15 June 1998, Volume 41 Issue 6

    

• Select all
  |

论文
• Select
  Representation of Congruences on Regular Semigroups with Inverse Transversals

  Li Min WANG(1);Xi Lin TANG(2)

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0174

  Abstract ( )   Knowledge map   Save

  For a regular semigroup with an inverse transversal S0, we have Saito's structure W(I, S°, A, *, α, β). We represented congruences on this kind of semigroups by the so called congruence assemblage abstractly which consist of congruences on the structure component parts I, S°and A. The structure of images of this type of semigroups is also presented.
• Select
  Counting Function Asymptotics and the Weak Weyl-Berry Conjecture for Connected Domains with Fractal Boundaries

  Hua CHEN

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0175

  Abstract ( )   Knowledge map   Save

  In this paper, we study the spectral asymptotics for connected fractal domains and Weyl-Berry conjecture. We prove, for some special connected fractal domains, the sharp estimate for second term of counting function asymptotics, which implies that the weak form of the Weyl-Berry conjecture holds for the case. Finally, we also study a naturally connected fractal domain, and we prove, in this case, the weak Weyl-Berry conjecture holds as well.
• Select
  On the Distribution of αp~3 Modulo One

  Ying Chun CAI

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0176

  Abstract ( )   Knowledge map   Save

  In this paper it is proved that the following inequality ‖αp3 -β‖ < P has infinitely many prime solutions for any irrational α and any real β, where ‖γ‖denotes the smallest distance from γ to integers. This result gives some improvement upon the previous one with the exponentdue to Baker and Harman.
• Select
  A.S. Convergence of Two-Parameter Banach Space Valued Martingales and the Radon-Nikodym Property of Banach Space

  Shi Xin GAN

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0177

  Abstract ( )   Knowledge map   Save

  In this paper, we prove that under the F4 condition, any Llog+ L bounded two-parameter Banach Space valued martingale converges almost surely to an integrable Banach Space valued random variable if and only if the Banach Space has the Radon-Nikodym property. We further prove that the above conclusion remains true if the F4 condition is replaced by the weaker local F4 condition.
• Select
  Generalization of Lawson-Hoffmann Duality

  Dong Sheng ZHAO(1);Bin ZHAO(2)

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0194

  Abstract ( )   Knowledge map   Save

  In this paper, we mainly prove that the category Of z-continuous posets is dually equivalent to a full subcategory of the category of all completely distributive lattices. Some other new properties of z-continuous posets are also investigated.
• Select
  Iterated Processes and Their Applications to Higher Order Differential Equations

  Enzo Orsingher(1);Xue Lei ZHAO

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0178

  Abstract ( )   Knowledge map   Save

  In this paper we construct models obtained by suitably combining Brownian motions and telegraphs in such a way that their transition functions satisfy. higher-order parabolic or hyperbolic equations of different types.Also equations with time-varying coefficients are dervied either considering processes endowed with drift or with suitable modifications of their structure.Finally the distribution of the maximum of the iterated Brownian motion (along with some other properties) is presented.
• Select
  Nonlinear Boundary Value Problems for Several Unknown Functions Vector in Clifford Analysis

  Sha HUANG(1);Hong Bing JIAO(1)

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0179

  Abstract ( )   Knowledge map   Save

  Letting fi(x), i = 1,..., p be function with value in a Clifford algebra An(R). we call F(x) = (f1, f2,.... fp) function vector, where f1, f2,..., fp are vector components for F(x). In this paper, by thinking of the vector-valued analysis, we discuss a four elements nonlinear boundary value problem for several unknown functions vector with shifts and conjugate and a corresponding linear boundary problem.Applying the method of integral equations and Shauder fixed-point theorem and contract mapping theorem, we prove the existence of solution for the nonlinear problem and the existence and uniqueness for the linear problem.
• Select
  The Uaited Form of the Strong Invariance and the Complete Convergence

  Li Xin ZHANG

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0180

  Abstract ( )   Knowledge map   Save

  The united form of the strong invariance and the complete convergence is established for sequences of i.i.d. random variables, and the complete convergence is studied via the strong invariance, many previous results on the strong invariance or the complete convergence are conclusions of the results obtained in this paper.
• Select
  Asymptotic Behavior of Gibbs Functions for M-band Wavelet Expansions

  Ze Yin ZHANG(1);Da Ren HUANG(1

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0181

  Abstract ( )   Knowledge map   Save

  It is given in this paper that the asympototic behavior of Gibbs function for a class of M-band wavelet expansion. In particular, the Daubechies' wavelets is included in this class.
• Select
  On the Oscillation of Second Order Linear Matrix Differential Systems

  Shao Wen ZHENG(1);Fan Wei MENG

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0182

  Abstract ( )   Knowledge map   Save

  In the present paper matrix differential system of the form (P(t)Y')' + Q(t)Y = 0, t ∈ [t0, ∞) is considered, where P,Q and Y are n x n real continuous matrix functions, p(t) and Q(t) are symmetric, and p(t) > 0, t ∈ [t0,∞). Using Riccati transformation generalized some new oscillation criteria for the system are established. The criteria obtained improve Erbe, Kong and Ruan's results in [4].
• Select
  Asymptotic Behavior of Solutions for a Class of Retarded Difference Equations

  Li Hong HUANG(1);Jian She YU(1

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0183

  Abstract ( )   Knowledge map   Save

  Consider the retarded difference equation xn-xn-1 = F(-f(xn) +g(xn-k )),where k is a positive integer, F, f, g: R→R are continuous, F and f are increasing on R, and uF(u) > 0 for all u≠0. We show that when f(y) > g(y) (resp. f(y) < g(y)) for y ∈ R, every solution of the equation tends to either a constant or-∞ (resp. ∞) as n →∞. Furthermore, if f(y) ≡ g(y) for y ∈ R, then every solution of the equation tends to a constant as n→∞.
• Select
  Positive Solutions of Singular Second Order Boundary Value Problems

  Ru Yun MA

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0184

  Abstract ( )   Knowledge map   Save

  This paper studies the nonlinear boundary value problem u″ + a(t)f(u) = 0,au(0)-αβu'(0) = 0, γu(1) + δu'(1) = 0, where a is allowed to be singular at both end pents t = 0 and t = 1 and f is either superlinear or sublinear. We show the existence of at least one positive solution of this problem.
• Select
  On Heat Kernels, Eigenvalues and Eigenfunctions of Compact Symmetric Spaces

  Yi HONG

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0185

  Abstract ( )   Knowledge map   Save

  In this paper, we study the heat kernels, eigenvalues and eigenfunctions of Lie groups and compact symmetric spaces by means of the representation theory of groups. Especially, we discuss the complex Grassmannian manifolds and the manifolds Sp(n)/U(n).
• Select
  On the Number of Solutions of the Generalized Ramanujan-Nagell Equation x~2 + D = k~n

  Xi Geng CHEN(1);Yong Dong GUO(

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0186

  Abstract ( )   Knowledge map   Save

  Let D, k be positive integers with gcd (D, k) = 1. In this paper, using some elementary methods, we prove that if D is a prime, then the equation x2 + D = kn has at most eight positive integer solutions (x, n).
• Select
  Positive Solutions of One-dimensional Singular p-Laplace Equations

  Qing Liu YAO(1);Hai Chen LU(2)

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0187

  Abstract ( )   Knowledge map   Save

  Two existence theorems about the positive solutions of the BVP for onedimensional singular P-Laplace equations (|y|p-2y')' + g(t, y) = 0, y(0) = g(1) = 0,p > 1 was established. The results are obtained by using the nonlinear alternative of Leray-Schauder and the lower-upper solution method.
• Select
  Weak Carathodory Solution of Differential Equations in Banach Spaces

  Fu Min SONG

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0188

  Abstract ( )   Knowledge map   Save

  In this paper, it presents the initial value problem of the ordinary differential equations U' = f(t, u) in general Banach spaces. We assume that f(t, u) is not continuous and only f(t, u) satisfies the weak Caratheodory condition, we proved, however,that the solution of the initial value problem can be obtained by the uniformly limit of the iterative sequences. The error estimate of the iterative sequences of approximation solution is given. And also we have obtained the similar result to the periodic boundary value problem.
• Select
  On the Existence and Blow-up Problem of Solution for Initial Problem of Semilinear Heat Equation with Singular Coefficient

  Su Wen Jian(1); Feng Zao YANG(

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0189

  Abstract ( )   Knowledge map   Save

  In this paper, we study the following initial problem whereγ> 1, σ> 0. f(x) is continuous, bounded, uonnegative, and not identically zero real function.We study the existence of nonnegative local solution and global nonexistence of nonnegative solution for the problem(1), (2). We prove nonexistence of nonnegative global solution when 0<σ<1 and; or σ=1 and ; or σ>1.
• Select
  Solvability of Elliptic Boundary Value Problems without the Standard Landesman-Lazer Condition

  Zhi Qing HAN

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0193

  Abstract ( )   Knowledge map   Save

  In this paper we prove a very general result concerning solvability of the resonant problem: △n + λku + g(x,u) = h(x); u = 0, x ∈ αΩ, which immediately gives three generalized Landesman-Lazer conditions. The most interesting application of the general result is concerned with the problem as λk = λ1, in which case we prove solvability results for it under conditions which are not the standard Landesman-Lazer condition or only partly enjoy it. Furthermore, we propose a new sign condition and give a comprehensive extension of a main result of Figueiredo and Ni.
• Select
  Asymptotic Expansion in Lp Norm for Multivariate Kantorovich Operators

  Chun Gou ZHANG

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0190

  Abstract ( )   Knowledge map   Save

  In this paper, a high order asymptotic expansion is given in Lp norm (1
• Select
  Global Asymptotic Stability of Nonautonomous Mathematical Ecological Equations with Distributed Deviating Arguments

  Jiao Wan LUO(1);Jian She YU(2)

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0191

  Abstract ( )   Knowledge map   Save

  In the present paper, we study the global asymptotic stability of the zero solution of the nonautonomous differential equation with distributed deviating arguments x'(t) = -g(t, x(t)) - f(t, x(t +s)du(s)) which includes manymathematical ecological equations. Our results generalize and improve the corresponding results given in some known literatures.
• Select
  The Functor ()°of Dual Comodules and Coreflexive Comodules

  Zhi Feng Hao(1);Liang Gui FENG

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0192

  Abstract ( )   Knowledge map   Save

  In this paper we show the structure of dual comodule M0. We proof that the contravariant functor ()° is left exactness. We also introduce the coreflexive comodule to investigate the coreflexive coalgebras. Then we study some homological properties for corefiexive coalgebras. Finally let char (F) = 0 and C = F[x1, x2,...,xn]°, we show that every finitely cogenerated injective right C-comodules in cofree.
• Select
  Commuting Involutions with Fixed Point Set of Constant Codimension

  Yan Ying WANG(1);Zhen De WU(1)

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0195

  Abstract ( )   Knowledge map   Save

  Special generators of the unoriented cobordism ring MO. are constructed to determine the groups J of n-dimensional cobordism classes in MOn containing a representative Mn admitting a (Z2 )k -action with fixed point set of constant codimension.
• Select
  Weak Galois Extensions and Opposite Smash Products

  Hui Xiang CHEN

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0196

  Abstract ( )   Knowledge map   Save

  In this paper, we discuss the weak Galois extension for any (H, K) -comodule algebra A, and prove that any free quadratic extension of k is a weak Galois extension. Then we discuss the projectivity of A, Galios extensions and their transitivity by using the Morita relation bewteen the opposite smash product #op(K, A) and the K-coinvariant subalgebra C.
• Select
  Well-posedness of the Cauchy Problem for the Coupled System of the Schrdinger-KdV Equations

  Bo Ling GUO(1);Chang Xing MIAO

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0197

  Abstract ( )   Knowledge map   Save

  This paper is devoted to the study of the Cauchy problem for the coupled system of the Schrodinger-KdV equations which describes the nonlinear dynamics of the one-dimensional Langmuir and ion-acoustic waves. Global well-posedness of the problem is established in the space Hk x Hk (k ∈ Z+), the first and second component of which correspond to the electric field of the Langmuir oscillations and low-frequency density perturbation respectively.
• Select
  Problems in Homoclinic Bifurcation with Higher Dimensions

  De Ming ZHU

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0198

  Abstract ( )   Knowledge map   Save

  In this paper, a suitable normal coordinate system is constructed by using exponential dichotomies and generalizing the Floquet method from periodic systems to nonperiodic systems. Then the Poincare map is established to solve various problems in homoclinic bifurcations with codimension one or two. Bifurcation diagrams and bifurcation curves are given.
• Select
  Fixed Point Theorems of Mixed Monotone Operators and Its Applications

  Zhi Tao ZHANG

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0200

  Abstract ( )   Knowledge map   Save

  In this paper, we use partial order theory to study mixed monotone operators,and get existence and uniqueness of fixed point without assuming the operator to be compact or continuous. And apply the new results to Hammerstain integral equations on RN.
• Select
  On the Number of Fair Triangulations

  Han REN(1);Yan Pei LIU(1)

  Acta Mathematica Sinica, Chinese Series. 1998, 41(6): 0-0+0. https://doi.org/10.12386/A1998sxxb0199

  Abstract ( )   Knowledge map   Save

  In this paper a special kind of triangulated maps on the sphere called fair triangulations were enumerated with the size of maps as parameter. Moreover, the number of several other kinds of triangulations was found.