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A Structure Theorem for Poorly Anticoncentrated Gaussian Chaoses and Applications to the Study of Polynomial Threshold Functions
Structure Theorem Anticoncentrated Gaussian Chaoses Study of Polynomial Threshold Functions
2012/4/18
We prove a structural result for degree-$d$ polynomials. In particular, we show that any degree-$d$ polynomial, $p$ can be approximated by another polynomial, $p_0$, which can be decomposed as some fu...
A Cartier-Gabriel-Kostant structure theorem for Hopf algebroids
Cartier-Gabriel-Kostant structure theorem Hopf algebroids
2011/3/1
In this paper we give an extension of the Cartier-Gabriel-Kostant structure theorem to Hopf algebroids.
Non-linear Group Actions with Polynomial Invariant Rings and a Structure Theorem for Modular Galois Extensions
Non-linear Group Polynomial Invariant Rings
2010/11/24
Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that...
A Zero Structure Theorem for Dierential Parametric Systems
A Zero Structure Theorem Dierential Parametric Systems
2013/9/9
We present a zero structure theorem for a dierential parametric system:p1 = 0; ￠ ￠ ￠ ; pr = 0; d1 6 = 0; ￠ ￠ ￠ ; ds 6 = 0 where pi and di are dierential polynomials in Kfu1; ￠ ￠ ￠ ; um; x1; ￠ ￠ ￠ ; xn...