电力市场输电阻塞管理问题的规划模型求解

针对CUMCM2 0 0 4B电力市场的输电阻塞管理问题,建立目标规划模型,详细给出利用MATLAB优化工具箱函数linprog及fgoalattain求解模型的方法,指出正确使用数学软件在建模活动中的重要性.     

An experimental study of approximation algorithms for the joint spectral radius

We describe several approximation algorithms for the joint spectral radius and compare their performance on a large number of test cases. The joint spectral radius of a set Σ of $n \times n$ matrices is the maximal asymptotic growth rate that can be obtained by forming products of matrices from Σ. This quantity is NP-hard to compute and appears in many areas, including in system theory, combinatorics and information theory. A dozen algorithms have been proposed this last decade for approximating the joint spectral radius but little is known about their practical efficiency. We overview these approximation algorithms and classify them in three categories: approximation obtained by examining long products, by building a specific matrix norm, and by using optimization-based techniques. All these algorithms are now implemented in a (freely available) MATLAB toolbox that was released in 2011. This toolbox allows us to present a comparison of the approximations obtained on a large number of test cases as well as on sets of matrices taken from the literature. Finally, in our comparison we include a method, available in the toolbox, that combines different existing algorithms and that is the toolbox’s default method. This default method was able to find optimal products for all test cases of dimension less than four.     

Extragradient Methods for Solving Equilibrium Problems,Variational Inequalities,and Fixed Point Problems

In this paper, we propose the new extragradient algorithms for an α-inverse-strongly monotone operator and a relatively nonexpansive mapping in Banach spaces. We prove convergence theorems by this methods under suitable conditions. Applying our algorithms, we find a zero paint of maximal monotone operators. Using FMINCON optimization toolbox in MATLAB, we give an example to illustrate the usability of our results.     

瞬态热传导的奇异边界法及其MATLAB实现

基于动力学问题时间依赖基本解的奇异边界法是一种无网格边界配点法.该方法引入源点强度因子的概念从而避免了基本解的源点奇异性,具有数学简单、编程容易、精度高等优点.将该方法用于瞬态热传导问题的数值模拟,运用MATLAB实现该问题的数值研究,并创建相应的MATLAB工具箱.针对二维和三维瞬态热传导问题,进行了基于反插值技术和经验公式的奇异边界法MATLAB算例实现.针对支撑圆坯低温瞬态温度场的模拟结果表明,瞬态热传导奇异边界法的MATLAB工具箱具有简单、方便、精确可靠的优点.研究成果有助于发展瞬态热传导的奇异边界法,并为瞬态热传导问题的数值分析和仿真提供了一种简单高效的模拟工具.     

Global exponential stability results for neutral-type impulsive neural networks

In this paper, by utilizing the Lyapunov–Krasovkii functional and combining with the linear matrix inequality (LMI) approach, we analyze the global exponential stability of neutral-type impulsive neural networks. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.     

Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type

In this paper, by using the Lyapunov-Krasovskii functional method, we investigate the global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type. Some new stability criteria are presented in terms of linear matrix inequality (LMI). Two numerical examples are also given to show the effectiveness of the obtained results using LMI control toolbox in MATLAB.     

Verifying approximate solutions to differential equations

It is now standard practice in computational science for large-scale simulations to be implemented and investigated in a problem solving environment (PSE) such as MATLAB or MAPLE. In such an environment, a scientist or engineer will formulate a mathematical model, approximate its solution using an appropriate numerical method, visualize the approximate solution and verify (or validate) the quality of the approximate solution. Traditionally, we have been most concerned with the development of effective numerical software for generating the approximate solution and several efficient and reliable numerical libraries are now available for use within the most widely used PSEs. On the other hand, the visualization and verification tasks have received little attention, even though each often requires as much computational effort as is involved in generating the approximate solution.In this paper, we will investigate the effectiveness of a suite of tools that we have recently introduced in the MATLAB PSE to verify approximate solutions of ordinary differential equations. We will use the notion of ‘effectivity index’, widely used by researchers in the adaptive mesh PDE community, to quantify the credibility of our verification tools. Numerical examples will be presented to illustrate the effectiveness of these tools when applied to a standard numerical method on two model test problems.     

Matlab implementation of a moving grid method based on the equidistribution principle

The objective of this paper is to report on the development of a method of lines (MOL) toolbox within MATLAB, and especially, on the implementation and test of a moving grid algorithm based on the equidistribution principle. This new implementation includes various spatial approximation schemes based on finite differences and slope limiters, the choice between several monitor functions, automatic grid adaptation to the initial condition, and provides a relatively easy tuning for the non-expert user. Several issues, including the sensitivity of the numerical results to the tuning parameters, are discussed. A few test problems characterized by solutions with steep moving fronts, including the Buckley-Leverett equation and an extended Fisher-Kolmogorov equation, are investigated so as to demonstrate the algorithm and software performance.     

Anymatrix: an extensible MATLAB matrix collection

Numerical Algorithms - Anymatrix is a MATLAB toolbox that provides an extensible collection of matrices with the ability to search the collection by matrix properties. Each matrix is implemented as...     

Stability analysis of fuzzy Markovian jumping Cohen–Grossberg BAM neural networks with mixed time-varying delays

In this paper, we investigate the robust stability of uncertain fuzzy Markovian jumping Cohen–Grossberg BAM neural networks with discrete and distributed time-varying delays. A new delay-dependent stability condition is derived under uncertain switching probabilities by Takagi–Sugeno fuzzy model. Based on the linear matrix inequality (LMI) technique, upper bounds for the discrete and distributed delays are calculated using the LMI toolbox in MATLAB. Numerical examples are provided to illustrate the effectiveness of the proposed method.     

A New Lower Bound for the Kirchhoff Index using a numerical procedure based on Majorization Techniques

In this note, we use a procedure, proposed in [Bianchi, M., and A. Torriero, Some localization theorems using a majorization technique, Journal of Inequalities and Applications 5 (2000), 433–446], based on a majorization technique, which localizes real eigenvalues of a matrix of order n. Through this information, we compute a lower bound for the Kirchhoff index (see [Bianchi M., A. Cornaro, J.L. Palacios and A. Torriero, Bounds for the Kirkhhoff index via majorization techniques, Journal of Mathematical Chemistry, (2012) online first]) that takes advantage of additional eigenvalues bounds. An algorithm has been developed with MATLAB software to evaluate the above mentioned bound. Finally, numerical examples are provided showing how tighter results can be obtained.     

带有变化分布时滞的复值神经网络Lagrange稳定性

研究了带有变化分布时滞的复值神经网络Lagrange稳定性问题.通过构造合适的Lyapunov Krasovskii泛函, 并使用矩阵不等式技巧,建立了网络全局指数Lagrange稳定性的判定条件.提供的判据是复值线性矩阵不等式, 能够使用MATLAB软件的YALMIP工具箱快速计算.     

Reversible maps and their symmetry lines

In this paper, we present some methods to determine whether a planar map is reversible. Using these methods, we show that four automorphisms are reversible including Cremona map, cubic Hénon map, Knuth map and McMillan map. Some of them are not polynomial automorphism. We give the recurrence formulas of their symmetry lines, draw their phase portraits and symmetry lines with MATLAB software. Some special properties of their symmetry lines are explained and their beauties are also visually displayed.     

Global asymptotic stability of stochastic Cohen-Grossberg-type BAM neural networks with mixed delays: An LMI approach

In this paper, we consider the stochastic Cohen-Grossberg-type BAM neural networks with mixed delays. By utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) approach, some sufficient LMI-based conditions are obtained to guarantee the global asymptotic stability of stochastic Cohen-Grossberg-type BAM neural networks with mixed delays. These conditions can be easily checked via the MATLAB LMI toolbox. Moreover, the obtained results extend and improve the earlier publications. Finally, a numerical example is provided to demonstrate the low conservatism and effectiveness of the proposed LMI conditions.     

The LMI method for stationary oscillation of interval neural networks with three neuron activations under impulsive effects

In this paper, we investigate the stationary oscillation of interval neural networks with three neuron activation functions and time-varying delays under impulsive perturbations. Several theorems are given which present some sufficient conditions to guarantee the existence, uniqueness, and global exponential stability of periodic solutions (i.e., stationary oscillation) based on Lyapunov functionals approach and inequality analysis techniques. The obtained results can be easily checked by the Linear Matrix Inequality control toolbox in MATLAB. Finally, an example is given to illustrate the advantage of the obtained results.     

钢管订购和运输问题的二次规划模型求解

就 CMCM2 0 0 0钢管订购和运输问题 ,建立二次规划模型 ,给出详尽的用 MATLAB优化工具箱函数 quadprog求解该模型的方法 ,并指出该模型有多个最优解     

应用MATLAB统计工具箱进行教学评价

根据某学院教务部门提供的教学评价数据,利用MATLAB统计工具箱的多元统计回归命令和逐步回归命令,建立了学生对教师总体评价与各评价项目之间的四个回归模型.这些模型简单有效且逐步改进,由此能给教师提供一些合理的建议,以提高教学质量.     

Retrieving the time-dependent thermal conductivity of an orthotropic rectangular conductor

The aim of this paper is to determine the thermal properties of an orthotropic planar structure characterized by the thermal conductivity tensor in the coordinate system of the main directions (Oxy) being diagonal. In particular, we consider retrieving the time-dependent thermal conductivity components of an orthotropic rectangular conductor from nonlocal overspecified heat flux conditions. Since only boundary measurements are considered, this inverse formulation belongs to the desirable approach of non-destructive testing of materials. The unique solvability of this inverse coefficient problem is proved based on the Schauder fixed point theorem and the theory of Volterra integral equations of the second kind. Furthermore, the numerical reconstruction based on a nonlinear least-squares minimization is performed using the MATLAB optimization toolbox routine lsqnonlin. Numerical results are presented and discussed in order to illustrate the performance of the inversion for orthotropic parameter identification.     

基于MTALAB的神经网络判别模型

判别分析是判别样品所属类型的一种统计方法.利用M ATLAB提供的神经网络工具箱为基础,设计了一个三层BP神经网络判别模型,提出了一种进行判别分析的新方法,实例表明,利用BP神经网络建立的判别模型是进行判别分析的有效方法.是对研究分类问题的方法的扩充.