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(s,t,d)-bi-Koszul algebras

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Science china.mathematics 2009年第11期52卷 2419-2431页

作者： SI JunRu department of mathematics,hangzhou dianzi university,hangzhou 310018,china 1. department of mathematics Hangzhou Dianzi University Hangzhou 310018 China

The paper focuses on the 1-generated positively graded algebras with non-pure resolutions and mainly discusses a new kind of algebras called(s,t,d)-bi-Koszul algebras as the generalization of bi-Koszul algebras. An(s,t,d)-bi-Koszul algebra can be obtained from two periodic algebras with pure resolutions. The generation of the Koszul dual of an(s,t,d)-bi-Koszul algebra is discussed. Based on it,the notion of strongly(s,t,d)-bi-Koszul algebras is raised and their homological properties are further discussed.

关键词： bi-Koszul algebra periodic algebra pure resolution 16E05 16E40 16S37 16W50

ON MULTIPLE POSITIVE SOLUTIONS FOR A NONLINEAR ELLIPTIC PROBLEM IN R^N

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Chinese Annals of mathematics,Series B 2000年第3期21卷 351-358页

作者： YANG HAITAO(department of mathematics, Zhejiang university, hangzhou 310027, china.) WU SHAOPING(department of mathematics, Zhejiang university, hangzhou 310027, china.) department of mathematics Zhejiang University Hangzhou 310027 China

By making use of Variational method, the authors obtain some results about existence of multiple positive solutions and their asymptotic behavior as the parameter →＋∞ for a semilinear elliptic problem in RN.

关键词： Critical point Asymptotic behavior Concentration

SOME FUNCTIONAL LIMIT THEOREMS FOR THE INFINITE SERIES OF OU PROCESSES

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Chinese Annals of mathematics,Series B 2003年第2期24卷 249-260页

作者： WANG WENSHENG LIN ZHENGYAN department of mathematics, Zhejiang university, hangzhou 310028, china. department of mathematics, hangzhou Teacher’s College, hangzhou 310012, china. E-mail: wswang@*** department of mathematics, Zhejiang university, hangzhou 310028, china. Zhejiang Univ Dept Math Hangzhou 310028 Peoples R China hangzhou Teachers Coll Dept Math Hangzhou 310012 Peoples R China

This paper obtains functional modulus of continuity and Strassen's functional LIL of theinfinite series of independent Ornstein-Uhlenbeck processes, which also imply the Levy's exactmodulus of continuity and LIL of th... 详细信息

关键词： Ornstein-Uhlenbeck processes Stationary Gaussian processes Modulus of continuity Law of the iterated logarithm

REMARKS ON h-TRANSFORM AND DRIFT

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Chinese Annals of mathematics,Series B 1998年第4期19卷 473-478页

作者： YING JIANGANG (department of mathematics, Zhejiang university, hangzhou 310027, china.) Zhejiang Univ Dept Math Hangzhou 310027 Peoples R China

The author studies the h-transforms of symmetric Markov processes and corresponding Dirichlet spaces, and also discusses the drift transformation of Fukushima and Takeda’s type[2] and improves their result by a diffe... 详细信息

关键词： Right processes Revuz measures h-transform

Effective generalized equations of secure hyperelliptic curve digital signature algorithms

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The Journal of china.Universities of Posts and Telecommunications 2010年第2期17卷 100-108,115页

作者： YOU Lin ,SANG Yong-xuan College of Communication Engineering,hangzhou dianzi university,hangzhou 310018,china [a] College of Communication Engineering Hangzhou Dianzi University Hangzhou 310018 China

A hyperelliptic curve digital signature algorithm （HECDSA） can be viewed as the hyperelliptic curve analogue of the standard digital signature algorithm （DSA）. This article discusses divisor evaluations, the basic HECDSA, variants, two HECDSA equations and a 4-tuple HECDSA scheme, and puts forward a generalized equation for HECDSA. From this generalized equation, seven general HECDSA types are derived based on the efficiency requirements. Meanwhile, the securities of these general HECDSA types are analyzed in detail.

关键词： hyperelliptic curve digital signature algorithm generalized equation hyperelliptic curve discrete logarithm problem

GLOBAL EXISTENCE AND ASYMPTOTICS BEHAVIOR OF SOLUTIONS FOR A RESONANT KLEIN-GORDON SYSTEM IN TWO SPACE DIMENSIONS

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Chinese Annals of mathematics,Series B 2005年第1期26卷 89-104页

作者： XUERUYING FANGDAOYUAN departmentofmathematics ZhejiangUniversityHangzhou310027China departmentofmathematics ZhejiangUniversityHangzhou310027China

The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth,compactly supported Cauchy data, and find that t... 详细信息

关键词： Klein-Gordon equation Asymptotic behavior Global existence

Interpolating triangular meshes by Loop subdivision scheme

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Science china.Information Sciences) 2010年第9期53卷 1765-1773页

作者： DENG ChongYang1* & WANG GuoZhao2 1Institute of Applied mathematics and Engineering Computations,hangzhou dianzi university,hangzhou 310018,china.2department of mathematics,Zhejiang university,hangzhou 310027,china 1. Institute of Applied mathematics and Engineering Computations Hangzhou Dianzi University Hangzhou 310018 China2. Department of Mathematics Zhejiang University Hangzhou 310027 China

Using the limit point formula of the Loop subdivision scheme,we propose a very simple and efficient method for constructing interpolation surface of triangular meshes by Loop subdivision *** excellent properties of the method are:(1) Locality:the perturbation of a given vertex only influences the surface shape near this vertex.(2) Efficiency:the locations of new points can be computed with explicit formulae.(3) Easiness in implementation:only the geometric rule of the first step should be modified.(4) Freedom:for each edge,there is one degree of freedom to adjust the shape of the interpolation surface.(5) Easiness in generalization:it is easy to generalize our method to other approximation subdivision schemes with explicit formulae to compute limit point.

关键词： computer aided geometric design subdivision surface approximating subdivision scheme Loop surface surface interpolating

LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE □u= u^k(u)~α

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Chinese Annals of mathematics,Series B 2005年第3期26卷 361-378页

作者： FANGDAOYUAN WANGCHENGBO departmentofmathematics ZhejiangUniversityHangzhou310027China

This paper undertakes a systematic treatment of the low regularity local well-posedness and ill-posedness theory in H3 and Hs for semilinear wave equations with polynomial nonlinearity in u and (?)u. This ill-posed re... 详细信息

关键词： Semilinear wave equation Low regularity Local well-posedness Ill-posedness

Almost sure central limit theorems for random functions

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Science china.mathematics 2006年第12期49卷 1788-1799页

作者： LU Chuanrong, QIU Jin & XU Jianjun School of mathematics and Statistics, Zhejiang university of Finance and Economics, hangzhou 310018, china.department of mathematics, Zhejiang university, hangzhou 310028, china 1. School of mathematics and Statistics Zhejiang University of Finance and Economics Hangzhou 310018 China 2. department of mathematics Zhejiang University Hangzhou 310028 China

Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|Rn| <∞and Rn = o(n^(1/2)) a.s., or Rn = O(n1/2-2γ) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc.

关键词： statistics,random function,almost sure central limit theorem,logarithm average.