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

The study aims to discuss the relation between imported inflation and international trade of Iraqi economy for the period (1990-2015) by using annual data. To achieve the study aim, statistical and Econometrics methods are used through NARDL model to explain non-linear relation because it’s a model assigned to measure non-linear relations and as we know most economic relations are non-linear, beside explaining positive and negative effects of imported inflation, and to reach the research aim deductive approach was adopted through using descriptive method to describe and determine phenomenon. Beside the inductive approach by g statistical and standard tools to get the standard model explains the

This study included isolation and characterization of extremely halophilic bacteria from Al-Massab Al-Aam region in South of Iraq Fifty isolates were identified by using numerical taxonomy 40 strains belonged to the genus Halobacterium which inclucted Hb. halobium Hb. cutirubrum Hb. salinarium Hb. saccharovorum Hb. valismortis and Hb. volcanii. Ten strains belonged to the genus Halococcus which included Hc. morrhuae Hc. saccharolyticus. Growth curves were sensitive mutants determined for wild type and salt Generation time in logarthmic phase was measured and found to be (10.37 2hr 7 0.59) for Hb. salinarium / 18 (6.490 hr 0.24) for Hb. cutirubrum / 32, (6.700 hr + 0.488) for Hb. valismortis / 20, (11.243 hr + 0.96) for Hb. volcanii / 7. (7

A high sensitivity, low power and low cost sensor has been developed for photoplethysmography (PPG) measurement. The PPG principle was applied to follow the dilatation and contraction of skin blood vessels during the cardiac cycle. A standard light emitting diodes (LEDs) has been used as a light emitter and detector, and in order to reduce the space, cost and power, the classical analogue-to-digital converters (ADCs) replaced by the pulse-based signal conversion techniques. A general purpose microcontroller has been used for the implementation of measurement protocol. The proposed approach leads to better spectral sensitivity, increased resolution, reduction in cost, dimensions and power consumption. The basic sensing configuration prese

Joints are among the most widespread geologic structures as they are found in most each exposure of rock. They differ greatly in appearance, dimensions, and arrangement, besides they occur in quite different tectonic environments. This study is important because joints provide evidence on what kind of stress produced them (history of deformation) and also because they change the characteristics of the rocks in which they occur. The Measured data of joints from the studied area which are located in the high folded zone – Northeast of Iraq, were classified according to their relationship with the tectonic axes by projecting them stereographically using Schmidt net in GEOrient ver.9.5.0 software. The joint systems revealed the orientation of

The effect of heat treatment on the optical properties of the bulk heterojunction blend nickel (II) phthalocyanine tetrasulfonic acid tetrasodium salt and Tris (8-hydroxyquinolinato) Aluminum (NiPcTs/Alq3) thin films which prepared by spin coating was described in this study. The films coated on a glass substrate with speed of 1500 rpm for 1.5 min and treated with different annealing temperature (373, 423 and 473) K. The samples characterized using UV-Vis, X ray diffraction and Fourier transform Infrared (FTIR) spectra, XRD patterns indicated the presence of amorphous and polycrystalline blend (NiPcTs/Alq3). The results of UV visible shows that the band gap increase with increasing the annealing temperature up to 373 K and decreases with