15 July 2013, Volume 29 Issue 7

    

• Select all
  |

Articles
• Select
  Rough Marcinkiewicz Integrals with Mixed Homogeneity on Product Spaces

  Feng LIU, Huo Xiong WU

  Acta Mathematica Sinica. 2013, 29(7): 1231-1244. https://doi.org/10.1007/s10114-013-1675-5

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, the parabolic Marcinkiewicz integral operators on the product spaces R^m×Rⁿ(m, n≥2) are studied. The L^p-boundedness for such operators are established under rather weak size conditions of the kernels, which essentially improve or extend certain previous results.
• Select
  Characterizing Centralizers and Generalized Derivations on Triangular Algebras by Acting on Zero Product

  Xiao Fei QI, Jin Chuan HOU

  Acta Mathematica Sinica. 2013, 29(7): 1245-1256. https://doi.org/10.1007/s10114-013-2068-5

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let U= Tri(A, M, B) be a triangular ring, where A and B are unital rings, and M is a faithful (A,B)-bimodule. It is shown that an additive map Φ on U is centralized at zero point (i.e., Φ(A)B = AΦ(B)=0 whenever AB=0) if and only if it is a centralizer. Let δ:U→U be an additive map. It is also shown that the following four conditions are equivalent: (1) δ is specially generalized derivable at zero point, i.e., δ(AB)=δ(A)B+Aδ(B)-Aδ(I)B whenever AB=0; (2) δ is generalized derivable at zero point, i.e., there exist additive maps τ₁ and τ₂ on U derivable at zero point such that δ(AB)=δ(A)B + Aτ₁(B)=τ₂(A)B+Aδ(B) whenever AB=0; (3) δ is a special generalized derivation; (4) δ is a generalized derivation. These results are then applied to nest algebras of Banach space.
• Select
  Derivatives of Meromorphic Functions with Multiple Zeros and Elliptic Functions

  Pai YANG, Shahar NEVO

  Acta Mathematica Sinica. 2013, 29(7): 1257-1278. https://doi.org/10.1007/s10114-013-2375-x

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let f be a nonconstant meromorphic function in the plane and h be a nonconstant elliptic function. We show that if all zeros of f are multiple except finitely many and T(r, h)=o{T(r, f)} as r→∞, then f'=h has infinitely many solutions (including poles).
• Select
  Ghost Length, Cone Length and Complete Level of DG Modules

  Xue Feng MAO

  Acta Mathematica Sinica. 2013, 29(7): 1279-1310. https://doi.org/10.1007/s10114-013-1306-1

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we introduce a new numerical invariant complete level for a DG module over a local chain DG algebra and give a characterization of it in terms of ghost length. We also study some of its upper bounds. The cone length of a DG module is an invariant closely related with the invariant level. We discover some important results on it.
• Select
  Some Classes of Kenmotsu Manifolds with Respect to Semi-symmetric Metric Connection

  D. G. PRAKASHA, Aysel TURGUT VANLI, C. S. BAGEWADI, D. A. PATIL

  Acta Mathematica Sinica. 2013, 29(7): 1311-1322. https://doi.org/10.1007/s10114-013-0326-1

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we study conharmonic curvature tensor in Kenmotsu manifolds with respect to semi-symmetric metric connection and also characterize conharmonically flat, conharmonically semisymmetric and φ-conharmonically flat Kenmotsu manifolds with respect to semi-symmetric metric connection.
• Select
  On a Criterion of Universal Spectra

  Jian Lin LI

  Acta Mathematica Sinica. 2013, 29(7): 1323-1328. https://doi.org/10.1007/s10114-013-0559-z

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  For positive integers N₁,N₂, . . . ,N_n, let L=Zⁿ+A and Λ = N₁Z × · · · × N_nZ + Γ be two rational periodic sets, where A(1/N₁)Z × · · · × (1/N_n)Z and Γ Zⁿ are finite sets with (A-A)∩Zⁿ={0} and (Γ-Γ)∩(N₁Z×· · ·×N_nZ)={0}. In this note, we shall determine conditions under which the tiling set L has universal spectrum Λ. We first obtain a criterion of universal spectra. This criterion combined with the properties of compatible pair yields many necessary and sufficient conditions for Λ to be a universal spectrum for L. We then show that, under some mild additional conditions, the conjecture of Lagarias and Szabó is true. The results here extend the corresponding results of Lagarias, Szabó and Wang.
• Select
  Generalized Notions of Character Amenability

  Hasan Pourmahmood AGHABABA, Luo Yi SHI, Yu Jing WU

  Acta Mathematica Sinica. 2013, 29(7): 1329-1350. https://doi.org/10.1007/s10114-013-0627-4

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, the concepts of approximate character amenability (contractibility), uniform approximate character amenability (contractibility) and w^*-approximate character amenability are introduced. We are concerned with the relations among the generalized concepts of character amenability for Banach algebras. We show that approximate character amenability, w^*-approximate character amenability and approximate character contractibility are the same properties, as uniform approximate character amenability and character amenability, as uniform approximate character contractibility and character contractibility. The general theory for these concepts is also developed. Moreover, approximate character amenability of several concrete classes of Banach algebras related to locally compact groups and also some discrete semigroups is considered.
• Select
  Generalized McKay Quivers of Rank Three

  Xiao Li HU, Naihuan JING, Wu Xing CAI

  Acta Mathematica Sinica. 2013, 29(7): 1351-1368. https://doi.org/10.1007/s10114-013-1005-y

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  For each finite subgroup G of SL_n(C), we introduce the generalized Cartan matrix A_G in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices have similar favorable properties such as positive semidefiniteness as in the classical case of affine Cartan matrices. The complete McKay quivers for SL(C) are explicitly described and classified based on representation theory.
• Select
  On the Rigidity Theorems for Lagrangian Translating Solitons in Pseudo-Euclidean Space I

  Rui Wei XU, Rong Li HUANG

  Acta Mathematica Sinica. 2013, 29(7): 1369-1380. https://doi.org/10.1007/s10114-013-1046-2

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let f be a smooth strictly convex solution of
  1369
  defined on a domain Ω ⊂ Rⁿ, where a_i, b_i and c are constants. Then the graph M_∇f of ∇f is a spacelike translating soliton for mean curvature flow in pseudo-Euclidean space R_n²ⁿ with the translating vector 1/n (a₁, a₂, . . . , a_n; b₁, b₂, . . . , b_n). In this paper, we will use affine technique to show a Bernstein Theorem: if the graph M_∇f is complete, then f(x) must be a quadratic polynomial and M_∇f is an affine n-plane.
• Select
  Orthogonality and Quintic Functional Equations

  Choonkil PARK, Jian Lian CUI, Madjid Eshaghi GORDJI

  Acta Mathematica Sinica. 2013, 29(7): 1381-1390. https://doi.org/10.1007/s10114-013-1061-3

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Using the fixed point method, we prove the Hyers-Ulam stability of an orthogonally quintic functional equation in Banach spaces and in non-Archimedean Banach spaces.
• Select
  On the Indecomposable Modules of U_q(sl(2)) Constructed via Ore-extension

  Zhi Hua WANG, Li Bin LI

  Acta Mathematica Sinica. 2013, 29(7): 1391-1400. https://doi.org/10.1007/s10114-013-1426-7

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let A be a subalgebra of U_q(sl(2)) generated by K,K^-1 and F and A^δ be a subalgebra of U_q(sl(2)) generated by K,K^-1 (and also F^d if q is a primitive d-th root of unity with d an odd number). Given an A^δ-module M, a U_q(sl(2))-module A⊗_A^δ M is constructed via the iterated Ore extension of U_q(sl(2)) in a unified framework for any q. Then all the submodules of A ⊗_A^δ M are determined for a fixed finite-dimensional indecomposable A^δ-module M. It turns out that for some indecomposable A^δ-module M, the U_q(sl(2))-module A⊗_A^δ M is indecomposable, which is not in the BGG-categories O_q associated with quantum groups in general.
• Select
  Block Sparse Recovery via Mixed l₂/l₁ Minimization

  Jun Hong, LIN Song LI

  Acta Mathematica Sinica. 2013, 29(7): 1401-1412. https://doi.org/10.1007/s10114-013-1564-y

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We consider efficient methods for the recovery of block sparse signals from underdetermined system of linear equations. We show that if the measurement matrix satisfies the block RIP with δ_2s < 0.4931, then every block s-sparse signal can be recovered through the proposed mixed l₂/l₁-minimization approach in the noiseless case and is stably recovered in the presence of noise and mismodeling error. This improves the result of Eldar and Mishali (in IEEE Trans. Inform. Theory 55: 5302-5316, 2009). We also give another sufficient condition on block RIP for such recovery method: δ_s < 0.307.
• Select
  A Nonclassical LIL for Geometrically Weighted Series in Banach Space

  Ke Ang FU, Xiao Rong YANG, Wei HUANG

  Acta Mathematica Sinica. 2013, 29(7): 1413-1420. https://doi.org/10.1007/s10114-013-1591-8

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let {X,X_n; n ≥ 0} be a sequence of independent and identically distributed random variables, taking values in a separable Banach space (B,‖·‖) with topological dual B^*. Considering the geometrically weighted series ξ(β)=Σ_n=0^∞ βⁿX_n for 0 < β < 1, and a sequence of positive constants {h(n), n ≥ 1}, which is monotonically approaching infinity and not asymptotically equivalent to log log n, a limit result for √1-β²‖ξ(β)‖/√2h(1/(1-β²)) is achieved.
• Select
  On Edge Colorings of 1-Toroidal Graphs

  Xin ZHANG, Gui Zhen LIU

  Acta Mathematica Sinica. 2013, 29(7): 1421-1428. https://doi.org/10.1007/s10114-013-1724-0

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  A graph is 1-toroidal, if it can be embedded in the torus so that each edge is crossed by at most one other edge. In this paper, it is proved that every 1-toroidal graph with maximum degree Δ ≥ 10 is of class one in terms of edge coloring. Meanwhile, we show that there exist class two 1-toroidal graphs with maximum degree Δ for each Δ ≤ 8.
• Select
  Homogenization of a Nonlinear Degenerate Parabolic Differential Equation

  Hai Tao CAO, Xing Ye YUE

  Acta Mathematica Sinica. 2013, 29(7): 1429-1436. https://doi.org/10.1007/s10114-013-2133-0

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  This paper is devoted to the homogenization of a nonlinear degenerate parabolic problem
  ?_tu^ε-div(D(x/ε, u^ε, ∇u^ε)+K(x/ε, u^ε))=f(x)
  with Dirichlet boundary condition. Here the operator D(y, s,∇s) is periodic in y and degenerated in ∇s. In the paper, under the two-scale convergence theory, we obtain the limit equation as ε → 0 and also prove the corrector results of ∇u^ε to strong convergence.