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For $\alpha \in (0,1)$, set $\omega:\mathbb{R^+}\times \mathbb{R^+} \to \mathbb{R}$ defined as following $$\omega(t;\tau):=1-\pi^{-1}\int_0^\infty \frac{e^{-rt-\tau r^\alpha \cos(\alpha \pi)}\sin(\tau r^{\alpha}\sin(\alpha \pi))}{\pi r}dr, \ t, \tau>0$$ Can we prove that exist $a$, $b$, $c$, $\al... 3 hours later… 3:41 AM 7 Uncomputable functions: Intro The last month I have been going down the rabbit hole of googology (mathematical study of large numbers) in my free time. I am still trying to wrap my head around the seeming paradox of the existence of natural numbers that are well-defined but uncomputable (in the s... 1 hour later… 4:57 AM 3 I have the following situation Let$N_1, N_2 \sim \mathcal{N}(0,1)$two independent r.v. Let$X = \frac{N_1}{\sqrt{N_{1}^{2} + N_2^2}}$and$Y = \frac{N_2}{\sqrt{N_{1}^{2} + N_2^2}}$. Now I know how show to that$X$and$Y$are not independent, but I don't know how to show$X$and$Y$are uncorre... 2 hours later… 6:45 AM @Feeds Answers to this question are eligible for a +250 reputation bounty. Knocker379 wants to draw more attention to this question: > Find the area of A with some explanation (I'll comment any questions I have about your answer. Bounty is 250) @Feeds Answers to this question are eligible for a +250 reputation bounty. Bernhard Boehmler wants to draw more attention to this question. @Feeds Answers to this question are eligible for a +100 reputation bounty. SAWblade wants to draw more attention to this question. @Feeds Answers to this question are eligible for a +100 reputation bounty. Jarbas Dantas Silva is looking for an answer from a reputable source: > if the constants requested in the conditions of the question,$a$,$b$,$c$and$\alpha$exist, the reason for their existence must be explained mathematically in detail. In the case of non-existence, it must also be explained with mathematical rigor and in detail. I do not accept gaps to be filled in and every result used must be cited. I thank any help. @HNQmath.se Removed from HNQ by adding MathJax. 3 hours later… 9:31 AM 4 I am trying to solve the following exercise. What I know:$\tau$is a vector bundle of dimension$n$over$\mathbb{R}P^n$. The same is true for the trivial bundle$\mathbb{R}P^n \times \mathbb{R}^n$. Then we find surjective smooth maps$$\pi: \tau \to \mathbb{R}P^n \\ \tilde{\pi}:\mathbb{R}P^n ... 9:56 AM 5 We consider the group$G = SL(2, 3) $i.e, the set of$2 \times2$matrices with determinant 1 and addition and multiplication are performed modulo 3 even in the determinant formula. One can show that$|G| = 24$a) Let$\alpha = \begin{pmatrix} 2 & 2\\ 2 & 1 \end{pmatrix}$show that$\alpha \in G$... 2 hours later… 11:47 AM 0 According to the Implicit Function Theorem ($2$dimensional case): if$F:U\subset \mathbb{R}^2\to \mathbb{R}$is a$C^1$function defined on the open set$U$and$(x_0,y_0)\in U$such that$F(x_0,y_0)=0$and$F_y(x_0,y_0)\neq 0$, then for some neighbourhoods$I,\,J$of$x_0,y_0$, respectively t... 0 Imagine I want to statistically characterise a set of converging points and still get an idea of the converging properties or shape of such set, for example The values of the mean or variance of the$y$coordinates don't really tell me anything specific about the converging shape of such set and... 2 hours later… 1:29 PM @Feeds Answers to this question are eligible for a +50 reputation bounty. Nikolaos Skout is looking for an answer from a reputable source. @Feeds Answers to this question are eligible for a +50 reputation bounty. sam wolfe wants to draw more attention to this question. 2:18 PM 0 During lectures, we got to show that$C_9$,$C_9 + 1$are subdirectly irreducible, where$C_n$:=$(\{0, 1, . . . , n − 1\}, (0 1 . . . n − 1))C_n + 1$:=$(\{0, 1, . . . , n − 1, n\}, (0 1 . . . n − 1)(n))$I know the usual definition of subdirect irreducibility - An algebra$A\$ is subdir...

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