中国科学院数学与系统科学研究院期刊网

15 September 2006, Volume 49 Issue 5
    

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  • Lan Zhe LIU(1); Shan Zhen LU(2
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 961-972. https://doi.org/10.12386/A2006sxxb0119
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    In this paper, we prove the endpoint boundedness for some multilinear operators related to certain non-convolution operators. The operators include Littlewood-Paley operator and Marcinkiewiecz operator.
  • Dong Xiang CHEN; Jie Cheng CHE
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 973-984. https://doi.org/10.12386/A2006sxxb0120
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    In this paper, the authors consider the commutators of fractional integrals defined by , where Kα(x,y) = d(x, y)α-1,m∈N and b(x) belongs to BMO(X,μ). We prove that Iα,bm maps the Orlicz space L(log L)m(X) into weak Lq(X), and so does the fractional maximal commutator Mα,bm.
  • Chang Yu LU(1); Jian Hong WU(2
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 985-988. https://doi.org/10.12386/A2006sxxb0121
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    This paper studies the influence ofβ0 which is the center of an ellipse to the admissibility of linear estimator in the situation of an incomplete non-central ellipsoidal restriction (β-β0)'N(β-β0)≤σ2,N≥0 in linear model (Y,Xβ,σ2V,V≥0). The results show that the class of admissible linear estimators with incomplete non-central ellipsoidal restriction of (β-β1)'N(β-β1)≤σ2,N≥0 is the same as the one with the restriction of (β-β2)'N(β-β2)≤σ2,N≥0 forβ1 andβ2 with certain structure.
  • Zong Xuan CHEN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 989-998. https://doi.org/10.12386/A2006sxxb0122
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    In this paper we investigate the problems on the hyper-order, the e-type order, the dependence relation of solutions for a class of higher order linear differential equations with periodic coefficients, and obtain some relations between e-type order and hyper-order, and precise relations between the two orders and coefficients. In this paper, using e-type order to estimate the growth of solutions of the equations is the first, the estimation is more precise than that using the order or the hyper-order.
  • Hua Ning LIU; Wen Peng ZHANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 999-100. https://doi.org/10.12386/A2006sxxb0123
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    In this paper, the generalized Dedekind sums and Hardy sums are defined. The arithmetic properties of the generalized Dedekind sums are studied, and the generalized Hardy sums are expressed in terms of the generalized Dedekind sums. Finally, the generalized Subrahmanyam's identities and Knopp's theorems are given and proved.
  • Zhe Feng XU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1009-101. https://doi.org/10.12386/A2006sxxb0124
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    Given a positive integer n, the definition of the famous Smarandache function is: S(n) = min{m : m∈N, n|m!}. The main purpose of this paper is to study the value distribution of the Smarandache function by using the elementary method, and give some interesting asymptotic formulae.
  • Wen Xiang WANG; Zu He SHEN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1013-102. https://doi.org/10.12386/A2006sxxb0125
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    By using the concept of Basin of Attraction as a main tool of our explosion in discussing the diffeomorphisms between Banach spaces, we change it into discussing the existence and finiteness of nonnegative solution of the scalar differential equation. In Section 2, an extension of the famous Hadamard-Levy theorem is given. In Section 3 and Section 4, the theorem is applied to interval analysis and differential equation respectively. The results of this paper generalize some existing theorems.
  • Wei CAO; Qi SUN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1021-102. https://doi.org/10.12386/A2006sxxb0126
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    Let I(d1,…,dn) denote the number of solutions of the equation∑i=1n xi/di≡0(mod 1),1≤xi≤di-1. If I(d1,…,dn)>0, let L(d1,…,dn) denote the least integer represented by∑i=1n xi/di(1≤xi≤di-1).I(d1,…,dn),L(d1,…,dn) and their estimations play an important role in studying the diagonal equations over the finite fields. This paper gives some sufficient conditions for whereωi=gcd(di, lcm[dj:j≠i])for i=1,...,n.
  • Dao Cun SUN; Zong Sheng GAO
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1027-103. https://doi.org/10.12386/A2006sxxb0127
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    In this paper, we define the addition of algebroidal functions, and investigate its operation. Furthermore, we extend the Yi Hongxun's uniqueness theorems of meromorphic functions with multiple values to the algebroidal functions by using our results in combination with Yang Lo's method.
  • Yan ZHENG; Li Shan LIU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1033-103. https://doi.org/10.12386/A2006sxxb0128
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    Using the cone and monotone iterative theory, the existence and uniqueness of solutions for three classes of systems of two binary operator equations in Banach space are discussed, and the error estimations for the convergent iterative sequence are also given. As a generalization, the solutions for some classes of n variable operator equations are also discussed.
  • Biao FANG; Jin Hua FEI; Ming Y
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1039-104. https://doi.org/10.12386/A2006sxxb0129
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    In this paper, we consider the following conjecture on Euler numbers: p≡1 mod 4, E(p-1)/2 (?) 0 mod p for any prime p. The conjecture has been proved true by using the properties of Euler numbers and Fourier series applied to Gauss sums.
  • Zhan Bing BAI(1); Wei Gao GE(2
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1045-105. https://doi.org/10.12386/A2006sxxb0130
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    We consider the boundary value problem:((?)p(x'(t)))'+q(t)f(t,x(t),x'(t))=0,P>1,t∈[0,1],with x(0)=x(1)=0 or x(0)=x'(1)=0. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The key point here is that the nonlinear term f is dependent on the first order derivative. An example is that also included to illustrate the importance of the results obtained.
  • Li HONG; Wei Min WANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1053-106. https://doi.org/10.12386/A2006sxxb0131
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    This paper treats of the second order semilinear elliptic system of the form -Δu=f1(v),-Δv=f2(u),x∈Rn(n≥3). Under the assumptions of fi(i=1,2), we obtain a Liouville-type theorem of this system.
  • Ping Yan CHEN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1061-106. https://doi.org/10.12386/A2006sxxb0132
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    Let {X,Xn,n≥0} be a sequence of pairwise independent identically distributed random variables, 11. In order to prove this result, the paper discusses the convergent rate of Cesaro strong law of large number for the sequence of pairwise negative correlational random variables and its is interested. The result also holds for identically distributed pairwise NQD sequences.
  • Yi Cheng LIU; Zhi Xiang LI
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1067-107. https://doi.org/10.12386/A2006sxxb0133
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    Several fixed point theorems for contraction type mapping are obtained in this paper, which generalize and improve the corresponding results in [1-5]. As an application, some existence results of positive almost periodic solutions for delay integral equations are obtained, which generalize the existing results.
  • Ying Chun JIANG(1); You Ming L
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1075-108. https://doi.org/10.12386/A2006sxxb0134
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    This paper studies the completeness of orthogonal wavelet systems in (?)2(Z), the main purpose is to find some easily checked sufficient conditions. To do that, the construction for p stage wavelet bases is firstly revisited; then a characterization for a wavelet system to be complete is shown, which improves Frazier's theorem, three sufficient conditions are finally received from that characterization.
  • Zong Guang LIU; Zun Wei FU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1085-109. https://doi.org/10.12386/A2006sxxb0135
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    In this note, the authors obtain some necessary and sufficient conditions for the weighted Hardy-Littlewood average operator, Uψ, to be bounded on Herz spaces Kqα,p(Rn), and give some estimates for the corresponding operator norms.
  • Yun Ge XU; Yuan Chen
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1091-109. https://doi.org/10.12386/A2006sxxb0136
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    Let Aq-k/(x2,xy + qyx,y2) be the generalized exterior algebra in two variables. Based the minimal projective bimodular resolution constructed by Buchweitz et al, the dimensions of all Hochschild homology groups of Aq are calculated explicitly.
  • Hong Ke DU; Chun Yuan DENG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1099-111. https://doi.org/10.12386/A2006sxxb0137
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    Suppose that U and V are two subspaces of a Hilbert space H. If there exists a subspace L such that L+ U=H, L+V=H and L∩U=L∩V= {0}, then L is said to be a common complement of U and V. In this paper, some new characteristics of common complements of two subspaces are obtained. Meanwhile, a necessary and sufficient condition for the equation H=[U∩(U⊥+ V⊥)]⊕[V⊕(U⊥∩V⊥)] to hold is given, which it is a complete answer to GroB's question.
  • Lv Ping CHEN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1113-112. https://doi.org/10.12386/A2006sxxb0138
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    In this paper, we obtain an integral representation of extensional Bochner-Martinelli kernel with weight factors of (0, q) differential form on bounded domains and strongly pseudoconvex domain with piecewise smooth boundary in Cn, that is, we obtain an extensional Koppelman-Leray-Norguet formula with weight factors. Then we obtain the weighted continuous solution of (?)-equation on bounded domains. Because of the introduction of weight factors, the applications of integral formula (such as the application of interpolation problem) are much more flexible.
  • Bi Cheng YANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1121-112. https://doi.org/10.12386/A2006sxxb0139
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    In this paper, by introducing some parameters and estimating the weight coefficient, we give a generalization of Hilbert's double series inequality with a best constant factor, which involves theβfunction. As its applications, we consider the equivalent form and some particular results.
  • Shu Feng YUAN(1); Gang Song LE
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1127-113. https://doi.org/10.12386/A2006sxxb0140
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    In this paper, we give a dual quermassintegral version of Busemann-Petty problem in Geometric convexity, and extend the Funk's section theorem to the dual quermassintegral.
  • Yu Feng ZHANG(1); Qing You YAN
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1133-114. https://doi.org/10.12386/A2006sxxb0141
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    A new loop algebra with 7 dimensions is constructed, which is devoted to two known Liouville integrable hierarchies. From which, the resulting four expanded integrable models are obtained by making use of Tu scheme and the definition of integrable couplings. In addition, the nonisospectral flows of one of the above known hierarchies are given by the use of Ma scheme.
  • Fei HE; De LIU; Yang Ming
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1145-115. https://doi.org/10.12386/A2006sxxb0142
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    In this paper, Drop theorem, Phelps' lemma, Ekeland's principle and Pareto efficiency theorem due to Isac are generalized to locally complete locally convex Hausdorff spaces. And the equivalence of these theorems is proved.
  • Wei JIANG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1153-116. https://doi.org/10.12386/A2006sxxb0143
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    In this paper, we discuss the nonlinear singular delay differential control systems. Firstly we give variation formula for first variation systems of nonlinear singular delay differential control systems, then for the function-controllability of first variation systems of nonlinear singular delay differential control systems, we give some criteria, and finally we give the criteria for the function-controllability of nonlinear singular delay differential control systems.
  • Shan Chao YANG(1); Yong Ming L
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1163-117. https://doi.org/10.12386/A2006sxxb0144
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    In this paper, we discuss the uniformly asymptotic normality of the weighted function estimate of the fixed design regression model for strong mixing samples. We give the rates of the uniformly asymptotic normality. The rate is near n-1/6.
  • Xue Ping WANG; Xiao Bing QU
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1171-118. https://doi.org/10.12386/A2006sxxb0145
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    In this paper, we first introduce a concept of continuous join-irreducible element (which is join-irreducible but not completely join-irreducible) in lattices and discuss some of its properties. Then we use the properties to describe the solution set of fuzzy relational equation A☉X = b (where both A=(aj)j∈J and b are known, b is a continuous join-irreducible element, X=(xj)j∈JT is unknown, "☉" represents "sup-inf", J is an infinite set) on complete Brouwerian lattices. First, we give a necessary and sufficient condition for the existence of attainable solutions (resp. unattainable solutions) and some properties of attainable solutions (resp. unattainable solutions). Then we describe further the solution set of fuzzy relational equations.
  • De Yu ZHANG; Wen Guang ZHAI
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1181-118. https://doi.org/10.12386/A2006sxxb0146
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    Letρ3(n)=∑n=|m|3-|l|3,(m,l)=1 1.In this paper we study the sum R3(x)=∑n≤xρ3(n)=A3x2/3+B3x1/2+E3(x), and we shall prove that if the Riemman Hypothesis (RH) is true, then E3(x)=O(x4/15+ε), which improves the previous result.
  • Yang Ming; Yong HE
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1189-119. https://doi.org/10.12386/A2006sxxb0147
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    Let 5 be a semigroup, and let B be a bi-ideal of 5 (i.e., B is a subsemigroup of 5 satisfying the condition that BSB(?)B). Then B is called a prime bi-ideal of 5 if, for any bi-ideals C, D of S, CD C B implies that either C(?)B or D(?)B. A band K is called a quasi-chain if it is a N-covered pure LR-band. We prove that all bi-ideals of S are prime if and only if it is an orthogroup whose idempotents form a quasi-chain.
  • Qin DENG
    Acta Mathematica Sinica, Chinese Series. 2006, 49(5): 1195-120. https://doi.org/10.12386/A2006sxxb0148
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    This paper studies the relative growth of adjacent coefficients of a univalent function. For the function f(z)∈S, 0<λ<1,when f is Bazilevic function, we obtain the exact estimate for the order of ||Dn+1|- |Dn||.