ﻻ يوجد ملخص باللغة العربية
A surprising result of FitzGerald and Horn (1977) shows that $A^{circ alpha} := (a_{ij}^alpha)$ is positive semidefinite (p.s.d.) for every entrywise nonnegative $n times n$ p.s.d. matrix $A = (a_{ij})$ if and only if $alpha$ is a positive integer or $alpha geq n-2$. Given a graph $G$, we consider the refined problem of characterizing the set $mathcal{H}_G$ of entrywise powers preserving positivity for matrices with a zero pattern encoded by $G$. Using algebraic and combinatorial methods, we study how the geometry of $G$ influences the set $mathcal{H}_G$. Our treatment provides new and exciting connections between combinatorics and analysis, and leads us to introduce and compute a new graph invariant called the critical exponent.
We study the following nonlinear critical curl-curl equation begin{equation}label{eq0.1} ablatimes ablatimes U +V(x)U=|U|^{p-2}U+ |U|^4U,quad xin mathbb{R}^3,end{equation} where $V(x)=V(r, x_3)$ with $r=sqrt{x_1^2+x_2^2}$ is 1-periodic in $x_3$ dire
The study of entrywise powers of matrices was originated by Loewner in the pursuit of the Bieberbach conjecture. Since the work of FitzGerald and Horn (1977), it is known that $A^{circ alpha} := (a_{ij}^alpha)$ is positive semidefinite for every entr
We prove a uniform bound on the topological Turan number of an arbitrary two-dimensional simplicial complex $S$: any $n$-vertex two-dimensional complex with at least $C_S n^{3-1/5}$ facets contains a homeomorphic copy of $S$, where $C_S > 0$ is an ab
In this article we introduce Variable exponent Fock spaces and study some of their basic properties such as the boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality.
The blow up problem of the semilinear scale-invariant damping wave equation with critical Strauss type exponent is investigated. The life span is shown to be: $T(varepsilon)leq Cexp(varepsilon^{-2p(p-1)})$ when $p=p_S(n+mu)$ for $0<mu<frac{n^2+n+2}{n