# All Questions

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### On linear integer onequalities with infinitely many solutions

Suppose that a linear system of inequalities $Ax \le b$, where $A\in Z^{m\times n}$ and $b\in Z^m$, have integral coefficients, has an infinite number of integral solutions $x$. Can one conclude ...
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### Prove the inequality, $\sqrt{n} \le (n!)^{\frac{1}{n}} \le \frac{n+1}{2}$ [on hold]

Prove the given inequality $$\sqrt{n} \le (n!)^{\frac{1}{n}} \le \frac{n+1}{2}$$ $$\forall \ \ \ n \in \mathbb{N}$$
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### An inequality improvement on AMM 11145

I have asked the same question in math.stackexchange, I am reposting it here, looking for answers: How to show that for $a_1,a_2,\cdots,a_n >0$ real numbers and for $n \ge 3$: ...
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### How to Wacth The Live Game? [on hold]

Another weekend, another individual of your just about all highly-anticipated fights of any year. even though Klitschko will be the heavy favorite and few tend to be picking against him, ...
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### Improper integral $\int_0^1 \frac{\exp(ctx)}{\sqrt{(\exp(bt)-1)(1-\exp(atx))-(1-\exp(at))(\exp(btx)-1)}} dx$ with $-a$ and $b$ positive

Is the following function real analytic in $t>0$: $$F(t)=\int_0^1\frac{\exp(ctx)}{\sqrt{(\exp(bt)-1)(1-\exp(atx))-(1-\exp(at))(\exp(btx)-1)}} dx,$$ where $-a$ and $b$ are positive, and $c\not=a$? ...
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### Uniform proof that a finite (irreducible real) reflection group is determined by its degrees?

Given a finite (irreducible real) group $G$ generated by reflections acting on euclidean $n$-space, it was shown by Chevalley in the 1950s that the algebra of invariants of $G$ in the associated ...
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### Time Hierarchy Theorem and P vs NP

One obvious strategy for proving P not equal to NP would be to show that there is some problem in NP which is hard for a time class strictly containing P (the origin of this question is the recent ...
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### Reference for holder estimate on parabolic equation with neumann boundary condition

I saw a type of holder estimate in Friedman's book: partial differential equations of parabolic type(page 200 3.24) as following: Suppose we have a uniformly parabolic equation with holder ...
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### Grothendieck's paper on principal bundles, reduction to a torus step

In Grothendieck's paper "Sur la Classification des Fibres Holomorphes sur la Sphere de Riemann", there is a step I don't understand in section 4, where he proves reduction to a torus. He states (lemma ...
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### Curve with Matlab [on hold]

I have posted this question: http://math.stackexchange.com/questions/1547373/curve-with-matlab but I have not answers. Can you help me?
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### Convex Optimization in an Ellipsoid

Suppose we want to minimize a linear objective inside an ellipsoid that is, $\min _x l^Tx$ such that $(x - \mu)^TA(x - \mu) \leq \beta ^2$. Here, A is PSD and $\mu$ is a fixed vector. Can this be ...
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### Operations via Morse Theory

I am interested in seeing if and how Morse Theory can "do everything". Some core things are handle decomposition, Bott periodicity, and Euler characteristic. But what do the normal (co)homology ...
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### Obtaining the metric from the mixed Ricci tensor $R^i{}_j$

In chapter 5 of the book "Einstein Manifolds", Arthur Besse discusses the possibility to find the metric $g$ when knowing the Ricci curvature tensor $Ric(g)$ ($=R_{ij}$). But what do we know about ...
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### Isometric embeddings of finite subsets of $\ell_2$ into infinite-dimensional Banach spaces

Question: Does there exist a finite subset $F$ of $\ell_2$ and an infinite-dimensional Banach space $X$ such that $F$ does not admit an isometric embedding into $X$? There are some results of the ...