关于产生式系统并行执行与收敛性问题的探讨

产生式系统引入并行技术后，出现了两个新的困难问题：相容性问题和收敛性问题。基于并行知识库机ＰＫＢＭ９５，为了解决收敛性问题，本文给出了一种称为规则顺序锁定的方法。另外，为了发现隐循环以及为了提高性能，我们给出一系列动态分析了测试的方法，如路径跟踪等等。     

组播网络的随机仿真

提出了一种能线性逼近现实网络特性的随机网络生成方法，研究内容包括：推证新的概率连通公式，证明其收敛性，并对模型的仿真效果进行实验和性能分析。事实证明此模型是一种可定制的通用网络仿真模型，较其他仿真模型而言，其收敛性更为优良，且能更加逼真地模拟现实网络的属性。     

一种新的非线性共轭梯度法及收敛性

在LS方法基础上,提出了一种新的求解无约束最优化问题的共轭梯度法.新方法通过一个新的公式计算参数,克服了LS方法的数值效果不稳定和收敛性弱的缺点,并且在强Wolfe线搜索下证明了该方法具有充分下降性和全局收敛性.大量的数值试验表明新方法是稳定的、有效的.     

一类非线性系统的模糊自适应滑模输出反馈控制

针对一类非线性系统，提出一种新的模糊自适应滑模输出反馈控制方法，该方法不需要非线性系统的状态可测的假设。基于李亚普诺夫函数方法，给出了模糊自适应输出反馈控制律以及在线调节的参数自适应律，证明了模物闭环系统的稳定性和跟踪误差的收敛性。     

基于定常线性迭代法的PSO算法收敛性分析

PSO算法本身是线性时变离散系统,现有的PSO算法收敛性条件的研究都是通过一定的假设将其转化为线性定常离散系统,线性定常离散系统的数学模型与求解线性方程组的单步定常线性迭代法的数学模型完全一致,这样对线性定常离散系统的稳定性分析就转化为对单步定常线性迭代格式的收敛性分析,为PSO算法的收敛性研究提供了一种新的思路和方法。     

改进遗传算法全局收敛性分析

传统的遗传算法大多数没有给出收敛性准则。一类新的改进的遗传算法被提出,该算法即考虑了优化问题的全局性要求——每一步构造一个新函数,而这往往却比局部最优理论和方法困难得多;同时通过对选择算子的改进,对遗传算法后期进化缓慢问题得到了有效控制,最后给出了算法的收敛性证明以及收敛性准则。实例证明该算法是有效的。     

模糊蕴涵的逼近性

证明了模糊蕴涵的收敛性与一致收敛性等价,借助所有的强否定刻画了任意连续蕴涵。特别地,发现了S-蕴涵完全被定义域中对角线上的值所决定。此外,还给出了一种新的构造模糊蕴涵的方法。     

初态学习下的迭代学习控制

提出一种新的初态学习律,以放宽常规迭代学习控制方法的初始定位条件．它允许一定的定位误差,在迭代中不需要定位在某一具体位置上,使得学习控制系统具有鲁棒收敛性．针对二阶LTI系统,给出了输入学习律及初态学习律的收敛性充分条件．依据收敛性条件,学习增益的选取需系统矩阵的估计值,但在一定建模误差下,仍能保证算法的收敛性．所提出的初态学习律本身及其收敛性条件均与输入矩阵无关．     

非线性系统辨识的改进双对角化最小二乘算法

本文提出了一种新的有效的非线性系统最小二乘辨识算法－－改进的双对角化最小二乘（ＭＢＬＳ）算法，在存在舍入误差的条件下，给出了算法的收敛性证明，事实上，算法的收敛性几何不受舍入误差的影响，算法是大范围数值稳定的，仿真结果说明了新算法的有效性。     

连续搅拌釜式生化反应器的非模型控制策略

本方提出了ＳＩＭＯ系统一种新的基于神经网络的非模型控制方法（ＭＦＣ），它包括线性策略和控制作用受限的非线性控制策略，讨论了非模型控制算法收敛性和非模型控制系统的稳定性，将其用于某连续搅拌釜式发酵器的产率最优反馈控制，仿真研究获得了满意的结果。ＭＦＣ方法我需对象模型，具有收敛快，自学习，强抗扰和鲁棒性好等特点。为难以建模的时变，非线性复杂生化过程的控制提供一条新的途径。     

SOME NEW ASPECT OF LYAPUNOV TYPE THEOREMS FOR STOCHASTIC DIFFERENCE EQUATIONS WITH CONTINUOUS TIME

Some new Lyapunov type theorems for stochastic difference equations with continuous time are proven. It is shown that these theorems simplify an application of Lyapunov functionals construction method.     

非线性连续联想记忆神经网络的分析和优化设计

研究非线性连续联想记忆神经网络的渐近稳定性,得出几个定理.在此基础上,提出了一种优化设计方法,并给出了理论证明.目前已有的若干结论是本文所得定理的特例.     

Convergence for nonnegative double splittings of matrices

In this paper, we investigate a class of iterative methods for solving linear systems. This iterative method is derived by double splittings of coefficient matrices. On the basis of convergence and comparison theorems for single splittings, we present some convergence and comparison theorems for nonnegative double splittings. The results are applied to the Jacobi double SOR method.     

Convergence and comparison theorems for double splittings of matrices

In this paper, some convergence theorems for the double splitting of a monotone matrix or a Hermitian positive definite matrix are presented. Two comparison theorems for two double splittings of a monotone matrix are obtained. Meanwhile, we establish a new sufficient condition for convergence of the Gauss-Seidel double SOR method for an H-matrix.     

Hierarchical sensitivity analysis of priority used in analytic hierarchy process

The analytic hierarchy process (AHP) initialed by Saaty (1980) has recently been attracting attention as a useful support method for multi-objective decision making. This paper presents some useful theorems for the sensitivity analysis of priority that is playing an important role in the AHP. These theorems are derived from the principle of hierarchical composition which is expressed in the form of a reachability matrix. Using the theorems, we can easily calculate the degrees of effects caused by local or global changes in the priorities of some criteria, and also we can examine the possibility of rank reversal among alternatives. Furthermore, by applying these theorems to a dwelling selection problem, this paper verifies their effectiveness.     

The convergence conditions of the psd iterative method for linear systems

In this paper, the PSD iterative method was proposed by Evans and Missirlis [4], for solving a large nonsingular system of linear equations Ax=b A general necessary condition for con-vergence of the PSD iterative method is obtained. The convergence theorems of the PSD iterative method are established under the condition that the coefficient matrix A is an H-matrix, our theorems improve and extend some known results.     

Improved convergence theorems of modulus-based matrix splitting iteration method for nonlinear complementarity problems of <Emphasis Type="Italic">H</Emphasis>-matrices

In this paper, the convergence conditions of the modulus-based matrix splitting iteration method for nonlinear complementarity problem of H-matrices are weakened. The convergence domain given by the proposed theorems is larger than the existing ones. Numerical examples show the advantages of the new theorems.     

A New Approach for Automatic Theorem Proving in Real Geometry

We present a new method for proving geometric theorems in the real plane or higher dimension. The method is derived from elimination set ideas for quantifier elimination in linear and quadratic formulas over the reals. In contrast to other approaches, our method can also prove theorems whose complex analogues fail. Moreover, the problem formulation may involve order inequalities. After specification of independent variables, nondegeneracy conditions are generated automatically. Moreover, when trying to prove conjectures that – apart from nondegeneracy conditions – do not hold in the claimed generality, missing premises are found automatically. We demonstrate the applicability of our method to nontrivial examples.     

Mathematics mechanization and applications after thirty years

The aim of mathematics mechanization is to develop symbolic algorithms for manipulating mathematical objects, proving and discovering theorems in a mechanical way. This paper gives a brief review of the major advances in the field over the past thirty years. The characteristic set method for symbolic solution of algebraic, differential, and difference equation systems are first introduced. Methods for automated proving and discovering geometry theorems are then reviewed. Finally, applications in computer-aided geometric design, computer vision, intelligent computer-aided design, and robotics are surveyed.     

Finding Proofs in Tarskian Geometry

We report on a project to use a theorem prover to find proofs of the theorems in Tarskian geometry. These theorems start with fundamental properties of betweenness, proceed through the derivations of several famous theorems due to Gupta and end with the derivation from Tarski’s axioms of Hilbert’s 1899 axioms for geometry. They include the four challenge problems left unsolved by Quaife, who two decades ago found some OTTER proofs in Tarskian geometry (solving challenges issued in Wos’s 1998 book). There are 212 theorems in this collection. We were able to find OTTER proofs of all these theorems. We developed a methodology for the automated preparation and checking of the input files for those theorems, to ensure that no human error has corrupted the formal development of an entire theory as embodied in two hundred input files and proofs. We distinguish between proofs that were found completely mechanically (without reference to the steps of a book proof) and proofs that were constructed by some technique that involved a human knowing the steps of a book proof. Proofs of length 40–100, roughly speaking, are difficult exercises for a human, and proofs of 100–250 steps belong in a Ph.D. thesis or publication. 29 of the proofs in our collection are longer than 40 steps, and ten are longer than 90 steps. We were able to derive completely mechanically all but 26 of the 183 theorems that have “short” proofs (40 or fewer deduction steps). We found proofs of the rest, as well as the 29 “hard” theorems, using a method that requires consulting the book proof at the outset. Our “subformula strategy” enabled us to prove four of the 29 hard theorems completely mechanically. These are Ph.D. level proofs, of length up to 108.