中国科学院数学与系统科学研究院期刊网
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15 June 2014, Volume 30 Issue 6
    

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  • Categorification of Integrable Representations of Quantum Groups
    Hao ZHENG
    Acta Mathematica Sinica. 2014, 30(6): 899-932. https://doi.org/10.1007/s10114-014-3631-4
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    We categorify the highest weight integrable representations and their tensor products of a symmetric quantum Kac-Moody algebra. As a byproduct, we obtain a geometric realization of Lusztig's canonical bases of these representations as well as a new positivity result. The main ingredient in the underlying geometric construction is a class of micro-local perverse sheaves on quiver varieties.
  • The Boundedness of Composition Operators on Triebel-Lizorkin and Besov Spaces with Different Homogeneities
    Wei DING
    Acta Mathematica Sinica. 2014, 30(6): 933-948. https://doi.org/10.1007/s10114-014-3280-7
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    In this paper, we introduce new Triebel-Lizorkin and Besov Spaces associated with the different homogeneities of two singular integral operators. We then establish the boundedness of composition of two Calderón-Zygmund singular integral operators with different homogeneities on these Triebel-Lizorkin and Besov spaces.
  • A Posterior Error Analysis for the Nonconforming Discretization of Stokes Eigenvalue Problem
    Shang Hui JIA, Fu Sheng LUO, He Hu XIE
    Acta Mathematica Sinica. 2014, 30(6): 949-967. https://doi.org/10.1007/s10114-014-3121-8
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    In this paper, we present a posteriori error estimator for the nonconforming finite element approximation, including using Crouzeix-Raviart element and extended Crouzeix-Raviart element, of the Stokes eigenvalue problem. With the technique of Helmholtz decomposition, we first give out a posteriori error estimator and prove it as the global upper bound and local lower bound of the approximation error. Then, by deleting a jump term in the indicator, another simpler but equivalent indicator is obtained. Some numerical experiments are provided to verify our analysis.
  • Relations between Simplicial Groups, 3-Crossed Modules and 2-Quadratic Modules
    Hasan ATİK, Erdal ULUALAN
    Acta Mathematica Sinica. 2014, 30(6): 968-984. https://doi.org/10.1007/s10114-014-3416-9
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    In this paper, we define two-quadratic module and explore the relations among twoquadratic modules, three-crossed modules and simplicial groups.
  • On the Hochstadt-Lieberman Theorem for Discontinuous Boundary-valued Problems
    Yu Ping WANG, Hikmet KOYUNBAKAN
    Acta Mathematica Sinica. 2014, 30(6): 985-992. https://doi.org/10.1007/s10114-014-3221-5
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    In this paper, we discuss the half inverse problem for Sturm-Liouville equations with boundary conditions dependent on the spectral parameter and a finite number of discontinuities inside the interval and prove the Hochstadt-Liberman type theorem for the above boundary-valued problem.
  • A Sufficient Condition for Planar Graphs with Maximum Degree 8 to Be 9-totally Colorable
    Jian Sheng CAI, Chang Chun TENG, Gui Ying YAN
    Acta Mathematica Sinica. 2014, 30(6): 993-1006. https://doi.org/10.1007/s10114-014-3170-z
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    A total k-coloring of a graph G is a coloring of V (G) ∪ E(G) using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ"(G) is the smallest integer k such that G has a total k-coloring. It is known that if a planar graph G has maximum degree Δ ≥ 9, then χ" (G) = Δ+1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without a fan of four adjacent 3-cycles, then χ"(G) = 9.
  • Stable Weakly Shadowable Volume-preserving Systems Are Volume-hyperbolic
    Mário BESSA, Manseob LEE, Sandra VAZ
    Acta Mathematica Sinica. 2014, 30(6): 1007-1020. https://doi.org/10.1007/s10114-014-3093-8
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    We prove that any C1-stable weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E ⊕ F. Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity.
  • The Limit Theorems for Maxima of Stationary Gaussian Processes with Random Index
    Zhong Quan TAN
    Acta Mathematica Sinica. 2014, 30(6): 1021-1032. https://doi.org/10.1007/s10114-014-2809-0
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    Let {X(t), t ≥ 0} be a standard (zero-mean, unit-variance) stationary Gaussian process with correlation function r(·) and continuous sample paths. In this paper, we consider the maxima M(T) = max{X(t), ∀t ∈ [0, T]} with random index TT, where TT/T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of M(TT) exists under some additional conditions related to the correlation function r(·).
  • On the Stability of a Mixed Functional Equation Deriving from Additive, Quadratic and Cubic Mappings
    Li Guang WANG, Kun Peng XU, Qiu Wen LIU
    Acta Mathematica Sinica. 2014, 30(6): 1033-1049. https://doi.org/10.1007/s10114-014-3335-9
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    In this paper, we investigate the general solution and the Hyers-Ulam stability of the following mixed functional equation f(2x + y) + f(2x - y) = 2f(2x) + 2f(x + y) + 2f(x - y) -4f(x) - f(y) - f(-y) deriving from additive, quadratic and cubic mappings on Banach spaces.
  • On the Convergence Behavior of Conformal Immersion Sequence from Cylinders
    Li CHEN
    Acta Mathematica Sinica. 2014, 30(6): 1050-1060. https://doi.org/10.1007/s10114-014-1614-0
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    In this paper, we are concerned with the convergence behavior of a sequence of conformal immersions {fn} from long cylinders Pn with Pn |Afn|2 + μ(fn(Pn)) < Λ. We show that if {fn} does not converge to a point, the total Gauss curvatures and the measures of the images of {fn} will not lose on the necks and each neck consists of a point.
  • Asymptotic Behavior of Impulsive Stochastic Functional Differential Equations
    Li Guang XU, Dan Hua HE
    Acta Mathematica Sinica. 2014, 30(6): 1061-1072. https://doi.org/10.1007/s10114-014-1099-x
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    In this paper, a nonlinear and nonautonomous impulsive stochastic functional differential equation is considered. By establishing a nonautonomous L-operator impulsive delay inequality and using the properties of ρ-cone and stochastic analysis technique, we obtain the p-attracting set and p-invariant set of the impulsive stochastic functional differential equation. An example is also discussed to illustrate the efficiency of the obtained results.
  • Low Dimensional Cohomology of Hom-Lie Algebras and q-deformed W(2, 2) Algebra
    La Mei YUAN, Hong YOU
    Acta Mathematica Sinica. 2014, 30(6): 1073-1082. https://doi.org/10.1007/s10114-013-2614-1
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    This paper aims to study low dimensional cohomology of Hom-Lie algebras and the q-deformed W(2, 2) algebra. We show that the q-deformed w(2, 2) algebra is a Hom-Lie algebra. Also, we establish a one-to-one correspondence between the equivalence classes of one-dimensional central extensions of a Hom-Lie algebra and its second cohomology group, leading us to determine the second cohomology group of the q-deformed w(2, 2) algebra. In addition, we generalize some results of derivations of finitely generated Lie algebras with values in graded modules to Hom-Lie algebras. As application, we compute all αk-derivations and in particular the first cohomology group of the q-deformed w(2, 2) algebra.
  • Non-wandering Expanding Maps on Branched 1-Manifolds and Smale-Williams Solenoids
    Xiao Ming DU
    Acta Mathematica Sinica. 2014, 30(6): 1083-1088. https://doi.org/10.1007/s10114-013-2434-3
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    In this paper, we give a criterion of whether there are non-wandering expanding maps on a given branched 1-manifold. As an application, we give an example of a dynamic on a 3-manifold having non-zero first Betti number, the non-wander sets of which are two Smale-Williams solenoids.
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