15 May 2012, Volume 28 Issue 5

    

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  On Tame Operators between Non-Archimedean Power Series Spaces

  Wieslaw ŚLIWA, Agnieszka ZIEMKOWSKA

  Acta Mathematica Sinica. 2012, 28(5): 869-884. https://doi.org/10.1007/s10114-011-0634-2

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  Let p ∈ {1,∞}. We show that any continuous linear operator T from A₁ (a) to A_p (b) is tame, i.e., there exists a positive integer c such that sup_x ‖T_x‖_k/|x|_ck < ∞ for every k ∈ N. Next we prove that a similar result holds for operators from A_∞ (a) to A_p (b) if and only if the set M_b,a of all finite limit points of the double sequence (b_i/a_j)_,j∈N is bounded. Finally we show that the range of every tame operator from A_∞(a) to A_∞ (b) has a Schauder basis.
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  Stability of Symmetric Closed Characteristics on Symmetric Compact Convex Hypersurfaces in R²ⁿ under a Pinching Condition

  Hui LIU

  Acta Mathematica Sinica. 2012, 28(5): 885-900. https://doi.org/10.1007/s10114-011-0494-9

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  In this paper, let Σ ⊂ R²ⁿ be a symmetric compact convex hypersurface which is (r,R)-pinched with R/r < √5/3. Then Σ carries at least two elliptic symmetric closed characteristics; moreover, Σ carries at least E[(n-1)/2]+E[(n-1)/3] non-hyperbolic symmetric closed characteristics.
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  A₁ Weights and d-Homogeneous Measures on Ahlfors d-Regular Space

  Yu Xia DAI, Sheng You WEN, Zhi Xiong WEN

  Acta Mathematica Sinica. 2012, 28(5): 901-908. https://doi.org/10.1007/s10114-011-0460-6

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  Let X be an Ahlfors d-regular space and m a d-regular measure on X. We prove that a measure μ on X is d-homogeneous if and only if μ is mutually absolutely continuous with respect to m and the derivative D_mμ (x) is an A₁ weight. Also, we show by an example that every Ahlfors d-regular space carries a measure which is d-homogeneous but not d-regular.
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  An L⁰(F,R)-valued Function’s Intermediate Value Theorem and Its Applications to Random Uniform Convexity

  Tie Xin GUO, Xiao Lin ZENG

  Acta Mathematica Sinica. 2012, 28(5): 909-924. https://doi.org/10.1007/s10114-011-0367-2

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  Let (Ω,F, P) be a probability space and L⁰(F, R) the algebra of equivalence classes of realvalued random variables on (Ω,F, P). When L⁰(F, R) is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L⁰(F, R) to L⁰(F, R). As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module (S, ‖·‖) is random uniformly convex iff L^p (S) is uniformly convex for each fixed positive number p such that 1 < p +∞.
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  Global Well-posedness of Compressible Bipolar Navier-Stokes-Poisson Equations

  Yi Quan LIN, Cheng Chun HAO, Hai Liang LI

  Acta Mathematica Sinica. 2012, 28(5): 925-940. https://doi.org/10.1007/s10114-011-0238-x

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  We consider the initial value problem for multi-dimensional bipolar compressible Navier-Stokes-Poisson equations, and show the global existence and uniqueness of the strong solution in hybrid Besov spaces with the initial data close to an equilibrium state.
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  The Degree Distribution of the Random Multigraphs

  Ai Lian CHEN, Fu Ji ZHANG, Hao LI

  Acta Mathematica Sinica. 2012, 28(5): 941-956. https://doi.org/10.1007/s10114-011-0144-2

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  In this paper, as a generalization of the binomial random graph model, we define the model of multigraphs as follows: let G (n; {p_k}) be the probability space of all the labelled loopless multigraphs with vertex set V={v₁, v₂, . . . , v_n}, in which the distribution of tvi,vj , the number of the edges between any two vertices v_i and v_j is {t_vi,vj=k}=p_k, k=0, 1, 2, . . . and they are independent of each other. Denote by X_d=X_d(G), Y_d=Y_d(G), Z_d=Z_d(G) and Z_cd=Z_cd(G) the number of vertices of G with degree d, at least d, at most d and between c and d. In this paper, we discuss the distribution of X_d, Y_d, Z_d and Z_cd in the probability space G(n; {p_k}).
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  *-Regular Leavitt Path Algebras of Arbitrary Graphs

  Gonzalo ARANDA PINO, Kulumani RANGASWAMY, Lia VAŠ

  Acta Mathematica Sinica. 2012, 28(5): 957-968. https://doi.org/10.1007/s10114-011-0106-8

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  If K is a field with involution and E an arbitrary graph, the involution from K naturally induces an involution of the Leavitt path algebra L_K(E). We show that the involution on L_K(E) is proper if the involution on K is positive-definite, even in the case when the graph E is not necessarily finite or row-finite. It has been shown that the Leavitt path algebra L_K(E) is regular if and only if E is acyclic. We give necessary and sufficient conditions for L_K(E) to be *-regular (i.e., regular with proper involution). This characterization of *-regularity of a Leavitt path algebra is given in terms of an algebraic property of K, not just a graph-theoretic property of E. This differs from the known characterizations of various other algebraic properties of a Leavitt path algebra in terms of graphtheoretic properties of E alone. As a corollary, we show that Handelman’s conjecture (stating that every *-regular ring is unit-regular) holds for Leavitt path algebras. Moreover, its generalized version for rings with local units also continues to hold for Leavitt path algebras over arbitrary graphs.
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  Bäcklund Transformation and Conservation Laws for the Variable-coefficient N-Coupled Nonlinear Schrödinger Equations with Symbolic Computation

  Xiang Hua MENG, Bo TIAN, Tao XU, Hai Qiang ZHANG

  Acta Mathematica Sinica. 2012, 28(5): 969-974. https://doi.org/10.1007/s10114-011-0531-8

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  Considering the integrable properties for the coupled equations, the variable-coefficient Ncoupled nonlinear Schrödinger equations are under investigation analytically in this paper. Based on the Lax pair with the nonisospectral parameter, a Bäcklund transformation for such a coupled system denoting in the Γ functions is constructed with the one-solitonic solution given as the application sample. Furthermore, an infinite number of conservation laws are obtained using symbolic computation.
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  The Least Regular Order with Respect to a Regular Congruence on Ordered Γ-Semigroups

  Manoj SIRIPITUKDET, Aiyared IAMPAN

  Acta Mathematica Sinica. 2012, 28(5): 975-982. https://doi.org/10.1007/s10114-011-9702-x

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  The motivation mainly comes from the conditions of congruences to be regular that are of importance and interest in ordered semigroups. In 1981, Sen has introduced the concept of the Γ-semigroups. We can see that any semigroup can be considered as a Γ-semigroup. In this paper, we introduce and characterize the concept of the regular congruences on ordered Γ-semigroups and prove the following statements on an ordered Γ-semigroup M: (1) Every ordered semilattice congruences is a regular congruence. (2) There exists the least regular order on the Γ-semigroup M/ρ with respect to a regular congruence ρ on M. (3) The regular congruences are not ordered semilattice congruences in general.
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  A C^*-Algebras with Non-stable K₁-Group Property

  Qing Zhai FAN, Xiao Chun FANG

  Acta Mathematica Sinica. 2012, 28(5): 983-988. https://doi.org/10.1007/s10114-011-9701-y

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  In this paper, we give a class of C^*-algebras with non-stable K₁-group property which include the example non-simple tracial topological rank zero and stable rank two C^*-algebra given by Lin and Osaka.
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  Regular Maps of Graphs of Order 4p

  Jin Xin ZHOU, Yan Quan FENG

  Acta Mathematica Sinica. 2012, 28(5): 989-1012. https://doi.org/10.1007/s10114-011-9528-6

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  A 2-cell embedding f: X→S of a graph X into a closed orientable surface S can be described combinatorially by a pair M=(X;ρ) called a map, where ρ is a product of disjoint cycle permutations each of which is the permutation of the arc set of X initiated at the same vertex following the orientation of S. It is well known that the automorphism group of M acts semi-regularly on the arc set of X and if the action is regular, then the map M and the embedding f are called regular. Let p and q be primes. Du et al. [J. Algebraic Combin., 19, 123-141 (2004)] classified the regular maps of graphs of order pq. In this paper all pairwise non-isomorphic regular maps of graphs of order 4p are constructed explicitly and the genera of such regular maps are computed. As a result, there are twelve sporadic and six infinite families of regular maps of graphs of order 4p; two of the infinite families are regular maps with the complete bipartite graphs K_2p,2p as underlying graphs and the other four infinite families are regular balanced Cayley maps on the groups Z_4p, Z₂²×Z_p and D_4p.
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  Spherical f-Tilings by Scalene Triangles and Isosceles Trapezoids, Ⅱ

  Catarina P. AVELINO, Altino F. SANTOS

  Acta Mathematica Sinica. 2012, 28(5): 1013-1032. https://doi.org/10.1007/s10114-011-9511-2

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  The study of the dihedral f-tilings of the sphere S² whose prototiles are a scalene triangle and an isosceles trapezoid was initiated in a previous work. In this paper we continue this classification presenting the study of all dihedral spherical f-tilings by scalene triangles and isosceles trapezoids in some cases of adjacency.
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  Product of Toeplitz Operators on the Harmonic Dirichlet Space

  Lian Kuo ZHAO

  Acta Mathematica Sinica. 2012, 28(5): 1033-1040. https://doi.org/10.1007/s10114-011-9300-y

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  In this paper, we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product of two Toeplitz operators is another Toeplitz operator only if one factor is constant.
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  An Empirical Likelihood Method in a Partially Linear Single-index Model with Right Censored Data

  Yi Ping YANG, Liu Gen XUE, Wei Hu CHENG

  Acta Mathematica Sinica. 2012, 28(5): 1041-1060. https://doi.org/10.1007/s10114-011-9157-0

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  Empirical-likelihood-based inference for the parameters in a partially linear single-index odel with randomly censored data is investigated. We introduce an estimated empirical likelihood for the parameters using a synthetic data approach and show that its limiting distribution is a mixture of central chi-squared distribution. To attack this difficulty we propose an adjusted empirical likelihood to achieve the standard χ²-limit. Furthermore, since the index is of norm 1, we use this constraint to reduce the dimension of parameters, which increases the accuracy of the confidence regions. A simulation study is carried out to compare its finite-sample properties with the existing method. An application to a real data set is illustrated.
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  The K°-relation on the Congruence Lattice of a Regular Semigroup with an Inverse Transversal

  Ying Ying FENG, Li Min WANG

  Acta Mathematica Sinica. 2012, 28(5): 1061-1074. https://doi.org/10.1007/s10114-011-9112-0

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  Let S be a regular semigroup with an inverse transversal S° and C(S) the congruence lattice of S. A relation K° on C(S) is introduced as follows: if ρ, θ ∈ C(S), then we say that ρ and θ are K°-related if Ker ρ°=Kerθ°, where ρ°=ρ|S°. Expressions for the least and the greatest congruences in the same K°-class as ρ are provided. A number of equivalent conditions for K° being a congruence are given.
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  The Spectral Gap for Quasi-birth and Death Processes

  Yong Hua MAO, Liang Hui XIA

  Acta Mathematica Sinica. 2012, 28(5): 1075-1090. https://doi.org/10.1007/s10114-011-9034-x

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  For a reversible quasi-birth and death process, we generalize and refine the decomposition method, by constructing a birth-death process and a sequence of restriction processes. The spectral gap for the quasi-birth and death process is estimated in terms of the spectral gaps for these processes, and in some special cases, the estimation is sharp. With the aid of the symmetrization procedure, the result is also applied to two queueing models: M/M/1 in random environment and M/M/c with synchronous vacation.