Method of particular solutions for linear,two-point boundary-value problems

The methods commonly employed for solving linear, two-point boundary-value problems require the use of two sets of differential equations: the original set and the derived set. This derived set is the adjoint set if the method of adjoint equations is used, the Green's functions set if the method of Green's functions is used, and the homogeneous set if the method of complementary functions is used.With particular regard to high-speed digital computing operations, this paper explores an alternate method, the method of particular solutions, in which only the original, nonhomogeneous set is used. A general theory is presented for a linear differential system ofnth order. The boundary-value problem is solved by combining linearly several particular solutions of the original, nonhomogeneous set. Both the case of an uncontrolled system and the case of a controlled system are considered.This research, supported by the NASA-Manned Spacecraft Center, Grant No. NGR-44-006-089, is a condensed version of the investigations described in Refs. 1 and 2.     

Dynamical level set method for parameter identification of nonlinear parabolic distributed parameter systems

This article considers a dynamical level set method for the identification problem of the nonlinear parabolic distributed parameter system, which is based on the solvability and stability of the direct PDE (partial differential equation) in Sobolev space. The dynamical level set algorithms have been developed for ill-posed problems in Hilbert space. This method can be regarded as a asymptotical regularization method as long as a certain stopping rule is satisfied. Hence, the convergence analysis of the method is established similar to the proof of convergence of asymptotical regularization. The level set converges to a solution as the artificial time evolves to infinity. Furthermore, the proposed level set method is proved to be stable by using Lyapunov stability theorem, which is constructed in my previous article.Numerical tests are discussed to demonstrate the efficacy of the dynamical level set method, which consequently confirm the level set method to be a powerful tool for the identification of the parameter.     

模糊集对分析用于脱硫除尘器的综合评价

提出了锅炉脱硫除尘器综合评价的模糊集对分析方法.评述了方法的基本原理和计算步骤,通过实例介绍了方法的应用.评价实例结果表明模糊集对分析用于脱硫除尘器综合评价是可行的.与密切值法相比,所得评价结果相同.该法具有计算简便和实用的特点.     

系统树中的近似Bayes方法

本文利用近似Ｂａｙｅｓ方法对一个具有树形结构的成败型系统的可靠性进行估计．本文证明了利用近似Ｂａｙｅｓ方法对系统的可靠性参数的估计，具点估计在Ｆｉｓｈｅｒ意义下是渐近有效的，其相应的置信下限也是Ｆｉｓｈｅｒ意义下渐近有效的．     

基于TOPSIS思想的技术创新方案的Vague集评价方法及其应用

为了得到理想的技术创新选择方案,论文从技术创新的实际出发,从实力、潜力和外部环境三个角度选择了一组反映技术创新项目实际情况的评价指标。并借助Vague集理论,通过TOPSIS中正负理想解的思想定义了任意创新方案的评价指标值,运用Vague集理论中距离的概念构建了新的评价方法,进而得到了满意的评价结果。该方法一方面体现了Vague集理论描述不确定性问题的优点,另一方面借助TOPSIS思想满足了方案评价的基本准则。这一思想和方法的提出不仅为Vague集理论研究提供了新的应用领域,也为技术创新的研究提供了新的思路和方法。     

Stability analysis of probabilistic Boolean networks with switching topology

This paper investigates the set stability of probabilistic Boolean networks (PBNs) with switching topology. To deal with this problem, two novel concepts, set reachability and the largest invariant set family, are defined. By constructing an auxiliary system, the necessary and sufficient conditions for verifying set reachability are given and the calculation method for the largest invariant set family is obtained. Based on these two results, an equivalent condition of set stability is derived, which can be used to determine whether a PBN with switching topology can be stabilized to a given set. In addition, the design method of switching signal is proposed by combining the characteristic of the largest invariant set family, and a numerical example is reported to demonstrate the efficiency of presented approach.     

基于Vague集的群决策方法研究

首先介绍了Vague集的基本概念,将直觉模糊集的一些运算规则重新在Vague集上作了定义,提出用Vague值表示的九级语言术语集.接着指出衡量Vague集(值)相似度要考虑的三个因素,提出了新的度量方法.在同时考虑专家决策结果的一致性和专家权重的基础上,提出了汇总各专家Vague意见的方法.最后以一个案例说明了所提出的方法.     

Finite bases for finitely generated,relatively congruence distributive quasivarieties

In [21], D. Pigozzi has proved in a non-constructive way that every relatively congruence distributive quasivariety of finite type generated by a finite set of finite algebras is finitely axiomatizable. In this paper we show that the non-constructive parts of Pigozzi's argument can be replaced by constructive ones. As a result we obtain a method of constructing a finite set of quasi-equational axioms for each relatively congruence distributive quasivariety generated by a given finite set of finite algebras of finite type. The method can also be applied to finitely generated congruence distributive varieties.Presented by Joel Berman.     

基于多项式组主项解耦消元法的几何定理机器证明

基于多项式组主项解耦消元法 ,将几何定理的假设条件 (多项式组 PS)化为主项只含主变元的三角型多项式组 DTS,可得到定理命题成立的不含变元的非退化条件 ,即充分必要或更接近充分必要的非退化条件 .由于多项式主系数不含变元 ,已不存在 DTS多项式之间的约化问题 ,故方法有普遍意义 .文中例为西姆松定理的机器证明 .     

A dual ascent procedure for the set partitioning problem

The set partitioning problem is a fundamental model for many important real-life transportation problems, including airline crew and bus driver scheduling and vehicle routing.In this paper we propose a new dual ascent heuristic and an exact method for the set partitioning problem. The dual ascent heuristic finds an effective dual solution of the linear relaxation of the set partitioning problem and it is faster than traditional simplex based methods. Moreover, we show that the lower bound achieved dominates the one achieved by the classic Lagrangean relaxation of the set partitioning constraints. We describe a simple exact method that uses the dual solution to define a sequence of reduced set partitioning problems that are solved by a general purpose integer programming solver. Our computational results indicate that the new bounding procedure is fast and produces very good dual solutions. Moreover, the exact method proposed is easy to implement and it is competitive with the best branch and cut algorithms published in the literature so far.     

A comparison of two methods for determining the weights of belonging to fuzzy sets

Saaty has solved a basic problem in fuzzy set theory using an eigenvector method to determine the weights of belonging of each member to the set. In this paper, a weighted least-square method is utilized to obtain the weights. This method has the advantage that it involves the solution of a set of simultaneous linear algebraic equations and is thus conceptually easier to understand than the eigenvector method. Examples are given for estimating the relative wealth of nations and the relative amount of foreign trade of nations. Numerical solutions are obtained using both the eigenvector method and the weighted least-square method, and the results are compared.Partial support of this research was provided by NIH Grant No. GM-23732.     

An improved approximate method for computing eigenvector derivatives

An improved approximate method for computing eigenvector derivatives has been developed. In this formulation an eigenvector derivative is assumed to be spanned by a set of truncated normal modes augmented by a residual static mode. The coefficients in the expansion are computed by a Bubnov-Galerkin method. The formulation has been implemented as a set of Direct Matrix Abstraction Programming alters for . Numerical examples show the method provides sufficient accuracy and reduced computation time when compared to the exact solution.     

Transient Bernoulli flow in multi-port fluid devices with arbitrary geometry

We present a method for the solution of transient flow in a multi-port fluid device with arbitrary geometry. The method is applicable to fluid devices where the fluid motion is primarily inviscid throughout the volume, but locally near a device port some accommodation to viscous flow is introduced. The internal flow is characterized by an array of purely geometrical factors between ports, essentially a set of generalized impedances; the state variables elicited are the average volume flow rates through the device ports. The method creates a set of coupled non-linear time-dependent ordinary differential equations. The solution to this set of equations is much faster, typically by orders of magnitude, than a single run of a transient CFD model. We demonstrate our method with a simple example; we show that the results of the method agree well with a full CFD calculation.     

A method of inference in approximate reasoning based on interval-valued fuzzy sets

This paper introduces and discusses a method of approximate inference which operates on the extension of the concept of a fuzzy set by the concept of an interval-valued fuzzy set. This method allows a formal, fuzzy representation to be built for verbal decision algorithms. Furthermore, it can have an effective computer representation. An example showing how this method operates is provided.     

多项式方程组的主项解耦消元法

本文提出多项式组符号求解的主项解耦 (主项只含主元 )消元法 :视多项式为变元不同幂积的线性组合 ,以主项解耦三角型多项式组 DTS为引导 ,用逐项伪除求余式 ,将多项式组 PS化为与其同解的 DTS.内容涉及 :消元算法、DTS的存在性与结构特性、零点集结构公式等 .亦对 Grobner基法、吴文俊消元法与本文方法之间的相互联系、区别以及特点进行了比较 .研究表明主项解耦消元法适用于一般多项式组且效率较高     

用基础解系解某些条件极值问题

通过对线性的目标函数在线性的约束条件下的极值问题的分析,得到这类极值问题一般是不能用拉格朗日乘数法求解.通过用基础解系的方法进行求解这类问题,实例表明,这种方法是可行有效的.     

Generating Sum-of-Ratios Test Problems in Global Optimization

A method is presented for the construction of test problems involving the minimization over convex sets of sums of ratios of affine functions. Given a nonempty, compact convex set, the method determines a function that is the sum of linear fractional functions and attains a global minimum over the set at a point that can be found by convex programming and univariate search. Generally, the function will have also local minima over the set that are not global minima.     

Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces

In this paper, we introduce and study some low computational cost numerical methods for finding a solution of a variational inequality problem over the solution set of an equilibrium problem in a real Hilbert space. The strong convergence of the iterative sequences generated by the proposed algorithms is obtained by combining viscosity-type approximations with projected subgradient techniques. First a general scheme is proposed, and afterwards two practical realizations of it are studied depending on the characteristics of the feasible set. When this set is described by convex inequalities, the projections onto the feasible set are replaced by projections onto half-spaces with the consequence that most iterates are outside the feasible domain. On the other hand, when the projections onto the feasible set can be easily computed, the method generates feasible points and can be considered as a generalization of Maingé’s method to equilibrium problem constraints. In both cases, the strong convergence of the sequences generated by the proposed algorithms is proven.     

The method of feasible directions for mathematical programming problems with preconvex constraints

The convergence of the method of feasible directions is proved for the case of the smooth objective function and a constraint in the form of the difference of convex sets (the so-called preconvex set). It is shown that the method converges to the set of stationary points, which generally is narrower than the corresponding set in the case of a smooth function and smooth constraints. The scheme of the proof is similar to that proposed earlier by Karmanov.     

共轭可交换性及其在集合形式单调类定理中的应用

引入了集列的极限运算与二元集运算之间的共轭可交换性的概念,讨论了常见的和重要的集列的极限运算与集代数运算之间所具有的共轭可交换性质,在一般的情形下证明了共轭可交换性是集类的极限运算生成类对集代数运算具有封闭性的一个充分条件,使得集合形式的单调类定理的理论得到了统一的解释,并且证明更简单,思路更清晰,最后还给出了一个新的集合形式的单调类定理.