不回归凸性

q-凹巴拿赫空间的李雅普诺夫定理

Lyapunov theorem for q-concave Banach spaces

证明了向量测度在具有无条件基的巴拿赫空间中的李雅普诺夫凸性定理的推广，其中向量测度对某些$q<\infty.$是q凹的

Constrained Functional Value under General Convexity Conditions with Applications to Distributed Simulation

We show a general phenomenon of the constrained functional value for densities satisfying general convexity conditions, which generalizes the observation in Bobkov and Madiman (2011) that the entropy per coordinate in a log-concave random vector in any dimension with given density at the mode has a range of just 1. Specifically, for general functions $ϕ$ and $ψ$, we derive upper and lower bounds of density functionals taking the form $I_ϕ(f) = \int_{\mathbb{R}^n} ϕ(f(x))dx$ assuming the convexity of $ψ^{-1}(f(x))$ for the density, and establish the tightness of these bounds under mild conditio…

四元数矩阵的上Bild的凸性

On the Convexity of the Upper Bild

本文证明了So和Thompson提出的四元数矩阵的上Bild的凸性，通过将问题简化为2×2矩阵，引入球面实坐标并结合凸、凹函数的极值分析完成证明。

Estimating the average of functions with convexity properties by means of a new center

In this article we show the following result: if $C$ is an $n$-dimensional convex and compact subset, $f:C\rightarrow[0,\infty)$ is concave, and $ϕ:[0,\infty)\rightarrow[0,\infty)$ is a convex function with $ϕ(0)=0$, we then characterize the class of sets and concave functions that attain the supremum \[ \sup_{C,f}\int_Cϕ(f(x))dx, \] where the supremum ranges over all sets $C$ with $n$-dimensional volume $|C|=c$ and the additional condition that $f(x_{C,f})=k$ for some point $x_{C,f}\in C$ that we introduce in the article, for two non-negative constants $c,k>0$. As a consequence, we extend som…

对数凹测度收敛模的等价性

On the equivalence of modes of convergence for log-concave measures

在最近的工作中，在渐近几何分析的一个重要主题是，许多经典的影响之间的不同类型的几何或功能不等式可以扭转凸性假设的存在。在这篇文章中，我们探讨了在对数凹分布中，不同的概率测度之间的距离概念在多大程度上是可比的。结果表明，当极限测度为高斯时，各向同性对数凹分布的弱收敛等价于全变差收敛，并进一步等价于相对熵收敛.

Banach 格中的凸性与凹性

Convexity and concavity in Banach lattices

本文系统介绍Banach格中(p,q)-凸性、(p,q)-凹性及上下p-估计等概念，阐述p-凸化与p-凹化技术，并给出相关算子的主要因子分解结果及其在重赋范与表示中的应用。