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Hypercube traversal algorithm

A recursive algorithm that I'm working on is based on traversing an $n$-dimensional hypercube. The quantity associated to each vertex can be computed by combining the values of all...

Mathematics Asked on 2 years ago

How do the Christoffel symbols on an abstract manifold relate to those on submanifolds?

Let $(M,g)$ be a Riemannian manifold of dimension $N$ with (Levi-Civita) connection $nabla$. I have seen the following definition of Christoffel symbols: For a given smooth moving...

Mathematics Asked on 2 years ago

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...

Mathematics Asked on 2 years ago

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...

Mathematics Asked by user13255 on 2 years ago

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 =...

Mathematics Asked by tmakino on 2 years ago

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...

Mathematics Asked by NotEinstein on 2 years ago

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...

Mathematics Asked on 2 years ago

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...

Mathematics Asked by Jsi23484 on 2 years ago

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...

Mathematics Asked on 2 years ago

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,...

Mathematics Asked by b_becsi on 2 years ago

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