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.

In this research we been estimated the survival function for data suffer from the disturbances and confusion of Iraq Household Socio-Economic Survey: IHSES II 2012 , to data from a five-year age groups follow the distribution of the Generalized Gamma: GG. It had been used two methods for the purposes of estimating and fitting which is the way the Principle of Maximizing Entropy: POME, and method of booting to nonparametric smoothing function for Kernel, to overcome the mathematical problems plaguing integrals contained in this distribution in particular of the integration of the incomplete gamma function, along with the use of traditional way in which is the Maximum Likelihood: ML. Where the comparison on the basis of the method of the Cen

The expression of the Proprotein Convertase Subtilisin/Kexin Type 9 gene (PCSK9) is inextricably related to lipid levels and a risk of atherosclerotic coronary artery disease (ASCAD). The present study aims to measure the quantity of PCSK9 gene expression and the effect of methylation on its expression level taking part in the pathogenesis of acute coronary artery disorder.

A current study included 150 subjects from the Iraqi population, 100 ASCAD patients and 50 healthy controls. The concentration of PCSK9 in each serum sample was determined by the ELISA technique, the expression levels of the PCSK9 gene in whole blood were estimated by RT-qPCR – Quantitative Reverse Transcription PCR method, and DNA

It was aimed to understand the interleukin-4 (IL-4) role in etio-pathogenesis of rheumatoid arthritis (RA). Two approaches were adopted. In the first one, a quantitative expression of IL4 gene was assessed by reverse transcription-quantitative polymerase chain reaction (RT-qPCR), and such findings were correlated with some demographic, clinical and laboratory parameters, which included gender, duration of disease, disease activity score (DAS-28), rheumatoid factors (RFs), C-reactive protein (CRP) and anti-cyclic citrullinated peptide (ACCP) antibodies. In the second approach, a single nucleotide polymorphism (SNP) of IL4 gene (rs2243250) was inspected by DNA sequencing using specific primers. Fifty-one Iraqi RA patients (22 males and 29 fem

Despite extensive investigations, an effective treatment for sepsis remains elusive and a better understanding of the inflammatory response to infection is required to identify potential new targets for therapy. In this study we have used RNAi technology to show, for the first time, that the inducible lysophosphatidylcholine acyltransferase 2 (LPCAT2) plays a key role in macrophage inflammatory gene expression in response to stimulation with bacterial ligands. Using siRNA- or shRNA-mediated knockdown, we demonstrate that, in contrast to the constitutive LPCAT1, LPCAT2 is required for macrophage cytokine gene expression and release in response to TLR4 and TLR2 ligand stimulation but not for TLR-independent stimuli. In addition, cells transfe

Coagulation is the most important process in drinking water treatment. Alum coagulant increases the aluminum residuals, which have been linked in many studies to Alzheimer's disease. Therefore, it is very important to use it with the very optimal dose. In this paper, four sets of experiments were done to determine the relationship between raw water characteristics: turbidity, pH, alkalinity, temperature, and optimum doses of alum [   .14 O] to form a mathematical equation that could replace the need for jar test experiments. The experiments were performed under different conditions and under different seasonal circumstances. The optimal dose in every set was determined, and used to build a gene expression model (GEP). The models were co

Two- dimensional numerical simulations are carried out to study the elements of observing a Dirac point source and a Dirac binary system. The essential features of this simulation are demonstrated in terms of the point spread function and the modulation transfer function. Two mathematical equations have been extracted to present, firstly the relationship between the radius of optical telescope and the distance between the central frequency and cut-off frequency of the optical telescope, secondly the relationship between the radius of the optical telescope and the average frequency components of the modulation transfer function.

The main idea of this paper is to define other types of a fuzzy local function and study the advantages and differences between them in addition to discussing some definitions of finding new fuzzy topologies. Also in this research, a new type of fuzzy closure has been defined, where the relation between the new type and different types of fuzzy local function has been studied

By use the notions pre-g-closedness and pre-g-openness we have generalized a class of separation axioms in topological spaces. In particular, we presented in this paper new types of regulαrities, which we named ρg­regulαrity and Sρg­regulαrity. Many results and properties of both types have been investigated and have illustrated by examples.

This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all