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Mathematics : Recent Questions and Answers (Page 12)

Find answers to your questions about Mathematics or help others by answering their Mathematics questions.

Rootspaces are $mathop{ad}$ nilpotent

$ DeclareMathOperator{ad}{ad}$Let $L$ be a semisimple Lie algebra with root space $L=H oplus bigoplus_{alpha in Phi}L_alpha$. Let $xin L_alpha$ with $alphaneq 0$. I want...

Asked on 01/01/2022

3 answer

extension of a function to a differentiable function

Suppose we have a map $f: S rightarrow mathbb{R}^{n}$, where $S subset mathbb{R}^{m}$, such that for each $a in S$ there exists an $m$ by $n$ matrix $A$ such that...

Asked on 01/01/2022 by user13255

1 answer

Is $-2^2$ equal to $-4$, or to $4$?

Is it always safe to assume that $-2^2 = -4$, or is this dependent on notation, i.e. would it be mathematically correct (albeit sloppy) to say $-2^2 = (-2)^2 =...

Asked on 01/01/2022 by tmakino

3 answer

Proof of $sum_{k=0}^m binom{n}{k}(-1)^k = (-1)^m binom{n-1}{m}$ for $n > m geq 0$

Let $n > m geq 0$ be integers. How can one prove the following equation? $$sum_{k=0}^m binom{n}{k}(-1)^k = (-1)^m binom{n-1}{m}$$ According to our script we have to use...

Asked on 01/01/2022 by NotEinstein

5 answer

Solving $0=sum_{T=0}^{L}(2u^2A-2Ou)$ for $O$

I know this seems like a very simple question, but I haven't been able to find anything online regarding the answer to this. Even WolframAlpha, which I usually use when...

Asked on 01/01/2022

0 answer

The meaning of definition written in the form ... is...

I am studying mathematics logic and i am now criticising all the things... I met some definitions which are in the form of ... is .... For example, A construction...

Asked on 01/01/2022 by Jsi23484

1 answer

Challenging problem: Find $a$ where $int_0^infty frac{cos(ax)ln(1+x^2)}{sqrt{1+x^2}}dx=0$.

What is the value of $ainmathbb{R}$ that makes the following integral true$$int_0^infty frac{cos(ax)ln(1+x^2)}{sqrt{1+x^2}}dx=0,?$$This question was proposed by my friend Khalef Ruhemi and I have no idea how...

Asked on 01/01/2022

3 answer

Sheldon Axler Measure Integration Real Analysis Section 2B Exercise 11

I apologize for the referential title, but the question is long and this book is freely available online. I'm referring to Sheldon Axler's new book, Measure, Integration, and Real Analysis,...

Asked on 01/01/2022 by b_becsi

1 answer

fibre of a scheme of finite type over a field being quasi-compact

Let $X,Y$ be schemes of finite type over a field $k$. In particular, they are quasi-compact. Let $f: X to Y$ be a morphism of finite type...

Asked on 01/01/2022

2 answer

What are the solutions of $frac{pi^e}{x-e}+frac{e^pi}{x-pi}+frac{pi^pi+e^e}{x-pi-e}=0$?

Prove that $$frac{pi^e}{x-e}+frac{e^pi}{x-pi}+frac{pi^pi+e^e}{x-pi-e}=0$$ has one real root in$(e,pi)$ and other in $(pi,pi+e)$.For $xin (-infty,e)$ the equation will be always be negative and for $xin (pi+e,infty)$...

Asked on 01/01/2022

1 answer

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