Regularity of the attractor for 3-D complex Ginzburg-Landau equation

In this paper,the existence of global attractor for 3-D complex Ginzburg Landau equation is considered.By a decomposition of solution operator,it is shown that the global attractor A_i in H~i(Ω) is actually equal to a global attractor Aj in H~j(Ω)(i≠j,i,j = 1,2,…m).     

3-list-coloring planar graphs of girth 4

In Thomassen (1995) [4], Thomassen proved that planar graphs of girth at least 5 are 3-choosable. In Li (2009) [3], Li improved Thomassen’s result by proving that planar graphs of girth 4 with no 4-cycle sharing a vertex with another 4- or 5-cycle are 3-choosable. In this paper, we prove that planar graphs of girth 4 with no 4-cycle sharing an edge with another 4- or 5-cycle are 3-choosable. It is clear that our result strengthens Li’s result.     

Cycle embedding in star graphs with more conditional faulty edges

The star graph is one of the most attractive interconnection networks. The cycle embedding problem is widely discussed in many networks, and edge fault tolerance is an important issue for networks since edge failures may occur when a network is put into use. In this paper, we investigate the cycle embedding problem in star graphs with conditional faulty edges. We show that there exist fault-free cycles of all even lengths from 6 to n! in any n-dimensional star graph S_n (n ? 4) with ?3n − 10 faulty edges in which each node is incident with at least two fault-free edges. Our result not only improves the previously best known result where the number of tolerable faulty edges is up to 2n − 7, but also extends the result that there exists a fault-free Hamiltonian cycle under the same condition.     

Fuzzy closure systems on L—ordered sets

In this paper, notions of fuzzy closure system and fuzzy closure L —system on L —ordered sets are introduced from the fuzzy point of view. We first explore the fundamental properties of fuzzy closure systems. Then the correspondence between fuzzy closure systems (fuzzy closure L —systems) and fuzzy closure operators is established. Finally, we study the connections between fuzzy closure systems and fuzzy Galois connections. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Parallel characteristic finite element method for time‐dependent convection–diffusion problem

Based on the overlapping‐domain decomposition and parallel subspace correction method, a new parallel algorithm is established for solving time‐dependent convection–diffusion problem with characteristic finite element scheme. The algorithm is fully parallel. We analyze the convergence of this algorithm, and study the dependence of the convergent rate on the spacial mesh size, time increment, iteration times and sub‐domains overlapping degree. Both theoretical analysis and numerical results suggest that only one or two iterations are needed to reach to optimal accuracy at each time step. Copyright © 2010 John Wiley & Sons, Ltd.     

推广的Kantorovich算子在Ba空间中的逼近

利用Ditzian-Totik光滑模,研究了推广的Kantorovich算子在Ba空间中的逼近,得到逼近的正定理与等价定理.所得结果改进、推广和统一了一些作者的结果.     

缺项样条插值(Ⅰ)

[1] proved that S_n(x) was uniquely determined, and gave the error bounds of approximation of f(x) ∈C~4 [0,1] by S_n(x). B. K. Swartz and R. S. Varga [2] also gave the degree of approximation of f(x) ∈C~6 [0, 1] by S_n(x). Z. R. Guo [3] obtained the saturation theorem for this approximation. Z. R. Guo [4-5] were also concerned in this kind of interpolation and gave the degree of approximation. In this paper we consider the general lacunary interpolation by quintic splines.     

A discussion on the conservatism of robust linear optimization problems

In 2004, Bertsimas and Sim proposed a robust approach that can control the degree of conservatism by applying a limitation Γ to the maximum number of parameters that are allowed to change. However, the robust approach can become extremely conservative even when Γ is relatively small. In this paper, we provide a theoretical analysis to explain why this extreme conservatism occurs. We further point out that the robust approach does not reach an extremely conservative state when Γ is less than k, where k is the number of nonzero components of the optimal solution of the extremely conservative robust approach. This research also shows that care must be taken when adjusting the value of Γ to control the degree of conservatism because the approach may result in greater conservatism than was intended. We subsequently apply our analysis to additive combinatorial optimization problems. Finally, we illustrate our results on numerical simulations.     

BP+基态和激发态的势能曲线和光谱性质的研究

本文利用量子化学中的多参考组态相互作用方法(MRCI), 在aug-cc-pVQZ级别计算了在环境科学中具有重要作用的离子BP⁺. 得到了对应三个离解极限B⁺(¹S_g)+P(⁴S_u), B⁺(¹S_g)+P(²D_u)以及B⁺(¹S_g)+P(²P_u)的6个Λ-S态势能曲线. 在计算中还考虑了Davidson修正(+Q)和标量相对论效应, 用以提高计算精度. 通过分析Λ-S态的电子结构, 确认了电子态的多组态特性. 计算中首次纳入了旋轨耦合效应, 获得了由BP⁺离子的6个Λ-S态分裂出的10个Ω 态的势能曲线. 计算得到的势能曲线表明相同对称性的Ω 态的势能曲线存在着明显的避免交叉. 在得到的Λ-S态和Ω 态的势能曲线的基础上, 运用LEVEL8.0程序通过求解核径向的Schrödinger 方程, 得到了相应的Λ-S态和Ω 态的光谱常数T_e, R_e, ω_e, ω_eχ_e, B_e和D_e, 其中基态X⁴∑^-的光谱常数与已有的理论值符合的非常好, 文中其他电子态的光谱常数均为首次报道. 关键词： 多参考组态相互作用方法(MRCI) 势能曲线 光谱常数 旋轨耦合效应