Hsu-Riordan 阵/partial monoid

本文首先对Shapiro的Riordan群进行了推广。给出了Hsu-Riordan partial monoid的概念，然后在此框架内，对徐利治先生的两类扩展型广义Stirling数偶进行了统一处理；建立了Hsu-Wang转换定理。Brown-Sprugnoli转换公式，以及广义Brown转换引理-它揭示了一些不同类型的Hsu-Riordan阵之间转换的方法。由此可产生大量的恒等式。     

许宝騄先生的学术成就——谨以此文纪念许宝騄先生诞辰100周年

许宝騄先生是我国概率统计学科的主要奠基人、中国科学院院士、北京大学一级教授.本文回顾许宝騄先生的毕生科研工作,着重阐述了许先生在数理统计学和概率论的10个方面的研究成果及其对学科发展的影响,以此纪念许宝騄先生诞辰100周年暨逝世40周年.     

某些二元互反关系及其对于插值公式的应用

This paper investigates the bivariate analogs of Gould-Hsu's inversions and obtains an inverse relation including five sets of free parameters which can be seen as a partial solution for Hsu's open problem. Some instances and applica-tions to interpolation theory are remarked .     

An integration by parts formula on path space over manifolds carrying geometric flow

We establish an integration by parts formula on the path space with reference measure P, the law of the(reflecting) diffusion process on manifolds with possible boundary carrying geometric flow, which leads to the standard log-Sobolev inequality for the associated Dirichlet form. To this end, we first modify Hsu's multiplicative functionals to define the damp gradient operator, which links to quasi-invariant flows; and then establish the derivative formula for the associated inhomogeneous diffusion semigroup.     

A univalent spiral-vortex model for separated flow past a polygonal obstacle

Summary A free-streamline flow model for flow past a polygonal obstacle with a near-wake terminating in Tulin's double spiral vortices is constructed. The flows are univalent for a large class of geometries. In addition a criterion is given for determining the underpressure as function of the Reynolds number using the Stokes solution for diffusion of a vortex sheet, and an extension of Tulin and Hsu's matching theory to transitional flows.

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Sunto Si costruisce un modello di flusso con scia e vortici a doppia spirale alla Tulin per un ostacolo poligonale arbitrario. Il flusso risulta univalente per un' ampia classe di geometrie. Inoltre viene proposto un criterio per correlare il parametro del modello al numero di Reynolds del corrispondente flusso viscoso, combinando la soluzione di Stokes per la diffusione di uno strato di vortici con la teoria di Tulin e Hsu (1980).

     

Recognizing Planar Strict Quasi-Parity Graphs

 A graph is a strict-quasi parity (SQP) graph if every induced subgraph that is not a clique contains a pair of vertices with no odd chordless path between them (an “even pair”). We present an O(n ³) algorithm for recognizing planar strict quasi-parity graphs, based on Wen-Lian Hsu's decomposition of planar (perfect) graphs and on the (non-algorithmic) characterization of planar minimal non-SQP graphs given in [9]. Received: September 21, 1998 Final version received: May 9, 2000     

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??This paper is based on ``Pao-Lu Hsu's lecture' (2019/3/22) at Peking University and the subsequent expansion of his reports. It begins with some recollections benefited of the author from Professor Hsu, and ends with thanking to a group of professors at Peking University for their support and help over the past decades. The middle part is the theme of the talk. It gives first an overview of personal cross research. Then, from a challenge of computing, the author reports on the study looking for a larger class of complex matrices which have real spectrum. This was done mainly in the last year. It involves the fields of computation, probability, statistical mechanics and quantum mechanics Next, the paper introduces the latest development of algorithms, which is another illustration of the intersection between probability theory and computational mathematics. As the end, it also outlines the understanding of the cross study.     

A polynomial algorithm for maximum weighted vertex packings on graphs without long odd cycles

The vertex packing problem for a given graph is to find a maximum number of vertices no two of which are joined by an edge. The weighted version of this problem is to find a vertex packingP such that the sum of the individual vertex weights is maximum. LetG be the family of graphs whose longest odd cycle is of length not greater than 2K + 1, whereK is any non-negative integer independent of the number (denoted byn) of vertices in the graph. We present an O(n ^2K+1) algorithm for the maximum weighted vertex packing problem for graphs inG 1. A by-product of this algorithm is an algorithm for piecing together maximum weighted packings on blocks to find maximum weighted packings on graphs that contain more than one block. We also give an O(n ^2K+3) algorithm for testing membership inG This work was supported by NSF grant ENG75-00568 to Cornell University. Some of the results of this paper have appeared in Hsu's unpublished Ph.D. dissertation [9].     

A global pinching theorem for compact surfaces inS 3 with constant mean curvature

LetM be a compact minimal surface inS ³. Y. J. Hsu^[5] proved that if S₂22, thenM is either the equatorial sphere or the Clifford torus, whereS is the square of the length of the second fundamental form ofM, ·₂ denotes theL ²-norm onM. In this paper, we generalize Hsu's result to any compact surfaces inS ³ with constant mean curvature.Supported by NSFH.     

Elastic constants of monotropic plastic foams. 1. Deformation parallel to foam rise direction. A mathematical model

A mathematical model of the deformative properties and structure of lightweight, monotropic (or isotropic in the limiting case) plastic foams with a pronounced strut-like structure has been elaborated in the linear theory of deformation. A selection of five independent elastic constants is described. For the integral characterization of the deformative properties of plastic foams as micrononhomogeneous composite materials, the elastic constants are introduced as the effective constants. In order to describe the plastic foam structure, a local model consisting of two parts is proposed, i.e., a model of a continuous medium for the calculation of stresses and a local structure model. Considering deformation parallel to the foam rise direction when the semiaxes hypothesis is assumed, the Young modulus and Poisson's ratio are determined.Institute of Polymer Mechanics. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 719–733, November–December, 1997.