Newest Questions - Mathematics Stack Exchange
2 days ago · Mathematics Stack Exchange is a platform for asking and answering questions on mathematics at all levels.
optimization - Minimizing KL-divergence against un-normalized ...
Jun 10, 2024 · Minimizing KL-divergence against un-normalized probability distribution Ask Question Asked 1 year, 7 months ago Modified 1 year, 7 months ago
Integral of factorial function - Mathematics Stack Exchange
Dec 19, 2022 · $$ \\mbox{What can we say about the integral}\\quad \\int_{0}^{a} x!\\,{\\rm d}x\\ ?. $$ Or something like $\\displaystyle\\int_{0}^{3} x!\\ {\\rm d}x\\ ?$.
(Un-)Countable union of open sets - Mathematics Stack Exchange
A remark: regardless of whether it is true that an infinite union or intersection of open sets is open, when you have a property that holds for every finite collection of sets (in this case, the union or …
modular arithmetic - Prove that that $U (n)$ is an abelian group ...
Prove that that U(n) U (n), which is the set of all numbers relatively prime to n n that are greater than or equal to one or less than or equal to n − 1 n 1 is an Abelian group. My thought …
For what $n$ is $U_n$ cyclic? - Mathematics Stack Exchange
17 Un U n is cyclic iff n n is 2 2, 4 4, pk p k, or 2pk 2 p k, where p p is an odd prime. The proof follows from the Chinese Remainder Theorem for rings and the fact that Cm ×Cn C m × C n is …
distance from a point to a hyperplane - Mathematics Stack Exchange
Mar 28, 2015 · I have an n-dimensional hyperplane: w′x + b = 0 w x + b = 0 and a point x0 x 0. The shortest distance from this point to a hyperplane is d = |w⋅x0+b| ||w|| d = w x 0 + b w. I …
$\\operatorname{Aut}(\\mathbb Z_n)$ is isomorphic to $U_n$.
Aug 3, 2023 · It might be using ring theory in a non-essential way, but it is conceptually simpler because the endomorphisms are easier to describe than the automorphisms, and since the …
study of the sequence (Un) defined by $U_{0}=a$ and …
Oct 7, 2020 · let a and b be real numbers such that a>0 and b>1. Consider the sequence (Un) defined by U0 = a U 0 = a and Un+1 = a + 1−b−n 2.Un U n + 1 = a + 1 b n 2 U n . Show that …
When is the group of units in $\\mathbb{Z}_n$ cyclic?
Let Un U n denote the group of units in Zn Z n with multiplication modulo n n. It is easy to show that this is a group. My question is how to characterize the n n for which it is cyclic. Since the …