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Population-size-dependent branching processes in Markovian random environments

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Chinese Science Bulletin 1998年第8期43卷 635-638页

作者： WANG Hanxing 1 and DAI Yonglong 2 1. department of mathematics, Shanghai university, Shanghai 201800, China 2. department of mathematics, Zhongshan university, Guangzhou 510275, China department of mathematics Shanghai University Shanghai China department of mathematics Zhongshan University Gunngzhou China

A branching model {Z n} n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1 as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. P(Z n=0 for some n)=1) and noncertain extinction (i.e. P(Z n=0 for some n)<1) are studied.

关键词： Markov chains in random environments stochastic population models branching processes.

Perturbations of the radical of nest algebras

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Chinese Science Bulletin 1998年第7期43卷 556-560页

作者： LU Fangyan 1 and LU Shijie 2 1. department of mathematics, Suzhou university, Suzhou 215006, China 2. department of mathematics, Zhejiang university, Hangzhou 310027, China department of mathematics Suzhou University Suzhou China department of mathematics Zhejiang University Hangzhou China

Let R N and K-N be the radical ideal and the compact operator ideal of nest algebra T(N) respectively. It is proved thatR-N+K-N=span{T∈T(N)∶TT(N)NCT}=span{T∈T(N): #σ′(ST)≤1, S∈T(N)}.

关键词： nest algebras radical perturbation.

The Degree of Symmetry of Certain Compact Smooth Manifolds II

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Chinese Annals of mathematics,Series B 2007年第2期28卷 195-204页

作者： Bin XU department of mathematics, university of Science and Technology of China, Hefei 230026, China Chern Institute of mathematics, Nankai university, Tianjin 300071, China department of mathematics, Johns Hopkins university, Baltimore, MD 21218, usa. department of mathematics University of Science and Technology of ChinaHefei 230026 China

We give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain compact fiber bundles with non-trivial four dimensional fibers in the sense of cobordism, by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau (Topology, 18, 1979, 361-380). As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree of symmetry of CP2×V, where V is a closed smooth manifold admitting a real analytic Riemannian metric of non-positive curvature. In addition, by the Albanese map, we obtain the sharp estimate of the degree of symmetry of a compact smooth manifold with some restrictions on its one dimensional cohomology.

关键词： Degree of symmetry Fiber bundle Cobordism Non-positive Curvature Harmonic map First cohomology

Automorphisms with order three of affine Lie algebras

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Chinese Science Bulletin 1998年第21期43卷 1793-1798页

作者： JIN Quanqin 1,2 and HOU Zixin 2 1. department of mathematics, Hebei university, Baoding 071002, China 2. department of mathematics, Nankai university, Tianjin 300071, China department of mathematics Hebei University Baoding China department of mathematics Nankai University Tianjin China

Some properties of automorphisms of affine Lie algebras are presented. Automorphisms with order three are classified up to conjugacy, and their fixed point sets are also computed. As a corollary, it is proved that two... 详细信息

关键词： affine Lie algebra automorphism of order three first (second) kind of automorphism.

Compact composition operators on BMOA（B_n）

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Science China mathematics 2009年第12期 2679-2687页

作者： LI Song-Ying1,2& LONG SuJuan2 1department of mathematics,university of california,irvine,ca 92697,usa 2School of mathematics and Computer Science,Fujian Normal university,Fuzhou 350007,China

The paper gives some characterization theorems for the compact composition operator on some function spaces over the unit ball Bn in ***,it gives a characterization for com- pact composition operators on BMOA(Bn),whic... 详细信息

关键词： compactness composition operators BMOA spaces

Large deviation principle for diffusion processes under a sublinear expectation

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Science China mathematics 2012年第11期55卷 2205-2216页

作者： CHEN ZengJing 1,2 & XIONG Jie 3,4,1 School of mathematics,Shandong university,Jinan 250100,China 2 department of Financial Engineering,Ajou university,Suwon 443749,Korea 3 department of mathematics,university of Macao,PO Box 3001,Macao,China 4 department of mathematics,university of Tennessee,Knoxville,TN 37996-1300,usa 1. School of mathematics Shandong University Jinan 250100 China 2. department of Financial Engineering Ajou University Suwon 443749 Korea 3. department of mathematics University of Macau PO Box 3001 Macau China 4. department of mathematics University of Tennessee Knoxville TN 37996-1300 USA

We represent the exponential moment of the Brownian functionals under a nonlinear expectation according to the solution to a backward stochastic differential *** an application,we establish a large deviation principle of the Freidlin and Wentzell type under the corresponding nonlinear probability for diffusion processes with a small diffusion coefficient.

关键词： large deviation principle backward stochastic differential equation g-expectation ambiguity

Eigenvalue approximation from below using non-conforming finite elements

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Science China mathematics 2010年第1期53卷 137-150页

作者： YANG YiDu 1 ,ZHANG ZhiMin 2 & LIN FuBiao 11 School of mathematics and Computer Science,Guizhou Normal university,Guiyang 550001,China 2 department of mathematics,Wayne State university,Detroit,MI 48202,usa 1. School of mathematics and Computer Science Guizhou Normal University Guiyang 550001 China2. Department of Mathematics Wayne State University Detroit MI 48202 USA

This is a survey article about using non-conforming finite elements in solving eigenvalue problems of elliptic operators,with emphasis on obtaining lower bounds. In addition,this article also contains some new materials for eigenvalue approximations of the Laplace operator,which include:1) the proof of the fact that the non-conforming Crouzeix-Raviart element approximates eigenvalues associated with smooth eigenfunctions from below;2) the proof of the fact that the non-conforming EQ rot1 element approximates eigenvalues from below on polygonal domains that can be decomposed into rectangular elements;3) the explanation of the phenomena that numerical eigenvalues λ 1,h and λ 3,h of the non-conforming Q rot1 element approximate the true eigenvalues from below for the L-shaped domain. Finally,we list several unsolved problems.

关键词： non-conforming element eigenvalue lower bound

Correlation of zeros of automorphic L-functions

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Science China mathematics 2008年第7期51卷 1147-1166页

作者： LIU JianYa1 & YE YangBo1,2 1 School of mathematics,Shandong university,Jinan 250100, China 2department of mathematics,The university of Iowa,Iowa City,IA 52242-1419,usa 1. School of mathematics Shandong University Jinan 250100 China 2. department of mathematics The University of Iowa Iowa City IA 52242-1419 USA

We compute the n-level correlation of normalized nontrivial zeros of a product of Lfunctions: L(s, π1) … L(s, π k ), where πj, j = 1, …, k, are automorphic cuspidal representations of GL mj (?A). Here the sizes of the groups GL mj (?A) are not necessarily the same. When these L(s, π j ) are distinct, we prove that their nontrivial zeros are uncorrelated, as predicted by random matrix theory and verified numerically. When L(s, π j ) are not necessarily distinct, our results will lead to a proof that the n-level correlation of normalized nontrivial zeros of the product L-function follows the superposition of Gaussian Unitary Ensemble (GUE) models of individual L-functions and products of lower rank GUEs. The results are unconditional when m 1, …, m k ? 4, but are under Hypothesis H in other cases.

关键词： automorphic L-function zero correlation Selberg’s orthogonality conjecture 11F70 11M26 11M41

Schwarz-Pick estimates for positive real part holomorphic functions on unit ball and polydisc

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Science China mathematics 2010年第4期53卷 1017-1024页

作者： LIU Yang 1,& CHEN ZhiHua 2 1 department of mathematics,Zhejiang Normal university,Jinhua 321004,China 2 department of mathematics,Tongji university,Shanghai 200092,China 1. department of mathematics Zhejiang Normal University Jinhua 321004 China2. Department of Mathematics Tongji University Shanghai 200092 China

We give higher order derivatives Schwarz-Pick estimates for all positive real part holomorphic functions on Bn and D n,and generalize early work on Schwarz-Pick estimate of higher order derivatives for holomorphic fun... 详细信息

关键词： Schwarz-Pick estimate holomorphic function Taylor expansion