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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...
V字型密度界面是一类常见的密度界面，如海沟、半地堑以及俯冲带之下的莫霍面，利用重力数据刻画此类密度界面形态对于区域构造研究、油气勘探以及物理海洋学等都具有重要意义.本文首先建立了Lp-范数形式的模型约束函数，并利用正则化原理将其与重力数据误差函数和已知深度约束函数结合形成V字型密度界面反演的目标函数，推导了目标函数的梯度表达式，并以非线性共轭梯度法为核心给出了反演流程.二维简单模型试算结果表明p=...
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...
基于广义高斯分布和非凸Lp范数正则化的地震稀疏盲反褶积
盲反褶积 Lp范数 预条件共轭梯度法 非凸正则化
2016/6/1
由于在大多数情形下反射系数的概率分布服从广义高斯分布,可由Lp范数作为度量(0.7< p< 1.3),且当p< 1时,广义高斯分布对弱反射信息的保留比修正柯西分布更好。为此,基于反射系数广义高斯分布的假设,从贝叶斯稀疏反演理论出发,建立了非凸Lp范数正则化的盲反褶积模型。在求解时通过交替松弛策略使反射系数和子波同步趋于真实解。为了稳定地求解反射系数,将非凸Lp范数(0< p< 1)正则化模型转变为...
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...
Decomposition Methods for Large Scale LP Decoding
LP Decoding Alternating Direction Method of Multipliers Information Theory
2012/4/18
When binary linear error-correcting codes are used over symmetric channels, a relaxed version of the maximum likelihood decoding problem can be stated as a linear program (LP). This LP decoder can be ...
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...