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 results of the effect of the type of feed showed a significant increase (P≤0.01) for palm fronds DM during the incubation period of 7, 14, 21 days, a high Mnp superiority in its incubation 14 days, and a significant superiority of Laccase in its incubation 21 days, while the effect of the enzyme concentration on DM was higher Significant at a concentration of 10% of the enzyme, and the interaction between the type of feed and the enzyme together showed a highly significant increase in the treated palm fronds Laccase and Lip in the incubation period of 7 days, and the treated palm fronds Mnp during incubation 14 days. %, 15% for the interaction between the type of coarse feed and the concentration of the enzyme

An investigation was conducted for the improvement of viscosity index of light lubricating oil fraction (40 stock)
obtained from vacuum distillation unit of lube oil plant of Daura Refinery, using solvent extraction process.
In this study furfural solvent was used to extract the undesirable materials which reduce the viscosity index of raw
lubricating oil fraction.
The studied effecting variables of extraction were extraction temperature range from 70 to 110°C, and solvent to oil
ratio range from 1:1 to 4:1 (wt/wt).
The n-d-M method was used for calculation of carbon distribution and structural group analysis of the raffinate
produced from furfural extraction.
Also the three component phase diagram for a mixed-ba

The primary purpose of this paper is to introduce the, N-coprobabilistic normed space, coprobabilistic dual space of N-coprobabilistic normed space and give some facts that are related of them.

The main object of this article is to study and introduce a subclass of meromorphic univalent functions with fixed second positive defined by q-differed operator. Coefficient bounds, distortion and Growth theorems, and various are  the obtained results.

 Most of the propositions, after the Arabic letter reached a position of integrity and proficiency, the calligrapher turned to the production of calligraphic formations in various aesthetic and expressive forms, investing the spiritual energies in what these calligraphic compositions show in artistic paintings. It carries a lot of meanings that are embodied in linear formations, and in order to reach these expressions and know the effective positions of space, this research is concerned with studying these technical treatments. The first chapter included the research problem, which included a question about the effectiveness of space in the linear painting, the importance of research and the temporal and spatial boundaries. As for the s

Some relations of inclusion and their properties are investigated for functions of type " -valent that involves the generalized operator of Srivastava-Attiya by using the principle of strong differential subordination.

In this paper, a modified derivation has been introduced to analyze the construction of C-space. The profit from using C-space is to make the process of path planning more safety and easer. After getting the C-space construction and map for two-link planar robot arm, which include all the possible situations of collision between robot parts and obstacle(s), the A* algorithm, which is usually used to find a heuristic path on Cartesian W-space, has been used to find a heuristic path on C-space map. Several modifications are needed to apply the methodology for a manipulator with degrees of freedom more than two. The results of C-space map, which are derived by the modified analysis, prove the accuracy of the overall C-space mapping and cons