In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

The main work of this paper is devoted to a new technique of constructing approximated solutions for linear delay differential equations using the basis functions power series functions with the aid of Weighted residual methods (collocations method, Galerkin’s method and least square method).

In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

             It is the regression analysis is the foundation stone of knowledge of statistics , which mostly depends on the ordinary least square method , but as is well known that the way the above mentioned her several conditions to operate accurately and the results can be unreliable , add to that the lack of certain conditions make it impossible to complete the work and analysis method and among those conditions are the multi-co linearity problem , and we are in the process of detected that problem between the independent variables using farrar –glauber test , in addition to the requirement linearity data and the lack of the condition last has been resorting to the

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.

Collective C2 transitions in 32S are discussed for higher
energy configurations by comparing the calculations of transition
strength B(CJ  )with the experimental data. These configurations
are taken into account through a microscopic theory including
excitations from the core orbits and the model space orbits with nħω
excitations.
Excitations up to n=10 are considered. However n=6 seems to
be large enough for a sufficient convergence. The calculations
include the lowest seven 2+0 states of 32S.

Abstract

In this work, diabetic glucose concentration level control under disturbing meal has been controlled using two set of advanced controllers. The first set is sliding mode controllers (classical and integral) and the second set is represented by optimal LQR controllers (classical and Min-, ax). Due to their characteristic features of disturbance rejection, both integral sliding mode controller and LQR Minmax controller are dedicated here for comparison. The Bergman minimal mathematical model was used to represent the dynamic behavior of a diabetic patient’s blood glucose concentration to the insulin injection. Simulations based on Matlab/Simulink, were performed to verify the performance of each controll

The efficient behavior of a low-concentrating photovoltaic-thermal system with a micro-jet channel (LCPV/T-JET) and booster mirror reflector is experimentally evaluated here. Micro-jets promote the thermal management of PV solar cells by implementing jet water as active cooling, which is still in the early stages of development. The booster mirror reflector concentrates solar irradiance into solar cells and improves the thermal, electrical, and combined efficiencies of the LCPV/T-JET system. The LCPV/T-JET system was tested under ambient weather conditions in the city of Bangi, Selangor, Malaysia, and all data was recorded between 10:00 a.m. and 4:00 p.m. Parametric studies were conducted to compare the performance of the LCPV/T-JET system