Unified Finite Integral Transform Analysis

A special matrix is introduced, the elements of which are zero or first-order operators. This matrix is used to define the initial boundary value problem which covers a wide class of engineering applications. To bring the solution of the problem within the realm of integral transform theory, a new finite integral transform and the corresponding inversion formula are developed. The necessary orthogonality relations is derived using an extension of the Gauss-Green theorem. The formal solution obtained here can be applied to study heat conduction problems, elasticity problems, etc.     

Iterative algorithms for optimal design of columns subject to a stress constraint

Two algorithms based on an integral equation formulation of the buckling optimization problem are formulated and implemented. The objective of the optimization is to maximize the buckling load of an elastically restrained column by optimally designing the cross-sectional area subject to a minimum cross-section or maximum stress constraint. The first approach involves solving the resulting integral equations iteratively taking into account the boundary conditions, the optimality criterion and the imposed constraints. In the second approach an iterative finite difference approximation scheme is developed.The column is elastically restrained at both ends which produce the simple support and clamped end conditions for the limiting cases leading to the optimal design of columns under general boundary conditions. The above problems do not have analytical solutions due to the complexity of the boundary conditions, constraints and the optimality conditions necessitating the formulation of computational schemes for their solution. Several numerical results are given and compared with available results in the literature. Moreover the accuracy of the methods is studied by comparing the iterative solutions with finite element ones and with exact results when available.     

A continuous integraph

A mechanical integraph has been developed which plots continuously the integral of the product of two functions. It uses the principle of the electrical integrating watthour-meter combined with a moving table. Errors of the machine have been reduced to an average of 1 per cent. for common uses. By cross-connecting the device in a simple mechanical way, it is possible to solve certain types of integral equations. A link motion has been added which plots the product of two given functions. Various uses have been made of the instrument for solving problems in connection with electrical circuits, continuous beams, etc., and certain problems involving integral equations.     

Direct transformation of variational problems into Cauchy systems—II. scalar-semi-quadratic case

This series of papers addresses three interrelated problems: the solution of a variational problem, the solution of integral equations, and the solution of an initial valued system of integrodifferential equations. It will be shown that a large class of variational problems requires the solution of a nonlinear integral equation. It has also been shown that the solution of a nonlinear integral equation is identical to the solution of a Cauchy system. In this paper, we by-pass the nonlinear integral equations and show that the minimization problems directly imply a solution of the Cauchy system. This second paper in the series looks at semi-quadratic functional and scalar functions.     

多元函数介值定理的推广

介值定理是数学分析的一个重要定理,对研究函数方程根的存在性、不动点和积分中值定理等问题起到重要作用。在多元函数中推广介值定理,并且将只有第一类间断点的函数的介值定理推广运用到积分中值定理中,推广了文[4]的结论。     

The solutions of vibration control problems using artificial neural networks

This paper introduces an alternative method artificial neural networks (ANN) used to obtain numerical solutions of mathematical models of dynamic systems, represented by ordinary differential equations (ODEs) and partial differential equations (PDEs). The proposed trial solution of differential equations (DEs) consists of two parts: The initial and boundary conditions (BCs) should be satisfied by the first part. However, the second part is not affected from initial and BCs, but it only tries to satisfy DE. This part involves a feedforward ANN containing adjustable parameters (weight and bias). The proposed solution satisfying boundary and initial condition uses a feedforward ANN with one hidden layer varying the neuron number in the hidden layer according to complexity of the considered problem. The ANN having appropriate architecture has been trained with backpropagation algorithm using an adaptive learning rate to satisfy DE. Moreover, we have, first, developed the general formula for the numerical solutions of nth-order initial-value problems by using ANN.For numerical applications, the ODEs that are the mathematical models of linear and non-linear mass-damper-spring systems and the second- and fourth-order PDEs that are the mathematical models of the control of longitudinal vibrations of rods and lateral vibrations of beams have been considered. Finally, the responses of the controlled and non-controlled systems have been obtained. The obtained results have been graphically presented and some conclusion remarks are given.     

融入基础力学内容的“计算方法”课程延拓性教学实践

在计算方法课程教学中融入理论力学、材料力学知识内容,提出延拓性教学的三个层次:一是由力学问题认识基本数学问题的来源与背景;二是掌握基本数学模型的数值求解方法与理论;三是通过编程实验环节将具体力学问题转化成数学模型求数值解。近几年的课程教学效果调查表明,采用延拓性教学法能有效提高学生的学习主动性、综合应用所学知识分析问题和解决问题的能力。     

A new approach to numerical integration by means of steady-state flux in a slab

The definite integral is generally interpreted geometrically as an “area”. An alternate interpretation as a steady-state “flux” through a unit slab is derived, which leads to a new method of numerical integration. The usual sum of a large number of approximate areas is replaced by the flux through a “single” increment.The method involves the solution of a system of linear finite difference equations. The coefficient matrix is tri-diagonal and is solved efficiently by the Thomas algorithm. During the iterative process the coefficients are determined by simple quadrature schemes applied to each increment.Error analysis revealed that an expression could be derived for the roundoff error associated with the final Thomas iteration. It is shown that the roundoff error is smallest when the matrix coefficients a_k\S>1. The method is shown to be superior to the classical methods due to its simplicity and tolerance for variable increment size. In addition, a new function is determined which is useful in diffusion studies. Numerical data are presented confirming these results.     

浅议求二次函数解析式的方法

历届中考的热点之一,就是运用二次函数解决数学问题或实际问题,此类题目经常需要用二次函数表达其中的变量关系,而求出二次函数的解析式是解题的关键。求二次函数解析式的方法有定义法、平移法、三点法、交点法、顶点法、对称法、旋转法、参数法、等量法等。     

Modeling of synchronous electric machines for real-time simulation and automotive applications

Recent research in the field of vehicle electrification has indicated that synchronous machines, which include the permanent magnet synchronous machine (PMSM) and the externally excited synchronous machine (EESM), represent a viable solution for electric propulsion. A challenging problem for synchronous machines drives employed in automotive applications is to obtain accurate mathematical models which can deal with parametric variation and which are suitable for real-time simulations and synthesis of control laws. The goal of this paper is to provide a mathematical modeling framework for synchronous machines that can answer to this challenging problem. To this end, using the rotor reference frame, the mathematical models of PMSMs and EESMs are constructed taking into account also the parametric variation due to magnetic saturation and temperature variation. Then, a complex state-space bilinear model for both EESM and PMSM with parametric variation due to magnetic saturation and temperature are developed. Considering the parametric variation as a polytopic bounded disturbance, it is then shown how to split the bilinear complex model in two PWA variable parameter state-space models suitable for a cascade control structure. Based on the developed models, a dynamic unified simulator was constructed in Matlab^®/Simulink^®. Measurement data obtained in a real test-bench system were used to verify the accuracy of the simulator. The discrete-time simulator was then integrated in an industrial hardware-in-the-loop test bench for real-time evaluation of a current control scheme in EESM drives.     

Question categorization and classification using grammar based approach

Question-answering has become one of the most popular information retrieval applications. Despite that most question-answering systems try to improve the user experience and the technology used in finding relevant results, many difficulties are still faced because of the continuous increase in the amount of web content. Questions Classification (QC) plays an important role in question-answering systems, with one of the major tasks in the enhancement of the classification process being the identification of questions types. A broad range of QC approaches has been proposed with the aim of helping to find a solution for the classification problems; most of these are approaches based on bag-of-words or dictionaries. In this research, we present an analysis of the different type of questions based on their grammatical structure. We identify different patterns and use machine learning algorithms to classify them. A framework is proposed for question classification using a grammar-based approach (GQCC) which exploits the structure of the questions. Our findings indicate that using syntactic categories related to different domain-specific types of Common Nouns, Numeral Numbers and Proper Nouns enable the machine learning algorithms to better differentiate between different question types. The paper presents a wide range of experiments the results show that the GQCC using J48 classifier has outperformed other classification methods with 90.1% accuracy.     

Distributed-parameter optimal control via mathematical programming

In this paper a variety of optimal control (OC) problems for distributed- parameter (DP) systems are approached using mathematical programming (MP). First, the principal DP models in current use are given, a variety of DP objective functions is provided, and the OC problems based on them are formulated. Second, these models and objective functions are converted in algebraic form, as required by MP, and the solution procedure of the OC problems via MP is outlined. Third, a representative set of nonlinear programming results applied to DP systems is presented, and finally, a numvber of application examples is given.     

Non-fragile sampled-data stabilization analysis for linear systems with probabilistic time-varying delays

This paper deals with the problem of non-fragile sampled-data stabilization analysis for a class of linear systems with probabilistic time-varying delays via new double integral inequality approach. Based on the auxiliary function-based integral inequality (AFBII) and with the help of some mathematical approaches, a new double integral inequality (NDII) is developed. Then, to demonstrate the merits of the proposed inequality, an appropriate Lyapunov–Krasovskii functional (LKF) is constructed with some augmented delay-dependent terms. By employing integral inequalities, an enhanced stability criterion for the concerned system model is derived in terms of linear matrix inequalities (LMIs). Finally, three benchmark illustrative examples are given to validate the effectiveness and advantages of the proposed results.     

融合分治法与支持向量机的“算法设计与分析”教学模式研究

"算法设计与分析"是计算机类本科生的专业必修课,内容涵盖递归、分治等多种算法的模型设计、代码实现和案例分析。有效掌握课程内容对日后从事机器学习方向的算法工程师岗位或进一步地科研深造等均具有十分重要的作用。然而,当前的课程内容缺乏与相关机器学习算法的关联性分析,导致学生难以将课程所学知识有效运用在实际应用或科研工作中。为此,本文以分治法为例,探讨将分治法的求解过程与运用支持向量机求解多类分类问题的一对一方法有效融合在一起。通过分析新的课程教学模式,进一步培养学生日后从事相关工作的能力。     

On two roles decision support systems can play in negotiations

This paper focuses on the role of the computer system in group decision-making. Two systems used in solving negotiating problems and three procedures which can be utilized to develop group decision support systems are analysed and a unified approach for the analysis is presented. The systems and procedures are based on multicriteria decision analysis and use mathematical programming models. They can play different roles: systems intervention in the negotiating process can be used merely to facilitate the process, or the system can actively mediate negotiations; both roles are discussed here.     

Managing the investment in information security technology by use of a quantitative modeling

This paper presents a mathematical model for an optimal security-technology investment evaluation and decision-making processes based on a quantitative analysis of the security risks and a digital-assets assessment in an organization. The model makes use of a quantitative analysis of different security measures that counteract individual risks by identifying the information-system processes in an enterprise and the potential threats. The model comprises the target security levels for all the identified core business processes and the probability of a security accident together with the possible loss the organization may suffer. The model allows in-depth analyses and computations providing quantitative assessments of different options for investments, which translate into recommendations that facilitate the selection of the best solution and the associated decision-making. The model was tested using empirical examples and mathematical simulations with data from a real business environment.     

浅谈“以学生为中心”教学法在机械基础教学中的应用

介绍了"以学生为中心"教学法在机械基础教学中的应用,从而克服了传统机械基础教学模式中存在的弊病,通常是对学生采用协作式、个别化、小组讨论等教学形式或采用多种教学形式相结合来进行教学。学生共同参与解决实际问题,激发了学生的学习兴趣,强调学生的主体性,培养学生分析和解决实际问题的能力、接受新知识的能力以及团结协作的社会能力。     

An efficient solution of hamiltonian boundary value problems by combined gauss pseudospectral method with differential continuation approach

Our paper deals with an effective application of the pseudospectral method to solution of Hamiltonian boundary value problems in optimal control theory. The developed numerical methodology is based on the celebrated Gauss pseudospectral approach. The last one makes it possible to reduce the conventional Hamiltonian boundary value problem to an auxiliary algebraic system. The implementable algorithm we propose is computationally consistent and moreover, involves numerically tractable results for a relative small discretization grids. However, the solution of the obtained algebraic equations system may has a low convergence radius. We next use the differential continuation approach in order to weaken the necessity of the well-defined initial conditions for the above algebraic system. The presented solution procedure can be extremely useful when the generic shooting-type methods fail because of sensitivity or stiffness. We discuss some numerical results and establish the efficiency of the proposed methodology.     

渗透数学思想教学，宣传数学文化作用

数学思想方法是数学的灵魂,是开启数学知识宝库的金钥匙,是用之不竭的数学发现的源泉。针对目前有不少学生不了解数学文化与作用,数学分析与解题能力较差,本文简要介绍数学文化作用,并拟用“应用数学思想解题,彰显创新解法优势”为例,说明数学思想在解题中的优越性与重要性。倡导教师在日常教学活动中,加强渗透数学思想教学,促进学生数学素质与解题能力的提高。     

Analysis of switching devices with bond graphs

Modelling and simulation of switching devices with bond graphs is a subject which has no totally satisfying solutions. In this paper, switching devices are represented by flow or effort sources, with a variable circuit topology at switching time. For the simulation, the usual method uses causality resistors to insure integral causality to energy storage elements. The choice of those resistors is quite arbitrary and can lead to stiff systems. We propose, for linear systems, an approach without such resistors. When components lose the integral causality, the order of the state vector changes, provoking the use of pulse variables. A solution is proposed to compute the amplitude of the pulse and the value of the new variables.