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Integral spinor norms in dyadic local fields Ⅲ

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Science china mathematics 2010年第9期53卷 2425-2446页

作者： L JianRui1 & XU Fei2.1department of mathematics,Jinan University,Guangzhou 510632.{2. 2.chool of mathematics,Capital normal University,Beijing 100048,{2. department of mathematics Jinan University Guangzhou China School of mathematics Capital Normal University Beijing China

In this paper we give an alternative computation of integral spinor norms over dyadic local fields by using the Jordan decomposition of *** particular,we emphasize the striking similarity between the theory over dyadi... 详细信息

关键词： integral lattice spinor norm Jordan decomposition

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

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Science china(Physics,Mechanics & Astronomy) 2004年第3期47卷 365-380页

作者： CHENG Chuanfu1, 2. SONG Hongsheng2. LIU Chunxiang2. REN Xiaorong2. ZHANG Ningyu3, TENG Shuyun1 & XU Zhizhan1 1. shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, P. O. Box 800-2.1, shanghai 2.1800, {2. 2. department of Physics, Shandong normal University, Jinan 2.0014, {2. 3. Shandong Institute of Architecture and Engineering, Jinan 2.0014, {2. shanghai Institute of Optics and Fine MechanicsChinese Academy of Sciencesshanghai{2. department of PhysicsShandong normal UniversityJinan{2. Shandong Institute of Architecture and EngineeringJinanchina

From Helmholtz equation of the harmonic electromagnetic waves, the integral equations of the light field at the medium boundaries are obtained by use of the Green's theorem and are discretized into linear equation set with the values of the light field and its derivative as the unknowns. On solving the linear equation set, we realize the rigorous computations of the light fields at the boundaries. Then the intensities of the light waves scattered by the random self-affine fractal surfaces in the optical near-field are calculated, and the propagation characteristics, the evolutions of the contrast and the intensity probability density function of the near-field speckles are studied in detail. The near-field speckles are much different from the conventional speckles in the diffraction regions and in the imaging systems. There are obvious local fluctuations in the intensity distributions of the near-field speckles and such fluctuations disappear after propagating a distance of one wavelength from the medium surfaces. For the random surfaces with smaller lateral correlation lengths, the speckle contrasts approach the saturation values and the speckle fields approach Gaussian distribution within the near-field, while for the random surfaces with larger lateral correlation lengths, such evolutions become comparatively slow.

关键词： speckle, near-field optics, first order statistics, Green's function.

N-Soliron-like Solution of Ito Equation

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Communications in Theoretical Physics 2004年第11期 641-644页

作者： ZHANG Yi~(1,2.) CHEN Deng-Yuan~2.~1department of mathematics,Zhejiang {2. University,Jinhua 32.004,china ~2.0} of mathematics,shanghai University,shanghai 2.0436,china department of mathematics，Zhejiang {2. University，Jinhua 32.004，china department of mathematics，{2. University，{2. 2.0436，china department of mathematics，{2. University，{2. 2.0436，china

By using the extended Hirota’s method,the N-soliton-like solution of the Ito equation is ***-thermore,we also investSgate the soliton-like solution interaction and find singularity.

关键词： soliton-like solution Ito equation Hirota method

Combined perturbation bounds:Ⅱ.Polar decompositions

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Science china mathematics 2007年第9期50卷 1339-1346页

作者： Wen LI~(1+) Wei-wei SUN~2.1 School of Mathematical Sciences,South china normal University,Guangzhou 510631,china 2.department of mathematics,City University of Hong Kong,Hong Kong,china School of Mathematical Sciences South China Normal University Guangzhou China department of mathematics City University of Hong Kong Hong Kong China

In this paper,we study the perturbation bounds for the polar decomposition A=QH where Q is unitary and H is *** optimal (asymptotic) bounds obtained in previous works for the unitary factor,the Hermitian factor and singular values of A areσ_r^2.|ΔQ||_F^2.||ΔA||_F^2. 1/2.|ΔH||_F^2.||ΔA||_F^2.and ||Δ∑||_F^2.||ΔA||_F^2.respectively,where∑=diag(σ_1,σ_2....,σ_r,0,...,0) is the singular value matrix of A andσ_r denotes the smallest nonzero singular *** we present some new combined (asymptotic) perturbation boundsσ_r^2.|ΔQ||_F^2.1/2.|ΔH||_F^2.||ΔA||_F^2.andσ_r^2.|ΔQ||_F^2.||Δ∑||_F^2.||ΔA||_F^2.which are optimal for each *** corresponding absolute perturbation bounds are also given.

关键词： polar decomposition perturbation singular value

THE TOPOLOGICAL AND DYNAMICAL PROPERTIES OF NONORIENTABLE SURFACES

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Chinese Annals of mathematics 1988年第2期9卷 197-206页

作者：朱德明 department of mathematics {2. china normal University shanghai china.

Four topological and dynamical properties of nonorientable surfaces are *** is that for every continuous flow defined on any nonorientable closed surface,thereexist periodic or singular closed *** the case of the projective plane,it confirms aconjecture of professor Ye Yian-qian in his lecture notes“dynamical systems on surfaces”.Secondly,the author gives an exact upper bound of the number of closed curves onnonorientable surfaces,which do not intersect each other and the complement of their sumis still *** third is concerned with the upper and lower bound of the number ofthe periodic or singular closed orbits with certain *** last is related to theconnectedness of the complement of a lifting curve on two-fold covering *** firstproperty may be considered as a generalization of Kneser theorem from Klein bottle togeneral nonorientable surfaces and the second as a generalization of[4]Theorem 9.3.6from orientable surfaces to nonorientable surfaces.

关键词： Th THE TOPOLOGICAL AND DYNAMICAL PROPERTIES OF NONORIENTABLE SURFACES PCO

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, Suzhou University, Suzhou 2.5006, {2. 2.ollege of mathematics and Information Science, Hebei normal University, Shijiazhuang 050016, {2. department of mathematics Suzhou University Suzhou China College of mathematics and Information Science Hebei Normal University Shijiazhuang 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 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

THE CODIMENSION FORMULA ON AF-COSUBMODULES

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Chinese Annals of mathematics,Series B 2002年第3期23卷 419-424页

作者： GUO KUNYU department of mathematics, Fudan University, {2. 2.0433, china department of mathematics Fudan University Shanghai 200433 China

Let M1, M2.be submodules of analytic Hilbert module X on ?(? Cn) such that M1 ? M2.and dimM1/M2.= k < '. If M2.is an AF-cosubmodule, then the codimension dimM1/M2.of M2.in M1 equals the cardinality of zeros of M2.rel... 详细信息

Let M1, M2.be submodules of analytic Hilbert module X on ?(? Cn) such that M1 ? M2.and dimM1/M2.= k 2.is an AF-cosubmodule, then the codimension dimM1/M2.of M2.in M1 equals the cardinality of zeros of M2.related to MI by counting multiplicities. The codimension formula has some interesting applications. In particular, the author calculates out the dimension of Rudin quotient module, which is raised in [14].

关键词： AF-cosubmodule Characteristic space Analytic Hilbert module

SADDLE VALUES AND INTEGRABILITY CONDITIONS OF QUADRATIC DIFFERENTIAL SYSTEMS

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Chinese Annals of mathematics 1987年第4期8卷 466-478页

作者：朱德明 department of mathematics {2. china normal University shanghai china.

In the first section of the paper,the first three saddle values R1,R2.R3 of the realquadratic differential system（QDE） are computed by use of the method with which Poincaréresearchs on Hopf *** the second section,by applying the method and results ofDulac seeking integrability conditions of QDE it is proved that the system is integrable ifand only if R1=R2.R3=0,and it is also true when the system is *** integrabilityconditions given here can be applied much more easily then Dulac’*** the last part ofthe paper,it is pointed out that iR1,iR2.iR3 are the first three focal values of the weakfocus of the complex *** the formulae of R1,R2.R3 and the result in section 2.one can easily give the formulae of the focal values for the real QDE with Bautin formand give a new proof of Bautin’s famous result.

关键词：鲁一 Za SADDLE VALUES AND INTEGRABILITY CONDITIONS OF QUADRATIC DIFFERENTIAL SYSTEMS

A note on the 2.connectivity in one-dimensional ad hoc networks

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Science china(Information Sciences) 2011年第1期54卷 123-128页

作者： SHANG YiLun department of mathematics,{2. Jiao Tong University, {2. 2.02.0,china department of mathematics Shanghai Jiao Tong University Shanghai China

2.connectivity is the basic graph theoretical metric for fault tolerance to node failures,and it is an extremely desirable property in network *** a one-dimensional finite ad hoc network formed by n nodes uniformly and independently distributed in a closed interval[0,z](z∈R+),we give a closed form expression for the probability that a connected one-dimensional finite ad hoc network becomes disconnected after removing a *** also sketch a procedure of finding the exact formula for 2.connectivity in a one-dimensional ad hoc network.

关键词： ad hoc network one-dimensional network 2.connectivity