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DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong Tian (department of mathematics, Shanghai normal university, Shanghai 200234, china) department of mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.

CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

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Journal of Computational mathematics 2001年第3期19卷 241-258页

作者： De-tong Zhu (department of mathematics, Shanghai normal university, Shanghai 200234, china) 上海师范大学上海 200234

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.

关键词： curvilinear paths trust region methods nonmonotonic technique unconstrained optimization

Note on the number of integral ideals in Galois extensions

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Science china mathematics 2010年第9期53卷 2417-2424页

作者： L GuangShi1,& WANG YongHui2 1School of mathematics,Shandong university,Jinan 250100,china 2department of mathematics,capital normal university,beijing 100048,china School of mathematics Shandong University department of mathematics Capital Normal University

Let K be an algebraic number field of finite degree over the rational filed *** ak be the number of integral ideals in K with norm *** this paper we study the l-th integral power sum of ak,i.e.,∑k≤ x akl(l = 2,3,...).We are able to improve the classical result of Chandrasekharan and *** an application we consider the number of solutions of polynomial congruences.

关键词： Dedekind zeta-function integral ideal congruences

Isolation, characterization and functional analysis of a cdc48 homologue from tobacco BY-2 cells

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Progress in Natural Science:Materials International 2007年第2期17卷 156-162页

作者： CHEN Zhiling, YU Yi, LIU Lina and XIA Guixian ( College of Life Science, capital normal university, beijing 100037, china Institute of Microbiology, Chinese Academy of Sciences, beijing 100080, china) College of Life Science Capital Normal University Beijing 100037 China. Institute of Microbiology Chinese Academy of Sciences Beijing 100080 China

The fission yeast Schizosaccharomyces pombe was used to identify genes from tobacco BY-2 cells that may play roles in cell cycle regulation. A cDNA encoding a protein homologous to the yeast CDC48 was isolated and the gene was designated as NtCDC48 . The cDNA contains an open reading frame coding for a predicted protein of 808 amino acids which comprises of two typical ATPase modules (aa 245-374 and aa 518-646) . Overexpression of NtCDC48 in tobacco BY-2 cells led to an increase in the mitotic index as well as to the formation of diffused mitotic spindles. NtCDC48-GFP fusion proteins are distributed ubiquitously through Gl to M phases, yet their subcellular localization varied regularly along with the cell cycle progression. These results indicate that NtCDC48 may play an important role in the regulation of cell cycle in BY-2 cells.

关键词： tobacco BY-2 suspension cells NtCDC48 spindle cell cycle.

Coupling, spectral gap and related topics (Ⅱ)

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Chinese Science Bulletin 1997年第18期42卷 1409-1416页

作者： CHEN Muf adepartment of mathematics, beijing normal university, beijing 100875, china department of mathematics Beijing Normal University Beijing 100875 China

THIS is the second one of a series of three reviews. The ideas introduced in the last review are used to study the estimate of spectral gap and four classes of typical eigenvalue problems on manifolds. The comparison ... 详细信息

关键词： diffusions manifold Markov chains spectral gap couplings.

Superprocesses arising from interactive stochastic flows

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Science china mathematics 2006年第4期49卷 451-476页

作者： YAN Guojun & LI Zhanbing Medical School, Shantou university, Shantou 515063, china department of mathematics, Bejing normal university, beijing 100875, china Medical School Shantou University Shantou China department of mathematics Bejing Normal University Beijing China

In this paper, we give a unified construction for superprocesses with dependent spatial motion constructed by Dawson, Li, Wang and superprocesses of stochastic flows constructed by Ma and Xiang. Furthermore, we also g... 详细信息

关键词： superprocess, interactive stochastic flows, martingale problem, dual processes.

ON THE VARIATIONS OF G_2

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Chinese Annals of mathematics,Series B 2003年第3期24卷 387-394页

作者： LIU DONG LIN LEI department of mathematics, East china normal university, Shanghai 200062, china. department of mathematics, East china normal university, Shanghai 200062, china. department of mathematics East China Normal University Shanghai 200062 China

In [1], Shen Guangyu constructed several classes of new simple Lie algebras of characteristic 2, which are called the variations of G2. In this paper, the authors investigate their derivation algebras. It is shown that G2 and its variations all possess unique nondegenerate associative forms. The authors also find some nonsingular derivations of ViG for i = 3,4, 5, 6, and thereby construct some left-symmetric structures on Vi G for i = 3,4,5,6. Some errors about the variations of sl(3, F) in [1] are corrected.

关键词： Variation Derivation Associative form Left-symmetric structure

Relations between Lipschitz functions and convex functions

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Science china mathematics 2005年第5期48卷 703-710页

作者： RUAN Yingbin department of mathematics, Fujian normal university, Fuzhou 350007, china Academy of mathematics and Systems Science, Chinese Academy of Sciences, beijing 100080, china department of mathematics Fujian Normal University Fuzhou China Academy of mathematics and Systems Science Chinese Academy of Sciences Beijing China

We discuss the relationship between Lipschitz functions and convex functions. By these relations, we give a sufficient condition for the set of points where Lipschitz functions on a Hilbert space is Frechet differenti... 详细信息

关键词： Lipschitz functions convex functions the Frechet differentiability.

Linear operators preserving the generalized decomposable numerical range

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Chinese Science Bulletin 1997年第1期42卷 22-26页

作者： LEI Tiangangdepartment of mathematics, beijing normal university, beijing 100875, china department of mathematics Beijing Normal University Beijing 100875 China

LET G be a subgroup of the symmetric group Sm. Denote by CG the set of all functions f: G→C. A function f∈CG is said to be positive semi-definite （p. s. d. ） if there exists c∈CG such that for all τ∈G. In particular, the irreducible complex characters of G are p. s. d. Let Cn×m denote the set of all n×m complex matrices. For f∈CG, the

关键词： decomposable numerical range linear operator positive semi-definite function generalized matrix function.