The main theme of this thesis could be divided into three objectives : The first is to define and classify integral equations with one and multiple delay, including Fredholm, Volterra and integro-differential equations (Retarded, Neutral and Mixed types). While the second and popular objective of this work is to study the inverse problems related to delay integral equations by using non-classical variational formulation method. Some examples are given for each of the discussed type of delay integral equations. Also, a study to the direct and inverse problems related to integral equations with multiple delay, also considered as a third objective. Several examples are given for each type of these equations. Finally, the suggested approach

Homomorphic encryption became popular and powerful cryptographic primitive for various cloud computing applications. In the recent decades several developments has been made. Few schemes based on coding theory have been proposed but none of them support unlimited operations with security.   We propose a modified Reed-Muller Code based symmetric key fully homomorphic encryption to improve its security by using message expansion technique. Message expansion with prepended random fixed length string provides one-to-many mapping between message and codeword, thus one-to many mapping between plaintext and ciphertext. The proposed scheme supports both (MOD 2) additive and multiplication operations unlimitedly.   We make an effort to prove

A new modified differential evolution algorithm DE-BEA, is proposed to improve the reliability of the standard DE/current-to-rand/1/bin by implementing a new mutation scheme inspired by the bacterial evolutionary algorithm (BEA). The crossover and the selection schemes of the DE method are also modified to fit the new DE-BEA mechanism. The new scheme diversifies the population by applying to all the individuals a segment based scheme that generates multiple copies (clones) from each individual one-by-one and applies the BEA segment-wise mechanism. These new steps are embedded in the DE/current-to-rand/bin scheme. The performance of the new algorithm has been compared with several DE variants over eighteen benchmark functions including sever

New evidence on nanotechnology has shown interest in the creation and assessment of nanoparticles for cancer treatment. Worldwide, a wide range of tumor-targeted approaches are being developed to reduce side effects and boost the efficacy of cancer therapy. One strategy that shows promise is the use of metallic nanoparticles to increase the radio sensitization of the cancer cells while reducing or maintaining the normal tissue complication probability during radiation therapy. In this study, atmospheric plasma was created using argon gas to create Au NPs using the plasma jet scheme, and their ability to induce apoptosis as an anticancer mechanism was tested. Aqueous gold tetrachloride salts (HAuCl4·3H2O) ere used to produce gold nanopartic

In this work, a joint quadrature for numerical solution of the double integral is presented. This method is based on combining two rules of the same precision level to form a higher level of precision. Numerical results of the present method with a lower level of precision are presented and compared with those performed by the existing high-precision Gauss-Legendre five-point rule in two variables, which has the same functional evaluation. The efficiency of the proposed method is justified with numerical examples. From an application point of view, the determination of the center of gravity is a special consideration for the present scheme. Convergence analysis is demonstrated to validate the current method.

This article studies the nonlocal inverse boundary value problem for a rectangular domain, a second-order, elliptic equation and a two-dimensional equation. The main objective of the article is to find the unidentified coefficient and provide a solution to the problem. The two-dimensional second-order, convection equation is solved directly using the finite difference method (FDM). However, the inverse problem was successfully solved the MATLAB subroutine lsqnonlin from the optimization toolbox after reformulating it as a nonlinear regularized least-square optimization problem with a simple bound on the unknown quantity. Considering that the problem under study is often ill-posed and that even a small error in the input data can hav

The accurate identification of internal and external pressures in thick-walled hyperelastic vessels is a challenging inverse problem with significant implications for structural health monitoring, biomedical devices, and soft robotics. Conventional analytical and numerical approaches address the forward problem effectively but offer limited means for recovering unknown load conditions from observable deformations. In this study, we introduce a Graph-FEM/ML framework that couples high-fidelity finite element simulations with machine learning models to infer normalized internal and external pressures from measurable boundary deformations. A dataset of 1386 valid samples was generated through Latin Hypercube Sampling of geometric and l

Intravascular embolisation of foreign bodies (FB) is a rare, serious complication that may occur during central venous line insertion. A 39-yearold male in a critical condition presented to casualty department with a through-and-through chest gunshot wound. Chest X-ray showed left haemothorax; an urgent chest tube was introduced and central venous access was introduced via the right femoral vein. The guided wire used in the procedure was unintentionally pushed to reach the right ventricular apex. Echocardiography confirmed FB location. Once stabilised, the patient was referred to Iraqi Centre of Cardiac Diseases, where transcatheter retrieval was performed. To stabilise the FB, a 6F pigtail catheter was used to create a U-shaped loop in the