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poisson's theory of Birkhoffian system

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Chinese Science Bulletin 1996年第8期41卷 641-645页

作者：梅凤翔 Department of Applied Mechanics Beijing Institute of Technology Beijing 100081 China

The poisson’s theory in classical analytical mechanics is an important integration theo-ry. The theory includes the definition of the poisson bracket for the Hamiltonian system,the poisson’s condition for the first integral and poisson’s theorem to construct from thepoisson bracket of two known integrals a third integral. The Birkhoffian system

关键词： analytical mechanics Birkhoffian system generalized poisson bracket.

poisson double extensions

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Science China Mathematics 2020年第4期63卷 701-720页

作者： Qi Lou Sei-Qwon Oh Shengqiang Wang School of Mathematical Sciences Fudan UniversityShanghai 200433China Department of Mathematics Chungnam National UniversityDaejeon 34134Republic of Korea Department of Mathematics East China University of Science and TechnologyShanghai 200237China

A double Ore extension was introduced by Zhang and Zhang(2008)to study a class of ArtinShelter regular *** we give a definition of poisson double extension which may be considered as an analogue of the double Ore extension,and show that algebras in a class of double Ore extensions are deformation quantizations of poisson double *** also investigate the modular derivations of poisson double extensions and the relationship between poisson double extensions and iterated poisson polynomial *** are illustrated by examples.

关键词： poisson double extension semiclassical limit deformation quantization

poisson kernel and Cauchy formula of a non-symmetric transitive domain

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Science China Mathematics 2010年第7期53卷 1678-1683页

作者： LU Qi-Keng Institute of Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190, China Institute of Mathematics Academy of Mathematics and System Science Chinese Academy of Sciences Beijing China

In 1965, Lu Yu-Qian discovered that the poisson kernel of the homogenous domain S m,p,q={Z∈Cm×m, Z1∈Cm×p,Z2 ∈Cq×m|2i1( Z-Z+)-Z1Z1′-Z2′Z2>0} does not satisfy the Laplace-Beltrami equation associated with the Bergman metric when S m,p,q is not symmetric. However the map T0:Z→Z, Z1→Z1 , Z2→Z2 transforms S m,p,q into a domain S I (m, m + p + q) which can be mapped by the Cayley transformation into the classical domains R I (m, m + p + q). The pull back of the Bergman metric of R I (m, m + p + q) to S m,p,q is a Riemann metric ds 2 which is not a Khler metric and even not a Hermitian metric in general. It is proved that the Laplace-Beltrami operator associated with the metric ds 2 when it acts on the poisson kernel of S m,p,q equals 0. Consequently, the Cauchy formula of S m,p,q can be obtained from the poisson formula.

关键词： poisson kernel Cauchy formula

Fast Solving the Cauchy Problems of poisson Equation in an Arbitrary Three-Dimensional Domain

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Computer Modeling in Engineering & Sciences 2018年第3期114卷 351-380页

作者： Cheinshan Liu Fajie Wang Wenzheng Qu Center for Numerical Simulation Software in Engineering and Sciences College of Mechanics and MaterialsHohai UniversityNanjing 211100China Department of Mechanical and Mechatronic Engineering National Taiwan Ocean UniversityKeelung 202-24Taiwan School of Electromechanic Engineering Qingdao UniversityQingdao 266071China Institute of Applied Mathematics Shandong University of TechnologyZibo 255049China

In this paper we propose a novel two-stage method to solve the threedimensional poisson equation in an arbitrary bounded domain enclosed by a smooth *** solution is decomposed into a particular solution and a homogeneous *** the first stage a multiple-scale polynomial method(MSPM)is used to approximate the forcing term and then the formula of Tsai et al.[Tsai,Cheng,and Chen(2009)]is used to obtain the corresponding closed-form solution for each polynomial *** in the second stage we use a multiple/scale/direction Trefftz method(MSDTM)to find the solution of Laplace equation,of which the directions are uniformly distributed on a unit circle 1,and the scales are determined a priori by the collocation points on *** examples of 3D data interpolation,and several numerical examples of direct and inverse Cauchy problems in complex domain confirm the efficiency of the MSPM and the MSDTM.

关键词： poisson equation multiple/scale/direction Trefftz method multiple-scale polynomial method irregular domain inverse Cauchy problem

Hardy–Littlewood–Sobolev Inequalities with the Fractional poisson Kernel and Their Applications in PDEs

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Acta Mathematica Sinica,English Series 2019年第6期35卷 853-875页

作者： Lu CHEN Guozhen LU Chunxia TAO School of Mathematics and Statistics Beijing Institute of Technology Department of Mathematics University of Connecticut School of Mathematical Sciences Beijing Normal University

The purpose of this paper is five-fold. First, we employ the harmonic analysis techniques to establish the following Hardy–Littlewood–Sobolev inequality with the fractional poisson kernel on the upper half space ■ where f ∈ L^p(?R_+~n), g ∈ Lq(R_+~n) and p, q'∈(1, +∞), 2 ≤α poisson kernel. Finally, by using the method of moving plane in integral forms, we prove that extremals of the Hardy–Littlewood–Sobolev inequality with the fractional poisson kernel must be radially symmetric and decreasing about some point ξ_0 ∈ ?R_+~n. Our results proved in this paper play a crucial role in establishing the Stein–Weiss inequalities with the poisson kernel in our subsequent paper.

关键词： Existence of extremal functions Hardy–Littlewood–Sobolev inequality Moving plane method poisson kernel

Reduced poisson actions

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Science China Mathematics 2000年第10期43卷 1026-1034页

作者：刘张炬杨奇林 Department of Mathematics Peking University Beijing 100871 China

A sufficient and necessary condition is given for the action of the quotient of a poisson-Lie group G on the quotient of a poisson G-space P to be a poisson action, where both the poisson structures on the quotient group and the quotient manifold are induced by Dirac structures. The left invariant Dirac structure and the left invariant tensor descriptions of poisson homogeneous spaces are proved to be equivalent.

关键词： poisson action Dirac structure reduction.

poisson Integrals as a (C_0) Semigroup on the Banach Space L^p(R^n) (1

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Chinese Science Bulletin 1993年第17期38卷 1414-1416页

作者：刘尚平 Institute of Mathematics Academia Sinica

1 The Operator（-△）1/2 In Ref.[1], we define the operator （-△）1/2 on the Banach space Lp（Rn） as follows:（-△）1/2sum from j=1 to n Rj Dj, its

关键词： poisson integral (C0) semigroup generator.

Central simple poisson algebras

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Science China Mathematics 2004年第2期47卷 245-263页

作者： SU Yucai & XU XiaopingDepartment of Mathematics, Shanghai Jiaotong University, Shanghai 200030, China Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China 1.Department of Mathematics Shanghai Jiaotong University 200030 Shanghai China 2.Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China

poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of poisson algebras has not been well developed. In this paper, we determine the structure of the central simple poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic *** Lie algebra structures of these poisson algebras are in general not finitely-graded.

关键词： poisson algebra, locally-finite operator, derivation, finitely-graded, isomorphism class.

Frobenius poisson algebras

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Frontiers of Mathematics in China 2019年第2期14卷 395-420页

作者： Juan LUO Shengqiang WANG Quanshui WU Mat hematics and Science College Shanghai Normal University Shanghai 200234 China Depar tmen t of Mat hematics East China University of Science and Technology Shanghai 200237 China School of Mat hematical Sciences Fudan University Shanghai 200433 China

This paper is devoted to study Frobenius poisson algebras. We introduce pseudo-unimodular poisson algebras by generalizing unimodular poisson algebras, and investigate Batalin-Vilkovisky structures on their cohomology algebras. For any Frobenius poisson algebra, all Eatalin-Vilkovisky opera tors on its poisson cochain complex are described explicitly. It is proved that there exists a Batalin-Vilkovisky operator on its cohomology algebra which is induced from a Batalin-Vilkovisky operator on the poisson cochain complex, if and only if the poisson st rue ture is pseudo-unimodular. The relation bet ween modular derivations of polynomial poisson algebras and those of their truncated poisson algebras is also described in some cases.

关键词： poisson algebra Frobenius algebra Batalin-Vilkovisky algebra poisson (co)homology modular derivation