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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。
In this talk, I will discuss the stability conditions for a free boundary problem of compressible Euler equations coupled with a nonlinear Poisson equation of electric potential. Under those stability...
We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order $s \in (0,1)$. We derive regularity results in weighted Sobolev spaces, where the wei...
How to select the active variables which have significant impact on the event of interest is a very important and meaningful problem in the statistical analysis of ultrahigh-dimensional data. In many ...
In this lecture, I will discuss some of the recent progresses in the level-set percolation of Gaussian free field in (d\geq 3), including the positivity of threshold and (if time permits) sharp phase ...
In this lecture, I will discuss some of the recent progresses in the level-set percolation of Gaussian free field in (d\geq 3), including the positivity of threshold and (if time permits) sharp phase ...
The (discrete) Gaussian free field (dGFF) on a transient graph, simply put, is the random Gaussian field with covariance given through Green’s function of the random walk on that graph. It is in many ...
Filtering is a key step for most applications of airborne LiDAR point clouds. Although lots of filtering algorithms have been put forward in recent years, most of them suffer from parameters setting o...
The workshop will explore large-N asymptotics of random matrices, in connection with the operator-algebra models of their limiting behavior that appear in free probability theory. The behavior or rand...
Holographic images of free-flowing air particles may help climate change and biological weapons watchdogs better monitor the atmosphere, according to a recent Kansas State University study.Principle i...
Imaging very small materials takes not only great skill on the part of the microscopist, but also great instruments and techniques. For a refined microscopic look at biological materials, the challeng...
Free boundary problems have vast and important applications in physics, mechanics, biology, engineering, and finance, etc. At the same time, there is a great challenge in their mathematical study whic...
This conference is the 14th International Conference on Free Boundary Problems: Theory and Applications, which is in the series of conferences beginning in Montecatini (Italy, 1981) and succeeding in ...
Background: Leucine co-ingestion with lower-protein (LP)–containing meals may overcome the blunted muscle protein synthetic response to food intake in the elderly but may be effective only in individu...
Some of the world’s most important discoveries – penicillin, vulcanized rubber and Velcro, to name a few – were made by accident. In fact, it’s been said that upward of half of all scientific discover...

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