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.

A content-based image retrieval (CBIR) is a technique used to retrieve images from an image database. However, the CBIR process suffers from less accuracy to retrieve images from an extensive image database and ensure the privacy of images. This paper aims to address the issues of accuracy utilizing deep learning techniques as the CNN method. Also, it provides the necessary privacy for images using fully homomorphic encryption methods by Cheon, Kim, Kim, and Song (CKKS). To achieve these aims, a system has been proposed, namely RCNN_CKKS, that includes two parts. The first part (offline processing) extracts automated high-level features based on a flatting layer in a convolutional neural network (CNN) and then stores these features in a

The aerodynamic characteristics of general three-dimensional rectangular wings are considered using non-linear interaction between two-dimensional viscous-inviscid panel method and vortex ring method. The potential flow of a two-dimensional airfoil by the pioneering Hess & Smith method was used with viscous laminar, transition and turbulent boundary layer to solve flow about complex configuration of airfoils including stalling effect. Viterna method was used to extend the aerodynamic characteristics of the specified airfoil to high angles of attacks. A modified vortex ring method was used to find the circulation values along span wise direction of the wing and then interacted with sectional circulation obtained by Kutta-Joukowsky theorem of

n this paper, we formulate three mathematical models using spline functions, such as linear, quadratic and cubic functions to approximate the mathematical model for incoming water to some dams. We will implement this model on dams of both rivers; dams on the Tigris are Mosul and Amara while dams on the Euphrates are Hadetha and Al-Hindya.

     In this article, we aim to define a universal set consisting of the subscripts of the fuzzy differential equation (5) except the two elements  and , subsets of that universal set are defined according to certain conditions. Then, we use the constructed universal set with its subsets for suggesting an analytical method which facilitates solving fuzzy initial value problems of any order by using the strongly generalized H-differentiability. Also, valid sets with graphs for solutions of fuzzy initial value problems of higher orders are found.

CD-nanosponges were prepared by crosslinking B-CD with diphenylcarbonate (DPC) using ultrasound assisted technique. 5-FU was incorporated with NS by freeze drying, and the phase solubility study, complexation efficiency (CE) entrapment efficiency were performed. Also, the particle morphology was studied using SEM and AFM. The in-vitro release of 5-FU from the prepared nanosponges was carried out in 0.1N HCl.

5-FU nanosponges particle size was in the nano size. The optimum formula showed a particle size of (405.46±30) nm, with a polydispersity index (PDI) (0.328±0.002) and a negative zeta potential (-18.75±1.8). Also the drug entrapment efficiency varied with the CD: DPC molar ratio from 15.6 % to 30%. The SEM an

This paper is concerned with the blow-up solutions of a system of two reaction-diffusion equations coupled in both equations and boundary conditions. In order to understand how the reaction terms and the boundary terms affect the blow-up properties, the lower and upper blow-up rate estimates are derived. Moreover, the blow-up set under some restricted assumptions is studied.

In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method.

In this paper the effect of engagement length, number of teeth, amount of applied load, wave propagation time, number of cycles, and initial crack length on the principal stress distribution, velocity of crack propagation, and cyclic crack growth rate in a spline coupling subjected to cyclic torsional impact have been investigated analytically and experimentally. It was found that the stresses induced due to cyclic impact loading are higher than the stresses induced due to impact loading with high percentage depends on the number of cycles and total loading time. Also increasing the engagement length and the number of teeth reduces the principal stresses (40%) and
(25%) respectively for increasing the engagement length from (0.15 to 0