In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

novel spectrofluorimetric flow injection analysis (FIA) method was developed for the selective quantification of ascorbic acid via fluorescence quenching of serotonin hydrochloride. The system employs a custom-designed photometric array comprising 16 irradiation sources arranged in a dual-axis matrix—eight aligned horizontally and eight orthogonally, enabling multi-angle excitation and enhanced spectral resolution. Fluorescence signals were captured using a twin-pair solar cell detector, offering high sensitivity and minimal optical interference. The method exhibited a linear calibration range of 0.1–30 limit of detection (LOD) of 0.025 μ μ g/mL with a correlation coefficient (r mol /L, equivalent to 4.403 * 10 4 μ 2 ) of 0.9966, a g

This paper presents a computer simulation model of a thermally activated roof (TAR) to cool a room using cool water from a wet cooling tower. Modeling was achieved using a simplified 1-D resistance-capacitance thermal network (RC model) for an infinite slab. Heat transfer from the cooling pipe network was treated as 2-D heat flow. Only a limited number of nodes were required to obtain reliable results. The use of 6^th order RC-thermal model produced a set of ordinary differential equations that were solved using MATLAB - R2012a. The computer program was written to cover all possible initial conditions, material properties, TAR system geometry and hourly solar radiation. The cool water supply was considered time

Despite the great economic and commercial importance given to real estate by virtue of its view of the landscape or public roads, US courts have differed in their position on compensation for damages resulting from blocking that view or vision by public projects. Some courts compensated for such damages, other courts approved such compensation. Hence, this research came to shed light on the extent of the possibility of compensation for blocking the view or vision as a result of public projects, and the research has supported us with many judicial decisions.

Investigations made and soil samples brought from 14 sites in different areas, including Abu Ghraib and Al Anbar. Tests and measurements made in the Microbiology Laboratory at the College of Agriculture, University of Anbar. Department of Soil Sciences and water Resources, in order to isolate bio-fertilizers and test isolates fixing nitrogen in atmosphere and solvents for phosphorous compounds efficiency. The experiment included isolating and diagnosis of bacteria from rhizosphere soils of different plants that were brought from different agricultural areas, 74 isolates obtained by soils alleviation, and then the bio-chemical morphological and microscopic characteristics of these soils studied. The results showed that the most abundant and