中国科学院数学与系统科学研究院期刊网

15 November 2004, Volume 47 Issue 6
    

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  • Riemann Type Integrals on Compact Hausdorff Measure Spaces
    Guo Jun WANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1041-105. https://doi.org/10.12386/A2004sxxb0130
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    The theory of Riemann type integrals is established on compact Hausdorff measure spaces. It is proved that a function is Riemann integrable if and only if it is continuous almost everywhere. The concept of computability of Riemann integrals is proposed and it is proved that Riemann integrals are computable if and only if the spaces are metrizable.
  • On the Optimal Values for Inequalities Involving Power Means
    Wan Lan WANG(1), Jia Jin WEN(1
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1053-106. https://doi.org/10.12386/A2004sxxb0131
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    Let Mn[r] (a) be the r-th power mean of a, O <α<θ<β. Then the largest number λ, satisfying [Mn[α](a)]1-λ[Mn[β](a)]λ≤Mn[θ](a), is λ≥{1+ (β-θ)/[m(θ-α)]}-1, where m = min{[2 + (n - 2)tβ]/[2 + (n - 2)tα], t∈ R++}; the smallest number λ, satisfying the reverse inequality, is λ= [β(θ-α)]/[θ(β-α)]. The method depends on the theory of majorization and analytic techniques. The optimality idea of establish-ing inequalities is displayed as many times as possible. As some applications, several inequalities (including improved Hardy's inequality) involving sums, integrals and ma-trices are obtained.
  • Absolute Stability of Lurie Indirect Control Systems with Multiple Variable Delays
    Mu Hua CHEN(1), Zhi Hong GUAN(
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1063-107. https://doi.org/10.12386/A2004sxxb0132
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    In this paper, by applying the properties of M-matrix and using the appropri-ate Lyapunov function, new delay-dependent/delay-independent sufficient conditions for absolute stability of Lurie-type indirect control systems with multiple variable de-lays are derived. Our results generalize and improve the existing ones.
  • On the Approximation by Reciprocals of Polynomials with Positive Coefficientes in L~1 Spaces
    Xue Feng MEI(1), Song Ping ZHO
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1071-107. https://doi.org/10.12386/A2004sxxb0133
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    The present paper investigates approximation by reciprocals of polynomials with positive coefficients in L[0,1]1, space and proves that if f(x)∈L[0,1]1, f(x)≥0, f(x)(?)0, then there exists a qn(x)∈Πn(+) such that ||f-1/qn||L1≤Cω(f,n-1/2)L1, where Πn(+) indicates all polynomials of degree n with positive coefficients.
  • Greedy Algorithm for Besov Classes
    He Ping WANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1079-108. https://doi.org/10.12386/A2004sxxb0134
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    The best m-term approximation of Besov classes MBpr,θ with respect to the tensor product periodic wavelet basis Wd is discussed. We prove that the orders of the best m-term approximation can be achieved by a simple greedy algoritmu.
  • On the Construction of Triadic Symmetric Bi-Orthogonal Wavelets with Pre-Assigned Fundamental Scaling Function
    Jian Wei WANG(1), Ze Yin ZHANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1089-109. https://doi.org/10.12386/A2004sxxb0135
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    In this paper, a design method of triadic bi-orthogonal symmetric wavelets is proposed. If both dual scaling function and scaling function are compact support, symmetric and interpolatory, then they are type-1 symmetric. And the general for-mulas of compact support dual scaling functions are given. The method of frequency optimization is brought forward to design scaling function and wavelet functions. It can be formulated as linear constrained minimization problem, which can be solved through Lagrange's method of multipliers.
  • Oscillation and Nonoscillation of Solutions of Second Order Damped Elliptic Differential Equations
    Zhi Ting XU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1099-110. https://doi.org/10.12386/A2004sxxb0136
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    By using Riccati technique, some necessary conditions are established for nonoscillation of solution of second order damped elliptic differential equation ∑i,j=1N. Di[aij(x)Djy] +∑i=1N bi(x)Diy + q(x)f(y)=0. Using these results, we obtain some oscillation criteria for the above equation.
  • Regularity of Degenerate Weak (L_1,L_2)-BLD Mappings
    Ju Ling LI(1), Hong Ya GAO(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1107-111. https://doi.org/10.12386/A2004sxxb0137
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    In this paper, we give the definition of degenerate weak (L1, L2)-BLD map-pings in space, and by using the technique of Hodge decomposition and weakly reverse Holder inequality we prove the following regularity result of degenerate weak (L1,L2)-BLD mappings: For every q1 such that 0< L2lnl/2l221+l×100n2[23l/2(24l+n+1)](l-q1) < 1 there exists integrable exponent p1 = p1(n,l,q1,L1,L2) >, such that every degenerate weak (L1,L2)-BLD mapping f∈Wloc1,q1(Ω,Rn) belongs to Wloc1,p1(Ω,Rn), that is, f is a degenerate (L1,L2)-BLD mapping in the usual sense.
  • Strong-CHIP and Characterization of the Best Approximation with Generalized Restrictions
    Dong Hui FANG(1), Chong LI(2),
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1115-112. https://doi.org/10.12386/A2004sxxb0138
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    The problem of the best approximation with generalized restrictions is in-vestigated. Under the assumption that l and u have finite intersection points, by introducing the concept of the sub-strong interior point condition and making use of the strong-CHIP from optimization theory, we study the relationship of the sub-strong interior point, the strong-CHIP and the characterization of the best approximation with generalized restrictions. Consequently, the characterization theorems of Kolmogorov's type and "0 belonging to the convex hull" type are obtained.
  • The Automorphism Groups of Generalized Witt Lie Superalgebras over a Field of Prime Characteristic
    Wen DE LIU, Yong Zheng ZHANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1123-113. https://doi.org/10.12386/A2004sxxb0139
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    Let W be the infinite-dimensional or finite-dimensional generalized Witt Lie superalgebra over a field of prime characteristic and Aut W the automorphism group. Employing the invariance of the natural filtration of W and the invariant dimension property of the base algebra of W, we prove that Aut W is isomorphic to the admissible automorphism group of the base algebra of W. Then it is proved that the group isomorphism sends the standard normal series of Aut W to the one of the admissible automorphism groups, and further properties of Aut W are given.
  • Existence of Periodic Solutions for Nonlinear nth Order Ordinary Differential Equations
    Bing Wen LIU(1), Li Hong HUANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1133-114. https://doi.org/10.12386/A2004sxxb0140
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    By applying the theory of topological degree, we establish the existence of 2π-periodic solutions for a class of nonlinear nth order ordinary differential equations.
  • Z-Connected Set System and Its Category Character
    Yun SHANG, Bin ZHAO
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1141-114. https://doi.org/10.12386/A2004sxxb0141
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    In this paper, the concepts of Z-connected set system is introduced, and then a series of properties of Z-connected continuous poset are discussed, we mainly prove that the category of Z-connected continuous posets is dually equivalent to a full subcategory of the category of completely distributive lattices.
  • Uniform Covers and Compact Images of Metric Spaces
    Ying GE(1), Shou LIN(2)
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1149-115. https://doi.org/10.12386/A2004sxxb0142
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    In this paper the structures of sequence-covering compact images of locally separable metric spaces are investigated by uniform covers, the main results are that (1) a space is a sequence-covering compact image of a locally separable metric space if and only if it has a uniform sn-network consisting of cosmic subspaces; (2) a space is a sequence-covering quotient compact image of a locally separable metric space if and only if it is a locally cosmic space and a sequence-covering quotient compact image of a metric space.
  • Representation and Duality of Finite Hopf C~*-Algebra
    Li Ning JIANG(1),　Zhong Yan L
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1155-116. https://doi.org/10.12386/A2004sxxb0143
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    Suppose that A is a finite dimensional Hopf C-algebra and H is a Hilbert space. If there exists an action γ of A on L(H) so that L(H) is a modular algebra with conjugate property and the inner-product on H is A-invariant, then there is a unique C-representation θ of A on H supplemented by the γ. The A-invariant subspace of L(H) is exactly the commutant of θ(A).
  • On the Continuity of Julia Sets and Hausdorff Dimension
    Wei ZHUANG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1161-116. https://doi.org/10.12386/A2004sxxb0144
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    Given d≥2 consider the family of monic polynomials Pc(z) = zd + c, for c ∈C. Let Kc={z∈C|{Pcn(z)}n≥0 is bounded} be the filled-in Julia set of Pc and Jc=(?)Kc be the Julia set of Pc. Denote by HD(Jc) the Hausdorff dimension of Jc. Let ω(0) be the set of accumulation points of the orbit of critical point 0, and Pc0 be expanding in ω(0). Suppose that 0∈Jc0 and |c0| > ε>0. If a sequence of cn→c0, then Jcn→Jc0 and Kcn→Jc0, in the Hausdorff topology. We also prove that if there is C1>0 such that for a sequence cn→c0, dist(cn, Jc0)≥C1|cn-c0|1+1/d then HD(Jcn)→ HD(Jc0).
  • Existence of Positive Solutions of Singular Semi-Positone Boundary Value Problems
    Guo Qing CHAI
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1167-117. https://doi.org/10.12386/A2004sxxb0145
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    Considering the singular Semi-Positone boundary value problems: y″= f(t,y,y′), t∈(0,1), y(0)=a >0, y(1)=0, by application of Schauder fixed point theorem, under appropriate conditions, the author establishes the theorems for existence of positive solutions.
  • Some Properties and Constructions of Quasi-Bent Functions
    Xi Yong ZHANG, Wen Bao Han
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1175-118. https://doi.org/10.12386/A2004sxxb0146
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    In this paper, we generalize the concept of quasi-bent function in elementary 2-groups to general finite abelian groups, and our quasi-bent function concept concludes nearly all concepts about bent functions up to now. Several constructions are given, and the deep relationship between bent functions and some kind of quasi-bent functions is found. In addition, we find some connection between relative difference sets and quasi-bent functions, and find a way to construct bent functions from quasi-bent functions. In the end, we present some quasi-bent functions by the usage of Galois ring and Building sets.
  • A Class of Typical Singular Permutation Polynomials in Several Indeterminates over Z/p~lZ
    Jian Jun JIANG, Qi SUN
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1185-119. https://doi.org/10.12386/A2004sxxb0147
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    In this note, the authors study a class of typical singular polynomials in several indeterminates modulo p and obtain a necessary and sufficient condition for them to be permutation polynomials modulo pl (l > 1). In particular, for any positive integer u > 1, the authors obtain a polynomial which is a permutation polynomial modulo pu but not modulo pu+1. These results are generalizations and improvement of some known results obtained by Zhang Qifan, Hu Yongzhong, et al.
  • On the Uniqueness of Limit Cycle of the General Lienard Equation
    Ping Guang ZHANG, Shen Qi ZHAO
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1193-120. https://doi.org/10.12386/A2004sxxb0148
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    In this paper, a theorem on the uniqueness of limit cycle of the general Lienard equation is proved. Applying the theorem to the predator-prey model with undercrowding effect, it is proved that the predator-prey system has at most one limit cycle around the positive weak singular point.
  • The Lower Bounds of the Maximum Genus on Graphs in Terms of Diameter and Girth
    Xiu Yan SHENG
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1201-120. https://doi.org/10.12386/A2004sxxb0149
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    This paper proves the following results: Let G be a simple graph with diameter d. If its girth is not less than d, then the Betti deficient number of G, ξ(G)≤1, when d (≥4) is even, i.e. G is upper embeddable; and the Betti deficient number of G, ξ(G)≤2, when d (≥3) is odd, i.e. the maximum genus of G, γM(G)≥1/2β(G) - 1.
  • On the Block Independence in g-Inverses of Block Matrices
    Wen Bin GUO, Yong Hui LIU, mu
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1205-121. https://doi.org/10.12386/A2004sxxb0150
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    This paper studies the block independence in g-inverses of block matrices. We derive the necessary and sufficient conditions of block independence in g-inverses of two and three complex matrices, and reveal the relations between the definitions of block independence.
  • The Divisor Problem on the Beatty Sequence
    Guang Shi Lv(1), Wen Guang ZHA
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1213-121. https://doi.org/10.12386/A2004sxxb0151
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    In this paper we study the divisor problem on the Beatty sequence. We prove that in the sense of Lebesgue measure for almost all θ≥1 and all k≥5, Dk(θ;x) = ∑n≤x/θdk([nθ]) =θ-1Dk(1;x)+O(x4/5+ε) holds uniformly.
  • Discreteness Criteria for Subgroups of Isometry Group of Pinched Hadamard Manifold
    Bin Lin DAI
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1217-122. https://doi.org/10.12386/A2004sxxb0152
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    In this paper, we study the discreteness of isometry groups of pinched Hadamard manifold and obtain several theorems about discreteness criteria and group convergence of subgroups of Isom(X).
  • A Note on James's Distortion Theorem
    Dong Yang CHEN
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1223-122. https://doi.org/10.12386/A2004sxxb0153
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    If a Banach space X is such that X contains a subspace isomorphic to C[0,1], then X contains almost isometric copies of C[0,1]. This result generalizes the results due to Dowling, Randrianantoanina and Turett.
  • Existence of Entropy Solutions to Some Parabolic Problems with L~1 Data
    Feng Quan LI
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1225-123. https://doi.org/10.12386/A2004sxxb0154
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    In this paper, an existence result of entropy solutions to some parabolic problems is established. The data belongs to L1 and no growth assumption is made on the lower order term in divergence form.
  • Nash Inequalities for Markov Processes in Dimension One
    Yong Hua MAO
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1231-123. https://doi.org/10.12386/A2004sxxb0155
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    In this paper, we give characterizations of Nash inequalities for birth-death process and diffusion process on the line. We prove that for these processes, transience implies that the semigroups P(t) decay as ||P(t)||1→∞≤Ct-1. Sufficient conditions for general Markov chains are also obtained.
  • Bifurcations of Rough Heteroclinic Loops with Three Saddle Points
    Yin Lai JIN, De Ming ZHU
    Acta Mathematica Sinica, Chinese Series. 2004, 47(6): 1237-124. https://doi.org/10.12386/A2004sxxb0156
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    In this paper, we study the bifurcation problems of rough heteroclinic loops connecting three saddle points for a higher-dimensional system. Under some transversal conditions and the nontwisted condition, the existence, uniqueness, and noncoexistence of the 1-heteroclinic loop with three or two saddle points, the 1-homoclinic loop and 1-periodic orbit near Γ are obtained. Meanwhile, the bifurcation surfaces and existence regions are also given. Moreover, the above bifurcation results are extended to the case for heteroclinic loop with l saddle points.
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