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Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips

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Science china Mathematics 2005年第2期48卷 248-260页

作者： SHUI Shuliang & ZHU Deming College of Mathematics and Physics, Zhejiang normal university, Jinhua 321004, china department of Mathematics, east china normal university, shanghai 2.0062, china 1. College of Mathematics and Physics Zhejiang Normal University 321004 Jinhua China 2. department of Mathematics East China Normal University 200062 Shanghai China

Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1-periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.

关键词： bifurcation, homoclinic orbit, non-resonance, inclination flip, 1-periodic orbit.

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

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.

Orbits Heteroclinic to Invariant Manifolds

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Acta Mathematica Sinica,English Series 1996年第4期12卷 372-373,375-378页

作者： Zhu Deming department of Mathematics east china normal university shanghai, 2.0062.china department of Mathematics East China Normal University Shanghai China

Using the theory of invariant manifolds, we give local expressions of the stable and unstable manifolds for normally hyperbolic invariant tori, and study the existence of transverse orbits heteroclinic to hyperbolic i... 详细信息

关键词： Invariant manifold Exponential dichotomy Heteroclinic orbit Transversality

The Relative Canonical Algebra for Genus 4 Fibrations

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Acta Mathematica Sinica,English Series 1995年第1期11卷 44-52页

作者： Cai Jinxing department of Mathematics east china normal university shanghai,2.0062.china harm.showa-u.ac.jp

In this paper,we prove that for the genus 4 fibration,the relative canonical algebra is generated in degrees ≤3.

关键词： HO The Relative Canonical Algebra for Genus 4 Fibrations

On Indecomposable Definite Unimodular Hermitian Forms

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Acta Mathematica Sinica,English Series 1994年第2期10卷 113-120页

作者： Zhu Fuzu department of Mathematics east china normal university shanghai, 2.0062.china 1. department of Mathematics East China Normal University 200062 Shanghai China

For any natural numbers m and n≥17 we can construct explicitly indecomposable definite unimodular normal Hermitian lattices of rank n over the ring of algebraic integers Rm in an imaginary quadratic field (-m1/2). It is proved that for any n （in case m=11, there is one exception n=3） there exist indecomposable definite unimodular normal Hermitian R15(R11- lattices of rank n, and we exhibit representatives for each class. In the exceptional case there are no lattices with the desired properties. The method given in this paper can solve completely the problem of constructing indecomposable definite unimodular normal Hermitian Rm-lattices of any rank n for each m.

关键词： show On Indecomposable Definite Unimodular Hermitian Forms Math

Short cycle structures for graphs on surfaces and an open problem of Mohar and Thomassen

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Science china Mathematics 2006年第2期49卷 212-224页

作者： REN Han & DENG Mo department of Mathematics, east china normal university, shanghai 2.0062, china College of Mathematics & Information Science, Northwest normal university, Lanzhou 730070, china 1. department of Mathematics East China Normal University Shanghai 200062 China 2. College of Mathematics & Information Science Northwest Normal University Lanzhou 730070 China

In this paper we investigate cycle base structures of a (weighted) graph and show that much information of short cycles is contained in an MCB (i.e., minimum cycle base). After setting up a Hall type theorem for base-transformation, we give a sufficient and necessary condition for a cycle base to be an MCB. Furthermore, we show that the structure of MCB in a (weighted)graph is unique. The property is also true for those having a longest length (although much work has been down in evaluating MCB, little is known for those having a longest length). We use those methods to find out some unknown properties for short cycles sharing particular properties in (unweighted) graphs. As applications, we determine the structures of short cycles in an embedded graph and show that there exist polynomially bounded algorithms in finding a shortest contractible cycle and a shortest two-sided cycle provided such cycles exist. Those answer an open problem of B. Mohar and C. Thomassen.

关键词： cycle base facial cycle graph embedding.

The Tracial Rokhlin Property for Automorphisms on Non-simple C~*-Algebras

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Chinese Annals of Mathematics,Series B 2010年第2期31卷 191-200页

作者： Jiajie HUA department of Mathematics East China Normal University Shanghai 200241 China.

Let A be a unital AF-algebra （simple or non-simple） and let α be an automorphism of A. Suppose that α has certain Rokhlin property and A is α-simple. Suppose also that there is an integer J ≥ 1 such that J α＊... 详细信息

关键词： Rokhlin property Tracial rank zero AF-algebra

Cholesterol oxidase biosensor based on a glassy carbon electrode modified with Nafion and methyl viologen

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Chinese Journal of chemistry 1994年第4期12卷 343-347页

作者： JIN, Li-Tong ZHAO, Gui-Zhu FANG, Yu-Zhidepartment of chemistry, east china normal university, shanghai 2.0062, china department of chemistry East China Normal University Shanghai 200062 China

Cholesterol oxidase biosensor has been constructed by using bovine serum albumin and glutaraldehyde as cross linker to immobilize cholesterol oxidase and cholesterol esterase on a glassy carbon electrode modified with Nafion and methyl viologen. The biosensor has been used to determine total cholesterol in blood. The linear range of the determination is 2.5×10~7 to 1.0×10-4 mol/L. The detection limit is about 5.0×10~8 mol/L. The response time is 12 s. This biosensor has the advantage of high selectivity, sensitivity and short response time.

关键词： Biosensor cholesterol oxidase enzyme electrode.