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Occupation Measures of Singularly Perturbed Markov Chains with Absorbing States

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Acta Mathematica Sinica,English Series 2000年第1期16卷 161-180页

作者： G.Yin~(1)) department of mathematics,Wayne State university,Detroit,MI 48202,usaQ.Zhang~(2)) department of mathematics,university of Georgia,Athens,GA 30602,usaG.Badowski~(3)) department of mathematics,Wayne State university,Detroit,MI 48202,usa department of mathematics Wayne State University Detroit MI 48202 USA department of mathematics University of Georgia Athens GA 30602 USA

This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing *** focuses on both unscaled and scaled occupation *** mild conditions,a mean-square estimate is *** averaging the fast components,we obtain an aggregated *** the aggregated process itself may be non-Markovian,its weak limit is a Markov chain with much smaller state ***,a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.

关键词： Singularly perturbed Markov chain Occupation measure Aggregation Absorbing state Weak convergence Switching diffusion

EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC EQUATIONS IN EXTERIOR DOMAINS

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Acta Mathematica Scientia 2010年第3期30卷 713-725页

作者：曾宪忠刘振海 department of mathematics and Computational Science Hunan University of Science and Technology department of mathematics Central South University

This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that pc = （σ ＋ m ）n / （ n-σ- 2 ） is its critical exponent provided max{-1, [ （1- m ）n- 2] / （ n ＋ l ） } 〈 σ 〈 n- 2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the elliptic type degenerate equations. Futhermore, we demonstrate that if max（1, σ ＋ m）〈 p 〈 pc, then every positive solution of the equations blows up in finite time; whereas for p 〉 pc, the equations admit global positive solutions for some boundary values and initial data. Meantime, we also demonstrate that its positive solutions blow up in finite time provided n〈σ＋2.

关键词： Degenerate parabolic equations exterior domains -inhomogeneous dirichlet boundary conditions critical exponent blow-up global existence

Comparison of PBDE congener profiles and concentration levels in human specimens from China and the US and identification of human exposure sources

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Science China Chemistry 2010年第5期53卷 995-1002页

作者： SHE JianWen 1,SHE YiFan 2 &SONG WenLu 2 1 Biochemistry Section,Environmental Health Laboratory Branch,california department of Public Health,Richmond,ca 94804,usa 2Chemistry Section,Food and Drug Laboratory Branch,california department of Public Health,Richmond,ca 94804,usa 1. Environmental Health Laboratory Branch California Department of Public Health Biochemistry Section Richmond CA 94804 USA2. Food and Drug Laboratory Branch California Department of Public Health Chemistry Section Richmond CA 94804 USA

In an effort to investigate the status of human exposure to PBDEs in China,available monitoring data in human specimens(including breast milk,serums,and blood) was collected from the general population as well as specific groups that are occupationally *** exposure profiles and concentration levels were compared with their counterparts in the United States of *** was found that PBDE burdens in general Chinese population are one order lower and have different congener profiles from that in the US,showing higher percentages of BDE-28 or BDE-153 in human specimens from *** and residents in electronic wastes recycling regions or areas of commercial PBDE manufacturing have the highest PBDE exposure levels reported worldwide,which are close or higher than the exposure levels of the general population in the US. Highly brominated congeners,such as BDE-207 and 209,are among the major PBDE congeners,and BDE-209 has the highest percentage(above 50%) for all occupational populations *** components analysis(Pca) demonstrates that the exposure of the general population in the US is closely related to penta-BDE while the human burden in China is *** PBDE in indoor air(gas phase) in the US is highly correlated with the PBDE burden in the general population in the US,indicating a major exposure *** the occupationally exposed populations in China,the congener profiles are closely related to the commercial deca-BDE *** of exposure profiles for general and occupational populations in China suggests that it is essential to include more highly brominated congeners,such as BDE-207 and 209,in future human exposure studies,in order to assess the real burdens and profiles of PBDEs exposure in *** pollution prevention and occupational protection procedures are in need in China to avoid the PBDE contamination problem that has occurred in the US.

关键词： human exposure PBDEs congener profiles concentration levels source source identification China and usa

On the direct path problem of s-elementary frame wavelets

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Science China mathematics 2010年第12期53卷 3187-3196页

作者： DAI XingDe 1 , DIAO YuanAn 1 & GUO XunXiang 2,1 department of mathematics and Statistics, university of North carolina at Charlotte, Charlotte, NC 28223, usa 2.department of mathematics, Southwestern university of Finance and Economics, Chengdu 611130, China 1. department of mathematics and Statistics University of North Carolina at Charlotte Charlotte NC 28223 USA2. Department of Mathematics Southwestern University of Finance and Economics Chengdu 611130 China

In this paper, we discuss the path-connectivity between two s-elementary normalized tight frame wavelets via the so-called direct paths. We show that the existence of such a direct path is equivalent to the non-existence of an atom of a σ-algebra defined over the defining sets of the corresponding frame wavelets, using a mapping defined by the natural translation and dilation operations between the sets. In particular, this gives an equivalent condition for the existence of a direct path between two s-elementary wavelets.

关键词： wavelets frame wavelets frame wavelet sets path-connectivity of wavelets direct path

Rational holomorphic maps from B^2 into B^N with degree 2

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Science China mathematics 2006年第11期49卷 1504-1522页

作者： CHEN Zhihua, Jl Shanyu & XU Dekang department of mathematics, Tongji university, Shanghai 200092, China department of mathematics, university of Houston, Houston, TX 77204, usa department of mathematics Tongji University Shanghai 200092 China department of mathematics University of Houston Houston TX 77204 United States

Rational proper holomorphic maps from the unit ball in C2 into the unit ball CN with degree 2 are studied. Any such map must be equivalent to one of the four types of maps.

关键词： rational holomorphic maps between balls.

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.