In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.

Orthogonal polynomials and their moments serve as pivotal elements across various fields. Discrete Krawtchouk polynomials (DKraPs) are considered a versatile family of orthogonal polynomials and are widely used in different fields such as probability theory, signal processing, digital communications, and image processing. Various recurrence algorithms have been proposed so far to address the challenge of numerical instability for large values of orders and signal sizes. The computation of DKraP coefficients was typically computed using sequential algorithms, which are computationally extensive for large order values and polynomial sizes. To this end, this paper introduces a computationally efficient solution that utilizes the parall

Background Over the past decade there has been a growing awareness of, and interest in, the trace element concentration differences between normal and diseased tissues. Significant changes in tissue concentrations of Zinc (Zn) and Copper (Cu) have been previously reported in inflammation and cancer of certain human tissues.
Aim:(1)To correlate between Zn and Cu concentrations and the histological picture of normal and certain inflamed human tissues, namely the gall bladder (GB) the vermiform appendix (VA), visceral adipose tissue (VAT) and subcutaneous adipose tissue (SAT). (2) to detect whether there is a difference in the above-mentioned parameters between VAT and SAT. (3) to obtain recordings for trace element levels in human tissu

In this paper, a theoretical study of the energy spectra and the heat capacity of one electron quantum dot with Gaussian Confinement in an external magnetic field are presented. Using the exact diagonalization technique, the Hamiltonian of the Gaussian Quantum Dot (GQD) including the electron spin is solved. All the elements in the energy matrix are found in closed form. The eigenenergies of the electron were displayed as a function of magnetic field, Gaussian confinement potential depth and quantum dot size. Explanations to the behavior of the quantum dot heat capacity curve, as a function of external applied magnetic field and temperature, are presented.

An idiom is a group of words whose meaning put together is different from the meaning of
individual words. English is a rich language when it comes to idioms, they represent variety. For
foreign learners, idioms are problematic because even if they know the meaning of individual
words that compose an idiom the meaning of it might be something completely different.
The present study investigates Iraqi third year college students’ recognition of idioms. To
achieve this, the researchers have conducted a test which comprises three questions. Certain
conclusions are reached here along with some suggestions and recommendations.

Background: The prediction of changes in the mandibular third molar position and eruption is an important clinical concern because third molar retention may be beneficial for orthodontic anchorage. The aims of this study were to assess the mandibular third molar position by using medical CT scan and lateral reconstructed radiograph and evaluate gender differences. Materials and Methods: The sample of present study consisted of 39 patients (18 males and 21 females) with age range 11-15 years who were attending at Al-Suwayra General Hospital/ the Computerized Tomography department. The distance from anterior edge of ramus to distal surface of permanent mandibular second molar and mesio-distal width of developing mandibular third molar were

The virulent genes are the key players in the ability of the bacterium to cause disease. The products of such genes that facilitate the successful colonization and survival of the bacterium in or cause damage to the host are pathogenicity determinants. This study aimed to investigate the prevalence of virulence factors (esp, agg, gelE, CylA) in E. faecalis isolated from diverse human clinical collected in Iraqi patient , as well as to assess their ability to form biofilm and to determine their haemolytic and gelatinase activities. Thirty-two isolates of bacteria Enterococcus faecalis were obtained, including 15 isolates (46.87%) of the urine, 6 isolates (18.75%) for each of the stool and uterine secretions, and 5 isolates (15.62%) of the wo