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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

Difference packing arrays and systematic authentication codes

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Science china mathematics 2004年第4期47卷 566-577页

作者： YIN Jianxingdepartment of mathematics, suzhou university, suzhou 215006, china department of mathematics Suzhou University Suzhou China

In this paper, a type of combinatorial design (called difference packing array)is proposed and used to give a construction of systematic authentication codes. Taking advantage of this construction, some new series of ... 详细信息

关键词： authentication codes, difference packing arrays, constructions.

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

MATHER SETS FOR SUBlINEAR DUFFING EQUATIONS

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Chinese Annals of mathematics,Series B 1994年第4期15卷 421-434页

作者： QIAN DINGBIAN(department of mathematics, suzhou university, 215006, china.) 苏州大学数学系江苏苏州 215006

The existence of Mather sets(generalized quasiperiodic solutions and uNlinked periodicsolutions)for sublinear Duffing equations is shown. Here the approach is based on the use ofaction-angle variables and the applicat... 详细信息

关键词： Sublinear Duffing equation Finite twist Aubry-Mather theorem Mather sets.

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.

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.

P_(4k-1)-factorization of bipartite multigraphs

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Science china mathematics 2006年第7期49卷 961-970页

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

letλKm,n be a bipartite multigraph with two partite sets having m and n vertices, respectively. A Pν-factorization ofλKm,n is a set of edge-disjoint Pν-factors ofλKm,n which partition the set of edges ofλKm,n. Whenνis an even number, Ushio, Wang and the second author of the paper gave a necessary and sufficient condition for the existence of a Pν-factorization ofλKm,n. When v is an odd number, we proposed a conjecture. However, up to now we only know that the conjecture is true forν= 3. In this paper we will show that the conjecture is true whenν= 4k-1. That is, we shall prove that a necessary and sufficient condition for the existence of a P4k-1-factorization ofλKm,n is (1) (2k-1)m≤2kn, (2) (2k-1)n≤2km, (3)m + n = 0 (mod 4k-1), (4)λ(4k-1)mn/[2(2k-1)(m + n)] is an integer.

关键词： bipartite multigraph, factor, factorization.