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模态框(Modal)标题

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ISSN 0583-1431 CN 11-2038/O1
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  • n-Parameter d-Dimension Random Walk (RW~d_n)
    Jin Ping ZHANG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(3): 517-524. DOI: 10.12386/A2000sxxb0066
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    In this paper, we studied n-parameter d-dimension radom walk marked by RW~d_n. Its various multiparameter Maxkov properties、Single-point and wide-past transition functions were discussed. A weak law of large numers of RW~1_n (B~1(p, q)) was obtained.
  • On the Dentability and Radon-Nikodym Property of Bounded Linear Operators
    Huan Guang ZHAO,Zhen Jie HONG
    Acta Mathematica Sinica, Chinese Series. 2000, 43(5): 955-960. DOI: 10.12386/A2000sxxb0123
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    In this paper, the method of vector measure is used to study the characteristics of dentable operator class and Radon-Nikodym operator class in Banach space. The results obtained are used to research into the structure of Banach space, giving out some new characteristics for Radon-Nikodym property of Banach space.
  • Normal Familles and Shared Values of Meromorphic Functions
    Qing De ZHANG; Chun Yan Qin
    Acta Mathematica Sinica, Chinese Series. 2008, 51(1): 145-152. DOI: 10.12386/A2008sxxb0018
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    On the basis of fundamental Nevanlinna theory the problem of normality of meromorphic functions that share three finite complex values with their k-th derivatives (k is any positive integer)is discussed and some examples are provided to show the result is sharp.
  • A Basis of the Section Space o
    Shi Kun WANG; Hui Ping ZHANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(1): 1-10. DOI: 10.12386/A2007sxxb0001
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    In this paper, we prove that a
  • Convergence Properties of Pairwise NQD Random Sequences
    Qun Ying WU
    Acta Mathematica Sinica, Chinese Series. 2002, 45(3): 617-624. DOI: 10.12386/A2002sxxb0080
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    In this paper, we extend the Kolmogorov-type inequality to the case of pairwise NQD random sequences. Moreover, we study the convergence properties of pairwise NQD random sequences. As a result, we extend Baum and Katz complete convergence, the three series theorem, Marcinkiewicz strong law of large number to the case pairwise NQD of random sequences.
  • On sn-Metrizable Spaces
    Ying GE
    Acta Mathematica Sinica, Chinese Series. 2002, 45(2): 355-360. DOI: 10.12386/A2002sxxb0045
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    In this paper, we investigate some closed mappings properties on sn-metri- zable spaces by using the characterizations of sn-metrizable spaces and the relations among sn-metrizable spaces, g-metrizable spaces and metrizable spaces. We prove that the closed image of a sn-metrizable space is sn-metrizable if it is sn-first countable. By this result, we prove that the finite-to-one closed mappings and the open-closed mappings preserve sn-metrizable spaces, and give a counterexample to show that the perfect mappings do not preserve, sn-metrizable spaces. In addition, we prove that sn-metrizable spaces satisfy the perfect inverse image Cδ-diagonal theorem.
  • Generalized Estimating Equation Estimators with Longitudinal Data
    Mu ZHAO, Bai Cheng CHEN, Yong ZHOU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 1-16. DOI: 10.12386/A2012sxxb0001
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    Generalized estimating equations method as a powerful method for estimating parameters, is wildly used in many fields, such as biostatistics, econometrics and medical insurance, and so on. For longitudinal data, We should take account into within-subject correlation structure in order to improve efficiency of a estimator. It is often useful to suppose that there is a parametric assumption within-subject correlation in longitudinal data analysis. But unreasonable assumptions made on within-subject correlation structure can result in inefficient estimation for parameters or even result in misspecification. For the generalized estimating equations with longitudinal data, we propose the extended GMM methods and extended EL methods and construct the large sample properties for our estimators. One of the proposed EL methods which is called block empirical likelihood is robust because of avoiding any assumptions on withinsubject correlation structure. We also provide two simulation examples to illustrate the finite properties for our estimators.  
  • An Existence and Uniqueness Result for BSDEs with Uniformly Continuous Generators in z
    Sheng Jun FAN, Long JIANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 187-194. DOI: 10.12386/A2011sxxb0020
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    This paper establishes an existence and uniqueness result for the solution to a one-dimensional backward stochastic differential equation (BSDE for short) whose generator satisfies Constantin’s condition in y and is uniformly continuous in z, which generalizes some known results.

     

  • A PROBLEM WITH VARIABLE END POINTS IN THE CALCULUS OF VARIATIONS
    KunSheng HU
    Acta Mathematica Sinica, Chinese Series. 1936, 1(1): 1-14. DOI: 10.12386/A1936sxxb0001
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    <正> 1.INTRODUCTION.Let g be an extremal arc with conjugateend points for the integral(?)In case n=1,the question whether or not g actually minimizes Ⅰrelative to arcs joining the ends of g has been discussed by Kneser(~1),Osgood(~2), Lindeberg(~3),and others by studying the shape of the en-velope of the extremals passing through an end point of g.In thecase n=2,Hahn(~4) has reduced the problem to that of an ordinaryminimum of a function of two variables by using a family of brokenextremals joining the ends of g.The method of Hahn is generaland can be extended in several directions as has been recently doneby Morse(~5)
  • Completion of Difference Substitution Method Based on Stochastic Matrix
    Jia XU, Yong YAO
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 219-226. DOI: 10.12386/A2011sxxb0023
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    In this paper, the principle of finite kernel is used to complete the successive difference substitution. Then a complete algorithm for deciding positive semi-definite polynomial is presented. This algorithm can be applied further to compute the global optimization of rational function. Being different from any other common methods of numerical optimization, the method in this paper gets accurate symbolic solution.

     

  • The Fundamental Solution for the Tricomi Operator
    Ai Fang QU
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 625-632. DOI: 10.12386/A2008sxxb0074
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    We give the fundamental solution of the Tricomi operator Tu=y(u_(x_1x_1)+u_(x_2x_2))+u_(yy)=0.(Ⅰ) It has stronger singularity than Tu=yu_(xx)+u_(yy)=0.We indicate that it is necessary to introduce the principal part of Cauchy integral to define the fundamental solution in the theory of distribution.
  • Best Proximity Point Theorems for Generalized Weak Contractive Mappings in Partially Ordered Menger PM-spaces
    Zhao Qi WU, Chuan Xi ZHU, Cheng Gui YUAN
    Acta Mathematica Sinica, Chinese Series. 2021, 64(2): 177-188. DOI: 10.12386/A2021sxxb0016
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    In this paper, some best proximity point theorems for generalized weakly contractive mappings which satisfy certain conditions by using three control functions in partially ordered Menger PM-spaces are obtained, and sufficient conditions to guarantee the uniqueness of the best proximity points are also given. Moreover, some corollaries are derived as consequences of the main results.

  • Existence Analysis of the Positive Steady-State Solutions for a Glycolysis Model
    Mei Hua WEI, Jian Hua WU
    Acta Mathematica Sinica, Chinese Series. 2011, 54(4): 553-560. DOI: 10.12386/A2011sxxb0056
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    This paper deals with a representative glycolysis model in biochemical reaction. We study the non-existence of non-constant positive steady-state solutions by using a priori estimates. A necessary condition for the existence of non-constant positive steady-state solutions is obtained. On the basis of Turing instability of constant steady-state solutions, the degree theory is combined with a priori estimates to give a sufficient condition for the existence of non-constant positive steady-state solutions.  
  • A Fundamental Inequality of the Theory of Meromorphic Function and Its Applications
    Jian Ping WANG(1), Hong Xun YI
    Acta Mathematica Sinica, Chinese Series. 2006, 49(2): 443-450. DOI: 10.12386/A2006sxxb0055
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    In this paper, we first prove a fundamental inequality of the theory of meromorphic function; as one of its applications, we then study the value distribution problem which is closely related to a theorem of Hayman and prove that if f is a transcendental meromorphic function all of whose zeros have multiplicities at least κ, then the function of the form ff(κ) assumes every finite nonzero value infinitely often, except for at most three positive integers k with 2≤κ≤4.
  • Computation of Topological Degree and Applications
    Zhi Lin YANG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(2): 275-280. DOI: 10.12386/A2005sxxb0032
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    In this paper, we compute, by using cone theory, the topological degree of a class of completely continuous fields where the condition on the lower boundedness of nonlinear operators is sharply weakened. Therefore our results substantially improve and generalize the existing ones in the literature. Finally we use our abstract results to establish the existence of nontrivial solutions for superlinear Hammerstein integral equations.
  • Normality Criteria and Multiple Values
    Yan XU, Jian Ming CHANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 265-270. DOI: 10.12386/A2011sxxb0027
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    Let F be a family of meromorphic functions defined in a domain D, let ψ ( 0) be a holomorphic function in D, and k be a positive integer. If, for every f ∈ F, f ≠ 0, f(k) ≠ 0 and all zeros of f(k)(z) - ψ(z) have multiplicities at least (k + 2)/k, then F is normal in D.  
  • On the Infinite Sum of Reciprocal Fibonacci Numbers
    Ting Ting WANG
    Acta Mathematica Sinica, Chinese Series. 2012, 55(3): 517-524. DOI: 10.12386/A2012sxxb0048
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    We use the elementary method and the properties of the floor function to study the infinite sums derived from the reciprocals of the cubic of the Fibonacci numbers, and give a new and interesting identity involving the reciprocals of this sums.
  • A Generalization of the Bernfeld-Haddock Conjecture and Its Proof
    Tai Shan YI Li; Hong HUANG
    Acta Mathematica Sinica, Chinese Series. 2007, 50(2): 261-270. DOI: 10.12386/A2007sxxb0031
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    In this paper,we study the convergence of solutions of a class of delay differ- ential equations.These equations have important practical applications and generalize those on which Bernfeld and Haddock conjectured that each solution of the equations tends.to a constant.We first give an example to point out the errors in several existing works on the convergence of solutions of the equations as well as their generalizations. Then we confirm the Bernfeld-Haddock conjecture under weaker conditions.Our re- sult corrects and improves the existing ones.An appendix by Professor Tongren Ding is also given to correct the mistakes in one of his works.
  • The Boundary Behavior of Isotonic Cauchy Type Integral in Clifford Analysis
    Min KU, Jin Yuan DU, Dao Shun WANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 177-186. DOI: 10.12386/A2011sxxb0019
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    The holomorphic functions of several complex variables are closely related to the so-called isotonic Dirac system in which different Dirac operators in the half dimension act from the left and from the right on the functions considered. In this paper we mainly study the boundary properties of the isotonic Cauchy type integral operator over the smooth surface in Euclidean space of even dimension with values in a complex Clifford algebra. We obtain Privalov theorem inducing Sokhotskii-Plemelj formula as the special case for the isotonic Cauchy type integral operator with Hölder density functions taking values in a complex Clifford algebra, and show that Privalov theorem of the classical Bochner-Martinelli type integral and the classical Sokhotskii- Plemelj formula over the smooth surface of Euclidean space for holomorphic functions of several complex variables may be derived from it.

     

  • Maximal Commutators for Multilinear Singular Integrals with Non-Smooth Kernels
    Xiao Li CHEN, Jie Cheng CHEN
    Acta Mathematica Sinica, Chinese Series. 2011, 54(4): 529-540. DOI: 10.12386/A2011sxxb0054
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    This paper is concerned with the Cotlar’s inequality for the maximal commutators of the m-linear Calderón-Zygmund operator with non-smooth kernels and the weighted norm inequalities for the commutators and the maximal commutators of multilinear singular integrals are established.  
  • Regular Semigroups with Regular *-Transversals
    Shou Feng WANG, Di ZHANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(4): 591-600. DOI: 10.12386/A2011sxxb0060
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    In this paper, some remarkable properties of regular semigroups with a regular *-transversal are given. A construction method of a regular semigroup with a quasi-ideal regular *-transversal is obtained. Furthermore, congruences on this class of semigroups are also considered by applying our structure theorem.  
  • Uniqueness Theorems of Meromorphic Functions Sharing Sets IM on Annuli
    Ting Bin CAO, Hong Xun YI
    Acta Mathematica Sinica, Chinese Series. 2011, 54(4): 623-632. DOI: 10.12386/A2011sxxb0064
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    The main purpose of this paper is to deal with the uniqueness problem for meromorphic functions on annuli. We obtain two general uniqueness theorems of meromorphic functions sharing sets from which an analog of Nevanlinna’s famous five-value theorem is proposed.  
  • The Representation of the Total Variation and the Metric Derivative for Fuzzy Bounded Variation Functions
    Zeng Tai GONG, Yu Juan BAI
    Acta Mathematica Sinica, Chinese Series. 2011, 54(4): 633-642. DOI: 10.12386/A2011sxxb0065
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    The metric derivative of the fuzzy-number-valued functions and the representation of the total variation for the fuzzy-number-valued function which is of bounded variation are defined and discussed. It is proved that the fuzzy absolutely continuous functions are metrically differentiable almost everywhere, and the integration of its metric derivative equals to the total variation of the primitive. Finally, the representation of the total variation for the fuzzy-number-valued functions which is of bounded variation is given.  
  • Von Koch Curve and Its Fractional Calculus
    Yong Shun LIANG, Wei Yi SU
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 227-240. DOI: 10.12386/A2011sxxb0024
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    An analytic expression of von Koch curve has been given. Based on this complex-valued function, we give estimation of fractal dimension of its fractional calculus. Graphs of Weyl-Marchaud fractional derivative of this function have been given. Such function can also be transferred into certain self-affine fractal function. Finally, we set up the linear connection between fractal dimension of this function and order of fractional calculus. Graphs and numerical results of certain examples have been shown.

     

  • The Invariant Subspaces of the Sobolev Disk Algebra
    Rui Fang ZHAO; Yong-fei Jin
    Acta Mathematica Sinica, Chinese Series. 2008, 51(3): 617-624. DOI: 10.12386/A2008sxxb0073
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    We study the invariant subspaces of the operator M_z on the Sobolev disk algebra R(D).First,we study the multiplication operator M_z restricted to the invariant subspace.Then we show that M_z restricted to one invariant subspace is unitarily equivalent to M_z restricted to another invariant subspace if and only if the two invariant subspaces are equal.We also characterize the invariant subspaces with common zeros on the boundary of the disk.
  • Global Well-posedness and Analyticity for the Generalized Rotating Navier-Stokes Equations
    Wei Hua WANG
    Acta Mathematica Sinica, Chinese Series. 2020, 63(5): 417-426. DOI: 10.12386/A2020sxxb0036
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    We establish the global well-posedness and analyticity of mild solution to the generalized three-dimensional incompressible Navier–Stokes equations for rotating fluids if the initial data are in Fourier–Herz spaces ?q1-2α (R3) under appropriate conditions for α and q. As corollaries, we also give the corresponding conclusions of the generalized Navier–Stokes equation.

  • Uniqueness of Meromorphic Functions in the Unit Disc Sharing Small Functions in One Angular Domain
    Hui Fang LIU, Dao Chun SUN
    Acta Mathematica Sinica, Chinese Series. 2010, 53(4): 663-674. DOI: 10.12386/A2010sxxb0074
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    In this paper, it is shown that two admissible meromorphic functions in the unit disc must be identical, provided that they share five small functions CM or five values IM in one angular domain.

  • Strong Convergence Theorems of the Modified Reich-Takahashi Iteration Method in Banach Spaces
    Liu Chuan ZENG
    Acta Mathematica Sinica, Chinese Series. 2005, 48(3): 417-426. DOI: 10.12386/A2005sxxb0051
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    Let E be a real Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Let D be a nonempty bounded closed convex subset of E and T : D → D be an asymptotically nonexpansive mapping. It is shown that under some suitable conditions, the sequence {xn} defined by the modified Reich-Takahashi iteration method (1.2) converges strongly to a fixed point of T, where x0 is any given point in D, and {αn}, {β} are real sequences in [0,1] with some restrictions.
  • Unitary Equivalence of Submodules and Stable Isomorphism of Corresponding Hereditary C*-Subalgebras
    Lun Chuan ZHANG, Mao Zheng GUO
    Acta Mathematica Sinica, Chinese Series. 2010, 53(6): 1041-1044. DOI: 10.12386/A2010sxxb0116
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    We obtain a Stone type theorem under the frame of Hilbert C*-module, such that the classical Stone theorem is our special case.

  • On Operators with Uniform Descent
    Jian Lan CHEN, Qiao Fen JIANG, Huai Jie ZHONG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(4): 625-634. DOI: 10.12386/A2010sxxb0070
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    We discuss the communicative quasinilpotent perturbation of operators with topological uniform descent: we obtain a counterexample to show that this kind of perturbation isn't stable; and we get the relations between super-ranges and super-kernels of operators with topological uniform descent and their perturbation; by means of these relations, we show that the communicative nilpotent perturbation of left (right) Drazin invertible operators is stable. At last, we also discuss the Ri-type Kato decomposition and Ri-type super-Kato decomposition of operators in the B-regularities BRi(1≤i≤13) on Banach spaces.

     

  • The Automorphism Group of a Generalized Extraspecial p-Group (II)
    Yu Lei WANG, He Guo LIU
    Acta Mathematica Sinica, Chinese Series. 2011, 54(4): 651-658. DOI: 10.12386/A2011sxxb0067
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    In this paper, the automorphism group of a generalized extraspecial p-group G is determined again, where p is a prime number. Assume that |G| = p2n+m and |ζG| = pm, where n ≥ 1 and m ≥ 2. Let AutcG be the normal subgroup of AutG consisting of all elements of AutG which act trivially on ζG. Then
    (i) If p is odd, then AutG = 〈θ〉  AutcG, where θ is of order (p - 1)pm-1; If p = 2, then AutG = 〈θ1, θ2〉 AutcG, where 〈θ1, θ2〉 = 〈θ1〉 × 〈θ2〉 Z2m-2 × Z2.
    (ii) If the exponent of G is equal to pm, then AutcG/InnG Sp(2n, p).
    (iii) If the exponent of G is equal to pm+1, then AutcG/InnG K Sp(2n - 2, p), where K is an extraspecial p-group of order p2n-1 (If p is odd) or an elementary abelian 2-group of order 22n-1. In particular, AutcG/InnG Zp when n = 1. 
  • Fredholm Perturbation of Spectra of 2 × 2-Upper Triangular Matrices
    Shi Fang ZHANG, Huai Jie ZHONG, Jun De WU
    Acta Mathematica Sinica, Chinese Series. 2011, 54(4): 581-590. DOI: 10.12386/A2011sxxb0059
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    Let H and K be complex infinite dimensional separable Hilbert spaces, A ∈ B(H), B ∈ B(K), C ∈ B(K,H) and MC = (0ABC). In this paper, we characterize completely the Fredholm perturbation for the Weyl spectrum, essential spectrum, spectrum, left spectrum, right spectrum, lower semi-Fredholm spectrum, lower semi-Weyl spectrum and upper semi-Weyl spectrum of the upper triangular operator matrices MC.  
  • The Fixed Point Theorem of Convex-Power Condensing Operator and Applications to Abstract Semilinear Evolution Equations
    Jing Xian SUN(1), Xiao Yan ZHA
    Acta Mathematica Sinica, Chinese Series. 2005, 48(3): 439-446. DOI: 10.12386/A2005sxxb0053
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    We give the definition of a kind of new operator-convex-power condensing operator for the need of applied questions and generalize the definition of condensing operator. The fixed point theorem of this kind of new operator is proved. This generalizes the famous Schauder fixed point theorem and Sadovskii fixed point theorem. As applications, the existence of global mild solutions and positive mild solutions of initial value problem for a class of semilinear evolution equations with noncompact semigroup in Banach spaces is obtained.
  • Non-commutative Poisson Algebra Structures on Extended Affine Lie Algebras
    Jie TONG, Quan Qin JIN
    Acta Mathematica Sinica, Chinese Series. 2011, 54(4): 561-570. DOI: 10.12386/A2011sxxb0057
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    Non-commutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In the paper, the non-commutative poisson algebra structures on extended affine Lie algebras are determined.  
  • Positive Solutions of Non-Positone Nonlinear Operator Equations and Its Applications
    Jing Xian SUN, Xi An XU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 55-64. DOI: 10.12386/A2012sxxb0005
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    In this paper, firstly some existence results for unbounded connected component of solutions set of some nonlinear operator equations with parameter be obtained by using the global bifurcation theories, and then some existence results for positive solutions of a non-positone operator equation be obtained by using the positive connected property of the operator. The main results can be applied to various of differential boundary value problems to obtain the existence results for positive solutions without the assumption that the nonlinear terms are positone.  
  • The Minimal Signless Lapacian Spectral Radius of Graphs with Diameter n - 4
    Xiao Li WU, Jing Jing JIANG, Ji Ming GUO, Shang Wang TAN
    Acta Mathematica Sinica, Chinese Series. 2011, 54(4): 601-608. DOI: 10.12386/A2011sxxb0061
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    In the paper [The minimal Lapacian spectral radius of trees with a given diameter, Theoretical Computer Science 410: 78-83], Liu, Lu and Shu (2009) determine the trees with minimal Lapacian spectral radii for the diameter belongs to {1, 2, 3, 4, n - 3, n - 2, n - 1}, respectively. This paper gives the unique graph with minimal signless Lapacian spectral radius among graphs with diameter n - 4. Furthermore as a corollary, we determine the tree with minimal Lapacian spectral radius among trees with diameter n - 4.  
  • Trigonometric Series with Piecewise Bounded Variation Coefficients
    Song Ping ZHOU(1); Dan Sheng YU2); Ping ZHOU(2)
    Acta Mathematica Sinica, Chinese Series. 2008, 51(4): 633-646. DOI: 10.12386/A2008sxxb0075
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    We generalize some classical results in convergence and integrability for the trigonometric series with non-negative coefficients to the series with varying coefficients (they may change signs),by introducing the so-called piecewise bounded variation sequences (PBVS).
  • The Regular Cryptogroup Construction and Congruence of a Rees Matrix Semigroup over a Clifford Semigroup with Identity
    Hong Wei LI
    Acta Mathematica Sinica, Chinese Series. 2011, 54(2): 195-210. DOI: 10.12386/A2011sxxb0021
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    We investigate the regular cryptogroup construction of the Rees matrix semigroup over a Clifford semigroup with identity; secondly prove that the two conditions are equivalent on a Rees matrix semigroup S over a Clifford semigroup with identity: (1) the congruence ρ of S is a completely simple semigroup congruence; (2) there is an order-preserving bijection from the congruences of S to the admissible triples of S; finally prove that the lattice of completely simple congruences on a Rees semigroup over a Clifford semigroup with identity is semimodular.

     

  • On an Extension of Hardy--Hilbert's Inequality
    Wei Guo GONG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(4): 635-642. DOI: 10.12386/A2010sxxb0071
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    This paper deals with an extension of Hardy--Hilbert's inequality with a best constant factor by using the method of weight coefficient, and also considers its particular results.

  • Global Attractors for Schrödinger Equation Arising in Nonlinear Optics
    Rui Feng ZHANG, Bian Min KOU
    Acta Mathematica Sinica, Chinese Series. 2012, 55(1): 17-26. DOI: 10.12386/A2012sxxb0002
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    We study a nonlinear Schrödinger equation modeling light waves propagating in a photorefractive crystal. We first construct the global weak attractor for this system. And then by exact analysis of the energy equation, we show that the global weak attractor is actually the global strong attractor. Further, we give the upper bound of the fractal and Hausdorff dimensions of the global attractor.  
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