Questions tagged [reference-request]

This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

14,568 questions
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$\exp: \mathfrak{so}(1,n) \rightarrow SO(1,n)$ is surjective

I am looking for a reference where it is proven that the exponential map described above is surjective. Here, I am denoting by $\mathfrak{so}(1,n)$ the Lie Algebra of the group $SO(1,n)$. So we have ...
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Gelfand Naimark Segal construction

Let $X$ be a von Neumann algebra. Let $f$ be a faithful semi-finite normal weight on $X$. $$N_f:=\{x \in X : f(x^*x) < \infty \}$$ $$n_f:=\{x \in X : f(x^*x)=0 \}$$ Most of operator algebras ...
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Set $\int_0^1{x^n\sqrt{1-x^2}}dx\quad (n=0,1,2,…)$. Prove that the sequence $(a_n)$ is monotonically decreasing; [closed]

Set $a_{n}$=$\int_0^1{x^n\sqrt{1-x^2}}dx \quad (n=0,1,2,....)$ $1.$ Prove that the sequence $(a_n)$ is monotonically decreasing; $2.$ Prove $a_{n}$ = $\frac{(n-1)}{(n+2)}a_{n-2}\quad (n=2,3,…）$ ...
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how to split a separable algebra?

I'm trying to factor ideals in a function field (more precisely, ideals in a maximal order of a function field), and I've come across a step in the published Buchman-Lenstra algorithm which works in ...
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Poincare's Inequality

Assume $\Omega \subset L_d$, for some $d > 0$. Then, for all $u \in W^{1,q}_0(\Omega)$ $1 \leq q \leq \infty$ , $\left \|u \right \|_p \leq (d/2)\left \| \nabla u \right \|_p$. Prove that the ...
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Group structure of an elliptic curve over a finite field

I'd be interested in a short proof of and a reference (first source, not a textbook as e.g. one of Silverman's monographs) for the following result: Let $q$ be a prime power and $C/F_q$ be an ...
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Primitive of a function for all but countable many points

Let $f$ be a real-valued function with $D(f) = D = <a,b>$. In our calculus course we introduce such definitions: Definition 1. $F$ is an exact primitive of $f$ iff $D(F) = D$, $F$ is ...
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Find the area between the graph $y=e^{-x}\sin x, x \geq 0$ and the $x$-axis. Calculate the area of ​the area.

Find the area between the graph $y=e^{-x}\sin x, x \geq 0$ and the $x$-axis. Calculate the area of ​​the area. answer： The part of the red line is marked out, how do you think of it? If you don’t ...
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Book recommendation to study topics of Linear Programming for self study

I need some reference book suitable for self-study with many solved examples and solutions preferably for exercise questions for following study. Need basic honours undergraduate level text , ...
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Axioms of Propositional Logic with as few negation axioms as possible

Could you direct me to an axiom system for propositional logic over the connectives $\land$, $\lor$, and $\lnot$ with as few axioms over negation as reasonably possible? I've done a fair bit of ...
Image of $T:E \rightarrow \alpha E + (1-\alpha) E$ where $\alpha>1$.
Fix a real number $\alpha>1$ and an integer $n \geq 1$. Let $T_\alpha$ be the mapping defined on the set $\mathcal{E}$ of closed convex subsets of $\mathbb{R}^n$ by \begin{equation*} T_\alpha(E) = \...