In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

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.

I have studied the relationship between blood groups in humans and disease Cutaneous injury for the first time in Iraq study showed the presence of a significant statistical relationship between them leather Bmsoy in hospitals in Baghdad and its suburbs

This paper exclusively deals with medical encounters. . Structurally and thematically, it manifests itself in five parts. The First part deals with medical encounters as well as essential speech activities which cover (a) frames (certain types of talk) (b) the patient’s account and the patient’s story or more precisely the patient telling his story and (c) the act of questioning the patient. The Second part revolves round genre and register. The former, in most cases, suggests that the format of medical encounters is conversational. With register; we have a converse reality that restrictively tries to narrow things and give them a certain flavor. The Third part realizes the technicalities of medical encounters (a) the setting of an inte

A water resources management for earthen canal/stream is introduced through creating a combination procedure between a field study and the scientific analytical concepts that distinguish the hydraulic problems on this type of stream with using the facilities that are available in HECRAS software; aiming to point the solutions of these problems. Al Mahawil stream is an earthen canal which is subjected to periodic changes in cross sections due to scour, deposition, and incorrect periodic dredging processes due to growth of the Ceratophyllum plants and weeds on the bed and banks of the stream; which affect the characteristics of the flow. This research aims to present a strategy of water resources management through a field study that conducte

In this paper, the problem of developing turbulent flow in rectangular duct is investigated by obtaining numerical results of the velocity profiles in duct by using large eddy simulation model in two dimensions with different Reynolds numbers, filter equations and mesh sizes. Reynolds numbers range from (11,000) to (110,000) for velocities (1 m/sec) to (50 m/sec) with (56×56), (76×76) and (96×96) mesh sizes with different filter equations. The numerical results of the large eddy simulation model are compared with k-ε model and analytic velocity distribution and validated with experimental data of other researcher. The large eddy simulation model has a good agreement with experimental data for high Reynolds number with the first, seco

In this study the new azo compounds (3compounds) for nitrogen bases (Adenine and Cytosine) are synthesized through two reaction steps (formation of diazonium salt and coupling reaction). The compounds have been characterized by FTIR, melting point, and ultra-violate (UV) spectra. All synthesized compounds have been estimated in vitro for their antimicrobial activities against two species of bacteria(E.coli, S.aureus)and one kind of fungi ( Aspergillus flavus) .The results show that these compounds have very good antibacterial and antifungal activities especially compounds 1 and 3.To study the effect of these compounds were making some physiological tests on rats are made ,the results of hematological study showed decreasing level of