The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives a good agreement.
Vitamin K-dependent protein (VKDP) contributes to the development of lung cancer. The purpose of this research was to better understanding of the role of blood matrix Gla protein (MGP), VKDPs, Malondialdehyde (MDA), Superoxide dismutase (SOD) and Vitamin K (Vit K) in Iraqi patients with lung cancer before and after the first cycle of chemotherapy. Blood samples were collected from Al amal National Hospital for cancer treatment from October 2021 to May 2022, and a total of 80 samples were collected, divided into two groups (40 patient before taking a chemotherapy and 40 patients after taking chemotherapy), ranging in age from 20 to 45 years old. The results showed that although there were highly statistically significant differences in MD
... Show MoreDrip irrigation is one of the conservative irrigation techniques since it implies supplying water directly on the soil through the emitter; it can supply water and fertilizer directly into the root zone. An equation to estimate the wetted area in unsaturated soil is taking into calculating the water absorption by roots is simulated numerically using HYDRUS (2D/3D) software. In this paper, HYDRUS comprises analytical types of the estimate of different soil hydraulic properties. Used one soil type, sandy loam, with three types of crops; (corn, tomato, and sweet sorghum), different drip discharge, different initial soil moisture content was assumed, and different time durations. The relative error for the different hydrauli
... Show MoreThis paper examines the finding of spacewise dependent heat source function in pseudoparabolic equation with initial and homogeneous Dirichlet boundary conditions, as well as the final time value / integral specification as additional conditions that ensure the uniqueness solvability of the inverse problem. However, the problem remains ill-posed because tiny perturbations in input data cause huge errors in outputs. Thus, we employ Tikhonov’s regularization method to restore this instability. In order to choose the best regularization parameter, we employ L-curve method. On the other hand, the direct (forward) problem is solved by a finite difference scheme while the inverse one is reformulated as an optimization problem. The
... Show Morethis work, a simple method was used to prepare the MnO2 nanoparticles. These nanoparticles then were characterized by several techniques, such as X-ray diffraction, Fourier transform infrared spectroscopy, scanning electron microscopy (SEM) and atomic force microscope (AFM). The results showed that the diffraction peak of MnO2 nanoparticles was similar to that of standard data. The images of AFM and SEM indicated that the MnO2 nanorods were growing from the MnO2 nano spherical shape. PVA-pentaerythritol/MnO2 nanocomposite films were fabricated by evaporating casting method. The dielectric constant and loss tangent of P-Ery/MnO2 films were measured between 10 kHz and 1 MHz using LCR. As the content of MnO2 increased, the dielectric constant
... Show MoreIn this paper, some conditions to guarantee the existence of bounded solution to the second order multi delayed arguments differential equation are given. The Krasnoselskii theorem used to the Lebesgue’s dominated convergence and fixed point to obtain some new sufficient conditions for existence of solutions. Some important lemmas are established that are useful to prove the main results for oscillatory property. We also submitted some sufficient conditions to ensure the oscillation criteria of bounded solutions to the same equation.
This Book is intended to be textbook studied for undergraduate course in multivariate analysis. This book is designed to be used in semester system. In order to achieve the goals of the book, it is divided into the following chapters (as done in the first edition 2019). Chapter One introduces matrix algebra. Chapter Two devotes to Linear Equation System Solution with quadratic forms, Characteristic roots & vectors. Chapter Three discusses Partitioned Matrices and how to get Inverse, Jacobi and Hessian matrices. Chapter Four deals with Multivariate Normal Distribution (MVN). Chapter Five concern with Joint, Marginal and Conditional Normal Distribution, independency and correlations. While the revised new chapters have been added (as the curr
... Show MoreThis Book is intended to be textbook studied for undergraduate course in multivariate analysis. This book is designed to be used in semester system. In order to achieve the goals of the book, it is divided into the following chapters (as done in the first edition 2019). Chapter One introduces matrix algebra. Chapter Two devotes to Linear Equation System Solution with quadratic forms, Characteristic roots & vectors. Chapter Three discusses Partitioned Matrices and how to get Inverse, Jacobi and Hessian matrices. Chapter Four deals with Multivariate Normal Distribution (MVN). Chapter Five concern with Joint, Marginal and Conditional Normal Distribution, independency and correlations. While the revised new chapters have been added (as the curr
... Show MoreTaking into account the significance of food chains in the environment, it demonstrates the interdependence of all living things and has economic implications for people. Hunting cooperation, fear, and intraspecific competition are all included in a food chain model that has been developed and researched. The study tries to comprehend how these elements affect the behavior of species along the food chain. We first examined the suggested model's solution properties before calculating every potential equilibrium point and examining the stability and bifurcation nearby. We have identified the factors that guarantee the global stability of the positive equilibrium point using the geometric approach. Additionally, the circumstances that would gu
... Show MoreThe problem of reconstruction of a timewise dependent coefficient and free boundary at once in a nonlocal diffusion equation under Stefan and heat Flux as nonlocal overdetermination conditions have been considered. A Crank–Nicolson finite difference method (FDM) combined with the trapezoidal rule quadrature is used for the direct problem. While the inverse problem is reformulated as a nonlinear regularized least-square optimization problem with simple bound and solved efficiently by MATLAB subroutine lsqnonlin from the optimization toolbox. Since the problem under investigation is generally ill-posed, a small error in the input data leads to a huge error in the output, then Tikhonov’s regularization technique is app
... Show MoreNuclear medicine is important for both diagnosis and treatment. The most common treatment for diseases is radiation therapy used against cancer. The radiation intensity of the treatment is often less than its ability to cause damage, so radiation must be carefully controlled. The interactions of alpha particle with matter were studied and the stopping powers of alpha particle with ovary tissue were calculated using Beth-Bloch equation, Zeigler’s formula and SRIM Software also the range and Liner Energy Transfer (LET) and ovary thickness as well as dose and dose equivalent for this particle were calculated by using Matlab language for (0.01-200) MeV alpha energy.