15 September 2015, Volume 31 Issue 9

    

• Select all
  |

Articles
• Select
  Constructions of 1(1/2)-designs from Symplectic Geometry over Finite Fields

  Zhao CHAI, Rong Quan FENG, Li Wei ZENG

  Acta Mathematica Sinica. 2015, 31(9): 1367-1378. https://doi.org/10.1007/s10114-015-4716-4

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we construct some 1(1/2)-designs, which are also known as partial geometric designs, using totally isotropic subspaces of the symplectic space and generalized symplectic graphs. Furthermore, these 1(1/2)-designs yield six infinite families of directed strongly regular graphs.
• Select
  A Local Hölder Estimate of (K₁,K₂)-Quasiconformal Mappings between Hypersurfaces

  Shen Zhou ZHENG

  Acta Mathematica Sinica. 2015, 31(9): 1379-1390. https://doi.org/10.1007/s10114-015-3519-y

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we prove a local Hölder estimate of (K₁,K₂)-quasiconformal mappings between n-dimensional hypersurfaces of Rⁿ⁺¹ under an assumption of bounded mean curvature of the original hypersurface M. With some new ingredients of the isoperimetric inequality and the co-area formula on manifolds, we extend Simon's work of quasiconformal mappings on surfaces of R³ to the setting of n-dimensional hypersurfaces of Rⁿ⁺¹.
• Select
  Noncompact 4-manifolds with Uniformly Positive Isotropic Curvature

  Liang Ming SHEN

  Acta Mathematica Sinica. 2015, 31(9): 1391-1414. https://doi.org/10.1007/s10114-015-1611-y

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we study Ricci flow on noncompact 4-manifolds with uniformly positive isotropic curvature and with no essential imcompressible space form. That means there is positive lower bound of isotropic curvature and bounded geometry. Then by Perelman's technique, we can analyze the structures of such manifolds.
• Select
  Singular Hyperbolicity of Star Flows on Surfaces

  Sheng Zhi ZHU

  Acta Mathematica Sinica. 2015, 31(9): 1415-1423. https://doi.org/10.1007/s10114-015-4709-3

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we prove that every star flow on the closed surface has finitely many chain recurrent classes. Furthermore, it is singular hyperbolic if every non-trivial singular chain component is a graph. As a consequence, every star flow on the 2-sphere or the projective plane is singular hyperbolic.
• Select
  Quasisymmetric Mappings on Moran Sets

  Yanzhe LI

  Acta Mathematica Sinica. 2015, 31(9): 1424-1434. https://doi.org/10.1007/s10114-015-4432-0

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  This paper studies the quasisymmetric mappings on Moran sets. We introduce a generalized form of weak quasisymmetry and prove that, on Moran set satisfying the small gap condition, a generalized weakly quasisymmetric mapping is quasisymmetric. We further give a criterion for the quasisymmetry of mappings between Moran sets with some regular structure.
• Select
  Viscosity Iterative Algorithm for Variational Inequality Problems and Fixed Point Problems of Strict Pseudo-contractions in Uniformly Smooth Banach Spaces

  Gang CAI

  Acta Mathematica Sinica. 2015, 31(9): 1435-1448. https://doi.org/10.1007/s10114-015-4623-8

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  The purpose of this paper is to study a new viscosity iterative algorithm based on a generalized contraction for finding a common element of the set of solutions of a general variational inequality problem for finite inversely strongly accretive mappings and the set of common fixed points for a countable family of strict pseudo-contractions in uniformly smooth Banach spaces. We prove some strong convergence theorems under some suitable conditions. The results obtained in this paper improve and extend the recent ones announced by many others in the literature.
• Select
  Convergence of the Modified Discrete Ordinates Method for the Anisotropic Scattering Transport Equation

  Xin ZHANG

  Acta Mathematica Sinica. 2015, 31(9): 1449-1460. https://doi.org/10.1007/s10114-015-4507-y

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Criticality problem of nuclear tractors generally refers to an eigenvalue problem for the transport equations. In this paper, we deal with the eigenvalue of the anisotropic scattering transport equation in slab geometry. We propose a new discrete method which was called modified discrete ordinates method. It is constructed by redeveloping and improving discrete ordinates method in the space of L¹(X). Different from traditional methods, norm convergence of operator approximation is proved theoretically. Furthermore, convergence of eigenvalue approximation and the corresponding error estimation are obtained by analytical tools.
• Select
  Some Notes on Amenability and Weak Amenability of Lau Product of Banach Algebras Defined by a Banach Algebra Morphism

  Prakash A. DABHI, Ali JABBARI, Kazem HAGHNEJAD AZAR

  Acta Mathematica Sinica. 2015, 31(9): 1461-1474. https://doi.org/10.1007/s10114-015-4429-8

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let A and B be Banach algebras and T : B → A be a continuous homomorphism. nweak amenability of the Banach algebra A×_T B (defined in Bade, W. G., Curtis, P. C., Dales, H. G.: Amenability and weak amenability for Beurling and Lipschitz algebras. Proc. London Math. Soc., 55(2), 359-377 (1987)) is studied. The new version of a Banach algebra defined with a continuous homomorphism is introduced and Arens regularity and various notions of amenability of this algebra are studied.
• Select
  On n-Widths of a Sobolev Function Class in Orlicz Spaces

  Xiao Li WANG, Ga Ridi WU

  Acta Mathematica Sinica. 2015, 31(9): 1475-1486. https://doi.org/10.1007/s10114-015-4231-7

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  This paper considers the problem of n-widths of a Sobolev function class Ω_∞^r determined by P_r(D) = D^σ∏_j=1^l(D²-t_j² I) in Orlicz spaces. The relationship between the extreme value problem and width theory is revealed by using the methods of functional analysis. Particularly, as σ = 0 or σ = 1, the exact values of Kolmogorov's widths, Gelfand's widths, and linear widths are obtained respectively, and the related extremal subspaces and optimal linear operators are given.
• Select
  Gaussian Fluctuations of Eigenvalues in Log-gas Ensemble: Bulk Case I

  Deng ZHANG

  Acta Mathematica Sinica. 2015, 31(9): 1487-1500. https://doi.org/10.1007/s10114-015-3685-y

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We study the central limit theorem of the k-th eigenvalue of a random matrix in the log-gas ensemble with an external potential V = q2m^x2m. More precisely, let P_n(dH) = C_ne^-nTrV(H)dH be the distribution of n × n Hermitian random matrices, ρV(x)dx the equilibrium measure, where C_n is a normalization constant, V (x) = q2m^x2m with q2m = (Γ(m)Γ(1/2))/(Γ((2m+1)/2), and m ≥ 1. Let x₁ ≤…≤ x_n be the eigenvalues of H. Let k := k(n) be such that (k(n))/n ∈ [a, 1-a] for n large enough, where a ∈ (0, 1/2). Define
  G(s) :=∫_-1^s ρV (x)dx, -1 ≤ s ≤ 1,
  and set t := G^-1(k/n). We prove that, as n→∞,
  (x_k-t)/(√logn/√2π²nρV (t)) → N(0, 1)
  in distribution. Multi-dimensional central limit theorem is also proved. Our results can be viewed as natural extensions of the bulk central limit theorems for GUE ensemble established by J. Gustavsson in 2005.
• Select
  On the Complexity of Expansive Measures

  C. A. MORALES

  Acta Mathematica Sinica. 2015, 31(9): 1501-1507. https://doi.org/10.1007/s10114-015-4725-3

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We prove that the existence of positively expansive measures for continuous maps on compact metric spaces implies the existence of e > 0 and a sequence of (m, e)-separated sets whose cardinalities go to infinite as m→∞. We then prove that maps exhibiting such a constant e and the positively expansive maps share some properties.
• Select
  On Support τ-tilting Modules over Endomorphism Algebras of Rigid Objects

  Wen CHANG, Jie ZHANG, Bin ZHU

  Acta Mathematica Sinica. 2015, 31(9): 1508-1516. https://doi.org/10.1007/s10114-015-4161-4

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We consider a Krull-Schmidt, Hom-finite, 2-Calabi-Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented category pr T of T and the set of isomorphism classes of basic τ -rigid pairs in the module category of the endomorphism algebra End_C(T)^op. As a consequence, basic maximal objects in pr T are one-to-one correspondence to basic support τ-tilting modules over End_C(T)^op. This is a generalization of correspondences established by Adachi-Iyama-Reiten.