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poisson stable motions of monotone nonautonomous dynamical systems

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Science China Mathematics 2019年第7期62卷 1391-1418页

作者： David Cheban Zhenxin Liu School of Mathematical Sciences Dalian University of Technology Dalian 116024 China Department of Mathematics Faculty of Mathematics and Informatics State University of Moldova Chisinau AfD-2009 Moldova

In this paper, we study the poisson stability(in particular, stationarity, periodicity, quasiperiodicity, Bohr almost periodicity, almost automorphy, recurrence in the sense of Birkhoff, Levitan almost periodicity, pseudo periodicity, almost recurrence in the sense of Bebutov, pseudo recurrence, poisson stability) of motions for monotone nonautonomous dynamical systems and of solutions for some classes of monotone nonautonomous evolution equations(ODEs, FDEs and parabolic PDEs). As a byproduct, some of our results indicate that all the trajectories of monotone systems converge to the above mentioned poisson stable trajectories under some suitable conditions, which is interesting in its own right for monotone dynamics.

关键词： topological dynamics comparability periodicity quasi-periodicity Bohr/Levitan almost periodicity almost automorphy poisson stability monotone nonautonomous dynamical systems

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 algebras.Here 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 extensions.We also investigate the modular derivations of poisson double extensions and the relationship between poisson double extensions and iterated poisson polynomial extensions.Results 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

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

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.

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.

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

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.

Multidimensional compound poisson distributions in free probability

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Science China Mathematics 2019年第5期62卷 921-934页

作者： Guimei An Mingchu Gao School of Mathematical Sciences and LPMC Nankai University School of Mathematics and Information Science Baoji University of Arts and Sciences Department of Mathematics Louisiana College

Inspired by Speicher's multidimensional free central limit theorem and semicircle families, we prove an in?nite dimensional compound poisson limit theorem in free probability, and de?ne in?nite dimensional compound free poisson distributions in a non-commutative probability space. In?nite dimensional free in?nitely divisible distributions are de?ned and characterized in terms of their free cumulants. It is proved that for a sequence of random variables, the following three statements are equivalent:(1) the distribution of the sequence is multidimensional free in?nitely divisible;(2) the sequence is the limit in distribution of a sequence of triangular trays of families of random variables;(3) the sequence has the same distribution as that of {a_1^((i)): i = 1, 2,...}of a multidimensional free L′evy process {{a_1^((i)): i = 1, 2,...} : t≥0}. Under certain technical assumptions, this is the case if and only if the sequence is the limit in distribution of a sequence of sequences of random variables having multidimensional compound free poisson distributions.

关键词： free probability multidimensional free poisson distributions multidimensional free infinitely divisible distributions