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The purpose of this paper is to discuss a numerical method for solving Fredholm integral equations of the first kind with degenerate kernels and convergence of this numerical method.

By using sinc collocation method in strip, the authors try to estimate a numerical solution for this kind of integral equation.

Some numerical results support the accuracy and efficiency of the stated method.

The paper presents a method for solving first kind integral equations which are ill‐posed.

The purpose of this paper is to answer the question that what the best shape of fuzzy sets is in fuzzy systems for function approximation which is essential in many applications of fuzzy systems.

The uniform approximation rates indicate the approximating capabilities of fuzzy systems for function approximation. By Fourier analysis, the uniform approximation rates are estimated for the fuzzy systems with various shapes of if‐part fuzzy sets in the case of single‐input and single‐output. Based on the approximation rates, the relationships between the approximating capabilities and the shapes of fuzzy sets are developed and compared.

The since functions as the input membership functions in fuzzy systems are proved to have the almost best approximation property in a particular class of membership functions.

From the viewpoint of function approximation, the input membership functions are not necessarily positive in fuzzy systems.

For engineers, the sinc‐shaped membership function is a good choice to improve their fuzzy systems in real applications.

The uniform approximation rates of fuzzy systems for function approximation are estimated. Mathematically, the relationships between the approximating capabilities and the shapes of fuzzy sets are analyzed for fuzzy systems.

The purpose of this paper is to derive a dynamic equation for modelling the behaviour of smectic‐C liquid crystals under the effect of an electric field.

The model equation is solved using a finite difference approximation, method of lines and pseudo‐spectral methods. The solutions are compared for accuracy and efficiency. Comparison is made of the efficiency of finite differences, method of lines and pseudo‐spectral methods.

The Fourier pseudo‐spectral method is shown to be the most efficient approach.

This work is original; a computational comparison of numerical schemes applied to liquid crystals has not been found in the literature.

This paper aims to present a numerical solution of non‐linear Burger's equation using differential quadrature method based on sinc functions.

Sinc Differential Quadrature Method is used for space discretization and four stage Runge‐Kutta algorithm is used for time discretization. A rate of convergency analysis is also performed for shock‐like solution. Numerical stability analysis is performed.

Sinc Differential Quadrature Method generates more accurate solutions of Burgers' equation when compared with the other methods.

This combination, Sinc Differential Quadrature and Runge‐Kutta of order four, has not been used to obtain numerical solutions of Burgers' equation.

The purpose of this paper is to build a phase-type risk model with stochastic return on investment and random observation periods to characterize the ruin quantities under which the insurance company may take effective investment strategies to avoid bankruptcy.

By the Markov property and Ito’s formula, this paper derives the integro-differential equations in which the interclaim times follow a phase-type distribution. Using the sinc method, this paper obtains the approximate solutions of the expected discounted penalty function. The numerical examples are given to verify the robustness of the proposed sinc method.

This paper discloses the relationship between the investment strategy and initial surplus level. The insurance company with a high initial surplus level prefers high risk portfolios to earn more profit. Contrarily, the insurance company would invest low risk portfolios to avoid bankruptcy. In addition, this paper shows that a short observation period would bring higher ruin probability.

The risk model is distinct in that a phase-type risk model is constructed with stochastic return on investment and random observation periods. These considerations in the risk model are in sharp contrast to the setting in which the stochastic return on investment is observed continuously. In practice, the insurance company only can periodically observe the surplus level to check the balance of the book. This setting, therefore, is difficult to adopt. This paper develops a sinc method to solve the approximate solutions of the expected discounted penalty function.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

This paper aims to propose a new numerical method for the solution of the Blasius and magnetohydrodynamic (MHD) Falkner-Skan boundary-layer equations. The Blasius and MHD Falkner-Skan equations are third-order nonlinear boundary value problems on the semi-infinite domain.

The approach is based upon modified rational Bernoulli functions. The operational matrices of derivative and product of modified rational Bernoulli functions are presented. These matrices together with the collocation method are then utilized to reduce the solution of the Blasius and MHD Falkner-Skan boundary-layer equations to the solution of a system of algebraic equations.

The method is computationally very attractive and gives very accurate results.

Many problems in science and engineering are set in unbounded domains. One approach to solve these problems is based on rational functions. In this work, a new rational function is used to find solutions of the Blasius and MHD Falkner-Skan boundary-layer equations.

In this work, a method to design a slotless permanent magnet machine (SPMM) based on the joint use of an analytical model and deterministic global optimization algorithms is addressed. The purpose of this study is to propose to include torque ripples as an extra constraint in the optimization phase involving de facto the study of a semi-infinite optimization problem.

Based on the use of a well-known analytical model describing the electromagnetic behavior of an SPMM, this analytical model has been supplemented by the calculus of the dynamic torque and its ripples to carry out a more accurate optimized sizing method of such an electromechanical converter. As a consequence, the calculated torque depends on a continuous variable, namely, the rotor angular position, resulting in the definition of a semi-infinite optimization problem. The way to solve this kind of semi-infinite problem by discretizing the rotor angular position by using a deterministic global optimization solver, that is to say COUENNE, via the AMPL modeling language is addressed.

In this study, the proposed approach is validated on some numerical tests based on the minimization of the magnet volume. Efficient global optimal solutions with torque ripples about 5% (instead of 30%) can be so obtained.

The analytical model does not use results from the solution of two-dimensional field equations. A strong assumption is put forward to approximate the distribution of the magnetic flux density in the air gap of the SPMM.

The problem to design an SPMM can be efficiently formulated as a semi-infinite global optimization problem. This kind of optimization problems are hard to solve because they involve an infinity of constraints (coming from a constraint on the torque ripple). The authors show in this paper that by using analytical models, a discretization method and a deterministic global optimization code COUENNE, this problem is efficiently tackled. Some numerical results show that the deterministic global solution of the design can be reached even if the step of discretization is small.

A modified version of an essentially non‐oscillatory high resolution scheme is applied to the simulation of two‐dimensional combustion waves. Through the splitting of the governing equations the method is applied to the homogeneous system and the source terms are approximated by means of a Runge‐Kutta third‐order scheme. The results obtained in the modelling of a high speed wave show an improvement with respect to a semi‐implicit scheme in the reconstruction of the shock propagation.

The purpose of this paper is to address the problem of polar quantization optimization. Particularly, the aim is to find the method for the optimal resolution‐constrained polar quantizer design.

The new iterative algorithm for determination of the optimal decision and representation magnitude levels and algorithm for optimization of number of phase cells within each magnitude level, is proposed.

At high rates, the new optimal polar quantizer outperforms the optimal polar compander for 0.2 dB, while the more significant gain should be expected at lower rates. In this paper, in order to enable practical implementation of quantizer model, algorithm which transforms real values for the optimal numbers of phase cells within magnitude levels into integer ones is also proposed. Moreover, the approximate closed form of signal‐to‐quantization ratio is derived.

Since circularly symmetric sources and complex presentation of signals arise in numerous applications, it can be concluded that the usage area of the suggested proposal is very wide (audio coding, image coding, spectral phase coding, synthetic aperture radars systems, coding of the discrete Fourier transform).

It should be emphasized that in contrast to earlier work, where models have been designed under high‐rate assumption, the obtained nonuniform unrestricted polar quantizer is optimal for all rates.