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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Sharp Lp estimates and size of nodal sets of generalized Steklov eigenfunctions
Steklov-eigenfunctions 尖锐 Lp 估计 节点集
2023/4/13
We prove sharp Lp estimates for the Steklov eigenfunctions on compact manifolds with boundary in terms of their L2 norms on the boundary. We prove it by establishing Lp bounds for the harmonic extensi...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Lp-Brunn-Minkowski conjecture for 0
0
2023/4/21
The Lp-Brunn-Minkowski conjecture for 0 < p < 1 states that the volume functional is concave when origin-symmetric convex bodies are Lp-added, where 0 < p < 1. This conjecture has garnered significant...
Lp estimates for quantities advected by a compressible flow
Lp estimates quantities advected compressible flow
2015/10/15
We consider the evolution of a quantity advected by a compressible flow and subject to diffusion. When this quantity is scalar it can be, for instance, the temperature of the flow or the concentration...
Consider estimating the mean vector from data Nn(; 2I ) with lq norm loss,
q 1, when is known to lie in an n-dimensional lp ball, p 2 (0; 1). For large
n, the ratio of minimax linear risk to...
基于部分基变量提出了LP问题的矩阵算法. 该算法以最优基矩阵的一个充分必要条件为基础，首先将一个初始矩阵转化为右端项和检验数均满足要求的矩阵，再转为检验数满足要求的基矩阵，最后转化为最优基矩阵.该算法具有使用范围广、计算规模小、计算过程简化、计算机易于实现的优势.矩阵算法的核心运算是求逆矩阵的运算，提出了矩阵算法的求逆问题，讨论并给出了求逆快速算法，该算法充分利用了矩阵算法迭代过程中提供的原来的逆...
Optimal relations between Lp-norms for the Hardy operator and its dual
Hardy operator Dual operator Best constants
2012/6/29
We obtain sharp two-sided inequalities between $L^p-$norms $(1
Approximation of functions from Lp(w)b by matrix means of their Fourier series
Rate of approximation summability of Fourier series Lipschitz classes
2012/4/16
We formulate some special conditions for the integrable functions and moduli of continuity. We give the results on rate of approximation of such functions by matrix means of their Fourier series, wher...
Interior partial regularity for minimal Lp-vectorfields with integer fluxes
Interior partial regularity minimal Lp-vectorfields integer fluxes
2012/4/17
We use a new combinatorial technique to prove the optimal interior partial regularity result for Lp-vectorfields with integer fluxes minimizing the Lp-energy. More precisely, we prove that the minimal...
Notes on a slice distance for singular Lp-bundles
Notes slice distance singular Lp-bundles Differential Geometry
2012/4/17
A slice distance for the class of weak abelian Lp-bundles in 3 dimensions was introduced in a previous article in collaboration with Tristan Rivi\`ere, where it was used to prove the closure of such c...
Property (T) with respect to non-commutative Lp-spaces
Haagerup non-commutative Lp(M)-spaces property (T) group representations Mazur map
2011/8/29
Abstract: We show that a group with Kazhdan's property $(T)$ has property $(T_{B})$ for $B$ the Haagerup non-commutative $L_{p}(\mathcal{M})$-space associated with a von Neumann algebra $\mathcal{M}$,...
Lp混合质心体均质积分和对偶均质积分Brunn-Minkowski不等式
Lp-质心体 Lp-混合质心体 Lp-混合投影体 均质积分 对偶均质积分 Lp-混合调和Blaschke加
2012/11/23
定义了新几何体Γ-p,iK和Lp-混合调和Blaschke加K+pL的概念,建立了Lp-混合质心体Γp,iK的均质积分和对偶均质积分的Brunn-Minkowski不等式,并研究了算子Γp,i和Γ-p,i 的单调性.