The aim of this paper is to study the combined effects of the concentration and the thermo-diffusion on the unsteady oscillation flow of an incompressible Carreau fluid through an inclined porous channel. The temperature is assumed to affect exponentially the fluid's viscosity. We studied fluid flow in an inclined channel under the non-slip condition at the wall. We used the perturbation series method to solve the nonlinear partial differential equations. Numerical results were obtained for velocity distribution, and through the graphs, it was found that the velocity of fluid has a direct relation with Soret number, Peclet number, and Grashof number, while it has a reverse variation with chemical reaction, Schmidt number, frequency of os

      This study aims to classify the critical points of functions with 4 variables and 8 parameters, we found the caustic for the certain function with the spreading of the critical points. Finally, as an application, we found the bifurcation solutions for the equation of sixth order with boundary conditions using the Lyapunov-Schmidt method in the variational case.

Mathematical integration techniques rely on mathematical relationships such as addition, subtraction, division, and subtraction to merge images with different resolutions to achieve the best effect of the merger. In this study, a simulation is adopted to correct the geometric and radiometric distortion of satellite images based on mathematical integration techniques, including Brovey Transform (BT), Color Normalization Transform (CNT), and Multiplicative Model (MM). Also, interpolation methods, namely the nearest neighborhood, Bi-linear, and Bi-cubic were adapted to the images captured by an optical camera. The evaluation of images resulting from the integration process was performed using several types of measures; the first type depend

This paper demonstrates a new technique based on a combined form of the new transform method with homotopy perturbation method to find the suitable accurate solution of autonomous Equations with initial condition.  This technique is called the transform homotopy perturbation method (THPM). It can be used to solve the problems without resorting to the frequency domain.The implementation of the suggested method demonstrates the usefulness in finding exact solution for linear and nonlinear problems. The practical results show the efficiency and reliability of technique and easier implemented than HPM in finding exact solutions.Finally, all algorithms in this paper implemented in MATLAB version 7.12.

New hydrazone derivatives of Fenoprofen were synthesized and evaluated for their anti-inflammatory activity by means of egg white induced paw edema method. All the synthesized target compounds were characterized by FT-IR spectroscopy, 1HNMR analysis and by measure of their physical properties. The synthesis of the target compounds(H1-H4) was accomplished by multistep reaction procedures. The synthesized target compounds were show activity in reducing paw edema thickness and their anti-inflammatory effect was comparable to that of the standard (Fenoprofen) except for compound H3 which show anti-inflammatory activity higher than Fenoprofen.

The Catharanthus roseus plant was extracted and converted to nanoparticles in this work. The Soxhlet method extracted alkaloid compounds from the plant Catharanthus roseus and converted them to the nanoscale. Chitosan polymer was used as a linking material and converted to Chitosan nanoparticles using Sodium TriPolyPhosphate (STPP). The extracted alkaloids were linked with Chitosan nanoparticles CSNPs by maleic anhydride to get the final product (CSNPs- Linker- alkaloids). The synthesized (CSNPs- Linker- alkaloids) was characterized using SEM spectroscopy UV–Vis., Zeta Potential, and HPLC High-Performance Liquid Chromatography. Scanning electron microscope (SEM) analysis shows that the Chitosan nanoparticles (CSNPs) have small dim

     Transformation and many other substitution methods have been used to solve non-linear differential fractional equations. In this present work, the homotopy perturbation method to solve the non-linear differential fractional equation with the help of He’s Polynomials is provided as the transformation plays an essential role in solving differential linear and non-linear equations. Here is the α-Sumudu technique to find the relevant results of the gas dynamics equation in fractional order. To calculate the non-linear fractional gas dynamical problem, a consumer method created on the new homotopy perturbation a-Sumudu transformation method (HP TM) is suggested. In the Caputo type, the derivative is evaluated. a-Sumudu homotopy pe

Developing and researching antenna designs are analogous to excavating in an undiscovered mine. This paper proposes a multi-band antenna with a new hexagonal ring shape, theoretically designed, developed, and analyzed using a CST before being manufactured. The antenna has undergone six changes to provide the best performance. The results of the surface current distribution and the electric field distribution on the surface of the hexagonal patch were theoretically analyzed and studied. The sequential approach taken to determine the most effective design is logical, and prevents deviation from the work direction. After comparing the six theoretical results, the fifth model proved to be the best for making a prototype. Measured results rep

In this research article, an Iterative Decomposition Method is applied to approximate linear and non-linear fractional delay differential equation. The method was used to express the solution of a Fractional delay differential equation in the form of a convergent series of infinite terms which can be effortlessly computable.
The method requires neither discretization nor linearization. Solutions obtained for some test problems using the proposed method were compared with those obtained from some methods and the exact solutions. The outcomes showed the proposed approach is more efficient and correct.

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

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