The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

The current study is designed to investigate the histological and immunohistochemical characteristics of the thyroid gland in adult male Sciurus anamalus. This study found that the thyroid gland of the Caucasian squirrel is located in the neck area, below the larynx, on both sides of the trachea. It has two lobes (right and left) with cylindrical shape. The histological studies revealed that the thyroid gland is surrounded by a capsule which consists of connective tissue and forming of two layers which are outer layer and inner layer, and a layer of adipose tissue appears overlapping the outer layer. The inner tissue of the gland consists of follicles with different shapes and sizes, and is lined with simple cuboidal epithelial tissue (foll

      The combined system of electrocoagulation (EC) and electro-oxidation (EO) is one of the most promising methods in dye removal. In this work, a solution of 200 mg/l of Congo red was used to examine the removal of anionic dye using an EC-EO system with three stainless steel electrodes as the auxiliary electrodes and an aluminum electrode as anode for the EC process, Cu-Mn-Ni Nanocomposite as anode for the EO process. This composite oxide was simultaneously synthesized by anodic and cathodic deposition of Cu (NO3)2, MnCl2, and Ni (NO3)2 salts with 0.075 M as concentrations of each salt with a fixed molar ratio (1:1:1) at a constant current density of 25 mA/cm2. The characteristics structure and surface morphology of the depo

Greywater is a possible water source that can be improved for meeting the quality required for irrigation. Treatment of greywater can range from uncomplicated coarse filtration to advanced biological treatment. This article presents a simple design of a small scale greywater treatment plant, which is a series of physical and natural processes including screening, aeration, sedimentation, and filtration using granular activated carbon filter and differentiates its performance with sand filter. The performance of these units with the dual filter media of (activated carbon with sand) in treatment of greywater from Iraqi house in Baghdad city during 2019 and that collected from several points including washbasins, kitchen si

Secure information transmission over the internet is becoming an important requirement in data communication. These days, authenticity, secrecy, and confidentiality are the most important concerns in securing data communication. For that reason, information hiding methods are used, such as Cryptography, Steganography and Watermarking methods, to secure data transmission, where cryptography method is used to encrypt the information in an unreadable form. At the same time, steganography covers the information within images, audio or video. Finally, watermarking is used to protect information from intruders. This paper proposed a new cryptography method by using thre

The research aims to know the impact of science, technology, engineering, and mathematics education on both creative thinking and mathematical achievement. To achieve it, the two researchers followed the quasi-experimental approach with an experimental design for two groups, one experimental and the other a control. The research sample consisted of (32) female students from the fourth scientific grade in Al-Intisar Preparatory School for Girls/ AlRasafa, First Directorate. The sample was chosen intentionally and was divided into two groups: a control group studying by the traditional method, their number (16), and an experimental group that applied the STEM approach, their number also (16). There was parity between the two research groups i

The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the stat