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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.

Effective and robust motion estimation with sub-pixel accuracy is essential in many image processing and computer vision applications. Due to its computational efficiency and robustness in the presence of intensity changes as well as geometric distortions, phase correlation in the Fourier domain provides an attractive solution for global motion estimation and image registration. The paper aims to discuss these issues.

In this paper, relevant sub-pixel strategies are categorized into three classes, namely, single-side peak interpolation, dual-side peak interpolation and curve fitting. The well-known images “Barbara” and “Pentagon” were used to evaluate the performance of eight typical methods, in which Gaussian noise was attached in the synthetic data.

For eight such typical methods, the tests using synthetic data have suggested that considering dual-side peaks in interpolation or fitting helps to produce better results. In addition, dual-side interpolation outperforms curve fitting methods in dealing with noisy samples. Overall, Gaussian-based dual-side interpolation seems the best in the experiments.

Based on the comparisons of eight typical methods, the authors can have a better understanding of the phase correlation for motion estimation. The evaluation can provide useful guidance in this context.

In this paper, a newly proposed hybridization algorithm namely constriction coefficient-based particle swarm optimization and gravitational search algorithm (CPSOGSA) has been employed for training MLP to overcome sensitivity to initialization, premature convergence, and stagnation in local optima problems of MLP.

In this study, the exploration of the search space is carried out by gravitational search algorithm (GSA) and optimization of candidate solutions, i.e. exploitation is performed by particle swarm optimization (PSO). For training the multi-layer perceptron (MLP), CPSOGSA uses sigmoid fitness function for finding the proper combination of connection weights and neural biases to minimize the error. Secondly, a matrix encoding strategy is utilized for providing one to one correspondence between weights and biases of MLP and agents of CPSOGSA.

The experimental findings convey that CPSOGSA is a better MLP trainer as compared to other stochastic algorithms because it provides superior results in terms of resolving stagnation in local optima and convergence speed problems. Besides, it gives the best results for breast cancer, heart, sine function and sigmoid function datasets as compared to other participating algorithms. Moreover, CPSOGSA also provides very competitive results for other datasets.

The CPSOGSA performed effectively in overcoming stagnation in local optima problem and increasing the overall convergence speed of MLP. Basically, CPSOGSA is a hybrid optimization algorithm which has powerful characteristics of global exploration capability and high local exploitation power. In the research literature, a little work is available where CPSO and GSA have been utilized for training MLP. The only related research paper was given by Mirjalili et al., in 2012. They have used standard PSO and GSA for training simple FNNs. However, the work employed only three datasets and used the MSE performance metric for evaluating the efficiency of the algorithms. In this paper, eight different standard datasets and five performance metrics have been utilized for investigating the efficiency of CPSOGSA in training MLPs. In addition, a non-parametric pair-wise statistical test namely the Wilcoxon rank-sum test has been carried out at a 5% significance level to statistically validate the simulation results. Besides, eight state-of-the-art meta-heuristic algorithms were employed for comparative analysis of the experimental results to further raise the authenticity of the experimental setup.

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.

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 authors propose a rather elementary method to compute a family of integrals on the half line, involving positive powers of sin x and negative powers of x, depending on the integer parameters n≥q≥1.

Combinatorics, sine and cosine integral functions.

The authors prove an explicit formula to evaluate sinc-type integrals.

The proof is not present in the current literature, and it could be of interest for a large audience.

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.

Cubic B‐spline differential quadrature methods have been introduced. As test problems, two different solutions of advection‐diffusion equation are chosen. The first test problem, the transportion of an initial concentration, and the second one, the distribution of an initial pulse, are simulated. The purpose of this paper is to simulate the test problems.

The cubic B‐spline functions are chosen as test functions in order to construct the differential quadrature method. The error between the numerical solutions and analytical solutions are measured using various error norms.

The cubic B‐spline differential quadrature methods have produced acceptable solution for advection‐diffusion equation.

The advection‐diffusion equation has never been solved by any differential quadrature method based on cubic B‐splines.