基于粗糙集理论的舰船研制方案总体评价

以系统评价思想为指导,提出了基于粗糙集理论的多目标评价方法,对舰船研制方案综合评价问题进行了研究,建立了综合评价模型,并通过算例表明,该方法用于舰船研制方案的总体评价比现行方法有明显的优越性.     

Uncertainty of measurement and legislative limits

 The uncertainty affecting analytical measurements has to be taken into account when evaluating compliance of suspect matrices to legislative limits. To this aim Type 1 and 2 errors must be considered. This necessarily leads to the evaluation of the minimum detectable inadmissible signal, from which the minimum detectable inadmissible concentration can be obtained. The signal of suspect matrices thus has to be compared with the minimum detectable inadmissible signal. This paper aims to discuss practical problems involved in the comparison.     

Portfolio selection under strict uncertainty: A multi-criteria methodology and its application to the Frankfurt and Vienna Stock Exchanges

In modern portfolio theory, it is common practice to first compute the risk-reward efficient frontier and then to support an individual investor in selecting a portfolio that meets his/her preferences for profitability and risk. Potential flaws include (a) the assumption that past data provide sufficient evidence for predicting the future performances of the securities under consideration and (b) the necessity to mathematically determine or approximate the investor’s utility function. In this paper, we propose a methodology whose initial phase filters portfolios that are inefficient from a historical perspective. While this is consistent with traditional approaches, the second phase differs from the standard approach as it uses a decision table constructed by considering multiple scenarios assuming strict uncertainty. The table cells measure consequences by a multi-criteria linear performance index of simulated future returns, which avoids difficulties with performance ratios. The real world applicability is illustrated through two studies based on data from the stock exchanges in Frankfurt and Vienna.     

模型不确定非线性随机系统的鲁棒性能准则设计

对于一类模型不确定非线性随机系统,用耗散性的观点发展了鲁棒性能准则理论.特别地,将确定性非线性系统理论中的耗散性概念引入到模型不确定随机非线性系统中,并以此作为基础来发展H∞理论.在精确模型随机非线性系统H∞基础上,建立了模型不确定系统L2增益和HJI不等式的可解性的关系.由于HJI偏微分方程难于求解,考虑模型参数满足某种适当匹配条件的系统的鲁棒性能准则问题,我们不需要通过求解HJI方程就可以得到此类系统的H∞控制律.     

Some aspects of gravitational quantum mechanics

String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle. Such a modified Heisenberg uncertainty principle is referred as gravitational uncertainty principle(GUP) in literatures. This proposal has some novel implications on various domains of theoretical physics. Here, we study some consequences of GUP in the spirit of Quantum mechanics. We consider two problem: a particle in an one-dimensional box and free particle wave function. In each case we will solve corresponding perturbational equations and compare the results with ordinary solutions.     

Some recent progress in applied mathematics(Ⅱ)

1　Unified information theoryOne characteristic of the 2 0 th century is its information revolution.With satellites,huge amounts of information are collected daily,proposing a challenge to our understandingof the information.Also,we realize that different ways of comprehension can be very mis-leading,since all information contains noise and our reasoning and sensing organs are limit-ed.To this end,Shannon and Weaver in 1949established the first theory of informationdealing with uncertainty on…     

Uncertainty relations for entangled states

A generalized uncertainty relation for an entangled pair of particles is obtained if we impose a symmetrization rule for all operators that we should employ when doing any calculation using the entangled wave function of the pair. This new relation reduces to Heisenberg’s uncertainty relation when the particles have no correlation and suggests that we can have new lower bounds for the product of position and momentum dispersions.     

An approach to constructing mathematical models of moving mechanical systems under uncertainty

The paper outlines an approach to constructing a mathematical model of moving mechanical systems under uncertainty. Generalized fuzzy differential equations are used to prove that the model is mathematically correct. The motion of a control oscillator under uncertainty is considered as an example __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 108–119, October 2007.     

Uncertainty of chemical oxygen demand determination in wastewater samples

 The measurement uncertainty of the result of chemical oxygen demand determination in wastewater was evaluated. The major sources of uncertainty of the result of measurement were identified as the purity of reagents, volumetric operations, gravimetric operations, bias, and the repeatability of the method. Identification and evaluation of uncertainty sources was followed by combined uncertainty calculations. The combined uncertainty was compared to the experimentally determined variation and good agreement was found, indicating that the major uncertainty sources had been identified. The results show that the major sources of uncertainty arose from repeatability at high concentration level and volumetric steps at low concentration level, thus revealing the target operations for reducing the measurement uncertainty of this determination. Received: 5 August 2002 Accepted: 5 November 2002 Acknowledgements This research was supported by the Ministry of Education, Science and Sport of the Republic of Slovenia (Project Z2–3530). Presented at CERMM-3, Central European Reference Materials and Measurements Conference: The function of reference materials in the measurement process, May 30–June 1, 2002, Rogaška Slatina, Slovenia Correspondence to A. Drolc     

Robust Analysis and Synthesis for the Nonexistence of Periodic Solutions in a Class of Nonlinear Systems

This paper considers the nonexistence of periodic solutions in a class of nonlinear uncertain systems. Based on the generalized Kalman–Yakubovich–Popov (GKYP) lemma, linear matrix inequalities (LMIs) characterizations are derived to guarantee the nonexistence of periodic solutions in a certain frequency range. The new LMI conditions do not involve any product of the Lyapunov matrix and the system matrices. Based on the results, a dynamic output feedback controller is designed to ensure the nonexistence of periodic solutions in such systems. A concrete application to the Chua circuit shows the applicability and validity of the proposed approach. This work was supported by the National Science Foundation of China under Grants 60404007 and 60334030.