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.

Pharmaceutical-instigated pollution is a major concern, especially in relation to aquatic environments and drugs such as meropenem antibiotics. Adsorbents, such as multi-walled carbon nanotubes, offer potential as means of removing polluting meropenem antibiotics and other similar compounds from water. In order to evaluate the effectiveness of multi-walled carbon nanotubes in this capacity, various experimental parameters, including contact time, initial concentration, pH, temperature and the dose of adsorbent have been investigated. The Langmuir and the Freundlich isotherm models have been used. The data obtained using a modified Langmuir model have been consistent with the experimental ones; the best pH value has been obtained to have the

Periodontitis is a multifactorial chronic inflammatory disease that affects tooth-supporting soft/hard tissues of the dentition. The dental plaque biofilm is considered as a primary etiological factor in susceptible patients; however, other factors contribute to progression, such as diabetes and smoking. Current management utilizes mechanical biofilm removal as the gold standard of treatment. Antibacterial agents might be indicated in certain conditions as an adjunct to this mechanical approach. However, in view of the growing concern about bacterial resistance, alternative approaches have been investigated. Currently, a range of antimicrobial agents and protocols have been used in clinical management, but these remain largely non-v

Since the introduction of the HTTP/3, research has focused on evaluating its influences on the existing adaptive streaming over HTTP (HAS). Among these research, due to irrelevant transport protocols, the cross-protocol unfairness between the HAS over HTTP/3 (HAS/3) and HAS over HTTP/2 (HAS/2) has caught considerable attention. It has been found that the HAS/3 clients tend to request higher bitrates than the HAS/2 clients because the transport QUIC obtains higher bandwidth for its HAS/3 clients than the TCP for its HAS/2 clients. As the problem originates from the transport layer, it is likely that the server-based unfairness solutions can help the clients overcome such a problem. Therefore, in this paper, an experimental study of the se

The research aims to analysis of the current financial crisis in Iraq through knowing its causes and then propose some solutions that help in remedy the crisis and that on the level of expenditures and revenues, and has been relying on the Federal general budget law of the Republic of Iraq for the fiscal year 2016 to obtain the necessary data in respect of the current expenditures and revenues which necessary to achieve the objective of the research , and through the research results has been reached to a set of conclusions which the most important of them that causes of the current financial crisis in Iraq , mainly belonging to increased expenditures and especially the current ones and the lack of revenues , especially non-oil o

In this paper, third order non-polynomial spline function is used to solve 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of this method, and to compare the computed results with other known methods.

The fractional order partial differential equations (FPDEs) are generalizations of classical partial differential equations (PDEs). In this paper we examine the stability of the explicit and implicit finite difference methods to solve the initial-boundary value problem of the hyperbolic for one-sided and two sided fractional order partial differential equations (FPDEs). The stability (and convergence) result of this problem is discussed by using the Fourier series method (Von Neumanns Method).

In the present study a series of some four-,five-and seven-membered heterocyclic compounds have been synthesized by the reaetion of Schiff bases (1a,b) with chloroacetyl chloride, sodium azide, thioglycolic acid or various anhydrides to give azetidinone (2a,b), tetrazole (3a,b), thiazolidinone (4a,b) and 1,3-oxazepine derivatives (5-8a,b) respectively. Schiff bases (1a,b)were prepared from the reaction of p-toluidine with aromatic aldehydes. All synthesized compounds were characterized by physical properties and spectral data.