关键词： 数学形态学   小波变换   小电流接地系统   配电网   接地故障   选线算法   选线判据  

摘要： 我国配电网广泛采用中性点不接地或经消弧线圈接地系统,即小电流接地系统。在配电网中,单相接地故障率最高,但由于故障后接地电流小,故障特征不明显,因此小电流接地系统单相接地故障选线问题虽已经研究多年却一直未能很好解决,严重阻碍了配电网供电可靠性和自动化水平的提高。\n 本文首先对以往的各种稳态选线算法和暂态选线算法进行综述并指出各种算法存在的缺陷,然后对小电流接地系统单相接地故障特征进行了深入的理论研究和实验分析,研究结果表明故障后暂态过程中含有大量的高频特征信息,对这些特征信息进行分析提取,可构成选线判据。由于小波分析具有时频同时局部化的特点,可以将信号分解到不同的频率带,因此特别适合分析非平稳信号和暂态信号。本文对小波理论进行了深入的理论研究,从而为故障特征的提取提供了理论依据。虽然小波分析算法能很好的滤除白噪声,但是对于脉冲噪声却无能为力,如果不滤除脉冲噪声,就会影响选线时刻的判断造成选线不正确。因此本文提出了一种基于数学形态学及小波变换综合的选线算法,该算法利用数学形态学滤波器对采集到的电压电流信号进行滤波,而后利用小波变换的奇异性理论和模极大值理论来构成接地选线算法,本算法很好地体现了形态学滤波器的噪声抑制能力和小波分解的奇异点检测能力。Matlab仿真结果表明,该算法不受中性点接地方式、故障时刻和线路参数的影响,且具有较强的承受过渡电阻的能力。同时本文还讨论了小波分析用于故障选线所碰到的一些问题,如小波函数的选取,分解尺度的选取依据和采样频率的选择等。

关键词： 超声传感器   T靶   声学定位   弹着点  

摘要： 建立一种基于超声测量法的开放式T靶的数学模型.弹丸在空气中飞行时产生声波,利用超声传感器测出T型阵列传感器接收到声波时的相对时间差,通过建立相应T靶的数学解算模型可求出弹丸穿过靶面的精确位置以实现弹丸的自动定位.分析了影响定位精度的诸因素及提高定位精度的办法.

关键词： 算法思想   数学教学   渗透   高中   数学素养   现代人  

摘要： 算法思想是现代人所应该具备的一种数学素养，高中教师应把握让中学生理解算法思想这一本质，在数学教学中渗透算法思想，让学生体会算法思想，并将算法思想融入到自己的生活中．

关键词： 算法多样化   小学数学   《数学课程标准》   价值   尊重学生   计算教学   学生创造性   生活背景  

摘要： 《数学课程标准》指出“由于学生生活背景和思考的角度不同，所使用的方法必然是多样化的，教师应尊重学生的想法，鼓励学生独立思考，提倡计算方法的多样化。”而算法多样化则是针对过去计算教学中往往只有一种算法的弊端提出来的。计算单一化忽视了个别差异，遏制了学生创造性。针对这种情况，《数学课程标准》提出了这一全新的理念，意味着计算教学翻开了新的一页。

关键词： 运筹学   最优路线   直达矩阵   换乘   最短路  

摘要： 公交线路选择问题是城市公共交通信息查询的重要内容,本文建立了满足不同公交线路查询者需求的最优线路选择模型并给出了相应的算法。首先通过引入各条公交线路直达最短距离矩阵构造了公交网络直达关系图(直达矩阵),在直达关系图(直达矩阵)上,利用修改了的最短路算法,即可求得最优换乘路线。根据出行者的不同需求,通过在直达关系图上定义不同的权系数,可以分别求得换乘次数最少的公交出行线路、经过站点最少的公交出行线路;通过修改最短路算法,可以求得出行耗时最少的线路及出行费用最低的线路,另外,本模型还可以综合考虑出行者的需求情况,求得出行者满意度最大的出行路线。

关键词： G-protein coupled receptors   promiscuous coupling   trafficking   genetic algorithm  

摘要： G-protein-coupled receptors (GPCRs) constitute a large and diverse family of proteins whose primary function is to transduce extracellular stimuli into intracellular signals. These receptors play a critical role in signal transduction, and are among the most important pharmacological drug targets. Upon binding of extracellular ligands, these receptor molecules couple to one or several subtypes of G-protein which reside at the intracellular side of the plasma membrane to trigger intracellular signaling events. The question of how GPCRs select and activate a single or multiple G-protein subtype(s) has been the topic of intense investigations. Evidence is also accumulating;however, that certain GPCRs can be internalized via lipid rafts and caveolae. In many cases, the mechanisms responsible for this still remain to be elucidated. In this work, we extend the mathematical model proposed by Chen et a]. [Modelling of signalling via G-protein coupled receptors: pathway-dependent agonist potency and efficacy, Bull. Math. Biol. 65 (5) (2003) 933-958] to take into account internalization, recycling, degradation and synthesis of the receptors. In constructing the model, we assume that the receptors can exist in multiple conformational states allowing for a multiple effecter pathways. As data on kinetic reaction rates in the signalling processes measured in reliable in vivo and in vitro experiments is currently limited to a small number of known values. In this paper, we also apply a genetic algorithm (GA) to estimate the parameter values in our model. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： matrix algebra   aggregation algorithms   modelling software  

摘要： The aggregation procedure is an important theoretical and empirical topic of economics. It appears in the Microeconomics and Macroeconomics, in Panel and Cross-Sectional Data Analysis, in Data Mining Analysis, in Input-Output and Agent-based Computational Economics Modelling. The question of the choice of algorithm is became important since the size of the sample data has became more important, and despite of the speed of the computers. In this paper we present the "classical" algorithm (the "matrix algebraic" one) of aggregation of the two-dimensional sample data, and compare it to the alternative algorithms (the "vectorial" one) we developed. Then we present some extensions to the multidimensional aggregation.

关键词： modelling   nonlinear regression   sensitivity analysis  

摘要： This paper presents an algorithm that generates families of mathematical models with nonlinear parameters, and includes the study of linear models, based on the experimental data of the intervening variables. The implementation of this algorithm has been named poly-model and is based on the application of the Gauss-Newton algorithm for obtaining the parameters of nonlinear models [Verdu F. Un Algoritmo para la construccion multiple de modelos matematicos no lineales y el estudio de su estabilidad. Doctoral Tesis. Universidad de Alicante, 2004]. One of its characteristics is a search among different nonlinear models within the parameters;unlike the methods found in the scientific literature [Camacho Rosales J. Estadistica con SPSS para windows. Ed. Ra-Ma, 2002;Mathsoft Inc. Splus-4. Guide to Statistics. Seattle, 1997], the user does not intervene in their generation. A pruning criteria has also been introduced that is based on the stability analysis of models generated from perturbations, applying studies carried out by the authors and published in [Verdu F, Villacampa Y. A computer program for a Monte Carlo analysis of sensitivity in equations of environmental modelling obtained from experimental data. Advances in Engineering Software, 2002]. Object-oriented Pascal has been used in Delphi 6. (c) 2007 Published by Elsevier Ltd.

关键词： option   pricing   lattice   combinatorics   exotic option  

摘要： Options are popular financial derivatives that play essential roles in financial markets. How to price them efficiently and accurately is very important both in theory and practice. Options are often priced by the lattice model. Although the prices computed by the lattice converge to the theoretical option value under the continuous-time model, they may converge slowly. Worse, for some options like barrier options, the prices can even oscillate wildly. For Such options, huge amounts of computational time are required to achieve acceptable accuracy. Combinatorial techniques have been used to improve the performance in pricing a wide variety of options. This paper uses vanilla options, power options, single-barrier options, double-barrier options, and lookback options as examples to show how combinatorics can help us to derive linear-time pricing algorithms. These algorithms compare favorably against popular lattice methods, which take at least quadratic time. (C) 2007 Elsevier Ltd. All rights reserved.

摘要： Any logical procedure that is used to reason or to infer either deductively or inductively, so as to draw conclusions or make decisions, can be called, in a broad sense, a realization process. A realization process usually assumes the recursive form that one state develops into another state by following a certain specific rule. Such an action is generally formalized as a dynamical system. In mathematics, especially for existence questions, a realization process often appears in the form of an iterative procedure or a differential equation. For years researchers have taken great effort to describe, analyse, and modify realization processes for various applications. The thrust in this exposition is to exploit the notion of dynamical systems as a special realization process for problems arising from the field of linear algebra. Several differential equations whose solutions evolve in submanifolds of matrices are cast in fairly general frameworks, of which special cases have been found to afford unified and fundamental insights into the structure and behaviour of existing discrete methods and, now and then, suggest new and improved numerical methods. In some cases, there are remarkable connections between smooth flows and discrete numerical algorithms. In other cases, the flow approach seems advantageous in tackling very difficult open problems. Various aspects of the recent development and application in this direction are discussed in this paper. © 2008 Cambridge University Press.