# Tagged Questions

**2**

votes

**1**answer

81 views

### Compactness of a semi algebraic set

Suppose I have a polynomial $p\in R[x_1,\ldots,x_n]$ and I look at the set $S:=\{ x\in R^n : p(x)\geq 0\}$. Are there algebraic certificates on $p$ that will certify that $S$ is compact?

**0**

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**0**answers

433 views

### A product sum inequality question

For any $x_{1},x_{2},\cdots x_{6}$ with $\sum_{i=1}^{6}x_{i}^{2}=1$
and $y_{1},y_{2},\cdots y_{6}$ in $\mathbb{R}$ with $\sum_{i=1}^{6}y_{i}^{2}=1$,
do there always exist $z_{1},z_{2},\cdots z_{6}$ in ...

**0**

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**0**answers

91 views

### minimizing the integral of a function over square sets.

Hi!
I'm interested in some problems, but to be honest i'm not sure of the field they belong to.
Let $h(x,y)$ be a bivariate function on $X^2$, where $X$ is some nice topological space (for instance ...