WEAK CONVERGENCE OF HENSTOCK INTEGRABLE SEQUENCES

Some relationships between pointwise and weak convergence of a sequence of Henstock integrable functions are studied, In particular it is provided an example of a sequence of Henstock integrable functions whose pointwise limit is different from the weak one. By introducing an asymptotic version of the Henstock equiintegrability notion it is given a necessary and sufficient condition in order that a pointwisely convergent sequence of Henstock integrable functions is weakly convergent to its pointwise limit.     

Convergence analysis of time-point relaxation iterates for linear systems of differential equations

We study convergence properties of time-point relaxation (TR) Runge-Kutta methods for linear systems of ordinary differential equations. TR methods are implemented by decoupling systems in Gauss-Jacobi, Gauss-Seidel and successive overrelaxation modes (continuous-time iterations) and then solving the resulting subsystems by means of continuous extensions of Runge-Kutta (CRK) methods (discretized iterations). By iterating to convergence, these methods tend to the same limit called diagonally split Runge-Kutta (DSRK) method. We prove that TR methods are equivalent to decouple in the same modes the linear algebraic system obtained by applying DSRK limit method. This issue allows us to study the convergence of TR methods by using standard principles of convergence of iterative methods for linear algebraic systems. For a particular problem regions of convergence are plotted.     

集合环

本文用集环来表现模糊集，得到了表现定理的新形式，并证明了这种表现可以有限化，即用有限个经典集近似刻划模糊集并且这样的刻划是同态的。最后，证明了集对方法是集环表现的特殊情形。     

Complete Surjections and Complete Epimorphisms over Completely Distributive Lattices

Generators and lattice properties of the poset of complete homomorphisic images of a completely distributive lattice are exploited via the localic methods. Some intrinsic and extrinsic conditions about this poset to be a completely distributive lattice are given. It is shown that the category of completely distributive lattices is co-well-powered,and complete epimorphisms on completely distributive lattice are not necessary to be surjections. Finally, some conditions about complete epimorphisms to be surjections are given.     

Approximation by a class of modified Szász-Durrmeyer operators

We modify Szász-Durrmeyer operators by means of three-diagonal generalized matrix which overcomes a difficulty in extending a Berens-Lorentz result to the Szász-Durrmeyer operators for second order of smoothness. The direct and converse theorems for these operators inL _p are also presented by Ditzian-Totik modulus of smoothness.This project is supported by Zhejiang Provincial Foundation of China.     

用于光学神经网络硬件系统误差纠正的虚拟神经网络

提出了一种用于修正光学神经网络硬件系统误差的虚拟神经网络模型，光学实验结果表明该网络能够有效地消除硬件系统误差对实验结果的影响。     

ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS

0.IntroductionThispaperisaimedatdevelopingthecohomologytheoryofmodularLiealgebrasandthendeterminingthefirstcohomologygroupsofCartantypeLiealgebras.AsgeneralizationoftheconceptofrestrictedLiealgebras,ageneralizedrestrictedLiealgebra(GRLiealgebra)wasintroducedin[21],whichisassociatedwithabasisandamappingofthebasisintotheLiealgebrasatisfyingthegeneralized-restrictednessconditions.Generalizedrestrictedrepresentations(GRrepresentations)werethenintroduced,whichcanbereducedtotherepresentationsofa…     

Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach

The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique. This work was supported by the National Natural Science Fund of China (No. 10371096) for ZM Gao and YC Ma.     

灰色模型的最优化及其参数的直接求法

基于灰色模型的内涵表达式和白化方程响应式均为等比级数的观点,提出了一种不用求ago值、均值,不涉及灰色微分方程,白化微分方程概念,直接求灰色模型参数a,c的方法,通过此方法建立的新模型不仅从理论上可保证是在满足给定评价标准为模拟绝对误差平方和最小(或模拟相对误差平方和最小)、给定精度条件下的最优化模型,从而结束了灰色模型只有更优,没有最优的历史.并从理论上证明了新模型具有白化指数律重合性、白化系数律重合性,伸缩变换一致性.最后通过实例编程验证该方法具有可操作性,且预测精度高,效果好.