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 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

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

Cervical ectropion is considered to be a physiologic condition caused by columnar epithelium migration from the cervical canal into the vaginal portion of the cervix and usually there is no treatement for clinically asymptomatic cervical ectropion . Treatment can be achieved by thermal cauterization (Electrocautery), Cryosurgery or laser vaporization. Aim of the study: To study the effectiveness of CO2 laser (10600nm) in treatment of symptomatic cervical ectropion . Setting: The study was carried out at Laser Medicine Research Clinic at the Institute of Laser for Postgraduate Studies, University of Baghdad between the first of August 2013 to the end of October 2013. Patients and Methods: Ten female Patients with age range between 25-48 y

Several types of laser are used in experimental works in order to study the effects of laser on blood vessel. They differ from each other by a lot of properties mainly in wavelength, energy of the laser and pulse duration. In this study argon laser (488 nm- 514 nm) and continuous Nd: YAG laSer (1064 nm), have been applied to 50 samples of sheep blgod tesselS. Histologically, tha results of the study were different According to the txpe of L`sar used; apgon larer had distrabtave effects on $he blood vessal while continuous Nd: YAG laser Appeaped to be the safesd one on the blmod vessel architecture. This study concluded that argoj laser has da-aging ef&ect on

Due to increased consumption of resources, especially energy it was necessary to find alternatives characterized by the same quality as well as being of less expensive, and most important of these alternatives are characterized by waste and the fact that humancannot stop consumption. So we  have consideredwaste as an  alternative and cheap economic resources and by using environmental index the MIP (input materials per unit ,unit / service) is based on the grounds that the product is not the end of itselfit is a product to meet the need  of a product or service, awarded a resource input and output within the five basic elements are the raw materials is ecological, Raw materials ecological, water, air and soil erosion for a

The root-mean square-radius of proton, neutron, matter and charge radii, energy level, inelastic longitudinal form factors, reduced transition probability from the ground state to first-excited 2⁺ state of even-even isotopes, quadrupole moments, quadrupole deformation parameter, and the occupation numbers for some calcium isotopes for A=42,44,46,48,50 are computed using fp-model space and FPBM interaction. ⁴⁰Ca nucleus is regarded as the inert core for all isotopes under this model space with valence nucleons are moving throughout the fp-shell model space involving 1f_7/2, 2p_3/2, 1f_5/2, and 2p_1/2 orbits. Model space is used to present calculations using FPBM intera

The invention relates to a coordinate measuring machine (CMM) for determining a measuring position of a probe. The AACMM isdepends on the robotkinematics (forward and reverse) in their measurementprinciple, i.e., using the AACMM links and joint angles todetermine the exact workspace or part coordinates. Hence, themeasurements are obtained using an AACMM will be extremely accurate and precise since that ismerely dependent on rigid structural parameters and the only source of measurement error is due to human operators. In this paper, a new AACMM design was proposed. The new AACMM design addresses common issues such as solving the complex kinematics, overcoming the workspace limitation, avoiding singularity, and eliminating the effects of

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.