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A novel Haar scale-3 wavelet collocation technique is proposed in this study for dealing with a specific type of parabolic Buckmaster second-order nonlinear partial differential equation in a dispersive system and Chafee-Infante second-order non-linear partial differential equation (PDE) in a solitary system. Using Haar scale-3 (HSW-3) wavelets, the system approximates the space and time derivatives. To develop both an implicit and explicit analytical model for the dispersive and solitary system, the collocation approach is employed in conjunction with the discretization of space and time variables. We have examined the effectiveness, applicability, and veracity of the proposed computational approach using a variety of numerical problems with nonlinearity and numerous significant source terms. Additionally, the outcomes are graphically presented and organized. We achieved accuracy with the proposed methods even with a small selection of collocation locations. [ABSTRACT FROM AUTHOR]

In the paper the speed‐in‐action problem is investigated for the second‐order nonlinear hyperbolic equation. The main feature of the paper is that for the first time the problem is considered with a nonlocal condition in differ from many works devoted the similar problems. A theorem on the existence of the optimal control is proved. Freshet differentiability of the corresponding functional is shown. The necessary optimality conditions are derived in the form of variational inequalities. [ABSTRACT FROM AUTHOR]

This article utilizes the Aboodh residual power series and Aboodh transform iteration methods to address fractional nonlinear systems. Based on these techniques, a system is introduced to achieve approximate solutions of fractional nonlinear Korteweg-de Vries (KdV) equations and coupled Burger's equations with initial conditions, which are developed by replacing some integer-order time derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. As a result, the Aboodh residual power series and Aboodh transform iteration methods for integer-order partial differential equations may be easily used to generate explicit and numerical solutions to fractional partial differential equations. The results are determined as convergent series with easily computable components. The results of applying this process to the analyzed examples demonstrate that the new technique is very accurate and efficient. [ABSTRACT FROM AUTHOR]

Damped Burger's equation describes the characteristics of one-dimensional nonlinear shock waves in the presence of damping effects and is significant in fluid dynamics, plasma physics, and other fields. Due to the potential applications of this equation, thus the objective of this investigation is to solve and analyze the time fractional form of this equation using methods with precise efficiency, high accuracy, ease of application and calculation, and flexibility in dealing with more complicated equations, which are called the Aboodh residual power series method and the Aboodh transform iteration method (ATIM) within the Caputo operator framework. Also, this study intends to further our understanding of the dynamic characteristics of solutions to the Damped Burger's equation and to assess the effectiveness of the proposed methods in addressing nonlinear fractional partial differential equations. The two proposed methods are highly effective mathematical techniques for studying more complicated nonlinear differential equations. They can produce precise approximate solutions for intricate evolution equations beyond the specific examined equation. In addition to the proposed methods, the fractional derivatives are processed using the Caputo operator. The Caputo operator enhances the representation of fractional derivatives by providing a more accurate portrayal of the underlying physical processes. Based on the proposed two approaches, a set of approximations to damped Burger's equation are derived. These approximations are discussed graphically and numerically by presenting a set of two- and three-dimensional graphs. In addition, these approximations are analyzed numerically in several tables, including the absolute error for each approximate solution compared to the exact solution for the integer case. Furthermore, the effect of the fractional parameter on the behavior of the derived approximations is examined and discussed. [ABSTRACT FROM AUTHOR]

The article focuses on investigating traveling wave solutions of the Gardner equation in physics using the (m + (1/G0))-expansion method. It discusses the importance of nonlinear partial differential equations in various fields and explores different methods used to examine the Gardner equation, such as Riccati equations and generalized exponential rational function methods.

In this paper, we present generalized versions of the Wirtinger inequality, which contains as particular cases many of the well-known versions of this classic isoperimetric inequality. Some applications and open problems are also presented in the work. [ABSTRACT FROM AUTHOR]

The present paper is the first of a series of works planned by the authors to study some qualitative properties of Liénard type equations solutions with derivatives of both natural and fractional order. In the present paper, we investigate the behaviour of limit cycles of the Biryukov equation, which is an important from the applicability standpoint special case of the classical Liénard equation. [ABSTRACT FROM AUTHOR]

The generalized equal width model is an important non-linear dispersive wave model which is naturally used to describe physical situations in a water channel. In this work, we implement the idea of the interpolation by radial basis function to obtain numerical solution of the non-linear time fractional generalized equal width model defined by Caputo sense. In this technique, firstly, a time discretization is accomplished via the finite difference approach and the non-linear term is linearized by a linearization method. Afterwards, with the help of the radial basis function approximation method is used to discretize the spatial derivative terms. The stability of the method is theoretically discussed using the von Neumann (Fourier series) method. Numerical results and comparisons are presented which illustrate the validity and accuracy of our proposed concepts. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of risk estimate and choice of the rational variants in the transportation using expert information systems. The pairwise comparison method (Saaty's method) is used to determine the weights of chosen criteria. An example is given that compares logistic risks in shipping, railway and aviation transport. The input data are taken in the example are formal and can be chosen for the concrete problems. This example is solved by both non-fuzzy and fuzzy approach. It is shown that with the set of data in the railway transport is the optimal option. The results demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The article highlights the 80th Birthday of Editorial Board member and mathematics professor, Hari Mohan Srivastava. Topics include his association with numerous international scientific research journals along with his teaching job at Department of Mathematics and Statistics University of Victoria, Victoria, British Columbia, Canada; and his contribution to many theorems and algorithms, especially in number theory.

The way people learn will play an essential role in the sustainable development of the educational system for the future. Utilizing technology in the age of information and incorporating it into how people learn can produce better learners. Implicit learning is a type of learning of the underlying rules without consciously seeking or understanding the rules; it is commonly seen in small children while learning how to speak their native language without learning grammar. This research aims to introduce a processing system that can systematically identify the relationship between implicit learning events and their Encephalogram (EEG) signal characteristics. This study converted the EEG signal from participants while performing cognitive task experiments into Multiscale Entropy (MSE) data. Using MSE data from different frequency bands and channels as features, the system explored a wide range of classifiers and observed their performance to see how they classified the features related to participants' performance. The Artificial Bee Colony (ABC) method was used for feature selection to improve the process to make the system more efficient. The results showed that the system could correctly identify the differences between participants' performance using MSE data and the ABC method with 95% confidence. [ABSTRACT FROM AUTHOR]

Biconvex programming (or inequality constrained biconvex optimization) is an important model in solving many engineering optimization problems in areas like machine learning and signal and information processing. In this paper, the partial exactness of the partial optimum for the penalty function of biconvex programming is studied. The penalty function is partially exact if the partial Karush–Kuhn–Tucker (KKT) condition is true. The sufficient and necessary partially local stability condition used to determine whether the penalty function is partially exact for a partial optimum solution is also proven. Based on the penalty function, an algorithm is presented for finding a partial optimum solution to an inequality constrained biconvex optimization, and its convergence is proven under some conditions. [ABSTRACT FROM AUTHOR]