In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

Abstract 

The Phenomenon of Extremism of Values ​​(Maximum or Rare Value) an important phenomenon is the use of two techniques of sampling techniques to deal with this Extremism: the technique of the peak sample and the maximum annual sampling technique (AM) (Extreme values, Gumbel) for sample (AM) and (general Pareto, exponential) distribution of the POT sample. The cross-entropy algorithm was applied in two of its methods to the first estimate using the statistical order and the second using the statistical order and likelihood ratio. The third method is proposed by the researcher. The MSE comparison coefficient of the estimated parameters and the probability density function for each of the distributions were

The paper aims at initiating and exploring the concept of extended metric known as the Strong Altering JS-metric, a stronger version of the Altering JS-metric. The interrelation of Strong Altering JS-metric with the b-metric and dislocated metric has been analyzed and some examples have been provided. Certain theorems on fixed points for expansive self-mappings in the setting of complete Strong Altering JS-metric space have also been discussed.

In this paper , some of lexical stylistic , syntactical stylistic  devices , and one phonetic stylistic device are going to be illustrated in the study of the aphorisms of “life and death” . These stylistic  devices are parallelism , hyperbole , alliteration , meiosis , irony , oxymoron , cliché , litotes , metalepsis , and loose sentences.  This paper aims at identifying the functions and the  frequencies of these devices. These stylistic devices make one speech and writing more interesting and help to get the attention of readers/ listeners

Allah, in his Holy Quran introduced great prophet stories so as to learn from. The greatness of these stories lies in Allah himself being the author. He portrays his characters, lays the plot, defines the tests and Al- Ibtilla, provides ways of being patient, using Duaa to end all hard tests and generously describing the greatness of his rewards to all those who are patient. The purpose of this research is to study selected English prophet stories for children on three levels, the stories ability to convey lessons and Islamic teachings to children who do not speak Arabic, the stories portray the Islamic concept of patience, the teaching and learning styles andstrategies that Allah uses with each prophet. The concept of patience is defined a

Among a variety of approaches introduced in the literature to establish duality theory, Fenchel duality was of great importance in convex analysis and optimization. In this paper we establish some conditions to obtain classical strong Fenchel duality for evenly convex optimization problems defined in infinite dimensional spaces. The objective function of the primal problem is a family of (possible) infinite even convex functions. The strong duality conditions we present are based on the consideration of the epigraphs of the c-conjugate of the dual objective functions and the ε-c-subdifferential of the primal objective functions.

In this article, performing and deriving te probability density function for Rayleigh distribution is done by using ordinary least squares estimator method and Rank set estimator method. Then creating interval for scale parameter of Rayleigh distribution. Anew method using   is used for fuzzy scale parameter. After that creating the survival and hazard functions for two ranking functions are conducted to show which one is beast.