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05 April 2011, Volume 27 Issue 4
    

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  • Distribution of a Certain Partition Function Modulo Powers of Primes
    Hei-Chi CHAN
    Acta Mathematica Sinica. 2011, 27(4): 625-634. https://doi.org/10.1007/s10114-011-8620-2
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    In this paper, we study a certain partition function a(n) defined by Σn≥0 a(n)qn :=Π n=1(1 - qn)-1(1 - q2n)-1. We prove that given a positive integer j ≥ 1 and a prime m ≥ 5, there are infinitely many congruences of the type a(An + B) ≡ 0 (mod mj ). This work is inspired by Ono’s ground breaking result in the study of the distribution of the partition function p(n).  
  • Halpern Iteration in CAT(κ) Spaces
    Bożena PIĄTEK
    Acta Mathematica Sinica. 2011, 27(4): 635-646. https://doi.org/10.1007/s10114-011-9312-7
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    In this paper we show that an iterative sequence generated by the Halpern algorithm converges to a fixed point in the case of complete CAT(κ) spaces. Similar results for Hadamard manifolds were obtained in [Li, C., López, G., Martín-Márquez, V.: Iterative algorithms for nonexpansive mappings on Hadamard manifolds. Taiwanese J. Math., 14, 541-559 (2010)], but we study a much more general case. Moreover, we discuss the Halpern iteration procedure for set-valued mappings.  
  • Quantizations of the W-Algebra W(2, 2)
    Jun Bo LI, Yu Cai SU
    Acta Mathematica Sinica. 2011, 27(4): 647-656. https://doi.org/10.1007/s10114-011-8080-8
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    We quantize the W-algebra W(2, 2), whose Verma modules, Harish-Chandra modules, irreducible weight modules and Lie bialgebra structures have been investigated and determined in a series of papers recently.  
  • Line-primitive Linear Spaces with Fang-Li Parameter gcd(k, r) at Most 12
    Sheng Lin ZHOU, Yan Bo MA, Wei Dong FANG
    Acta Mathematica Sinica. 2011, 27(4): 657-670. https://doi.org/10.1007/s10114-011-8085-3
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    Let G be a subgroup of the automorphism group of a non-trivial finite linear space S. In this paper we prove that if G is line-primitive with Fang-Li parameter gcd(k, r) = 11 and 12, then G is also point-primitive. This extends the results of Fang and Li (1993) and Li and Liu (2001) which combined gives the result for gcd(k, r) ≤ 10.  
  • Bounds for Hardy Type Differences
    Neven ELEZOVIĆ, Kristina KRULIĆ, JosipPEČARIĆ
    Acta Mathematica Sinica. 2011, 27(4): 671-684. https://doi.org/10.1007/s10114-011-9707-5
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    Let Ak be an integral operator defined by  where k : Ω1 × Ω2 → R is a general nonnegative kernel, (Ω1,Σ1, μ1), (Ω2,Σ2, μ2) are measure spaces with σ-finite measures and  In this paper improvements and reverses of new weighted Hardy type inequalities with integral operators of such type are stated and proved. New Cauchy type mean is introduced and monotonicity property of this mean is proved.  
  • A Hopf Type Classification Theorem for Isovariant Maps from Free G-manifolds to Representation Spheres
    Ikumitsu NAGASAKI, Fumihiro USHITAKI
    Acta Mathematica Sinica. 2011, 27(4): 685-700. https://doi.org/10.1007/s10114-011-0235-0
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    An isovariant map is an equivariant map preserving the isotropy subgroups. In this paper, we develop an isovariant version of the Hopf classification theorem; namely, an isovariant homotopy classification result of G-isovariant maps from free G-manifolds to representation spheres under a certain dimensional condition, the so-called Borsuk-Ulam inequality. In order to prove it, we use equivariant obstruction theory and the multidegree of an isovariant map.  
  • Labelings of Plane Graphs Containing Hamilton Path
    Martin BAČA, Ljiljana BRANKOVIC, Andrea SEMANIČOVÁ-FEŇOVČÍKOVÁ
    Acta Mathematica Sinica. 2011, 27(4): 701-714. https://doi.org/10.1007/s10114-011-9451-x
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    This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. A weight of a face is the sum of the label of a face and the labels of the vertices and edges surrounding that face. In a super d-antimagic labeling the vertices receive the smallest labels and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s appearing in the graph.
    The paper examines the existence of such labelings for plane graphs containing a special Hamilton path.  
  • Finite Groups with Some Pronormal Subgroups
    Zhen Cai SHEN, Wu Jie SHI
    Acta Mathematica Sinica. 2011, 27(4): 715-724. https://doi.org/10.1007/s10114-011-9310-9
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    A subgroup H of finite group G is called pronormal in G if for every element x of G, H is conjugate to Hx in H,〈Hx〉. A finite group G is called PRN-group if every cyclic subgroup of G of prime order or order 4 is pronormal in G. In this paper, we find all PRN-groups and classify minimal non-PRN-groups (non-PRN-group all of whose proper subgroups are PRN-groups). At the end of the paper, we also classify the finite group G, all of whose second maximal subgroups are PRN-groups.  
  • Fibonacci and Lucas Congruences and Their Applications
    Refik KESKİN Bahar, DEMİRTÜRK BİTİM
    Acta Mathematica Sinica. 2011, 27(4): 725-736. https://doi.org/10.1007/s10114-011-9744-0
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    In this paper we obtain some new identities containing Fibonacci and Lucas numbers. These identities allow us to give some congruences concerning Fibonacci and Lucas numbers such as L2mn+k ≡ (-1)(m+1)n Lk (mod Lm), F2mn+k ≡ (-1)(m+1)n Fk (mod Lm), L2mn+k ≡ (-1)mn L2mn+k(mod Fm) and F2mn+k ≡ (-1)mn Fk (mod Fm). By the achieved identities, divisibility properties of Fibonacci and Lucas numbers are given. Then it is proved that there is no Lucas number Ln such that Ln = L2ktLmx2 for m > 1 and k ≥ 1. Moreover it is proved that Ln = LmLr is impossible if m and r are positive integers greater than 1. Also, a conjecture concerning with the subject is given.  
  • Mackey First Countability and Docile Locally Convex Spaces
    Carlos BOSCH GIRAL, Thomas E. GILSDORF, Claudia GÓMEZ-WULSCHNER
    Acta Mathematica Sinica. 2011, 27(4): 737-740. https://doi.org/10.1007/s10114-011-8540-1
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    We define a generalization of Mackey first countability and prove that it is equivalent to being docile. A consequence of the main result is to give a partial affirmative answer to an old question of Mackey regarding arbitrary quotients of Mackey first countable spaces. Some applications of the main result to spaces such as inductive limits are also given.  
  • On the Gauss-Weierstrass Summability of Multiple Trigonometric Series at μ-smoothness Points
    Sinem SEZER, Ilham A. ALIEV
    Acta Mathematica Sinica. 2011, 27(4): 741-746. https://doi.org/10.1007/s10114-011-9399-x
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    The notion of μ-smoothness points of periodic functions of several variables is introduced and the rate of convergence of the Gauss-Weierstrass means of relevant Fourier series at these points is investigated  
  • Constant Angle Surfaces in the Heisenberg Group
    Johan FASTENAKELS, Marian Ioan MUNTEANU, Joeri VAN DER VEKEN
    Acta Mathematica Sinica. 2011, 27(4): 747-756. https://doi.org/10.1007/s10114-011-8428-0
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    In this article we extend the notion of constant angle surfaces in S2 × R and H2 × R to general Bianchi-Cartan-Vranceanu spaces. We show that these surfaces have constant Gaussian curvature and we give a complete local classification in the Heisenberg group.  
  • Morita Contexts and Galois Theory for Weak Hopf Comodulelike Algebras
    Qiao Ling GUO, Shuan Hong WANG
    Acta Mathematica Sinica. 2011, 27(4): 757-772. https://doi.org/10.1007/s10114-011-8286-9
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    We investigate the Morita context and graded cases for weak group corings and derive some equivalent conditions for μ to be surjective. Furthermore, we develop Galois theory for weak group corings. As an application, we give Galois theory for comodulelike algebras over a weak Hopf group coalgebra.  
  • Global Existence of Solutions for Stochastic Impulsive Differential Equations
    Li Juan SHEN, Ji Tao SUN
    Acta Mathematica Sinica. 2011, 27(4): 773-780. https://doi.org/10.1007/s10114-011-8650-9
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    In this paper we obtain some results on the global existence of solution to It?o stochastic impulsive differential equations in M([0,∞),Rn) which denotes the family of Rn-valued stochastic processes x satisfying supt∈[0,∞)E|x(t)|2 < ∞ under non-Lipschitz coefficients. The Schaefer fixed point theorem is employed to achieve the desired result. An example is provided to illustrate the obtained results.  
  • Removable Edges in Cycles of a k-Connected Graph
    Li Qiong XU, Xiao Feng GUO
    Acta Mathematica Sinica. 2011, 27(4): 781-788. https://doi.org/10.1007/s10114-011-9278-5
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    An edge e of a k-connected graph G is said to be a removable edge if G θ e is still kconnected, where G θ e denotes the graph obtained from G by deleting e to get G - e, and for any end vertex of e with degree k - 1 in G - e, say x, delete x, and then add edges between any pair of non-adjacent vertices in NG-e(x). The existence of removable edges of k-connected graphs and some properties of 3-connected graphs and 4-connected graphs have been investigated. In the present paper, we investigate some properties of k-connected graphs and study the distribution of removable edges on a cycle in a k-connected graph (k ≥ 4).  
  • Strong Mixing Subshift of Finite Type and Hausdorff Measure of Its Chaotic Set
    Wan Gan SONG, Zhi HU, Hua Ming WU
    Acta Mathematica Sinica. 2011, 27(4): 789-798. https://doi.org/10.1007/s10114-011-9203-y
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    We present a sufficient and necessary condition for the subshift of finite type to be a measure-preserving transformation or to be a strong mixing measure-preserving transformation with respect to the Hausdorff measure. It is proved that a strong mixing subshift of finite type has a chaotic set with full Hausdorff measure.  
  • Partial Isometries and an Invariant of C*-algebras
    Hong Liang YAO, Xiao Chun FANG
    Acta Mathematica Sinica. 2011, 27(4): 799-806. https://doi.org/10.1007/s10114-011-8053-y
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    In this paper, we will discuss some properties of biprojection-commutative elements which are relevant to the classification of certain infinite C*-algebras, and define an important invariant s(A) of C*-algebra A as well as give some basic properties with regard to s(A). Moreover we prove that the invariant s(A) has continuity.
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