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简要介绍概率论中的耦合方法及其在基础数学中的应用。引入新的变测度耦合,以简单的随机微分方程为例,将其应用于建立无穷维Harnack不等式、Bisnut导数公式和分布积分公式。
We report the work “Duality between the pseudoeffective and the movable cone of a projective manifold” of Witt Nystrom, where he proved the transcendental Morse inequality for projective manifolds.
The logarithmic Brunn-Minkowski inequality conjecture is one of the most intriguing challenges in convex geometry since 2012. Notably, this conjectured inequality is stronger than the celebrated Brunn...
I will discuss the Hardy-Littlewood integral inequality with sharp constant on the Heisenberg goup proved by Frank and Lieb. I will outline a simpler proof which bypasses the sophisticated argument fo...
In 2012, Boroczky, Lutwak, Yang, and Zhang posed the log-Brunn-Minkowski conjecture, which represents an enhanced version of the classical Brunn-Minkowski inequality for convex bodies. We will recall ...
KPZ limit for one-dimensional weakly asymmetric Ginzburg-Landau model was studied by Diehl-Gubinelli-Perkowski in a setting of martingale (energy) solution. Our goal is to apply a path-wise approach b...
Unmitigated climate change will make the United States poorer and more unequal, according to a new study published today in the journal Science. The poorest third of counties could sust...
The aim of this paper is to measure the spatial accessibility to public health care facilities in Greece. We look at population groups disaggregated by age and socioeconomic characteristics. The purpo...
The Schrodinger’s cat thought experiment highlights the counterintuitive concept of entan-glement in macroscopically distinguishable systems. The hallmark of entanglement is the detection of strong co...
The purpose of this note is to present an extension and an alternative proof to Theorem 1.3 from G. Battle (Appl. Comput. Harmonic Anal. 4 (1997) 119–146). This extension applies to wavelet Bessel set...
We exploit duality considerations in the study of singular combinatorial 2-discs ("diagrams") and are led to the following innovations concerning the geometry of the word problem for finite presentati...
Let M be a complete non-compact Riemannian manifold. For p ∈ (1,+∞), let Δp be the p-Laplace operator on M. One says that M is p-hyperbolic if there exists a Green function for Δp (see [Ho1,2]); oth...
The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment desig...
In this article we consider the linear regression model y = X,B + a, where e is N(O, a21). In this context we derive exact tests of the form H: Rft ? r versus K: f E R K for the case in which a2 i...

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