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Mobius Isoparametric Hypersurfaces in S^(n+1) with Two Distinct Principal Curvatures

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Acta Mathematica Sinica,English Series 2002年第3期18卷 437-446页

作者： Hai Zhong LI department of mathematics, Tsinghua University. Beijing 100084. P. R. China Hui Li LIU department of mathematics, Northeastern University. Shenyang 110000. P. R. China Chang Ping WANG Key Laboratory of pure and Applied mathematics, School of Mathematical Sciences. Peking University, Beijing 100871, P. R. China Guo Song ZHAO department of mathematics, Sichuan University, Chengdu 610064. P. R. China department of mathematics Tsinghua University Beijing P. R. China department of mathematics Northeastern University Shenyang P. R. China Key Laboratory of pure and Applied mathematics School of Mathematical Sciences Peking University Beijing P. R. China department of mathematics Sichuan University Chengdu P. R. China

A hypersurface x: M→S^(n+1) without umbilic point is called a Mbius isoparametric hypersurface if its Mbius form Φ=-ρ^(-2)∑_i(ei(H)+∑_j(h_(ij)-Hδ_(ij))e_j(logρ))θ_i vanishes and its Mbius shape operator S=ρ^(-1)(S-Hid) has constant eigenvalues. Here {e_i} is a local orthonormal basis for I=dx·dx with dual basis {θ_i}, II=∑_(ij)h_(ij)θ_iθ_J is the second fundamental form, H=1/n∑_i h_(ij), ρ~2=n/(n-1)(‖II‖~2-nH^2) and S is the shape operator of x. It is clear that any conformal image of a (Euclidean) isoparametric hypersurface in S^(n+1) is a Mbius isoparametric hypersurface, but the converse is not true. In this paper we classify all Mbius isoparametric hypersurfaces in S^(n+1) with two distinct principal curvatures up to Mbius transformations. By using a theorem of Thorbergsson [1] we also show that the number of distinct principal curvatures of a compact Mbius isoparametric hypersurface embedded in S^(n+1) can take only the values 2, 3, 4, 6.

关键词： Mobius geometry Isoparametric hypersurface Principal curvature

ASYMPTOTIC BEHAVIOUR OF EIGENVALUES FOR THE DISCONTINUOUS BOUNDARY-VALUE PROBLEM WITH FUNCTIONAL-TRANSMISSION CONDITIONS

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Acta Mathematica Scientia 2002年第3期22卷 335-345页

作者： O.Sh.Mukhtarov department of mathematics, Science and Arts Faculty, Gaziosmanpasa University, Tokat, TurkeyMustafa Kandemir department of mathematics, Faculty of A mas y a Education, Ondokuz Mayis University, Amasya, Turkey Gaziosmanpasa Univ Sci & Arts Fac Dept Math Tokat Turkey Ondokuz Mayis Univ Fac Amasya Educ Dept Math Amasya Turkey

In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and linear functionals is investigated. So, the problem is not pure boundary-value. The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence of infinit number eigenvalues. Also the asymptotic formulas for eigenvalues are found.

关键词： Asymptotic behaviour of eigenvalues boundary-value problems functional-conditions discontinuous coefficients

TRANSPORTATION NETWORKS:OLD AND NEW

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Applied mathematics(A Journal of Chinese Universities) 1996年第3期11卷 251-272页

作者： LIU YANPEI(department of mathematics,Northern Jiaotong University, Beijing 100044) department of mathematics Northern Jiaotong University Beijing

This paper shows a number of Problems in pure and applied mathematicsthat are solved by constructing transportation ***,it also shows thatall the solutions are characterized by forbidden configurations which are not ***,all the characterizations are much related to the graphic method which wasfound by Chinese for solving a kind of the transportation problem in the fifties.

关键词： Mathematical programming,transportation problem,network graphic method forbidden configuration.

The spectrum for large sets of pure directed triple systems

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Science China mathematics 2006年第8期49卷 1103-1127页

作者： ZHOU Junling, CHANG Yanxun & Jl Lijun Institute of mathematics, Beijing Jiaotong University, Beijing 100044, China department of mathematics, Suzhou University, Suzhou 215006, China 1. Institute of mathematics Beijing Jiaotong University Beijing 100044 China 2. department of mathematics Suzhou University Suzhou 215006 China

An LPDTS(υ) is a collection of 3(υ - 2) disjoint pure directed triple systems on the same set of υ elements. It is showed in Tian's doctoral thesis that there exists an LPDTS(υ) for υ≡ 0,4 (mod 6), υ≥ 4. In this paper, we establish the existence of an LPDTS(υ) for υ≡ 1, 3 (mod 6), υ＞ 3. Thus the spectrum for LPDTS(υ) is completely determined to be the set {υ:υ≡0, 1 (mod 3),υ≥4}.

关键词： large set, oriented triple system, pure, directed candelabra system.

On the 3-rank of tame kernels of certain pure cubic number fields

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Science China mathematics 2010年第9期53卷 2381-2394页

作者： LI YuanYuan & QIN HouRong department of mathematics,Nanjing University,Nanjing 210093,China 1. department of mathematics Nanjing University Nanjing 210093 China

In this paper,we present some explicit formulas for the 3-rank of the tame kernels of certain pure cubic number fields,and give the density results concerning the 3-rank of the tame *** examples are given in Tables 1 ... 详细信息

关键词： the 3-rank of the tame kernels pure cubic fields density

Some Properties of Divisible and pure Fuzzy Subgroups

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模糊系统与数学 1992年第1期 48-53页

作者： Gu Wen-xiang Lu Tu (department of mathematics of Northeast Normal University) (department of mathematics of Chang Chun Teachers training College)

In [3] F. I. Sidky & M. Atif Mishref introduce the concepts of divisible and pure fuzzy subgroups and prove some of their properties. In this paper we further prove following results: Let f: G→G’ be an isomorphism of groups and A’ be a divisible (pure) fuzzy subgroup of G’ under Min, then f(A’) is a divisible (pure) fuzzy subgroup of G; Let B be a divisible fuzzy subgroup of divisible subgroup H of group G, G=H(?)H’, then there exists a fuzzy subgroup B’ of H’ such that B+B’=A is a fuzzy subgroup of G; If G is a divisible cyclic group, then G is finite group; If A is a fuzzy subgroup of divisible cyclic group, then A is trivial; suppose group G=G×G×…×G, Gis a divisible cyclic subgroup of G, i=1, 2, …, m, A is a divsiible (pure) fuzzy subgroup of G under Min, then A is trivial.

关键词： Some Properties of Divisible and pure Fuzzy Subgroups

ABSOLUTELY E-pure MODULES AND E-pure SPLIT MODULES

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Acta Mathematica Scientia 2011年第1期31卷 207-220页

作者：阎舫宇 department of mathematics Nanjing University department of Basic Courses China Pharmaceutical University

We first introduce the concepts of absolutely E-pure modules and E-pure split modules. Then, we characterize the IF rings in terms of absolutely E-pure modules. The E-pure split modules are also characterized.

关键词： Absolutely E-pure module E-pure split module IF ring copure flat module

Simulation of nuclei morphologies for binary alloy

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Science China mathematics 2010年第11期53卷 2927-2936页

作者： LI DaMing1, & ZHANG PingWen2 1department of mathematics, Shanghai Jiaotong University, Shanghai 200240, China 2Key Lab of mathematics and Applied mathematics, Center for Applied Physics and Technology and School of Mathematical Sciences, Peking University, Beijing 100871, China 1. department of mathematics Shanghai Jiaotong University Shanghai 200240 China2. Key Lab of Mathematics and Applied Mathematics Center for Applied Physics and Technology and School of Mathematical Sciences Peking University Beijing 100871 China

We study the critical nuclei morphologies of a binary alloy by the string method. The dynamic equation of the string, connecting the metastable phase (liquid) and stable phase (solid), is governed by Helmholtz free energy for the binary alloy system at a given temperature. The stationary string through the critical nucleus (saddle point) is obtained if the relaxation time of the string is su?ciently large. The critical nucleus radius and energy barrier to nucleation of a pure alloy with isotropic interface energy in two and three dimensions are calculated, which are consistent with the classical nucleation theory. The critical nuclei morphologies are sensitive to the anisotropy strength of interface energy and interface thickness of alloy in two and three dimensions. The critical nucleus and energy barrier to nucleation become smaller if the anisotropy strength of the interface energy is increased, which means that it is much easier to form a stable nucleus if the anisotropy of the interface energy is considered.

关键词： nucleation crystal morphology string method

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

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Science China mathematics 2009年第4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

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