基础模糊命题演算系统BL~*的改进系统

基础模糊命题演算系统BL*是一个和基础命题演算系统BL相对独立的命题演算系统。命题演算系统L*是系统BL*的扩张,但不是系统BL的扩张。通过对系统BL*及其它模糊命题演算系统的研究,本文对BL*系统进行了修正,进一步改进了BL*系统中的公理体系。     

A comprehensive analytical approach for policy analysis of system dynamics models

Formal tools to link system dynamics model’s structure to the system modes of behavior have recently become available. In this paper, we aim to expand the use of these tools to perform the model’s policy analysis in a more structured and formal way than the exhaustive exploratory approaches used to date. We consider how a policy intervention (a parameter change) affects a particular behavior mode by affecting the gains of particular feedback loops as well as how it affects the presence of that mode in the variable of interest. The paper demonstrates the utility of considering both of these aspects since the analysis provides an assessment of the overall impact of a policy on a variable and explains why the impact occurs in terms of structural changes in the model. Particularly in the context of larger models, this method enables a much more efficient search for leverage policies, by ranking the influence of each model parameter without the need for multiple simulation experiments.     

Availability optimization of a redundant system through dependency modeling

This paper presents a constructive approach to optimize the availability of a system through modeling the dependency of the components. Our goal is to minimize the system cost under the constraint that system availability must not be less than a given level. In particular, the components are dependent of each other. A function noted as the dependence function is introduced to model the dependency. It is demonstrated that, for a general form of the system cost, the dependence function guarantees a finite set of feasible solutions. An approach is then developed with the help of the dependence function to obtain the optimal solution. The resolution is illustrated by an interesting example, in which the system cost depends on the strength of the dependency. Our study reveals that the dependency is an essential and effective option to improve system reliability. Moreover, the modeling of dependency, i.e. the introduction of the dependence function is valuable for resolving the optimization problem.     

Recursive computational formulas of the least squares criterion functions for scalar system identification

The paper discusses recursive computation problems of the criterion functions of several least squares type parameter estimation methods for linear regression models, including the well-known recursive least squares (RLS) algorithm, the weighted RLS algorithm, the forgetting factor RLS algorithm and the finite-data-window RLS algorithm without or with a forgetting factor. The recursive computation formulas of the criterion functions are derived by using the recursive parameter estimation equations. The proposed recursive computation formulas can be extended to the estimation algorithms of the pseudo-linear regression models for equation error systems and output error systems. Finally, the simulation example is provided.     

Dilations for systems of imprimitivity acting on Banach spaces

Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued system of imprimitivity has a dilation to a probability spectral system of imprimitivity acting on a Banach space. This completely generalizes a well-known result which states that every frame representation of a countable group on a Hilbert space is unitarily equivalent to a subrepresentation of the left regular representation of the group. We also prove that isometric group representation induced framings on a Banach space can be dilated to unconditional bases with the same structure for a larger Banach space. This extends several known results on the dilations of frames induced by unitary group representations on Hilbert spaces.     

GENERALIZED MATRIX MULTISPLITTING RELAXATION METHODS AND THEIR CONVERGENCE

In this paper, we set up a general framework of parallel matrix mullisplitting relaxation methods for solving large scale system of linear equations. We investigate the convergence properties of this framework and give several sufficient conditions ensuring it to converge as well as diverge. At last, we conclude a necessary and sufficient condition for the convergence of this framework when the coefficient matrix is an L-matrix.     

规范变换与有限维可积系统间的变换

本文表明，利用两个特征值问题的规范变换，不仅可以建立和它们相联系的势的约束之间以及相应的有限维Ｈａｍｉｌｔｏｎ系统间的变换关系式，而且可以由一个可积系统的对合守恒积分导出另一个系统的守恒积分     

First Order System of Equations of Mixed Type and Second Order Equation of Mixed Type

A system of first order equations of mixed type, which may be reduced to a general second order equation of mixed type, is considered. Uniqueness of solution to the generalized Tricomi problem is proved by the method of auxiliary function. Existence of H¹ strong solution is based on a characteristic problem and is proved by the Fredholm's alternative properties.     

积逻辑系统中的广义重言式

讨论积逻辑系统中的广义重言式理论 ,给出积逻辑系统中子代数和广义重言式的一系列性质。本文的主要结果表明 ,在几个重要的逻辑系统中 ,标准积逻辑系统具有最简单的广义重言式结构 ,而在推理过程中 ,它具有较差的真值传递性。