15 March 2015, Volume 58 Issue 2

    

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  The Crossing Number of Link in Thickened Surface

  Xin Ming YAN

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 177-182. https://doi.org/10.12386/A2015sxxb0019

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  We estimate the crossing number of framed link in thickened surface, we define the span of framed link in Kauffman bracket skein module, which may give a lower bound of the crossing number.
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  The Construction of Modified Green Function in a Cone and Its Application

  Lei QIAO, Guo Shuang PAN, Yan Hui ZHANG

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 183-194. https://doi.org/10.12386/A2015sxxb0020

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  Our first aim in this paper is to construct a modified Green function in a cone and give the growth property of it. As an application, we next give the general solutions of the Dirichlet problem. Finally, we prove that this solution is unique.
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  Laguerre Isoparametric Hypersurface in Rⁿ with Three Distinct Principal Curvatures

  Ding Xing ZHONG, Xian Hua XIE, Hai Lian CHEN

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 195-212. https://doi.org/10.12386/A2015sxxb0021

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  An umbilical free oriented hypersurface x:M→Rⁿ with nonzero princi-pal curvatures is called Laguerre isoparametric hypersurface if its Laguerre form C=∑_i C_iw_i =∑_iρ^-1(E_i(logρ)(r-r_i)-E_i(r))w_i vanishes and Laguerre shape operator S=ρ^-1(S-rid has constant eigenvalues. Here ρ²=∑_i(r-r_i)²,r=r₁+r₂+…+r_n-1/n-1 is the mean curvature radius and S is the shape operator of x, E_i is local orthogonal basis for Laguerre metric g with dual basis w_i. In this paper, we classify all Laguerre isoprametric hypersurfaces in Rⁿ with three distinct Laguerre principal curvatures up to Laguerre transformation.
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  Strong Convergence of Multi-Valued Bregman Totally Quasi-Asymptotically Nonexpansive Mappings

  Shi Sheng ZHANG, Lin WANG, Yun He ZHAO, Gang WANG

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 213-226. https://doi.org/10.12386/A2015sxxb0022

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  We propose an algorithms for finding a common fixed point of a finite family of multi-valued Bregman total quasi-φ-asymptotically nonexpansive mappings in reflexive Banach spaces. The results presented in the paper improve and extend the corresponding new results announced by many authors. The algorithms are based on the Bregman distance related to a well-chosen convex function. As applications, we apply our results to a system of equilibrium problems and zero point problem of maximal monotone mappings in reflexive Banach spaces.
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  Global Attractor for a Class of Semi-Discrete System of Nonlinear Schrödinger-BBM Equations

  Ming Hao ZHAO, Chao Sheng ZHU, Yang Rong LI

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 227-242. https://doi.org/10.12386/A2015sxxb0023

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  This paper is devoted to the large time behavior and especially to the regularity of the global attractor for the semi-discrete in time Crank-Nicolson scheme to discretize a class of system of nonlinear Schrödinger-BBM equations on R × R. We first prove that such a semi-discrete system provides a discrete infinite-dimensional dynamical system in H¹ × H¹ that possesses a global attractor A_τ in H¹ × H¹. We also show that the global attractor A_τ is regular, i.e. A_τ is actually included, bounded and compact in H^(3/2)-ε×H².
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  Algebraic Extensions of nth Root of Class A Operators are Subscalar

  Jun Li SHEN, Alatancang

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 243-250. https://doi.org/10.12386/A2015sxxb0024

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  Algebraic extension of nth root of class A operator is studied. Specifically, we obtain that every algebraic extension of nth root of class A operator is subscalar. The proof uses the space decomposition technique. As a consequence, we consider the Weyl type theorems and the hyperinvariant subspace for such operator.
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  On a Jensen-quadratic Functional Equation and Its Hyers-Ulam Stability

  Pei Sheng JI, Ying Zi ZHAO

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 251-260. https://doi.org/10.12386/A2015sxxb0025

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  We obtain the general solution and stability of the Jensen-quadratic functional equation f((x₁+x₂)/2,y₁+y₂)+f((x₁+x₂)/2,y₁-y₂)=f(x₁,y₁)+f(x₁,y₂)+f(x₂,y₁)+f(x₂,y₂).
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  The Solutions for Semipositone (k,n-k) Conjugate Boundary Value Problems

  Hua SU, Li Shan LIU

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 261-270. https://doi.org/10.12386/A2015sxxb0026

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  We consider the existence of positive solutions to the following semiposi-tone (k,n-k) conjugate boundary value problems (SCBVP): 
  
  where n≥2, 1<k<n-1. The nonlinear function f may change sign for 0 < t < 1, i.e., we allow that the nonlinear term f is both semipositone and lower unbounded. Without making any monotone-type assumption, by using the fixed-point index theory, the existence of positive solution and many positive solutions are obtained.
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  Estimates on Higher Order Damped Wave Equation

  Wei Liang XIAO, Xu Huan ZHOU, Tao Tao ZHENG

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 271-286. https://doi.org/10.12386/A2015sxxb0027

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  This paper focus on the L^p estimates of the higher order damped wave equation. Using tools from harmonic analysis, especially the method of oscillatory integral, we calculated the point-wise estimates for the kernel related to the solution of the homogeneous equation. Also we apply these estimates to study the space-time estimates and the global solution to the Cauchy problem of the nonlinear equation.
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  C-Filters in Enriched Union Semi-Lattice with Its Applications

  Hong Bo WU, Hai Yan KOU

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 287-300. https://doi.org/10.12386/A2015sxxb0028

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  Firstly, the concept of upper covering relation in a union semi-lattice and upper coverage defined by the forme in an enriched union semi-lattice are introduced, the basic properties of them are discussed in enriched union semi-lattices. Secondly, the concept of C-filters is introduced in enriched union semi-lattices through upper coverage, it is proved that C-filters are usual filters, but usual filters are not C-filters in an enriched union semi-lattice. Thirdly, the relationships between morphisms of enriched union semi-lattice and co-Frames are investigated. At last, the isomorphism theorem between co-Frames and its C_S-filter co-Frames is proved.
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  Filtrations and Classifications for the Non-Simple Lie Superalgebras of Type W or S

  Xiu Qiang ZHANG, Wen De LIU

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 301-308. https://doi.org/10.12386/A2015sxxb0029

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  Let F be a field and char F = p > 3. Let g denote the Lie superalgebra which is the tensor product of an exterior superalgebra and a finite-dimensional generalized Witt algebra or special Lie algebra over F. In this paper it is proved that the standard filtration of the non-simple Lie superalgebra g is invariant under the automorphism group of g by means of investigating the ad nilpotent elements. Finally, the superalgebras of type W or S are classified by means of the parameters defining them.
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  Some Boundedness of Homogeneous Fractional Integrals onVariable Exponent Function Spaces

  Jian TAN, Zong Guang LIU

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 309-320. https://doi.org/10.12386/A2015sxxb0030

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  In this paper, the authors establish some boundedness of homogeneous fractional integrals on some variable exponent function spaces, such as variable Lebesgue spaces, variable Hardy spaces and variable Herz-type Hardy spaces.
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  On Non-Commuting Sets in a Finite p-Group with a Cyclic Center

  Yu Lei WANG, He Guo LIU

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 321-328. https://doi.org/10.12386/A2015sxxb0031

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  Let G be a group. A subset X in G is said to be non-commuting if xy≠yx for any x, y ∈ X with x ≠y. Furthermore, if |X| ≥ |Y| for any other non-commuting subset Y in G, then X is said to be a maximal non-commuting set. In this paper, the bound for the cardinality of a maximal non-commuting set in a finite p-group with a cyclic center is determined.
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  Affine Factorable Surfaces in Three-Dimensional Euclidean Space

  Peng ZONG, Lin XIAO, Hui Li LIU

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 329-336. https://doi.org/10.12386/A2015sxxb0032

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  Affine factorable surfaces in Euclidean 3-space were defined. The classification of surfaces with zero Gauss curvature and nonzero constant mean curvature and minimal affine factorable surfaces was given.
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  A Reconsideration on the Ptolemy Constant of Absolute Normalized Norms

  Zhan Fei ZUO

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 337-344. https://doi.org/10.12386/A2015sxxb0033

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  We determine and estimate the Ptolemy constant of absolute normalized norms on some new conditions. The new results which not only contain the previous results, but also give some new results in some concrete Banach spaces.
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  Normal Families Concerning Exceptional Functions and Shared Functions

  Hui Ling QIU, Cai Yun FANG, Ming Liang FANG

  Acta Mathematica Sinica, Chinese Series. 2015, 58(2): 345-352. https://doi.org/10.12386/A2015sxxb0034

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  Let F be a family of meromorphic functions in a domain D, let a(z), b(z), c(z) be three distinct meromorphic functions in D, one may be ∞, and for any z∈ D, a(z)= b(z), a(z) = c(z), b(z) = c(z), and let S = {a(z), b(z), c(z)}. If for any two functions f, g∈F, f and g share the set S in D, then F is normal in D. This extends the famous Montel's criterion.