A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimi

Frequently, load associated mode of failure, rutting and fatigue, are the main failure types found in some newly constructed roads within Baghdad, the capital of Iraq, and some suburban areas. The use of excessive amount of natural sand in asphalt concrete mixes which is attractive to local contractors could be one of the possible causes to the lack of strength properties of the mixes resulting in frustration in the pavement performance. In this study, the performance properties of asphalt concrete mixes with two natural sand types, desert and river sands, were evaluated. Moreover, five replacement rates of 0, 25, 50, 75, and 100% by weight of the fine aggregate finer than 4.75 were used. The performance properties including moisture susc

In the theoretical part, removal of direct yellow 8 (DY8) from water solution was accomplished using Bentonite Clay as an adsorbent. Under batch adsorption, the adsorption was observed as a function of contact time, adsorbent dosage, pH, and temperature. The equilibrium data were fitted with the Langmuir and Freundlich adsorption models, and the linear regression coefficient R2 was used to determine the best fitting isotherm model. thermodynamic parameters of the ongoing adsorption mechanism, such as Gibb's free energy, enthalpy, and entropy, have also been measured. The batch method was also used for the kinetic calculations, and the day's adsorption assumes first-order rate kinetics. The kinetic studies also show that the intrapar

Incorporating waste byproducts into concrete is an innovative and promising way to minimize the environmental impact of waste material while maintaining and/or improving concrete’s mechanical characteristics and strength. The proper application of sawdust as a pozzolan in the building industry remains a significant challenge. Consequently, this study conducted an experimental evaluation of sawdust as a fill material. In particular, sawdust as a fine aggregate in concrete offers a realistic structural and economical possibility for the construction of lightweight structural systems. Failure under four-point loads was investigated for six concrete-filled steel tube (CFST) specimens. The results indicated that recycled lightweight co

In this paper, I highlight the bishops mentioned in the Bible in its sections
(The Old and New Testaments) where these books still retain the remaining remnant of the Bible
Issuing the prophets who preceded the mission of the Prophet Muhammad (peace and blessings of Allaah be upon him) and they must pray
And peace, as those bishops were mentioned in the Book of Formation through the recitation of the psalms
To Habakkuk, Malakhi, and Hajji.
As well as in the New Testament, which we see clearly in the four Angels: Matthew, Luke,
Disco, John.
Then the male lamented what was said of those bishops by expressing the eternal heavenly book (the Qur'an)
Al - Karim) as he focuses on this subject from multiple angles and exp

Background: Knowledge about the prevalence and distribution of pathologies in a particular location is important when a differential diagnosis is being formulated. The aim of this study was to describe the prevalence and the clinicopathological features of odontogenic cysts and tumors affecting the maxilla and to discuss the unusual presentation of those lesions within maxillary sinus.

Materials and Methods: A multicenter retrospective analysis was performed on pathology archives of patients who were diagnosed with maxillary odontogenic cysts and tumors from 2010 to 2020. Data were collected with respect to age, gender and location.

Result: A total of 384 cases was identified, 320 (83.3%) cases were diagnosed as odontogenic

Iron , Cobalt , and Nickel powders with different particle sizes were subjected to sieving and He-Ne laser system to determine the particle size . 1wt% from each powders was blended carefully with 99wt% from Iraqi oil . Microscopic examination were carried for all samples to reveal the particle size distribution . A Siemens type SRS sequential wavelength dispersive(WDS) X-ray spectrometer was used to analyze all samples , and the XRF intensity were determined experimentally and theoretically for all suspended samples , Good agreement between theoretical and experimental results were found .