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SINGLE BIRTH PROCESSES

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Chinese Annals of Mathematics,Series B 1999年第1期20卷 77-82页

作者： CHEN MUFA(department of Mathematics,Beijing normal {2.,Beijing 100875,china) Beijing normal Univ Dept Math Beijing 100875 Peoples R China

The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2.(this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied

关键词： Markov chains Single birth process Uniqueness criterion

The geodetic numbers of graphs and digraphs

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Science china Mathematics 2007年第8期50卷 1163-1172页

作者： Chang-hong LU~(1,2. 1 department of Mathematics,East china {2. university,Shanghai 2.0062.china 2.Institute of Theoretical Computing,East china Narnal university,Shanghai 2.0062.china 1. department of Mathematics East China Normal University Shanghai 200062 China 2. Institute of Theoretical Computing East China Narnal University Shanghai 200062 China

For every two vertices u and v in a graph G, a u-v geodesic is a shortest path between u and v. Let I(u, v) denote the set of all vertices lying on a u-v geodesic. For a vertex subset S, let I(S) denote the union of all I(u, v) for u, v ∈ S. The geodetic number g(G) of a graph G is the minimum cardinality of a set S with I(S) = V (G). For a digraph D, there is analogous terminology for the geodetic number g(D). The geodetic spectrum of a graph G, denoted by S(G), is the set of geodetic numbers of all orientations of graph G. The lower geodetic number is g ?(G) = minS(G) and the upper geodetic number is g +(G) = maxS(G). The main purpose of this paper is to study the relations among g(G), g ?(G) and g +(G) for connected graphs G. In addition, a sufficient and necessary condition for the equality of g(G) and g(G × K 2. is presented, which improves a result of Chartrand, Harary and Zhang.

关键词： convex set digraph distance geodesic geodetic number 05C12 05C2.

Synthesis and Crystal Structure of CoCl(ieaa)(C_(10)H_7-ieai)(C_(10)H_7NH_2.

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Chinese Journal of Structural Chemistry 2002年第1期21卷 22-25页

作者： FENG Yun-Long (department of Chemistry, Zhejiang normal {2. Jinhua 2.1004,china) department of Chemistry Zhejiang Normal University Jinhua 231004

The title complex CoCl(ieaa)(C10H7-ieai)(C10H7NH2., C32.32.lCoN4O7, Mr= 679.00; (ieaa- and C10H7-ieai- are the anions of isonitrosoethylacetoacetate and its N-a- naphthylamine derivative of Schiff base, respectively, C10H7NH2.is a-naphthylamine), crystallizes in the monoclinic system, space group P2./n with a=11.846(2., b=2..912.5), c=12.783(3)? b=116.54(3), V=32.9(1)?, Dc=1.392./cm3, F(000)=1408, Mr=679.00, m(MoKa)=0.665mm-1, Z=4, final R=0.0584 and wR=0.1388 for 4177 observed reflections (I ≥ 2.(I)). A nitrogen atom of the ieaa- ligand and two nitrogen atoms of the C10H7-ieai- ligand define one of the triangular faces in the distorted octahedral geometry about the cobalt atom. The title complex contains isonitroso-b-ketoimine.

关键词： cobalt complex isonitroso-b-ketoimine Schiff base crystal structure

Kinetic energy and charge state effects in the X-ray emission of Mo surface induced by Xe^(q+)(q=2.,2.) ions

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Science china(phys.cs,Mechanics & Astronomy) 2008年第9期51卷 1240-1244页

作者： CUI Ying1,YANG ShengSheng2.YANG ZhiHu3,XU JinZhang1,ZHANG HongQiang1,XU Xu1,SHAO JianXiong1,LIU ZhaoYuan1,XIAO GuoQing3,ZHANG XiaoAn4,ZHAO YongTao3,ZHANG YanPing3 & CHEN XiMeng1 1 department of Modern phys.cs,Lanzhou {2.,Lanzhou 730000,china 2.National Key Laboratory of Vacuum & Cryogenics Technology and phys.cs,Lanzhou 730000,china 3 Institute of Modern phys.cs,Chinese Academy of Sciences,Lanzhou 730000,china 4 normal College of xianyang,xianyang 713000,china department of Modern phys.cs Lanzhou University Lanzhou 730000 China National Key Laboratory of Vacuum & Cryogenics Technology and phys.cs Lanzhou 730000 China Institute of Modern phys.cs Chinese Academy of Sciences Lanzhou 730000 China normal College of xianyang Xianyang 713000 China

L-shell X-ray spectra of Mo surface induced by Xe2.+ and Xe2.+ were measured. The X-ray intensity was obtained in the kinetic energy range of the incident ions from 350 to 600 keV. The relationship of X-ray intensity ... 详细信息

关键词： X-ray surface kinetic energy and charge state effect Xeq+

Spectral anomalies and spectral switches of partially coherent and polychromatic light diffracted at an aperture

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Science china(phys.cs,Mechanics & Astronomy) 2004年第1期47卷 24-35页

作者： Lü Baida1, 3 & PAN Liuzhan1, 2.1. Institute of Laser phys.cs and Chemistry, Sichuan university, Chengdu 610064,{2. 2. department of phys.cs, Luoyang normal College, Luoyang 47102.,{2. 3. State Key Laboratory of Laser Technology, Huazhong university of Science and Technology, Wuhan 430074,{2. Correspondence should be addressed to L Baida (email: badalu@***) Received July 10, 2.03 1. Institute of Laser phys.cs and Chemistry Sichuan University 610064 Chengdu China 2. State Key Laboratory of Laser Technology Huazhong University of Science and Technology 430074 Wuhan China 3. department of phys.cs Luoyang Normal College 471022 Luoyang China

Based on the propagation theory of partially coherent light in the space-frequency domain, the anomalous spectral behavior and spectral switches in the far field of partially coherent and polychromatic light diffracted at an aperture are studied. It is shown that, as compared with spatially fully coherent and polychromatic light whose spectral anomalies are induced only by aperture diffraction, the spectral anomalies and spectral switches of partially coherent and polychromatic light depend on the aperture diffraction, spatial correlationβ and bandwidth of the original spectrum. Detailed numerical calculations are made to illustrate the behavior of spectral switches of partially coherent and polychromatic light, and the results for spatially fully coherent and polychromatic light are treated as a special case ofβ=1 and included in our theory.

关键词： spectral anomaly spectral switch partially coherent and polychromatic light far field aperture diffraction

CONSTRUCTION OF INDECOMPOSABLEDEFINITE HERMITIAN FORMS

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Chinese Annals of Mathematics,Series B 1994年第3期15卷 349-360页

作者： ZHU FUZU (department ofMathematics, East china {2. university Shanghai 2.0062.china) E china normal UNIV DEPT MAHTSHANGHAI 200062PEOPLES R CHINA

This Paper gives a method to construct indecomposable positive definite integral Hermitianforman imnginary quadratic field Q with gin discriminant and g。n *** is shown that for ally natural numbers n and a, there are n-ary Indecomposable positivedefinite intopal Herlllltian lattices over Q(resp. Q)with discriminant a, exceptfor four(resp. one) exceptions. In these exceptional cases there are no lattices with the desiredproperties.

关键词： Indecomposable lattice(form) Minimum of a lattice(form) Minimal、ctor Irreduclble vector.

On Holomorphic Automorphisms of a Class of Non-homogeneous Rigid Hypersurfaces in C^(N+1)

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Chinese Annals of Mathematics,Series B 2010年第2期31卷 201-210页

作者： Qingyan WU department of Mathematics,Linyi normal {2.,Linyi 2.6005,Shandong,china department of Mathematics,Zhejiang {2.,Hangzhou 31002.,china department of Mathematics Linyi Normal University Linyi 276005 Shandong China department of Mathematics Zhejiang University Hangzhou 310027 China

The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in CN+1 near the origin,and the connected component containing the identity transformation of al... 详细信息

关键词： Real-analytic infinitesimal CR automorphisms Rigid hypersurfaces Holomorphic automorphisms

Image space analysis for variational inequalities with cone constraints and applications to traffic equilibria

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Science china Mathematics 2012年第4期55卷 851-868页

作者： LI Jun 1,& HUANG NanJing 2.1 College of Mathematics and Information,china West normal {2.,Nanchong 637009,china 2.department of Mathematics,Sichuan {2.,Chengdu 610064,china 1. College of Mathematics and Information China West Normal University Nanchong 637009 China2. Department of Mathematics Sichuan University Chengdu 610064 China

In this paper,the image space analysis (for short,ISA) is employed to investigate variational in- equalities (for short,VI) with cone *** separation for VI with cone constraints is characterized by using the normal cone to a regularization of the image,and saddle points of the generalized Lagrangian func- ***-type necessary and sufficient optimality conditions for VI with cone constraints are presented by using a separation *** functions and weak sharpness for VI with cone constraints are also investi- ***,the obtained results are applied to standard and time-dependent traffic equilibria introduced by Daniele,Maugeri and Oettli.

关键词： variational inequality image space analysis linear separation necessary and sufficient optimalitycondition traffic equilibrium

A differentiable sphere theorem with positive Ricci curvature and reverse volume pinching

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Science china Mathematics 2011年第3期54卷 603-610页

作者： WANG PeiHe1 & WEN YuLiang2.1School of Mathematical Sciences, Qufu normal university, Qufu 2.3165,{2. 2.3} of Mathematics, East{2. normal university, Shanghai 2.02.1,{2. 1. School of Mathematical Sciences Qufu Normal University Qufu 273165 China2. Department of Mathematics East China Normal University Shanghai 200241 China

Let Mn be a compact, simply connected n (≥3)-dimensional Riemannian manifold without bound-ary and Sn be the unit sphere Euclidean space Rn+1. We derive a differentiable sphere theorem whenever themanifold concerned satisfies that the sectional curvature KM is not larger than 1, while Ric(M)≥n+2.4 and the volume V (M) is not larger than (1 + η)V (Sn) for some positive number η depending only on n.

关键词： k-th Ricci curvature Hausdorff convergence differentiable sphere theorem harmonic coordinate harmonic radius