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.

Background: Cervical ectopy advanced to erosion is one of the common conditions in gynecological and pathological study. It is considered as a physiologic condition resulting from columnar epithelium migration from the cervical canal into the vaginal portion of the cervix, in which no treatment for asymptomatic cervical ectropion can be given. Treatment can be accomplished via thermal cauterization (Electro cautery), Cryosurgery. CO₂ laser therapy is another modality of treatment.

Objective: To study the effectiveness of CO₂ laser therapy and evaluate it as a biomedical tool for the treatment of cervical ectropion. The study was done at Laser Medicine Research Clinic at the

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

Business organizations have faced many challenges in recent times, most important of which is information technology, because it is widely spread and easy to use. Its use has led to an increase in the amount of data that business organizations deal with an unprecedented manner. The amount of data available through the internet is a problem that many parties seek to find solutions for. Why is it available there in this huge amount randomly? Many expectations have revealed that in 2017, there will be devices connected to the internet estimated at three times the population of the Earth, and in 2015 more than one and a half billion gigabytes of data was transferred every minute globally. Thus, the so-called data mining emerged as a

The technological development in the field of information and communication has been accompanied by the emergence of security challenges related to the transmission of information. Encryption is a good solution. An encryption process is one of the traditional methods to protect the plain text, by converting it into inarticulate form. Encryption implemented can be occurred by using some substitute techniques, shifting techniques, or mathematical operations. This paper proposed a method with two branches to encrypt text. The first branch is a new mathematical model to create and exchange keys, the proposed key exchange method is the development of Diffie-Hellman. It is a new mathematical operations model to exchange keys based on prime num

This work includes the synthesis and identification of ligand {3-((4-acetylphenyl)amino)-5,5-dimethylcyclohex2-en-1-one} (HL* ) by the treatment of 5,5-dimethylcyclohexane-1,3-dione with 4-aminoacetophenone under reflux. The ligand (HL* ) was identified via FTIR, Mass spectrum, elemental analysis (C.H.N.), 1H and 13C-NMR spectra, UV-Vis spectroscopy, TGA and melting point. The complexes were synthesized from ligand (HL* ) mixed with 3-aminophenol (A) and metal ion M(II), where M(II) = (Mn, Co, Ni, Cu, Zn and Cd) at alkaline medium to produce complexes of general formula [M(L* )(A)] with (1:1:1) molar ratio. These complexes were detected via FT-IR spectra, UV-Vis spectroscopy as well as elemental analysis (A.A) and melting point, conductivit

Concentrations 25, 50 and 100 mg of nano-capsules linolenic acid and non-capsulated fatty acid for 1kg of Milk was used for yogurt manufacture. The results showed no significant differences in the ratio of titration acidity and pH values between all processed treatments at the beginning and during of period storage. The treatments was added to it coated omega-3 by nano method were the least exposed to the oxidation process from the non-capsules omega-3, And for shield of The poly lactic acid had a significant role in the protection of alpha-linolenic acid against lipolysis by the formation of a protective layer to protect the acid from the activity of lipases enzymes, and the addition of fatty acid linolenic to milk was determined the gr

  This study deals with the measurement of the specific activity radiation for beryllium -7 isotope in Baghdad city for samples of surface soils, by using gamma ray spectrometer technique.       Twenty one samples were collected from surface soil of Baghdad city from Risafa and Karkh sides, (7) samples from  Risafa side and(14) samples from Karkh side, where the axis for locations which are fixed by using (G.P.S.) .  Gamma-ray spectrometry system (DSA 2000) with high purity germanium detector was used, which has (50%) efficiency and resolution of (2.2 keV) at gamma line (1332 keV) of 60Co source.        The specific activity values for beryllium -7  isotope in surface soil of  R