In this paper, a new class of nonconvex sets and functions called strongly -convex sets and strongly -convex functions are introduced. This class is considered as a natural extension of strongly -convex sets and functions introduced in the literature. Some basic and differentiability properties related to strongly -convex functions are discussed. As an application to optimization problems, some optimality properties of constrained optimization problems are proved. In these optimization problems, either the objective function or the inequality constraints functions are strongly -convex. 

     This paper is used for solving component Volterra nonlinear systems by means of the combined Sumudu transform with Adomian decomposition process. We equate the numerical results with the exact solutions to demonstrate the high accuracy of the solution results. The results show that the approach is very straightforward and effective.

Abstract This research scrutinizes the impact of external magnetic field strength variations on plasma jet parameters to enhance its performance and flexibility. Plasma jets are widely used for their high thermal and kinetic energy in both medical and industrial fields. The study employs optical emission spectroscopy to measure electron temperature, electron density, and plasma frequency in a plasma jet subjected to varying magnetic field strengths (25, 50, 100, 150, and 250 mT). The results indicate that a stronger magnetic field results in higher electron temperature (1.485 to 1.991 eV), electron density (5.405 × 1017 to 7.095 × 1017), and plasma frequency 7.382 × 1012 to 8.253 × 1012 Hz. As well as the research investigates the influ

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This study is dedicated to solving multicollinearity problem for the general linear model by using Ridge regression method. The basic formulation of this method and suggested forms for Ridge parameter is applied to the Gross Domestic Product data in Iraq. This data has normal distribution. The best linear regression model is obtained after solving multicollinearity problem with the suggesting of 10 k value.

This paper aims to study the quaternary classical continuous optimal control problem consisting of the quaternary nonlinear parabolic boundary value problem, the cost function, and the equality and inequality constraints on the state and the control. Under appropriate hypotheses, it is demonstrated that the quaternary classical continuous optimal control ruling by the quaternary nonlinear parabolic boundary value problem has a quaternary classical continuous optimal control vector that satisfies the equality constraint and inequality state and control constraint. Moreover, mathematical formulation of the quaternary adjoint equations related to the quaternary state equations is discovered, and then the weak form of the quaternary adjoint

A hybrid particulate swarm optimization (hybrid) combination of an optimization algorithm of the particle swarm and a variable neighborhood search algorithm is proposed for the multi-objective permutation flow shop scheduling problem (PFSP) with the smallest cumulative completion time and the smallest total flow time. Algorithm for hybrid particulate swarm optimization (HPSO) is applied to maintain a fair combination of centralized search with decentralized search. The Nawaz-Enscore-Ham )NEH) heuristic algorithm in this hybrid algorithm is used to initialize populations in order to improve the efficiency of the initial solution. The method design is based on ascending order (ranked-order-value, ROV), applying the continuous PSO algorithm

The climate is one of the natural factors affecting agriculture, and the success of the cultivation of any agricultural crop depends on the nature of the prevailing climate in the area of its ​​cultivation. If the main elements of climate: temperature, rain and humidity, affect the various agricultural activities that can be practiced, and the stages of growth of agricultural crops and also determine the areas of spread. When the climatic requirements of any crop are well available, its cultivation is successful and comfortable. The research starts from the problem of spatial variation of date production spatially in the study area and the reason for choosing dates because of its economic importance, so the research will be based on