05 January 2007, Volume 23 Issue 1

    

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  On the Predator-Prey System with Holling-(n + 1) Functional Response

  Wei WANG, Jian Hua SUN

  Acta Mathematica Sinica. 2007, 23(1): 1-6. https://doi.org/10.1007/s10114-005-0603-8

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  The qualitative properties of a predatorprey system with Holling-(n + 1) functional response and a fairly general growth rate are completely investigated. The necessary and sufficient condition to guarantee the uniqueness of limit cycles is given. Our work extends the previous relevant results in the reference.
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  Remarks on g-functions on Hⁿ

  Ming Ju LIU, Shan Zhen LU

  Acta Mathematica Sinica. 2007, 23(1): 7-16. https://doi.org/10.1007/s10114-005-0760-9

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  In this paper, the authors study some properties of Littlewood-Paley g-functions g_ψ (f), Lusin area functions S_ψ,α (f) and Littlewood-Paley g_ψ,λ^* (f) functions defined on Hⁿ, where α, λ >0 and ψ, f are suitable functions. They are the generalization of the corresponding operators on Rⁿ.
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  Algebraic Independence of Certain Generalized Mahler Type Numbers

  Yao Chen ZHU

  Acta Mathematica Sinica. 2007, 23(1): 17-22. https://doi.org/10.1007/s10114-005-0766-3

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  In this paper the generalized Mahler type number M_h(g;A, T) is defined, and in the case of multiplicatively dependent parameters g_i, h_i(1 ≤ i ≤ s) the algebraic independence of the numbers M_hi(gi;A, T)(1 ≤ i ≤ s) is proved, where A and T are certain infinite sequences of non-negative integers and of positive integers, respectively. Furthermore, the algebraic independence result on values of a certain function connected with the generalized Mahler type number and its derivatives at algebraic numbers is also given.
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  Circulant Double Coverings of a Circulant Graph of Valency Five

  Rong Quan FENG, Jin Ho KWAK

  Acta Mathematica Sinica. 2007, 23(1): 23-28. https://doi.org/10.1007/s10114-005-0773-4

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  Enumerating the isomorphism classes of several types of graph covering projections is one of the central research topics in enumerative topological graph theory. A covering of G is called circulant if its covering graph is circulant. Recently, the authors [Discrete Math., 277, 73-85 (2004)] enumerated the isomorphism classes of circulant double coverings of a certain type, called a typical covering, and showed that no double covering of a circulant graph of valency three is circulant. Also, in [Graphs and Combinatorics, 21, 386-400 (2005)], the isomorphism classes of circulant double coverings of a circulant graph of valency four are enumerated. In this paper, the isomorphism classes of circulant double coverings of a circulant graph of valency five are enumerated.
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  Rényi’s Problem in Short Intervals

  Wen Guang ZHAI

  Acta Mathematica Sinica. 2007, 23(1): 29-36. https://doi.org/10.1007/s10114-005-0857-1

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  In this paper, we study Rényi's problem and other related problems about the additive functions in short intervals. As corollaries, we improve Ivic's results.
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  The Strongly Simple Cycles with Given Rotation Pairs of an Interval Map

  Tai Xiang SUN, Hong Jian XI, Xiao Yan ZHANG

  Acta Mathematica Sinica. 2007, 23(1): 37-40. https://doi.org/10.1007/s10114-005-0803-2

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  In this paper, we introduce the notion of the strongly simple cycles with some rotation pair for interval maps and prove that, if an interval map has a cycle with given rotation pair, then it has a strongly simple cycle with the same rotation pair.
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  The Invariance Principle for p-θ Chain

  Di He HU, Zheng Yan XIAO

  Acta Mathematica Sinica. 2007, 23(1): 41-56. https://doi.org/10.1007/s10114-005-0735-x

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  There are two parts in this paper. In the first part we construct the Markov chain in random environment(MCRE), the skew product Markov chain and p-θ chain from a random transition matrix and a two-dimensional probability distribution, and in the second part we prove that the invariance principle for p-θ chain, a more complex non-homogeneous Markov chain, is true under some reasonable conditions. This result is more powerful.
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  Integrated Groups and Smooth Distribution Groups

  Pedro J. MIANA

  Acta Mathematica Sinica. 2007, 23(1): 57-64. https://doi.org/10.1007/s10114-005-0784-1

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  In this paper, we prove directly that α-times integrated groups define algebra homomorphisms. We also give a theorem of equivalence between smooth distribution groups and α-times integrated groups.
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  On Basic Constraint Qualifications for Infinite System of Convex Inequalities in Banach Spaces

  Xin Tao YE, Chong LI

  Acta Mathematica Sinica. 2007, 23(1): 65-76. https://doi.org/10.1007/s10114-005-0709-z

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  The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided.
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  General Kloosterman Sums and the Difference Between an Integer and Its Inverse Modulo Q

  Hua Ning LIU, Wen Peng ZHANG

  Acta Mathematica Sinica. 2007, 23(1): 77-82. https://doi.org/10.1007/s10114-005-0724-0

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  The main purpose of this paper is to use the generalized Bernoulli numbers, Gauss sums and the mean value theorems of Dirichlet L-functions to study the asymptotic property of one class of number-theoretic functions, and to give four interesting hybrid mean value formulae.
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  p-adic Measures of Algebraic Independence for the Values of Ramanujan Functions and Klein Modular Functions

  Tian Qin WANG, Guang Shan XU

  Acta Mathematica Sinica. 2007, 23(1): 83-88. https://doi.org/10.1007/s10114-005-0708-0

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  In this paper, we give the p-adic measures of algebraic independence for the values of Ramanujan functions and Klein modular functions at algebraic points.
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  Finite Degree Holomorphic Covers of Compact Riemann Surfaces

  Jouni PARKKONEN, Vesa RUUSKA

  Acta Mathematica Sinica. 2007, 23(1): 89-94. https://doi.org/10.1007/s10114-005-0824-x

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  A conjecture of Ehrenpreis states that any two compact Riemann surfaces of genus at least two have finite degree unbranched holomorphic covers that are arbitrarily close to each other in moduli space. Here we prove a weaker result where certain branched covers associated with arithmetic Riemann surfaces are allowed, and investigate the connection of our result with the original conjecture.
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  Adjacency Preserving Bijection Maps of Hermitian Matrices over any Division Ring with an Involution

  Li Ping HUANG

  Acta Mathematica Sinica. 2007, 23(1): 95-102. https://doi.org/10.1007/s10114-005-0770-7

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  Let D be any division ring with an involution, H_n(D) be the space of all n × n hermitian matrices over D. Two hermitian matrices A and B are said to be adjacent if rank(A-B) = 1. It is proved that if ψ is a bijective map from H_n(D)(n ≥ 2) to itself such that ψ preserves the adjacency, then ψ^-1 also preserves the adjacency. Moreover, if H_n(D) = f₃ (F₂), then ψ preserves the arithmetic distance. Thus, an open problem posed by Wan Zhe-Xian is answered for geometry of symmetric and hermitian matrices.
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  On the Equivalence of Weyl Theorem and Generalized Weyl Theorem

  M. BERKANI

  Acta Mathematica Sinica. 2007, 23(1): 103-110. https://doi.org/10.1007/s10114-005-0720-4

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  We know that an operator T acting on a Banach space satisfying generalized Weyl's theorem also satisfies Weyl's theorem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl's theorem, then it also satisfies generalized Weyl's theorem. We give also a similar result for the equivalence of a-Weyl's theorem and generalized a-Weyl's theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators.
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  The Weighted Transience and Recurrence of Markov Processes

  Min Zhi ZHAO, Hui Zeng ZHANG

  Acta Mathematica Sinica. 2007, 23(1): 111-126. https://doi.org/10.1007/s10114-005-0808-x

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  Transience and recurrence are among the most important concepts in Markov processes. In this paper, we study the transience and recurrence for right processes with a given weight function, and characterize them by potentials, excessive functions, first hitting times and last exit times of the process. We also study the properties of recurrent states.
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  A Berry-Esseen Theorem and a Law of the Iterated Logarithm for Asymptotically Negatively Associated Sequences

  Jian Feng WANG, Li Xin ZHANG

  Acta Mathematica Sinica. 2007, 23(1): 127-136. https://doi.org/10.1007/s10114-005-0800-5

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  Negatively associated sequences have been studied extensively in recent years. Asymp-totically negative association is a generalization of negative association. In this paper a Berry-Esseen theorem and a law of the iterated logarithm are obtained for asymptotically negatively associated sequences.
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  Linear Time Algorithms for Parallel Machine Scheduling

  Zhi Yi TAN, Yong HE

  Acta Mathematica Sinica. 2007, 23(1): 137-146. https://doi.org/10.1007/s10114-005-0838-4

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  This paper addresses linear time algorithms for parallel machine scheduling problems. We introduce a kind of threshold algorithms and discuss their main features. Three linear time threshold algorithm classes DT, PT and DTm are studied thoroughly. For all classes, we study their best possible algorithms among each class. We also present their application to several scheduling problems. The new algorithms are better than classical algorithms in time complexity and/or worst-case ratio. Computer-aided proof technique is used in the proof of main results, which greatly simplifies the proof and decreases case by case analysis.
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  Prime Submodules and Flat Modules

  A. Azizi

  Acta Mathematica Sinica. 2007, 23(1): 147-152. https://doi.org/10.1007/s10114-005-0813-0

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  In this paper, some characterizations of prime submodules in flat modules and, particularly, in free modules are given. Furthermore, the height of prime submodules and some saturated chain of prime submodules are also given.
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  On the Fourth Power Mean of the Character Sums Over Short Intervals

  Wen Peng ZHANG, Xiao Ying WANG

  Acta Mathematica Sinica. 2007, 23(1): 153-164. https://doi.org/10.1007/s10114-005-0893-x

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  The main purpose of this paper is to study the mean value properties of the character sums over the interval [1,p/8) by using the mean value theorems of the Dirichlet L-functions, and give an interesting mean value formula for this study.
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  Optimal Preemptive Online Algorithms for Scheduling with Known Largest Size on Two Uniform Machines

  Yong HE, Yi Wei JIANG, Hao ZHOU

  Acta Mathematica Sinica. 2007, 23(1): 165-174. https://doi.org/10.1007/s10114-005-0829-5

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  In this paper, we consider the semi-online preemptive scheduling problem with known largest job sizes on two uniform machines. Our goal is to maximize the continuous period of time (starting from time zero) when both machines are busy, which is equivalent to maximizing the minimum machine completion time if idle time is not introduced. We design optimal deterministic semi-online algorithms for every machine speed ratio s ∈ [1,∞), and show that idle time is required to achieve the optimality during the assignment procedure of the algorithm for any s > (s ² + 3s + 1 / (s ² + 2s + 1). The competitive ratio of the algorithms is (s ² + 3s + 1) / (s ² + 2s + 1), which matches the randomized lower bound for every s ≥ 1. Hence randomization does not help for the discussed preemptive scheduling problem.
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  On Banach Spaces Whose Unit Sphere Determines Polynomials

  Jesús FERRER

  Acta Mathematica Sinica. 2007, 23(1): 175-188. https://doi.org/10.1007/s10114-005-0832-x

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  In this paper we study the problem of characterizing the real Banach spaces whose unit sphere determines polynomials, i.e., if two polynomials coincide in the unit sphere, is this sufficient to guarantee that they are identical? We show that, in the frame of spaces with unconditional basis, non-reflexivity is a sufficient, although not necessary, condition for the above question to have an affirmative answer. We prove that the only l_pⁿ spaces having this property are those with p irrational, while the only l_p spaces which do not enjoy it are those with p an even integer. We also introduce a class of polynomial determining sets in any real Banach space.
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  Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over Twisted Heisenberg-Virasoro Algebra

  Ran SHEN, Yu Cai SU

  Acta Mathematica Sinica. 2007, 23(1): 189-192. https://doi.org/10.1007/s10114-005-0807-y

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  We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenberg-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module (and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series).