Sep 2008, Volume 3 Issue 3

    

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• Attractors for stochastic lattice dynamical systems with a multiplicative noise

  CARABALLO Tomás, LU Kening

  2008, 3(3): 317-335. https://doi.org/10.1007/s11464-008-0028-7

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  In this paper, we consider a stochastic lattice differential equation with diffusive nearest neighbor interaction, a dissipative nonlinear reaction term, and multiplicative white noise at each node. We prove the existence of a compact global random attractor which, pulled back, attracts tempered random bounded sets.
• Leibniz central extension on centerless twisted Schr?dinger-Virasoro algebra

  LI Junbo, SU Yucai

  2008, 3(3): 337-344. https://doi.org/10.1007/s11464-008-0031-z

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  In this paper, we present all the Leibniz 2-cocycles of the centerless twisted Schrödinger-Virasoro algebra L, which determine the second Leibniz cohomology group of L.
• Bernstein type result for constant mean curvature hypersurface

  LIU Huaqiao, MENG Qingyu

  2008, 3(3): 345-353. https://doi.org/10.1007/s11464-008-0030-0

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  We prove a Bernstein type theorem for constant mean curvature hypersurfaces in Rⁿ⁺¹ under certain growth conditions for n ≤ 3. Our result extends the case when M is a minimal hypersurface in the same condition.
• Characterization of simple -groups

  SHAO Changguo, SHI Wujie, JIANG Qinhui

  2008, 3(3): 355-370. https://doi.org/10.1007/s11464-008-0025-x

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  In this paper, we prove that a group G is isomorphic to M, where M is a simple K₄-group, if and only if the following hold: (1) ##G## = ##M##, (2) nse(G) = nse(M).
• Construct irreducible representations of quantum groups (())

  TANG Xin

  2008, 3(3): 371-397. https://doi.org/10.1007/s11464-008-0027-8

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  In this paper, we construct families of irreducible representations for a class of quantum groups U_q(f_m(K)). First, we give a natural construction of irreducible weight representations for U_q(f_m(K)) using methods in spectral theory developed by Rosenberg. Second, we study the Whittaker model for the center of U_q(f_m(K)). As a result, the structure of Whittaker representations is determined, and all irreducible Whittaker representations are explicitly constructed. Finally, we prove that the annihilator of a Whittaker representation is centrally generated.
• Junction trees of general graphs

  WANG Xiaofei, GUO Jianhua

  2008, 3(3): 399-413. https://doi.org/10.1007/s11464-008-0023-z

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  In this paper, we study the maximal prime subgraphs and their corresponding structure for any undirected graph. We introduce the notion of junction trees and investigate their structural characteristics, including junction properties, induced-subtree properties, running-intersection properties and maximum-weight spanning tree properties. Furthermore, the characters of leaves and edges on junction trees are discussed.
• A posteriori error estimates of constrained optimal control problem governed by convection diffusion equations

  YAN Ningning, ZHOU Zhaojie

  2008, 3(3): 415-442. https://doi.org/10.1007/s11464-008-0029-6

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  In this paper, we study a posteriori error estimates of the edge stabilization Galerkin method for the constrained optimal control problem governed by convection-dominated diffusion equations. The residual-type a posteriori error estimators yield both upper and lower bounds for control u measured in L²-norm and for state y and costate p measured in energy norm. Two numerical examples are presented to illustrate the effectiveness of the error estimators provided in this paper.
• Asymptotics for solutions of a defective renewal equation with applications

  YIN Chuancun, ZHAO Xianghua

  2008, 3(3): 443-459. https://doi.org/10.1007/s11464-008-0024-y

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  In this paper, we derive non-exponential asymptotic forms for solutions of defective renewal equations. These include as special cases asymptotics for compound geometric distribution and the convolution of a compound geometric distribution with a distribution function. As applications of these results, we study the Gerber-Shiu discounted penalty function in the classical risk model and the reliability of a two-unit cold standby system in reliability theory.
• OD-Characterization of all simple groups whose orders are less than 10

  ZHANG Liangcai, SHI Wujie

  2008, 3(3): 461-474. https://doi.org/10.1007/s11464-008-0026-9

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  Let M be a simple group whose order is less than 10⁸. In this paper, we prove that if G is a finite group with the same order and degree pattern as M, then the following statements hold: (a) If M ≠ A₁₀, U₄(2), then G ≅ M; (b) If M = A₁₀, then G ≅ A₁₀ or J₂ × Z₃; (c) If M = U₄(2), then G is isomorphic to a 2-Frobenius group or U₄(2). In particular, all simple groups whose orders are less than 10⁸ but A₁₀ and U₄(2) are OD-characterizable. As a consequence of this result, we can give a positive answer to a conjecture put forward by W. J. Shi and J. X. Bi in 1990 [Lecture Notes in Mathematics, Vol. 1456, 171–180].