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Smoothness for the collision local times of bifractional Brownian motions

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Science china mathematics 2011年第9期54卷 1859-1873页

作者： SHEN GuangJun 1,2,& YAN LiTan 3 1 department of mathematics,east china university of Science and Technology,shanghai 200237,china 2 department of mathematics,Anhui normal university,Wuhu 241000,china 3 department of mathematics,Donghua university,shanghai 201620,china 1. department of mathematics East China University of Science and Technology Shanghai 200237 China2. Department of Mathematics Anhui Normal University Wuhu 241000 China3. Department of Mathematics Donghua University Shanghai 201620 China

Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2 be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and wang in 2009, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2K2} 〈-1/3.

关键词： bifractional Brownian motion collision local time intersection local time chaos expansion

A LINE SEARCH FILTER SECANT METHOD FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION

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Journal of Systems Science & Complexity 2010年第2期23卷 343-361页

作者： Zhujun wang Detong ZHU department of mathematics Shanghai Normal University Shanghai 200234 China. Business College Shanghai Normal University Shanghai 200234 China.

This paper formulates and analyzes a line search method for general nonlinear equalityconstrained optimization based on filter methods for step acceptance and secant methods for *** feature of the new algorithm is that the secant algorithm is used to produce a searchdirection,a backtracking line search procedure is used to generate step size,some filtered rules areused to determine step acceptance,second order correction technique is used to reduce infeasibility andovercome the Maratos *** convergence properties of this method are analyzed:under mildassumptions it is showed that every limit point of the sequence of iterates generated by the algorithmis feasible,and that there exists at least one limit point that is a stationary point for the ***,it is also established that the Maratos effect can be overcome in our new approach by addingsecond order correction steps so that fast local superlinear convergence to a second order sufficient localsolution is ***,the results of numerical experiments are reported to show the effectivenessof the line search filter secant method.

关键词： Filter method nonlinear programming secant algorithm second order correction.

A categorical interpretation of Yetter-Drinfel'd modules

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Chinese Science Bulletin 1999年第9期44卷 771-778页

作者： KAN Haibin and wang ShuanhongInstitute of mathematics , Fudan university , shanghai 200433 , china department of mathematics , Henan normal university, Xinxiang 453002, china Institute of mathematics Fudan Univrrsity Shanghai China Dcpartment of mathematics Henun Normal University Xinxiang China

It is known that any strict tensor category （C, I） can determine a strict braided tensor category Z （ C）, the centre of C. When A is a finite Hopf algebra, Drinfel’d has proved that Z（AM） is equivalent to D（A）M as a braided tensor category, where AM is the left A-module category, and D （A） is the Drinfel’d double of A. This is the categorical interpretation of D （A）.Z（4M） is proved to be equivalent to the Yetter-Drinfel’ d module category AY D4 as a braided tensor category for any Hopf algebra A. Furthermore, for right A-comodule category MA , Z（MA） is proved to be equivalent to the Yetter-Drinfel’ d module category AY D4 as a braided tensor category. But, in the two cases, the Yetter-Drinfel’ d module category AY DA has different braided tensor structures.

关键词： Yetter-Drinfel’d module tensor category equivalence.

JACOBI SPECTRAL METHODS FOR MULTIPLE- DIMENSIONAL SINGULAR DIFFERENTIAL EQUATIONS

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Journal of Computational mathematics 2003年第3期21卷 325-338页

作者： Li-Han wang Ben-yu Guo (department of mathematics, shanghai normal university, shanghai 200234, china) department of mathematics Shanghai Normal University 上海 200234

Jacobi polynomial approximations in multiple dimensions are investigated. They are applied to numerical solutions of singular differential equations. The convergence analysis and numerical results show their advantages.

关键词： Jacobi approximations Multiple dimensions.

FLOATING QUANTIZATION EFFECTS ON MULTIRATE SAMPLED-DATA NONLINEAR CONTROL SYSTEMS

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Acta Mathematica Scientia 2007年第3期27卷 635-644页

作者：余宏旺汪志鸣 department of mathematics East China Normal University

In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.

关键词： Multirate sampled-data control systems quantization Schur stable uniformly ultimately bounded

Third-order optical nonlinearities for lanthanum (Ⅲ) complexes with 1,10-phenanthroline components

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Chinese Science Bulletin 1998年第5期43卷 399-402页

作者： SUN Zhenrong, wang Shenyi, HUANG Yanping, LIN Jiyun,DING Liangen and wang ZugengLaboratory for Quantum Optics, east china normal university, National Education Commission department of Physics, east china normal university, shanghai 200062, china Laboratory for Quantum Optics East China Normal University National Education Commission China department of Physics East China Normal University Shanghai China

The nonlinear refractive indexes n 2 for the ethanol solutions of 1,10-phenanthroline (2.0×10 -3 mol·L -1), [bis(1,10-phenanthroline) lanthanum (Ⅲ)] nitrate (1.0×10 -3 mol·L -1), and [nitrato-fluoracil-bis (1,10-phenanthroline) lanthanum (Ⅲ)] nitrate (1.0×10 -3 mol·L -1) are first measured, the third-order nonlinear optical susceptibilities χ (3) and are calculated, and the mechanisms of the third-order optical nonlinearities enhanced by lanthanum (Ⅲ) are discussed preliminarily.

关键词： Z-scan third-order optical nonlinearity lanthanum (Ⅲ) 1 10-phenanthroline.

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 273165, china 2department of mathematics, east china normal university, shanghai 20024., china 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

Two-photon Induced UV Fluorescence in Photo-active Spiropyran Molecules

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Chinese Journal of Lasers 1995年第2期B4卷 101-104页

作者： CHI Lunguang wang Zugeng(department of Physics, east china normal university,Joint Laboratory for Quantum Optics, shanghai Institute of Optics &. Fine mechanics,Academia Sinica and east china normal university, shanghai 200062, china) east china normal Univ Shanghai China

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关键词： spiropyran merocyanine two-photon absorption UV fluorescence

THE (ｕ＋κ)-ORBIT OF ESSENTIALLY normal OPERATORS AND COMPACT PERTURBATIONS OF STRONGLY IRREDUCIBLE OPERATORS

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Chinese Annals of mathematics,Series B 2000年第2期21卷 237-248页

作者： JIYOUQING JIANGCHUNLAN wangZONGYAO departmentofmathematics JilinUniversityChangchun130023China. departmentofmathematics JilinUniversityChangchun130023China. departmentofmathematics EastChinaUniversityofScienceandTechnologyShanghai200237＂China.

Let н be a complex, separable, infinite dimensional Hilbert space, T　ε（Ｈ）. （ｕ＋Ｋ）（T） denotes the （ｕ＋ｋ）-orbit of T, i.e., （ｕ＋ｋ）（T） = {R-1TR: R is invertible and of the form unitary plus compact}. Let be an analytic and simply connected Cauchy domain in C and n ε N. A（, n） denotes the class of operators, each of which satisfies （i） T is essentially normal; （ii） σ（T） =,　ρF（T）　∩ σ（T） = ; （iii） ind （λ-T） = -n, nul （λ-T） = 0 （λ∈Ω ）. It is proved that given T1, T2 ε A（, n） and ε > 0, there exists a compact operator K with K <ε such that T1 +Kε （ｕ＋ｋ）（T2）. This result generalizes a result of P. S. Guinand and L. Marcoux [6,15]. Furthermore, the authors give a character of the norm closure of （ｕ＋Ｋ）（T）, and prove that for each T ε A（, n）, there exists a compact （SI） perturbation of T whose norm can be arbitrarily small.

关键词： Essentially normal (u+k)-orbit Compact perturbation Spectrum Strongly irreducible operator