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CLASSICAL SOLUTION OF QUASI-STATIONARY STEFAN PROBLEM

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Chinese Annals of mathematics,Series B 1996年第2期17卷 175-186页

作者： YI FAHUAI Department of mathematics, suzhou university, suzhou 215006, china. Department of mathematics Suzhou University Suzhou 215006 China

This paper considers the quasi-stationary Stefan problem:△u(x,t)=0 in space-time domain,u=0 and Vv +(?)u/(?)u=0 on the free boundary.Under the natural conditions the existence of classical solution locally in time is proved bymaking use of the property of Frechet derivative operator and fixed point theorem. For thesake of simplicity only the one-phase problem is dealt with. In fact two-phase problem can bedealt with in a similar way with more complicated calculation.

关键词： Classical solution Quasi-stationary Stefan problem Frechet derivative

A RANDOM FUNCTIONAL CENTRAL LIMIT THEOREM FOR PROCESSES OF PRODUCT SUMS OF LINEAR PROCESSES GENERATED BY MARTINGALE DIFFERENCES

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Chinese Annals of mathematics,Series B 2003年第4期24卷 449-456页

作者： WANG YUEBAO YANG YANG ZHOU HAIYANG Department of mathematics, suzhou university, suzhou 215006, Jiangsu, china. Department of mathematics, suzhou university, suzhou 215006, Jiangsu, china. Department of mathematics Suzhou University Suzhou 215006 Jiangsu China

A random functional central limit theorem is obtained for processes of partial sums andproduct sums of linear processes generated by non-stationary martingale differences. It devel-ops and improves some corresponding results on processes of partial sums of linear processesgenerated by strictly stationary martingale differences, which can be found in [5].

关键词： Ilandom functional central limit theorem Processes of product sums

Weight modules over some Block algebras

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Science china mathematics 2009年第3期52卷 517-525页

作者： L RenCai Department of mathematics, suzhou university, suzhou 215006, china Department of mathematics Suzhou University Suzhou China

In this paper, the Harish-Chandra modules and Verma modules over Block algebra $ \mathfrak{L} $ [G] are investigated. More precisely, the irreducibility of the Verma modules over $ \mathfrak{L} $ [G] is completely det... 详细信息

关键词： Block algebra weight module highest weight module Harish-Chandra module 17B10 17B65 17B68

The nonwandering set of some Hénon map

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Chinese Science Bulletin 1999年第7期44卷 590-594页

作者： CAO YongluoDepartment of mathematics , suzhou university, suzhou 215006, china Department of mathematics Suzhou University Suzhou China

For the Hnon map Ta , b（x, y） = （1- ax2 + y, bx）, Benedicks and Carleson proved that for （ a, b） near （2, 0） and b > 0, there exists a set E with positive Lebesgue measure, whose corresponding map Ta,b possesses a strange attractor. Viana conjectured that if （a, b）∈ E, then the nonwandering set of the map Ta, b, Ω（Ta, b） = Aa,b U {qa, b},where A（a, b） is the strange attractor, qa, b is a hyperbolic fixed point in the third quadrant. It is proved that this conjecture holds true for a positive measure set E1 E.

关键词： strange attractor nonwandering set. basin of attraction.

A characterization of the finite simple groups with set of indices of their maximal subgroups

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Science china mathematics 2004年第4期47卷 508-522页

作者： LI XianhuaDepartment of mathematics, suzhou university, suzhou 215006, china (email: xhli@***) Department of mathematics Suzhou University Suzhou China

We study the problem concerning the influence of indices of maximal subgroups of a simple group on the structure of a group. We obtain a characterization property of all finite simple groups.

关键词： Finite simple group, maximal subgroup, index.

The Abundance of Strange Attractor in the Families of Nearby Singular Diffeomorphism

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Acta Mathematica Sinica,English Series 1997年第1期13卷 90-96页

作者： Cao Yongluo (Department of mathematics,suzhou university,suzhou 215006,china) Department of mathematics Suzhou University Suzhou China

In this paper,we consider the families of nearby singular diffeomorphism and the measure of a set in the parameter space,such that for each point of the set the corresponding diffeomorphism possesses strange *** some families of one-dimensional mapping satisfying certain transversality condition,we prove that there is a positive measure set in the parameter space, such that the system in the corresponding families of nearly singular diffeomorphism has strange ***,we study the dynamics of this type of strange attractor.

关键词： Transversal homoclinic point Strange attractor The families of nearby singular dif-

HYPERCYCLIC OPERATORS ON QUASI-MAZUR SPACES

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Acta Mathematica Scientia 2010年第5期30卷 1709-1720页

作者：丘京辉 Department of mathematics Suzhou University

Modifying the method of Ansari, we give some criteria for hypercyclicity of quasi-Mazur spaces. They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces. For some special locally convex spaces, for example, KSthe （LF）-sequence spaces and countable inductive limits of quasi-Mazur spaces, we investigate their hypercyclicity. As we see, bounded biorthogonal systems play an important role in the construction of Ansari. Moreover, we obtain characteristic conditions respectively for locally convex spaces having bounded sequences with dense linear spans and for locally convex spaces having bounded absorbing sets, which are useful in judging the existence of bounded biorthogonal systems.

关键词： hypercyclic operator bounded biorthogonal systems quasi-Mazur space inductive limit Kothe (LF)-sequence space

Generalized Steiner Triple Systems with Group Size g ≡0, 3 (mod 6)

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 561-568页

作者： Gen-nian GeDepartment of mathematics, suzhou university, suzhou 215006, china Department of mathematics Suzhou University Suzhou China

Generalized Steirier triple systems, GS(2,3,n,g), are equivalent to maximum constant weight codes over an alphabet of size g+1 with distance 3 and weight 3 in which each codeword has length n. The necessary conditions for the existence of a GS(2,3,n,g) are (n-1)g≡0 (mod 2), n(n-1)g2≡0 (mod 6), and n≥g+2. These necessary conditions are shown to be sufficient by several authors for 2≤g≤11. In this paper, three new results are obtained. First, it is shown that for any given g, g≡0 (mod 6) and g≥12, if there exists a GS(2.3.n.g) for all n, g+2≤n≤7g+13. then the necessary conditions are also sufficient. Next, it is also shown that for any given g, g≡3 (mod 6) and g≥15, if there exists a GS(2,3,n,g) for all n, n≡1 (mod 2) and g+2≤n≤7g+6, then the necessary conditions are also sufficient. Finally, as an application, it is proved that the necessary conditions for the existence of a GS(2,3,n,g) are also sufficient for g=12,15.

关键词： Generalized Steiner triple system constant weight codes singular indirect product disjoint

P_(4k-1)-factorization of complete bipartite graphs

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Science china mathematics 2005年第4期48卷 539-547页

作者： DU Beiliang & WANG Jian Department of mathematics, suzhou university, suzhou 215006, china Nantong Vocational College, Nantong 226007, china Department of mathematics Suzhou University Suzhou China Nantong Vocational College Nantong China

Let Km,n be a complete bipartite graph with two partite sets having m and n vertices, respectively. A Pv-factorization of Km,n is a set of edge-disjoint pv-factors of Km,n which partition the set of edges of Km,n. When v is an even number, Wang and Ushio gave a necessary and sufficient condition for the existence of Pv-factorization of Km,*** v is an odd number, Ushio in 1993 proposed a conjecture. However, up to now we only know that Ushio Conjecture is true for v = 3. In this paper we will show that Ushio Conjecture is true when v = 4k - 1. That is, we shall prove that a necessary and sufficient condition for the existence of a P4k-1-factorization of Km,n is (1) (2k - 1)m ≤ 2kn, (2) (2k -1)n≤2km, (3) m + n ≡ 0 (mod 4k - 1), (4) (4k -1)mn/[2(2k -1)(m + n)] is an integer.

关键词： complete bipartite graph, factorization, Ushio Conjecture.