L-fuzzy拓扑空间的层浓度

在Ｌ－ｆｕｚｙ拓扑学中引入了层稠密集、层第一纲集、层Ｂａｉｒｅ空间、层浓度、及层可分空间等概念，研究了它们的基本性质，讨论了它们与分明拓扑学中相应概念的关系．     

层合板壳脱层曲面的有限元分析

通过建立一类新的参考面有限单元,得到适应于分析层合板壳脱层屈曲问题的有限元方法,指出了利用Ｍｉｎｄｌｉｎ假设意义下的变形协调条件,可以将大多数胜任层合板壳分析的一般板壳单元改造为相应的参考面单元,这一方法确保了位移场的合理性和协调条件满足,为验证参考而单元的有效性和协调还对壳体脱层屈曲的几个算例作了数值分析。     

一类二层凸规划的对偶二层规划

本文讨论上层目标函数以下层子系统目标函数的最优值作为反馈的一类二层凸规划的对偶规划问题 ,在构成函数满足凸连续可微等条件的假设下 ,建立了二层凸规划的 Lagrange对偶二层规划 ,并证明了基本对偶定理 .     

奇摄动非线性系统的角层和冲击层现象

研究一类具有转向点的二阶非线性系统的角层和冲击层现象,在适当的假设条件下,利用微分不等式方法证明了解的存在性,并得到了解的按分量的一致有效的渐近估计.     

外部压力作用下复合材料层合圆柱壳的脱层扩展分析

含脱层的层合圆柱壳在承受外部压力作用时,容易发生脱层扩展,进而引起结构失效．基于可动边界变分原理并考虑脱层间的接触效应对圆柱壳在外部压力作用下的脱层扩展进行了分析,同时应用Griffith准则,导出了脱层前缘各点处的能量释放率表达式,且以轴对称脱层层合圆柱壳为例进行了数值计算,讨论了脱层大小、脱层深度、几何尺寸、材料性质及纤维铺层方式等因素对脱层扩展的影响．     

二层凸规划的基本性质

本文研究了一类抛述二层决策问题的二层数学规划模型，在一定条件下讨论了下层极值函数和上层复合目标函数的凸性和连续性，给出了二层决策问题优决策的存在条件。     

关于k-半层空间的一些结果

给出了对k-半层空间及c-半层空间的一些等价刻画,并给出kβ空间成为k-半层空间的一些条件.     

层合板壳脱层屈曲的有限元分析

通过建立一类新的参考面有限单元,得到适用于分析层合板壳脱层屈曲问题的有限元方法。指出了利用Mindlin假设意义下的变形协调条件,可以将大多数胜任层合板壳分析的一般板壳单元改造为相应的参考面单元。这一方法确保了位移场的合理性和协调条件的满足。为验证参考面单元的有效性,还对壳体脱层屈曲的几个算例作了数值分析。     

对称复合材料层合板弯曲的三维数值分析

本文采用三维各向异性有限单元模拟纯弯曲载荷下的复合材料层合板，给出了应力、应变沿厚度方向的变化规律。分析结果表明，在斜交对称铺层层合板的中心区域（远离加载端和自由边的区域），板的层间粘接界面附近，有根强的应力集中现象，可称之为层间效应。层间界面处力学性质的突变导致了层间应力的产生，并使层合板处于三向应力状态。三维数值模型给出的应变分布不同于基于Ｋｉｒｃｈｈｏｆｆ－Ｌｏｖｅ直法线假设的经典层合板理论给出的应变分布。     

具有初始层间压力的层合圆筒的热冲击研究

采用一种解析方法求解具有初始层间压力的双层层合圆筒内的动态热应力的瞬态响应·　首先,将由自紧装配双层层合圆筒引起的初始层间压力考虑作为热弹性动力学方程的初始条件·　其次,利用一个简便的数学变换方法求解具有初始应力场的单层圆筒的热弹性动力学解,然后利用层合圆筒的边界条件和连接条件,得到具有初始层间压力的双层层合圆筒的热冲击解·     

THE PLATEAU-B(E)ZIER PROBLEM WITH WEAK-AREA FUNCTIONAL

In this paper, we present a new method to solve the Plateau-Bézier problem. A new energy functional called weak-area functional is proposed as the objective functional to obtain the approximate minimal Bézier surface from given boundaries. This functional is constructed based on Dirichlet energy and weak isothermal parameterization condition. Experimental comparisons of the weak-area functional method with existing Dirichlet, quasi-harmonic, the strain energy-minimizing, harmonic and biharmonic masks are performed which show that the weak-area functional method are among the best by choosing appropriate parameters.     

Functional reproducing kernel Hilbert spaces for non-point-evaluation functional data

Motivated by the need of processing non-point-evaluation functional data, we introduce the notion of functional reproducing kernel Hilbert spaces (FRKHSs). This space admits a unique functional reproducing kernel which reproduces a family of continuous linear functionals on the space. The theory of FRKHSs and the associated functional reproducing kernels are established. A special class of FRKHSs, which we call the perfect FRKHSs, are studied, which reproduce the family of the standard point-evaluation functionals and at the same time another different family of continuous linear (non-point-evaluation) functionals. The perfect FRKHSs are characterized in terms of features, especially for those with respect to integral functionals. In particular, several specific examples of the perfect FRKHSs are presented. We apply the theory of FRKHSs to sampling and regularized learning, where non-point-evaluation functional data are used. Specifically, a general complete reconstruction formula from linear functional values is established in the framework of FRKHSs. The average sampling and the reconstruction of vector-valued functions are considered in specific FRKHSs. We also investigate in the FRKHS setting the regularized learning schemes, which learn a target element from non-point-evaluation functional data. The desired representer theorems of the learning problems are established to demonstrate the key roles played by the FRKHSs and the functional reproducing kernels in machine learning from non-point-evaluation functional data. We finally illustrate that the continuity of linear functionals, used to obtain the non-point-evaluation functional data, on an FRKHS is necessary for the stability of the numerical reconstruction algorithm using the data.     

Sobolev空间W^m,p（Ω）中残差泛函的极值理论

本文在Sobolev空间中讨论残差泛函J(u)的概念及性质,论证了残差泛函J(u)的弱紧性、强制性和下半连续性及凸性条件.根据临界点理论在Sobolev空间中建立起该残差泛函的极值原理,给出J(u)=0极小值存在定理.此外还证明了等价定理和J(R_n(c))=0的五种等价形式.     

Representing risk preferences in expected utility based decision models

Users of expected utility based decision models frequently find it useful or necessary to specify a functional form that represents the risk preferences of a decision maker. Having additional functional forms from which to choose would be helpful. The literature so far has provided several such functional forms for the utility function itself. The discussion presented here indicates that providing a functional form for the marginal utility function is an alternate and equally useful way to represent risk preferences. Furthermore, functional forms for marginal utility are easier to provide, and there exist functional forms for marginal utility that represent simple risk preferences for which there is no associated functional form for the utility function. Several functional forms for marginal utility are suggested, and the class of isoelastic risk preferences is identified and discussed.     

On the solvability of a functional equation

This article studies properties of solutions of a functional equation arising in dynamic programming of multistage decision processes. A sufficient condition for the existence, uniqueness and iterative approximation of solutions of the functional equation is established. A few other behaviours of solutions for certain functional equations which are particular cases of the functional equation are discussed. The results presented in this article extend, improve and unify some known results in literature.     

A package for symbolic solution of real functional equations of real variables

Summary This paper discusses the problems associated with the symbolic treatment of functional equations and presents a Mathematica package for the solution of real functional equations of real variables. The package includes a minimal basic database which contains a reduced set of functional equations with its four components: equation, domain, class and the corresponding solution. The word minimal is used in the sense that any equation that is solvable by the system using non-searching methods is excluded from the database. The package incorporates a searching algorithm which can solve functional equations independently of their notation and their algebraic representation. Not only general solutions but particular and candidate solutions are dealt with. This implies a careful analysis of domains and classes. The package includes some methods for solving functional equations, which are used when the input functional equations are not found in the database. Some methods have been implemented internally and some are in an external package. Finally, some examples illustrate the use of the package.     

On solvability of functional equations and system of functional equations arising in dynamic programming

The purpose of this paper is to study solvability of two classes of functional equations and a class of system of functional equations arising in dynamic programming of multistage decision processes. By using fixed point theorems, a few existence and uniqueness theorems of solutions and iterative approximation for solving these classes of functional equations are established. Under certain conditions, some existence theorems of coincidence solutions for the class of system of functional equations are shown. Some examples are given to demonstrate the advantage of our results than existing ones in the literature.     

Error Estimates for a Class of Elliptic Optimal Control Problems

In this article, functional type a posteriori error estimates are presented for a certain class of optimal control problems with elliptic partial differential equation constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state equation. The functional a posteriori error estimates developed by Repin in the late 1990s are applied to estimate the cost function value from both sides without requiring the exact solution of the state equation. Moreover, a lower bound for the minimal cost functional value is derived. A meaningful error quantity coinciding with the gap between the cost functional values of an arbitrary admissible control and the optimal control is introduced. This error quantity can be estimated from both sides using the estimates for the cost functional value. The theoretical results are confirmed by numerical tests.     

Functional Limit Theorems for Multiparameter Fractional Brownian Motion

We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional Lévy’s modulus of continuity and many other results are its particular cases. Applications to approximation theory are discussed.      

Local smoothing regression with functional data

Kernel estimates of a regression operator are investigated when the explanatory variable is of functional type. The bandwidths are locally chosen by a data-driven method based on the minimization of a functional version of a cross-validated criterion. A short asymptotic theoretical support is provided and the main body of this paper is devoted to various finite sample size applications. In particular, it is shown through some simulations, that a local bandwidth choice enables to capture some underlying heterogeneous structures in the functional dataset. As a consequence, the estimation of the relationship between a functional variable and a scalar response, and hence the prediction, can be significantly improved by using local smoothing parameter selection rather than global one. This is also confirmed from a chemometrical real functional dataset. These improvements are much more important than in standard finite dimensional setting.