Periodic solutions for fourth-order nonlinear functional difference equations

By using the critical point method, some new criteria are obtained for the existence and multiplicity of periodic solutions for fourth-order nonlinear functional difference equations. The proof is based on the linking theorem in combination with variational technique. Recent results in the literature are generalized and significantly improved. Copyright © 2013 John Wiley & Sons, Ltd.     

The extrapolation of band-limited signals in L2 with sampling errors

In this paper we will provide a theory for an extrapolation algorithm of band-limited signals with sampling errors or low noises. The main result is as follows: Suppose thatf(t) is in L² and is a continuous Ω band-limited signal. Then for any positive numbers T, A(>T) and ε, there exists a δ>0 such that when the sampling errors (or noises) off(t) on [−T, T] is less than δ we can extrapolate the values off(t) on the interval [−A, A] such that the difference between the extrapolated value and the exact value off(t) does not exceed ε.     

Synchronization of Takagi–Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays

In this paper, we propose and investigate a new general model of fuzzy stochastic discrete-time complex networks (SDCNs) described by Takagi–Sugeno (T–S) fuzzy model with discrete and distributed time-varying delays. The proposed model takes some well-studied models as special cases. By employing a new Lyapunov functional candidate, we utilize some stochastic analysis techniques and Kronecker product to deduce delay-dependent synchronization criteria that ensure the mean-square synchronization of the proposed T–S fuzzy SDCNs with mixed time-varying delays. These sufficient conditions are computationally efficient as it can be solved numerically by the LMI toolbox in Matlab. A numerical simulation example is provided to verify the effectiveness and the applicability of the proposed approach.     

向量优化中改进集的一些拓扑性质

主要研究改进集的一些拓扑运算性质。首先在改进集条件下给出了拓扑向量空间中两个非空集之和的拓扑内部的一些运算性质。进一步,利用改进集获得了 Flores-Baz′an 和 Hern′andez 提出的假定 B 的一个加强形式。此外,给出了一些例子对主要结果进行了解释。     

鞅方法在一类破产问题中的应用

本文从鞅条件出发 ,推导出了总理赔过程分别为复合 Poisson过程与复合二项过程 ,利率强度波动为带跳的 Poisson过程情形下的调节方程 ,并由此得到了一些有趣的结果。     

NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD, the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1-and L2-norm space estimates and the 0((△t)2) estimate for time variable are obtained.     

紧矩阵量子群G的余表示与其对偶量子群(A)的关系

设 G=（A,△）为紧矩阵量子群,G为A的所有有限维光滑的、不可约余表示等价类的集合.本文通过（A,△）的一个余表示Vo构造了两个相互配对的集合,利用Hilbert C＊-模的理论证明它们分别为A和Baaj与Skandalis构造的量子群A,并且证明了对任意的α∈G,在A中都对应一个有限维投影算子Pα,满足 dim（α）=dim（pα）.     

Minimal Martingale Measures for Discrete-time Incomplete Financial Markets

Abstract In this note, we give a characterization of the minimal martingale measure for a general discrete-time incomplete financial market.Then we concretely work out the minimal martingale messure for a specificdiscrete-time market model in which the assets'returns in different times are independent.     

面板数据公共变点的非参数最大似然估计

Gao Pengli;Xia Zhiming(School of Mathematics,Northwest University,Xi'an 710127,China)