中国科学院数学与系统科学研究院期刊网
AMS

15 June 2013, Volume 29 Issue 6
    

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  • Total Restrained Bondage in Graphs
    Nader JAFARI RAD, Roslan HASNI, Joanna RACZEK, Lutz VOLKMANN
    Acta Mathematica Sinica. 2013, 29(6): 1033-1042. https://doi.org/10.1007/s10114-013-1085-8
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    A subset S of vertices of a graph G with no isolated vertex is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V(G)-S is also adjacent to a vertex in V(G)-S. The total restrained domination number of G is the minimum cardinality of a total restrained dominating set of G. In this paper we initiate the study of total restrained bondage in graphs. The total restrained bondage number in a graph G with no isolated vertex, is the minimum cardinality of a subset of edges E such that G-E has no isolated vertex and the total restrained domination number of G-E is greater than the total restrained domination number of G. We obtain several properties, exact values and bounds for the total restrained bondage number of a graph.
  • Commutator of Hypersingular Integral with Rough Kernels on Sobolev Spaces
    Yan Ping CHEN, Yong DING, Xin Xia WANG
    Acta Mathematica Sinica. 2013, 29(6): 1043-1054. https://doi.org/10.1007/s10114-013-2127-y
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    In this paper, the authors give the boundedness of the commutator of hypersingular integral Tγ from the homogeneous Sobolev space LγP(Rn) to the Lebesgue space LP (Rn) for 1 < p < ∞ and 0 < γ < min{n/2, n/p}.
  • Modular Filter Convergence Theorems for Urysohn Integral Operators and Applications
    Antonio BOCCUTO, Xenofon DIMITRIOU
    Acta Mathematica Sinica. 2013, 29(6): 1055-1066. https://doi.org/10.1007/s10114-013-1443-6
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    We prove some versions of modular convergence theorems for nonlinear Urysohn-type integral operators with respect to filter convergence. We consider pointwise filter convergence of functions giving also some applications to linear and nonlinear Mellin operators. We show that our results are strict extensions of the classical ones.
  • Blow-up of Solutions for a Time-space Fractional Evolution System
    Yong Qiang XU, Zhong TAN
    Acta Mathematica Sinica. 2013, 29(6): 1067-1074. https://doi.org/10.1007/s10114-013-1433-8
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    In this paper, firstly, we study the local existence and uniqueness of mild solutions for fractional evolution systems with nonlocal in time nonlinearity. Then, we claim that such a mild solution is weak solution of this system. Finally, we prove a blow-up result under some conditions.
  • Existence of Diffusion Orbits in a Lattice System
    Ji LI
    Acta Mathematica Sinica. 2013, 29(6): 1075-1088. https://doi.org/10.1007/s10114-013-2168-2
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    We study a model which is a periodic lattice system with nearest neighbors coupling. Using the variational methods, we show the existence of diffusion orbits under a generic perturbation of time periodic.
  • Existence of Weakly Pandiagonal Orthogonal Latin Squares
    Yong ZHANG, Wen LI, Jian Guo LEI
    Acta Mathematica Sinica. 2013, 29(6): 1089-1094. https://doi.org/10.1007/s10114-013-2274-1
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    A weakly pandiagonal Latin square of order n over the number set {0, 1,..., n-1} is a Latin square having the property that the sum of the n numbers in each of 2n diagonals is the same. In this paper, we shall prove that a pair of orthogonal weakly pandiagonal Latin squares of order n exists if and only if n ≡ 0, 1, 3 (mod 4) and n ≠ 3.
  • A Note on Multitype Branching Process with Bounded Immigration in Random Environment
    Hua Ming WANG
    Acta Mathematica Sinica. 2013, 29(6): 1095-1110. https://doi.org/10.1007/s10114-013-1350-x
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    In this paper, we study the total number of progeny, W, before regenerating of multitype branching process with immigration in random environment. We show that the tail probability of |W| is of order t-κ as t → ∞, with κ some constant. As an application, we prove a stable law for (L-1) random walk in random environment, generalizing the stable law for the nearest random walk in random environment (see "Kesten, Kozlov, Spitzer: A limit law for random walk in a random environment. Compositio Math., 30, 145-168 (1975)").
  • Parameter Dependence of Stable Manifolds for Nonuniform (μ, ν)-dichotomies
    Ji Min ZHANG, Meng FAN, Xiao Yuan CHANG
    Acta Mathematica Sinica. 2013, 29(6): 1111-1130. https://doi.org/10.1007/s10114-013-1408-9
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    We construct stable invariant manifolds for semiflows generated by the nonlinear impul-sive differential equation with parameters x' = A(t)x + f(t, x, λ), t ≠ τi and x(τi+) = Bix (τi) + gi(x (τi), λ), i ∈ N in Banach spaces, assuming that the linear impulsive differential equation x' = A(t)x, t ≠ τi and x (τi+) = Bix (τi), i ∈ N admits a nonuniform (μ, ν)-dichotomy. It is shown that the stable invariant manifolds are Lipschitz continuous in the parameter λ and the initial values provided that the nonlinear perturbations f, g are sufficiently small Lipschitz perturbations.
  • The Configuration of Shock Wave Reflection for the TSD Equation
    Li WANG
    Acta Mathematica Sinica. 2013, 29(6): 1131-1158. https://doi.org/10.1007/s10114-013-1489-5
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    In this paper, we mainly study the nonlinear wave configuration caused by shock wave reflection for the TSD (Transonic Small Disturbance) equation and specify the existence and nonexistence of various nonlinear wave configurations. We give a condition under which the solution of the RR (Regular reflection) for the TSD equation exists. We also prove that there exists no wave configuration of shock wave reflection for the TSD equation which consists of three or four shock waves. In phase space, we prove that the TSD equation has an IR (Irregular reflection) configuration containing a centered simple wave. Furthermore, we also prove the stability of RR configuration and the wave configuration containing a centered simple wave by solving a free boundary value problem of the TSD equation.
  • Blow-up Criterion for Three-dimensional Compressible Viscoelastic Fluids with Vacuum
    Sheng Quan LIU, Jun Ning ZHAO
    Acta Mathematica Sinica. 2013, 29(6): 1159-1174. https://doi.org/10.1007/s10114-013-1569-6
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    In this paper, we study a Cauchy problem for the equations of 3D compressible viscoelastic fluids with vacuum. We establish a blow-up criterion for the local strong solutions in terms of the upper bound of the density and deformation gradient.
  • Conjugate Points on a Type of Kähler Manifolds
    Wei Ming LIU, Fu Sheng DENG
    Acta Mathematica Sinica. 2013, 29(6): 1175-1184. https://doi.org/10.1007/s10114-013-1695-1
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    We study conjugate points on a type of Kähler manifolds, which are submanifolds of Grassmannian manifolds. And then we give the applications to the study of the index of geodesics and homotopy groups.
  • Relaxation and Nonoccurrence of the Lavrentiev Phenomenon for Nonconvex Problems
    Farhad HÜSSEINOV
    Acta Mathematica Sinica. 2013, 29(6): 1185-1198. https://doi.org/10.1007/s10114-013-1721-3
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    The paper studies a relaxation of the basic multidimensional variational problem, when the class of admissible functions is endowed with the Lipschitz convergence introduced by Morrey. It is shown that in this setup, the integral of a variational problem must satisfy a classical growth condition, unlike the case of uniform convergence. The relaxations constructed here imply the existence of a Lipschitz convergent minimizing sequence. Based on this observation, the paper also shows that the Lavrentiev phenomenon does not occur for a class of nonconvex problems.
  • Subgroup Separability of Certain Generalized Free Products of Nilpotent-by-finite Groups
    Wei ZHOU, Goansu KIM
    Acta Mathematica Sinica. 2013, 29(6): 1199-1204. https://doi.org/10.1007/s10114-013-0547-3
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    In this paper, we show that certain generalized free products of nilpotent-by-finite groups are subgroup separable when the amalgamated subgroup is <h> × D where D is in the center of both factors.
  • New Periodic Solutions for a Class of Singular Hamiltonian Systems
    Peng Fei YUAN, Shi Qing ZHANG
    Acta Mathematica Sinica. 2013, 29(6): 1205-1218. https://doi.org/10.1007/s10114-013-0601-1
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    In this paper, we apply a variant of the famous Mountain Pass Lemmas of AmbrosettiRabinowitz and Ambrosetti-Coti Zelati with (PSC)c type condition of Palais-Smale-Cerami to study the existence of new periodic solutions with a prescribed energy for symmetrical singular second order Hamiltonian conservative systems with weak force type potentials.
  • Mutation on Knots and Whitney's 2-Isomorphism Theorem
    Zhi Yun CHENG, Hong Zhu GAO
    Acta Mathematica Sinica. 2013, 29(6): 1219-1230. https://doi.org/10.1007/s10114-013-0679-5
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    Whitney's 2-switching theorem states that any two embeddings of a 2-connected planar graph in S2 can be connected via a sequence of simple operations, named 2-switching. In this paper, we obtain two operations on planar graphs from the view point of knot theory, which we will term "twisting" and "2-switching" respectively. With the twisting operation, we give a pure geometrical proof of Whitney's 2-switching theorem. As an application, we obtain some relationships between two knots which correspond to the same signed planar graph. Besides, we also give a necessary and sufficient condition to test whether a pair of reduced alternating diagrams are mutants of each other by their signed planar graphs.
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