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The stationarity and invertibility of a class of nonlinear ARMA models

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Science china Mathematics 2011年第3期54卷 469-478页

作者： CHEN DanQing1,2 & WANG HaiBin2 1Department of Mathematics and Physics, Fujian university of Technology, Fuzhou 350108, china 2 school of mathematical sciences, xiamen university, xiamen 361005, china 1. Department of Mathematics and Physics Fujian University of Technology Fuzhou 350108 China2. School of Mathematical Sciences Xiamen University Xiamen 361005 China

We investigate some probabilistic properties of a new class of nonlinear time series models. A sufficient condition for the existence of a unique causal, strictly and weakly stationary solution is derived. To understand the proposed models better, we further discuss the moment structure and obtain some Yule-Walker difference equations for the second and third order cumulants, which can also be used for identification purpose. A sufficient condition for invertibility is also provided.

关键词： auto-covariance invertibility stationarity time series Yule-Walker difference equation

Laplacian on Complex Finsler Manifolds

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Chinese Annals of Mathematics,Series B 2011年第4期32卷 507-520页

作者： Jinxiu XIA Tongde ZHONG Chunhui QIU Department of Applied Mathematics Tongji University Shanghai 200092 China. school of mathematical sciences Xiamen University Xiamen 361005 Fujian China.

In this paper, the Laplacian on the holomorphic tangent bundle T 1,0 M of a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric is defined and its explicit expression is obtained by using the Chern Finsler connection associated with (M, F ). Utilizing the initiated "Bochner technique", a vanishing theorem for vector fields on the holomorphic tangent bundle T 1,0 M is obtained.

关键词： Laplacian Strongly pseudoconvex complex Finsler metric Chern Finsler connection

Laplacians on the holomorphic tangent bundle of a Kaehler manifold

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Science china Mathematics 2009年第12期52卷 2841-2854页

作者： ZHONG ChunPing school of mathematical sciences,xiamen university,xiamen 361005,china 1. school of mathematical sciences Xiamen University Xiamen 361005 China

Let M be a connected complex manifold endowed with a Hermitian metric *** this paper,the complex horizontal and vertical Laplacians associated with the induced Hermitian metric on the holomorphic tangent bundle T 1,0M of M are defined,and their explicit expressions are *** the complex horizontal and vertical Laplacians associated with the Hermitian metric on T 1,0M,we obtain a vanishing theorem of holomorphic horizontal p forms which are compactly supported in T 1,0M under the condition that g is a Kaehler metric on M.

关键词： Kaehler manifold complex horizontal Laplacian vanishing theorem 32Q15 32L20

Every Banach space with a w*-separable dual hasa 1+ε-equivalent norm with the ball covering property

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Science china Mathematics 2009年第9期52卷 1869-1874页

作者： CHENG LiXin, SHI HuiHua & ZHANG Wen school of mathematical sciences, xiamen university, xiamen 361005, china school of mathematical sciences Xiamen University Xiamen China

A normed space is said to have ball-covering property if its unit sphere can be contained in the union of countably many open balls off the origin. This paper shows that for every ε>0 every Banach space with a w*-sep... 详细信息

关键词： ball-covering property renorming Banach space

The Koppelman-Leray formula on complex Finsler manifolds

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Science china Mathematics 2005年第6期48卷 847-863页

作者： QIU Chunhui & ZHONG Tongde school of mathematical sciences, xiamen university, xiamen 361005, china Academy of Mathematics and System sciences, Chinese Academy of sciences, Beijing 100080, china 1. school of mathematical sciences Xiamen University 361005 Xiamen China 2. Academy of Mathematics and System sciences Chinese Academy of Sciences 100080 Beijing China

By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation theory on complex Finsler manifolds, theKoppelman and Koppelman-Leray formulas are obtained, and the - -equations are solved.

关键词： complex Finsler manifold, Chern-Finsler connection, invariant integral kernel, Koppelman-Lerayformulas, - -equation.

REMOVABLE EARS OF 1-EXTENDABLE GRAPHS

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Journal of Systems Science & Complexity 2010年第2期23卷 372-378页

作者： Shaohui ZHAI Xiaofeng GUO Department of Mathematics and Physics Xiamen University of Technology Xiamen 361024 China. school of mathematical sciences Xiamen University Xiamen 361005 China.

Carvalho, Lucchesi and Murty proved that any 1-extendable graph G different from K2 and C2n has at least A（G） edge-disjoint removable ears, and any brick G distinct from K4 and C6 has at least A（G） - 2 removable edges, where A（G） denotes the maximum degree of G. In this paper, we improve the lower bounds for numbers of removable ears and removable edges of 1-extendable graphs. It is proved that any 1-extendable graph G different from K2 and C2n has at least x′（G） edge-disjoint removable ears, and any brick G distinct from Ka and Ce has at least x′（G） - 2 removable edges, where x′（G） denotes the edge-chromatic number of G. Key words 1-extendable graphs, removable ear, removable edge.

关键词： 1-extendable graphs removable ear removable edge.

STRONG SOLUTIONS FOR THE INCOMPRESSIBLE FLUID MODELS OF KORTEWEG TYPE

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Acta Mathematica Scientia 2010年第3期30卷 799-809页

作者：谭忠王焰金 school of mathematical sciences Xiamen University

In this article, we are concerned with the strong solutions for the incompress- ible fluid models of Korteweg type in a bounded domain Ω СR^3. We prove the existence and uniqueness of local strong solutions to the initial boundary value problem. We point out that in this article we allow the existence of initial vacuum provided initial data satisfy a compatibility condition.

关键词： Korteweg model strong solutions incompressible fluids Navier-Stokes equations vacuum

Tubular algebras and affine Kac-Moody algebras

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Science china Mathematics 2007年第4期50卷 521-532页

作者： Zheng-xin CHEN & Ya-nan LIN school of Mathematics and Computer Science, Pujian Normal university, Fuzhou 350007, china school of mathematical sciences, xiamen university, xiamen 361005, china 1. school of Mathematics and Computer Science Fujian Normal University Fuzhou 350007 China 2. school of mathematical sciences Xiamen University Xiamen 361005 China

The purpose of this paper is to construct quotient algebras L(A) 1 ? /I(A) of complex degenerate composition Lie algebras L(A) 1 ? by some ideals, where L(A 1 ? is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A) 1 ? /I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra L re(A) 1 ? generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A) 1 ? generated by simple A-modules.

关键词： tubular algebras affine Kac-Moody algebras Hall algebras degenerate composition Lie algebras modules with real root 16G70 17B67

AN ITERATION METHOD FOR INCOMPRESSIBLEVISCOUS/INVISCID COUPLED PROBLEM VIA A SPECTRALAPPROXIMATION

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Journal of Computational Mathematics 1999年第4期17卷 379-396页

作者： Chuan-jn Xu(Department of Mathematics, xiamen university, xiamen 361005, china) 厦门大学数学系福建厦门 361005

An efficient iteration-by-subdomain method (known as the Schwarz alternating algorithm) for incompressible viscous/inviscid coupled model is presented. Appropriate spectral collocation approximations are proposed. The convergence analysis show that the iterative algorithms converge with a rate independent of the polynomial degree used.

关键词： coupled equations Navier-Stokes equations Euler equations cllocation approximation Schwarz alternating algorithm