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An analysis of merging-splitting group dynamics by Bernstein function theory
澳门新葡8455最新网站:2014年07月17日 00:00 点击数:

报告人:刘建国

报告地点:澳门新葡8455最新网站615室

报告澳门新葡8455最新网站:2014年07月28日星期四10:30-11:30

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报告摘要:

We study coagulation-fragmentation equations inspired by a simple model derived in fisheries science to explain data on the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no H-theorem, we are able to develop a rather complete description of equilibrium profiles and large-time behavior, based on complex function theory for Bernstein and Pick functions. The generating function for discrete equilibrium profiles also generates the Fuss-Catalan numbers (derived by Lambert in 1758) that count all ternary trees with $n$ nodes. The structure of equilibrium profiles and other related sequences is explained through a new and elegant characterization of the generating functions of completely monotone sequences as those Pick functions analytic and nonnegative on (-\infty,1).

主讲人概况:

刘建国,美国杜克大学数学系教授。清华大学数学科学中心特邀客座教授。复旦大学数学学士、美国UCLA数学博士。国际著名应用数学家,在偏微分方程的理论、计算和模型等多个研究领域都做出了很多重要研究成果。

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