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Variational construction of unbounded orbits in Lagrangian systems

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science China mathematics 2010年第3期53卷 617-624页

作者： CHENG Chong-Qing 1, & LI Xia 2.1 department of mathematics, Nanjing {2., Nanjing 2.0093, China 2.department of mathematics, suzhou univ.r.ity of science and technology, suzhou 2.5001, China 1. department of mathematics Nanjing University Nanjing 210093 China2. Department of Mathematics Suzhou University of Science and Technology Suzhou 215001 China

We show the existence of unbounded orbits in perturbations of generic geodesic flow in T2.by a generic periodic potential. Different from previous work such as in Mather (1997), the initial values of the orbits obtain... 详细信息

关键词： positive definite Lagrangian variational method unbounded orbit

Finite groups in which elements of the same order outside the center are conjugate

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science China mathematics 2007年第10期50卷 1493-1500页

作者： Xing-zhong YOU~1 Guo-hua QIAN~2.Wu-jie SHI~(3+) ~1 School of mathematics and Computing science,Changsha {2. of science and technology,Changsha 410076,China ~2.department of mathematics,Changshu Institute of technology,Changshu 2.5500,China ~3 School of mathematics,suzhou {2.,suzhou 2.5006,China 1. School of mathematics and Computing science Changsha University of Science and Technology Changsha 410076 China 2. department of mathematics Changshu Institute of Technology Changshu 215500 China 3. School of mathematics Suzhou University Suzhou 215006 China

We prove that if G is a finite group in which the elements of the same order outside the center are conjugate, then either G is abelian or G ≌ S3.

关键词： finite group, rational group, conjugacy class

λ-fold indecomposable large sets of Steiner triple systems

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science China mathematics 2010年第11期53卷 2877-2888页

作者： JI LiJun1, TIAN ZiHong2. & KANG QingDe2.1department of mathematics, {2. univ.r.ity, {2. 2.5006, China 2.ollege of mathematics and Information science, Hebei Normal univ.r.ity, Shijiazhuang 050016, China 1. department of mathematics Suzhou University Suzhou 215006 China2. College of Mathematics and Information Science Hebei Normal University Shijiazhuang 050016 China

A family (X, B1), (X, B2., . . . , (X, Bq) of q STS(v)s is a λ-fold large set of STS(v) and denoted by LSTSλ(v) if every 3-subset of X is contained in exactly λ STS(v)s of the collection. It is indecomposable and denoted by IDLSTSλ(v) if there exists no LSTSλ (v) contained in the collection for any λ riggs and rosa posed a problem: For which values of λ > 1 and orders v ≡ 1, 3 (mod 6) do there exist IDLSTSλ(v)? In this paper, we use partitionable candelabra systems (PCSs) and holey λ-fold large set of STS(v) (HLSTSλ(v)) as auxiliary designs to establish a recursive construction for IDLSTSλ(v) and show that there exists an IDLSTSλ(v) for λ = 2. 3, 4 and v ≡ 1, 3 (mod 6).

关键词： Steiner triple system large set candelabra system indecomposable

Conservation laws for mechanical systems with unilateral holonomic constraints

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Progress in Natural science:Materials International 2004年第1期14卷 56-60页

作者： ZHANG Yi*(department of Civil Engineering, univ.r.ity of {2. and technology of suzhou, suzhou 2.5011, China) univ Sci & Technol suzhou Dept Civil Engn Suzhou 215011 Peoples R China

A general approach to the construction of conservation laws for mechanical systems with unilateral holonomic constraints by finding corresponding integrating factors is presented. The definition of integrating factors for the routh equations of motion of the systems is given, and the necessary conditions for the existence of conserved quantities of the unilateral holonomic constraint systems are studied in detail. The conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results.

关键词： unilateral holonomic constraint integrating factor conservation theorem Killing equation

Plateau of α-function and c-minimal homoclinic orbits

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science China mathematics 2006年第7期49卷 922-931页

作者： LI Xia & CUI Xiaojun department of mathematics, {2. of science and technology of suzhou, suzhou 2.5009, China Mathematical research Institute, Fudan {2., Shanghai 2.0433, China 1. department of mathematics University of Science and Technology of Suzhou Suzhou 215009 China 2. Mathematical research Institute Fudan University Shanghai 200433 China

We consider the construction of the plateau of the α-function in a hyperbolic and positive definite Lagrangian system, and link the boundries of the α-function's plateau with the distribution of c-minimal homoclinic... 详细信息

关键词： α-function, β-function, plateau, Aubry sets.

The spectrum for overlarge sets of directed triple systems

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science China mathematics 2007年第10期50卷 1369-1381页

作者： Zi-hong TIAN~(1+) Li-jun JI~2.~1 Institute of mathematics,Hebei Normal univ.r.ity,Shijiazhuang 050016,China ~{2.,suzhou univ.r.ity,suzhou 2.5006,China 1. Institute of mathematics Hebei Normal University Shijiazhuang 050016 China 2. department of mathematics Suzhou University Suzhou 215006 China

A directed triple system of order v, denoted by DTS(v, λ), is a pair (X,B) where X is a v-set and B is a collection of transitive triples on X such that every ordered pair of X belongs to λ triples of B. An overlarge set of disjoint DTS(v, λ), denoted by OLDTS(v, λ), is a collection {(Y\{y}, Ai)}i,such that Y is a (v + 1)-set, each (Y\{y}, Ai) is a DTS(v, λ) and all Ai's form a partition of all transitive triples of Y. In this paper, we shall discuss the existence problem of OLDTS(v, λ) and give the following conclusion: there exists an OLDTS(v, λ) if and only if either λ = 1 and v = 0, 1 (mod 3), or λ = 3 and v≠2.

关键词： overlarge set directed triple system directed candelabra system

The decomposition of K_v into K_2.× K_5's

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science China mathematics 2007年第10期50卷 1382-1388页

作者： Yang LI~1 Jian-xing YIN~1 ru-cong ZHANG~2.Gen-nian GE~(2.) ~1 department of mathematics,{2. univ.r.ity,{2. 2.5006,China ~2.department of mathematics,Zhejiang univ.r.ity,Hangzhou 31002.,China 1. department of mathematics Suzhou University Suzhou 215006 China 2. department of mathematics Zhejiang University Hangzhou 310027 China

The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2.and c = 5, and show that such a de... 详细信息

关键词： decomposition, the complete graph Kv, product graph Kr×Kc, DNA library screening

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, {2. univ.r.ity, {2. 2.5006, Jiangsu, China. department of mathematics, {2. univ.r.ity, {2. 2.5006, Jiangsu, China. suzhou univ Dept Math Suzhou 215006 Peoples R 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

The spectrum of path factorization of bipartite multigraphs

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science China mathematics 2007年第7期50卷 1045-1054页

作者： Jian WANG~1 Bei-liang DU~(2.) 1 Nantong Vocational College,Nantong 2.6007,China 2.department of mathematics,suzhou {2.,suzhou 2.5006,China 1. Nantong Vocational College Nantong 226007 China 2. department of mathematics Suzhou University Suzhou 215006 China

Let λK m,n be a bipartite multigraph with two partite sets having m and n vertices, respectively. A P v-factorization of λK m,n is a set of edge-disjoint P v-factors of λK m,n which partition the set of edges of λK m,n . When v is an even number, Ushio, Wang and the second author of the paper gave a necessary and sufficient condition for the existence of a P v-factorization of λK m,n . When v is an odd number, we have proposed a conjecture. Very recently, we have proved that the conjecture is true when v = 4k ? 1. In this paper we shall show that the conjecture is true when v = 4k + 1, and then the conjecture is true. That is, we will prove that the necessary and sufficient conditions for the existence of a P 4k+1-factorization of λK m,n are (1) 2.m ? (2. + 1)n, (2. 2.n ? (2. + 1)m, (3) m + n ≡ 0 (mod 4k + 1), (4) λ(4k + 1)mn/[4k(m + n)] is an integer.

关键词： bipartite multigraph factorization 05B30 05C70