I solved this integral with a substitution rule: $u=ln x$, $du=dx/x$ $$int_1^2 frac{(1+ln x)^5}{x}dx=int_0^{ln 2} (1+u)^5 du$$ solved and...
Asked on 02/15/2021 by Adilah
1 answerFor a single variable function expanded about the point $x_0$, the radius of convergence is the radius of the largest disk around $x_0$ in which $f(z)$ is...
Asked on 02/15/2021 by Elster
0 answerFor a research project I was given a result, which describes the time distribution for the meeting time of two superdiffusive random walks (superdiffusive random walks don't have a standard...
Asked on 02/15/2021 by DeltaChief
0 answerA few days ago, I posted the following problems Prove thatbegin{equation}int_0^{pi/2}ln^2(cos x),dx=frac{pi}{2}ln^2 2+frac{pi^3}{24}\[20pt]-int_0^{pi/2}ln^3(cos x),dx=frac{pi}{2}ln^3 2+frac{pi^3}{8}ln 2 +frac{3pi}{4}zeta(3)end{equation} and the OP receives some good answers even...
Asked on 02/15/2021 by Anastasiya-Romanova 秀
7 answerI recently saw the following inequality,$$frac{(a-1)(c+1)}{1+bc+c}+frac{(b-1)(a+1)}{1+ca+a} + frac{(c-1)(b+1)}{1+ab+b} geq 0 tag1$$for all $abc=1$ and $a,b,c in mathbb{R}_+ setminus {0 }$. To prove this inequality, I...
Asked on 02/14/2021 by Darius Chitu
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