High-order kinetic flux vector splitting schemes in general coordinates for ideal quantum gas dynamics

A class of high-order kinetic flux vector splitting schemes are presented for solving ideal quantum gas dynamics based on quantum statistical mechanics. The collisionless quantum Boltzmann equation approach is adopted and both Bose–Einstein and Fermi–Dirac gases are considered. The formulas for the split flux vectors are derived based on the general three-dimensional distribution function in velocity space and formulas for lower dimensions can be directly deduced. General curvilinear coordinates are introduced to treat practical problems with general geometry. High-order accurate schemes using weighted essentially non-oscillatory methods are implemented. The resulting high resolution kinetic flux splitting schemes are tested for 1D shock tube flows and shock wave diffraction by a 2D wedge and by a circular cylinder in ideal quantum gases. Excellent results have been obtained for all examples computed.     

基于结构元的复模糊数及其序列极限

复模糊数是模糊复分析中的基本概念,在模糊复分析中,它的运算是基于扩张原理的形式给出的,是对元素遍历某个条件所对应的结果进行运算,这种遍历过程给实际操作带来了很多的不便,因此,在一定程度上也阻碍了模糊复分析理论的应用.对此,本文基于模糊结构元的理论基础,探讨了复模糊数运算的另一种新的途径,这种方法简化了复模糊数的运算,也...     

Imaginary quadratic function fields

In Bautista-Ancona and Diaz-Vargas (2006) [B-D] a characterization and complete listing is given of the imaginary quadratic extensions K of k(x), where k is a finite field, in which the ideal class group has exponent two and the infinite prime of k(x) ramifies. The objective of this work is to give a characterization and list of these kind of extensions but now considering the case in which the infinite prime of k(x) is inert in K. Thus, we get all the imaginary quadratic extensions of k(x), in which the ideal class group has exponent two.     

Algorithmic inference: From information granules to subtending functions

To get a true hybrid framework for taking operational decisions from data, we extend the Algorithmic Inference approach to the Granular Computing paradigm. The key idea is that whether or not we need to make decisions instead of mere computations depends on the fact that collected data are not sufficiently definite; rather, they are representative of whole sets of data that could be virtually observed, and we need to manage this indeterminacy. The distinguishing feature is that we face indeterminacy exactly where it affects the quality of the decision. This gives rise to a family of inference algorithms which can be tailored to many specific decisional problems that are generally solved only in approximate ways. In the paper we discuss the bases of the paradigm and provide some examples of its implementation.     

On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

This paper provides a thorough investigation on the resolution of a finite system of fuzzy relational equations with sup-T composition, where T is a continuous triangular norm. When such a system is consistent, although we know that the solution set can be characterized by a maximum solution and finitely many minimal solutions, it is still a challenging task to find all minimal solutions in an efficient manner. Using the representation theorem of continuous triangular norms, we show that the systems of sup-T equations can be divided into two categories depending on the involved triangular norm. When the triangular norm is Archimedean, the minimal solutions correspond one-to-one to the irredundant coverings of a set covering problem. When it is non-Archimedean, they only correspond to a subset of constrained irredundant coverings of a set covering problem. We then show that the problem of minimizing a linear objective function subject to a system of sup-T equations can be reduced into a 0–1 integer programming problem in polynomial time. This work generalizes most, if not all, known results and provides a unified framework to deal with the problem of resolution and optimization of a system of sup-T equations. Further generalizations and related issues are also included for discussion.     

Investment optimization on port’s development by fuzzy integer programming

In this research, the main purpose is to formulate a model to determine the optimum investment on port development from national investment prospective; on the other hand, costs and benefits are calculated from consumer and investor’s viewpoint. The formulated model is an integer-programming model. The emphasis is on how to formulate an investment optimization problem where cargo operation, investment costs, cargo-handling capacity, cargo transportation network, and the world maritime fleet constraints are included. Fuzzy numbers are used for cargo forecast study results. The output of the model is the type of design ships and design berths which are needed in each sub period, so that the port planner (the government) will find out the optimum development plan of port in each sub period when there is uncertainty in cargo handling forecast (fuzzy numbers).     

复Fuzzy数列的度量收敛与水平收敛

研究复Ｆｕｚｚｙ数列科技的收敛性，讨论复Ｆｕｚｚｙ数列度量收敛与水平收敛的等价性问题。为复Ｆｕｚｚｙ分析的进一上研究打下良好的基础。     

模糊信息处理在舰艇等级评估中的应用

采用模糊信息综合处理的方法，对舰艇主要设备技术状态作综合处理，评估舰艇的技术状态等级，促进舰艇等级评估趋向科学化、规范化。     

L-拓扑空间中的相对强F紧性与相对超F紧性

In this paper,two concepts of relative compactness-the relative strong fuzzy compactness and the relative ultra-fuzzy compactness are defined in L-topological spaces for an arbitrary L-set.Properties of relative strong fuzzy sets and relative ultra-fuzzy compact sets are studied in detail and some characteristic theorems are given.Some examples are illustrated.     

模糊线性系统的扰动分析

使用谱范数分析了模糊线性系统在三种情形下的扰动: (1)右端模糊向量有扰动, 系数矩阵不变; (2)系数矩阵有扰动,右端模糊向量不变; (3)系数矩阵和右端模糊向量都有扰动,并通过数值实例验证给出的扰动界的估计.