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

The local resolving neighborhood  of a pair of vertices  for  and  is if there is a vertex  in a connected graph  where the distance from  to  is not equal to the distance from  to , or defined by . A local resolving function  of  is a real valued function   such that  for  and . The local fractional metric dimension of graph  denoted by , defined by  In this research, the author discusses about the local fractional metric dimension of comb product are two graphs, namely graph  and graph , where graph  is a connected graphs and graph  is a complate graph &

Background:

Multiple sclerosis is a chronic disease believed to be the result of autoimmune disorders of the central nervous system, characterised by inflammation, demyelination, and axonal transection, affecting primarily young adults. Disease modifying therapies have become widely used, and the rapid development of these drugs highlighted the need to update our knowledge on their short- and long-term safety profile.

Objective:

The study aim is to evaluate the impact of disease-modifying treatments on thyroid functions and thyroid autoantibodies with subsequent effects on the outcome of the disease.

Materials and Methods:

A retro prospective study

Water pollution as a result of contamination with dye-contaminating effluents is a severe issue for water reservoirs, which instigated the study of biodegradation of Reactive Red 195 and Reactive Blue dyes by E. coli and Bacillus sp. The effects of occupation time, solution pH, initial dyes concentrations, biomass loading, and temperature were investigated via batch-system experiments by using the Design of Experiment (DOE) for 2 levels and 5 factors response surface methodology (RSM). The operational conditions used for these factors were optimized using quadratic techniques by reducing the number of experiments. The results revealed that the two types of bacteria had a powerful effect on biodegradable dyes. The regression analysis reveale

In this paper, we proposed a new class of weighted Rayleigh distribution based on two parameters, scale and shape parameters which are introduced in Rayleigh distribution. The main properties of this class are investigated and derived.

The research presents a case study of collecting materials and raw materials in a visual space that allows them to form a perception and meanings that inform the recipient by reconstructing them and inserting them into the surface of the artistic work and in such a way that the aesthetic act consists of a variety of media, touches and surfaces. The overlap of races within an environment characterized by unity. That is why the researcher in chapter one presented the problem of research, and the focus was on studying the multiplicity of materials and their aesthetic and functional role in the structure of creative work. The aim of the research is enhanced to identify the aesthetic performance function of the multiplicity of ores in the col

The experiences in the life are considered important for many fields, such as industry, medical and others. In literature, researchers are focused on flexible lifetime distribution.

In this paper, some Bayesian estimators for the unknown scale parameter  of Inverse Rayleigh Distribution have been obtained, of different two loss functions, represented by Suggested and Generalized loss function based on Non-Informative prior using Jeffery's and informative prior represented by Exponential distribution. The performance of   estimators is compared empirically with Maximum Likelihood estimator, Using Monte Carlo Simulation depending on the Mean Square Error (MSE). Generally, the preference of Bayesian method of Suggeste

    The using of the parametric models and the subsequent estimation methods require the presence of many of the primary conditions to be met by those models to represent the population under study adequately, these prompting researchers to search for more flexible models of parametric models and these models were nonparametric models.

    In this manuscript were compared to the so-called Nadaraya-Watson estimator in two cases (use of fixed bandwidth and variable) through simulation with different models and samples sizes.  Through simulation experiments and the results showed that for the first and second models preferred NW with fixed bandwidth fo

One of the most important methodologies in operations research (OR) is the linear programming problem (LPP). Many real-world problems can be turned into linear programming models (LPM), making this model an essential tool for today's financial, hotel, and industrial applications, among others. Fuzzy linear programming (FLP) issues are important in fuzzy modeling because they can express uncertainty in the real world. There are several ways to tackle fuzzy linear programming problems now available. An efficient method for FLP has been proposed in this research to find the best answer. This method is simple in structure and is based on crisp linear programming. To solve the fuzzy linear programming problem (FLPP), a new ranking function (R