中国科学院数学与系统科学研究院期刊网

15 July 2008, Volume 24 Issue 7
    

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  • P. J. FITZSIMMONS
    Acta Mathematica Sinica. 2008, 24(7): 1057-1066. https://doi.org/10.1007/s10114-007-6466-4
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    In the context of a symmetric diffusion process X, we give a precise description of the Dirichlet form of the process obtained by subjecting X to a drift transformation of gradient type. This description relies on boundary-type conditions restricting an associated reflecting Dirichlet form.
  • Thomas VOUGIOUKLIS
    Acta Mathematica Sinica. 2008, 24(7): 1067-1078. https://doi.org/10.1007/s10114-007-6481-5
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    The hyperoperations, called theta-operations (), are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define -operations. In this paper, we continue our study on the -operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using -operations one obtains, mainly, HV -structures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special HV -rings or HV-fields, so these hyperstructures can be used. Moreover, we study the relation of these -structures with other classes of hyperstructures, especially with the HV-structures.
  • Jing Xian SUN, Ke Mei SUN
    Acta Mathematica Sinica. 2008, 24(7): 1079-1088. https://doi.org/10.1007/s10114-007-5506-4
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    In this paper, by the fixed point index theory, the number of fixed points for sublinear and asymptotically linear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least nine or seven distinct fixed points for sublinear and asymptotically linear operators is proved. Finally, the theoretical results are applied to a nonlinear system of Hammerstein integral equations.
  • Ali GHAFFARI
    Acta Mathematica Sinica. 2008, 24(7): 1089-1096. https://doi.org/10.1007/s10114-007-6071-6
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    In this paper, among other things, the author studies the weak*-closed left translation invariant complemented subspace of semigroup algebras and group algebras. Also, the author studies the relationships between projections and amenability.
  • Yun Ge XU, Dan WANG
    Acta Mathematica Sinica. 2008, 24(7): 1097-1106. https://doi.org/10.1007/s10114-007-6072-5
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    Let Λ = kQ/I be a finite-dimensional Nakayama algebra, where Q is an Euclidean diagram Ãn for some n with cyclic orientation, and I is an admissible ideal generated by a single monomial relation. In this note we determine explicitly all the Hochschild homology and cohomology groups of Λ based on a detailed description of the Bardzell complex. Moreover, the cyclic homology of Λ can be calculated in the case that the underlying field is of characteristic zero.
  • Kun Chuan WANG
    Acta Mathematica Sinica. 2008, 24(7): 1107-1116. https://doi.org/10.1007/s10114-007-6136-6
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    We consider expansions of the type arising from Wilson bases. We characterize such expansions for L2(R). As an application, we see that such an expansion must be orthonormal, in contrast to the case of wavelet expansions generated by translations and dilation.
  • M. R. DARAFSHEH
    Acta Mathematica Sinica. 2008, 24(7): 1117-1126. https://doi.org/10.1007/s10114-007-6143-7
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    The author will prove that the group2Dp(3) can be uniquely determined by its order components, where p ≠ 2m + 1 is a prime number, p ≥ 5. More precisely, if OC(G) denotes the set of order components of G, we will prove OC(G) = OC(2Dp(3)) if and only if G is isomorphic to2Dp(3). A main consequence of our result is the validity of Thompson's conjecture for the groups under consideration.
  • V. A. MENEGATTO, C. P. OLIVEIRA, Ana P. PERON
    Acta Mathematica Sinica. 2008, 24(7): 1127-1138. https://doi.org/10.1007/s10114-007-6227-4
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    Let m and n be fixed, positive integers and f a space composed of real polynomials in m variables. The authors study functions f: R→R which map Gram matrices, based upon n points of Rm, into matrices, which are nonnegative definite with respect to f. Among other things, the authors discuss continuity, differentiability, convexity, and convexity in the sense of Jensen, of such functions.
  • Wei WU
    Acta Mathematica Sinica. 2008, 24(7): 1139-1154. https://doi.org/10.1007/s10114-007-6354-y
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    The author generalizes the Arzelà-Ascoli theorem to the setting of matrix order unit spaces, extending the work of Antonescu-Christensen on unital C*-algebras. This gives an affirmative answer to a question of Antonescu and Christensen.
  • Shi Feng DING
    Acta Mathematica Sinica. 2008, 24(7): 1155-1162. https://doi.org/10.1007/s10114-007-1027-4
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    Let Γ be a simple connected graph and let G be a group of automorphisms of Γ. Γ is said to be (G, 2)-arc transitive if G is transitive on the 2-arcs of Γ. It has been shown that there exists a family of non-quasiprimitive (PSU3(q), 2)-arc transitive graphs where q = 23m with m an odd integer. In this paper we investigate the case where q is an odd prime power.
  • Chao LIANG, Geng LIU
    Acta Mathematica Sinica. 2008, 24(7): 1163-1174. https://doi.org/10.1007/s10114-007-6445-9
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    In this paper, we give a partial answer to the problem proposed by Lan Wen. Roughly speaking, we prove that for a fixed i, f has C1 persistently no small angles if and only if f has a dominated splitting of index i on the C1 i-preperiodic set P*i (f). To prove this, we mainly use some important conceptions and techniques developed by Christian Bonatti. In the last section, we also give a characterization of the finest dominated splitting for linear cocycles.
  • Mourad BELLASSOUED
    Acta Mathematica Sinica. 2008, 24(7): 1175-1192. https://doi.org/10.1007/s10114-007-6468-2
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    In this paper, we shall investigate the decay property of the solutions to the initial-boundary value problem for the elastic wave equation with a local time-dependent nonlinear damping. We give some decay rate of the energy when the damping term is effective only in a neighborhood of a suitable subset of the boundary. The results obtained in this paper extend, in particular, the known results for the scalar wave equation.
  • Rong Hua ZHANG, Shou Feng ZHANG
    Acta Mathematica Sinica. 2008, 24(7): 1193-1204. https://doi.org/10.1007/s10114-007-6550-9
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    Let S be a regular semigroup, So an inverse subsemigroup of S. So is called a generalized inverse transversal of S, if V(x) ∩ SoØ. In this paper, some properties of this kind of semigroups are discussed. In particular, a construction theorem is obtained which contains some recent results in the literature as its special cases.
  • Özer TALO, Feyzi BAsŞAR
    Acta Mathematica Sinica. 2008, 24(7): 1205-1212. https://doi.org/10.1007/s10114-007-6552-7
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    Recently, the space bvp of real or complex numbers consisting of all sequences whose differences are in the space lp has been studied by Başar, Altay [Ukrainian Math. J. 55(1)(2003), 136-147], where 1 ≤ p ≤ ∞. The main purpose of the present paper is to introduce the space bvp(F) of sequences of p-bounded variation of fuzzy numbers. Moreover, it is proved that the space bvp(F) includes the space lp(F) and also shown that the spaces bvp(F) and lp(F) are isomorphic for 1 ≤ p ≤ ∞. Furthermore, some inclusion relations have been given.
  • Wai Chee SHIU, Gui Zhen LIU
    Acta Mathematica Sinica. 2008, 24(7): 1213-1220. https://doi.org/10.1007/s10114-007-6555-4
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    Plesnik in 1972 proved that an (m-1)-edge connected m-regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m-1 edges. Alder et al. in 1999 showed that if G is a regular (2n + 1)-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n. In this paper we obtain some sufficient conditions related to the edge-connectivity for an n-regular graph to have a k-factor containing a set of edges and (or) excluding a set of edges, where 1 ≤ kn/2. In particular, we generalize Plesnik's result and the results obtained by Liu et al. in 1998, and improve Katerinis' result obtained 1993. Furthermore, we show that the results in this paper are the best possible.
  • B. YOUSEFI, H. REZAEI
    Acta Mathematica Sinica. 2008, 24(7): 1221-1232. https://doi.org/10.1007/s10114-007-6601-2
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    Let B(X) be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or *-strong topology. We give sufficient conditions for a continuous linear mapping L: B(X) → B(X) to be supercyclic or *-supercyclic. In particular our condition implies the existence of an infinite dimensional subspace of supercyclic vectors for a mapping T on H. Hypercyclicity of the operator algebra with strong operator topology was studied by Chan and here we obtain an analogous result in the case of *-strong operator topology.