05 May 2011, Volume 27 Issue 5

    

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  Finiteness of Mapping Degree Sets for 3-Manifolds

  Pierre DERBEZ, Hong Bin SUN, Shi Cheng WANG

  Acta Mathematica Sinica. 2011, 27(5): 807-812. https://doi.org/10.1007/s10114-011-0416-x

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  By constructing certain maps, this note completes the answer of the question: For which closed orientable 3-manifold N, is the set of mapping degrees D(M,N) finite for any closed orientable 3-manifold M?  
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  (Co)Homology and Universal Central Extension of Hom-Leibniz Algebras

  Yong Sheng CHENG, Yu Cai SU

  Acta Mathematica Sinica. 2011, 27(5): 813-830. https://doi.org/10.1007/s10114-011-9626-5

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  Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory (such as (co)homology groups, universal central extensions) of Hom-Leibniz algebras based on some works of Loday and Pirashvili.  
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  Ortho-u-monoids

  Chun Mei GONG, Yu Qi GUO, K. P. SHUM

  Acta Mathematica Sinica. 2011, 27(5): 831-844. https://doi.org/10.1007/s10114-011-9437-8

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  In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E(S)-semiabundant semigroups. After introducing the concept of (~)-Green’s relations, and obtaining some important properties of (~)-Green’s relations and super E(S)-semiabundant semigroups, we have given the semilattice decomposition of ortho-u-monoids and a structure theorem for regular ortho-u-monoids. The main techniques that we used in the study are the (~)-Green’s relations, and the semi-spined product of semigroups.  
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  Numerical Blow-up for a Nonlinear Heat Equation

  Firmin K. N’GOHISSE, Théodore K. BONI

  Acta Mathematica Sinica. 2011, 27(5): 845-862. https://doi.org/10.1007/s10114-011-8464-9

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  This paper concerns the study of the numerical approximation for the following initialboundary value problem where f(s) is a positive, increasing, C¹ convex function for the nonnegative values of s, f(0) > 0, We find some conditions under which the solution of a semidiscrete form of the above problem blows up in a finite time and estimate its semidiscrete blow-up time. We also prove the convergence of the semidiscrete blow-up time to the theoretical one. A similar study has been also undertaken for a discrete form of the above problem. Finally, we give some numerical results to illustrate our analysis.  
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  Geometric Realization of Adams Maps

  Xian Zu LIN

  Acta Mathematica Sinica. 2011, 27(5): 863-870. https://doi.org/10.1007/s10114-011-0164-y

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  Let G/P be a homogenous space with G a compact connected Lie group and P a connected subgroup of G of equal rank. As the rational cohomology ring of G/P is concentrated in even dimensions, for an integer k we can define the Adams map of type k to be l_k : H^*(G/P,Q) → H^*(G/P,Q), l_k(u) = k^#em/em#u, u ∈ H^2#em/em#(G/P,Q). We show that if k is prime to the order of the Weyl group of G, then l_k can be induced by a self map of G/P. We also obtain results which imply the condition that k is prime to the order of the Weyl group of G is necessary.  
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  On a Sharp Volume Estimate for Gradient Ricci Solitons with Scalar Curvature Bounded Below

  Shi Jin ZHANG

  Acta Mathematica Sinica. 2011, 27(5): 871-882. https://doi.org/10.1007/s10114-011-9527-7

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  In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota’s argument we obtain a local lower bound estimate of the scalar curvature for the Ricci flow on complete manifolds. Consequently, one has a sharp estimate of the scalar curvature for expanding Ricci solitons; we also provide a direct (elliptic) proof of this sharp estimate. Moreover, if the scalar curvature attains its minimum value at some point, then the manifold is Einstein.  
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  Clique-Transversal Sets in 4-Regular Claw-Free Graphs

  Er Fang SHAN, Li Ying KANG

  Acta Mathematica Sinica. 2011, 27(5): 883-890. https://doi.org/10.1007/s10114-011-9478-z

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  A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted by τ_c(G), is the minimum cardinality of a cliquetransversal set in G. In this paper we give the exact value of the clique-transversal number for the line graph of a complete graph. Also, we give a lower bound on the clique-transversal number for 4-regular claw-free graphs and characterize the extremal graphs achieving the lower bound.  
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  Some Sufficient Conditions on the Number of Non-abelian Subgroups of a Finite Group to be Solvable

  Jiang Tao SHI, Cui ZHANG

  Acta Mathematica Sinica. 2011, 27(5): 891-896. https://doi.org/10.1007/s10114-011-9476-1

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  Thompson’s theorem indicates that a finite group with a nilpotent maximal subgroup of odd order is solvable. As an important application of Thompson’s theorem, a finite group is solvable if it has an abelian maximal subgroup. In this paper, we give some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable.  
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  Bounds of Deviation for Branching Chains in Random Environments

  Wei Gang WANG

  Acta Mathematica Sinica. 2011, 27(5): 897-904. https://doi.org/10.1007/s10114-011-9444-9

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  We consider non-extinct branching processes in general random environments. Under the condition of means and second moments of each generation being bounded, we give the upper bounds and lower bounds for some form deviations of the process.  
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  On the Period Function of a Class of Reversible Quadratic Centers

  Hai Hua LIANG, Yun Lin ZHAO

  Acta Mathematica Sinica. 2011, 27(5): 905-918. https://doi.org/10.1007/s10114-011-9364-8

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  This paper is devoted to the study of the period function for a class of reversible quadratic system We determine the monotonicity of the period function for each k ∈ R. It is proved that the period function has at most one critical point.  
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  Chromatic Uniqueness of Certain Complete Tripartite Graphs

  G. C. LAU, Y. H. PENG

  Acta Mathematica Sinica. 2011, 27(5): 919-926. https://doi.org/10.1007/s10114-011-8507-2

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  Let P(G, λ) be the chromatic polynomial of a graph G. A graph G is chromatically unique if for any graph H, P(H, λ) = P(G, λ) implies H is isomorphic to G. Liu et al. [Liu, R. Y., Zhao, H. X., Ye, C. F.: A complete solution to a conjecture on chromatic uniqueness of complete tripartite graphs. Discrete Math., 289, 175-179 (2004)], and Lau and Peng [Lau, G. C., Peng, Y. H.: Chromatic uniqueness of certain complete t-partite graphs. Ars Comb., 92, 353-376 (2009)] show that K(p - k, p - i, p) for #em/em# = 0, 1 are chromatically unique if p ≥ k + 2 ≥ 4. In this paper, we show that if 2 ≤ #em/em# ≤ 4, the complete tripartite graph K(p - k, p - i, p) is chromatically unique for integers k ≥ #em/em# and p ≥ k²/4 + #em/em# + 1.  
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  On Imbalances in Oriented Tripartite Graphs

  S. PIRZADA, T. A. NAIKOO, Nasir A. SHAH

  Acta Mathematica Sinica. 2011, 27(5): 927-932. https://doi.org/10.1007/s10114-011-8459-6

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  An oriented tripartite graph is the result of assigning a direction to each edge of a simple tripartite graph. For any vertex x in an oriented tripartite graph D(U, V,W), let d_x⁺ and d_x^- denote the outdegree and indegree respectively of x. Define as the imbalances of the vertices u_{em in U, vj in V and wk in W respectively. In this paper, we obtain criteria for sequences of integers to be the imbalances of some oriented tripartite graph.}  
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  Strict Topology over the Space of Measures with Continuous Translations on a Locally Compact Foundation Semigroup

  S. MAGHSOUDI, R. NASR-ISFAHANI

  Acta Mathematica Sinica. 2011, 27(5): 933-942. https://doi.org/10.1007/s10114-011-8404-8

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  Let S be a locally compact semigroup, ω be a weight function on S, and M_a(S, ω) be the weighted semigroup algebra of S. Let L₀^∞ (S;M_a(S, ω)) be the C*-algebra of all M_a(S, ω)-measurable functions g on S such that g/ω vanishes at infinity. We introduce and study a strict topology β¹(S, ω) on M_a(S, ω) and show that the Banach space L₀^∞ (S;M_a(S, ω)) can be identified with the dual of M_a(S, ω) endowed with β¹(S, ω). We finally investigate some properties of the locally convex topology β¹(S, ω) on M_a(S, ω).  
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  Notes on Piecewise-Koszul Algebras

  Jia Feng Lü, Xiao Lan YU

  Acta Mathematica Sinica. 2011, 27(5): 943-952. https://doi.org/10.1007/s10114-011-8238-4

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  The relationships between piecewise-Koszul algebras and other “Koszul-type” algebras are discussed. The Yoneda-Ext algebra and the dual algebra of a piecewise-Koszul algebra are studied, and a sufficient condition for the dual algebra A^! to be piecewise-Koszul is given. Finally, by studying the trivial extension algebras of the path algebras of Dynkin quivers in bipartite orientation, we give explicit constructions for piecewise-Koszul algebras with arbitrary “period” and piecewise-Koszul algebras with arbitrary “jump-degree”.  
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  Derivation of Lower Critical Magnetic Field for Anisotropic Ginzburg-Landau Model in Superconductivity

  Yan Lei KOU, Shi Jin DING

  Acta Mathematica Sinica. 2011, 27(5): 953-982. https://doi.org/10.1007/s10114-011-8206-z

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  In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field H_C1 which is the first critical value of h_ex corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter κ, and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers.  
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  Orthosymplectic Quantum Function Superalgebras OSP_q(2l+1|2n)

  Jun Li LIU, Shi Lin YANG

  Acta Mathematica Sinica. 2011, 27(5): 983-1004. https://doi.org/10.1007/s10114-011-8037-y

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  By the R-matrix of orthosymplectic quantum superalgebra U_q(osp(2l+1|2n)) in the vector representation, we establish the corresponding quantum Hopf superalgebra OSP_q(2l + 1|2n). Furthermore, it is shown that OSP_q(2l + 1|2n) is coquasitriangular.  
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  A New Characterization of p-Smoothable Banach Spaces

  Yan Bo REN, You Liang HOU

  Acta Mathematica Sinica. 2011, 27(5): 1005-1010. https://doi.org/10.1007/s10114-011-8026-1

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  In this paper an atomic decomposition theorem for Banach-space-valued weak Hardy regular martingale space w_pH_α^S (X) is given. As an application, p-smoothable Banach spaces are characterized in terms of bounded sublinear operators defined on Banach-space-valued weak Hardy regular martingale space w_pH_α^S (X)  
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  Wavelets with Differential Relation

  Zhi-Tao CHUANG, Youming LIU

  Acta Mathematica Sinica. 2011, 27(5): 1011-1022. https://doi.org/10.1007/s10114-010-8188-2

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  Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli’s work.