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

In this paper, the first integrals of Darboux type of the generalized Sprott ET9 chaotic system will be studied. This study showed that the system has no polynomial, rational, analytic and Darboux first integrals for any value of . All the Darboux polynomials for this system were derived together with its exponential factors. Using the weight homogenous polynomials helped us prove the process.

This study aimed at comparing the performance of vertical, horizontal and hybrid subsurface flow systems in secondary treatment for the effluent wastewater from the primary basins at Al-Rustumia wastewater treatment plant, Baghdad, Iraq. The treatments were monitored for six weeks while the testsduration were from 4 to 12 September 2018 under continuous wastewater feeding for chemical oxygen demand (COD), total suspended solid (TSS),ammonia-nitrogen(NH₄-N) and phosphate (PO₄-P) in comparison with FAO and USEPA standards for effluent discharge to evaluate the suitability of treated water for irrigation purposes. Among the systems planted with Phragmites Australia, the hybrid subsurface flow system which cons

Abstract

The population is sets of vocabulary common in character or characters and it’s study subject or research . statistically , this sets is called study population (or abridgement population ) such as set of person or trees of special kind of fruits or animals or product  any country for any commodity through infinite temporal period term ... etc.

The population maybe finite if we can enclose the number of its members such as the students of finite school grade . and maybe infinite if we can not enclose the number of it is members such as stars or aquatic creatures in the sea . when we study any character for population the statistical data is concentrate by two metho

This document provides an examination of research, on combining orthogonal frequency division multiplexing (OFDM) and optical fibers in communication networks. With the increasing need for data speeds and efficient use of bandwidth experts have been exploring the connection between OFDM, valued for its ability to handle multipath interference and optimize spectral usage and optical fiber technology which provides superior data transmission capabilities with low signal loss and strong protection, against electromagnetic disturbances. The review summarizes discoveries from studies examining the pros and cons of using OFDM, in optical communication networks. It discusses obstacles like fiber nonlinearity, chromatic dispersion and the effects o