An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.

Self-criticism is that a person confronts himself with his mistakes in order to reform and develop them for the better, motivate them and inspire hope in them to push them forward and continue to give in this life. The Holy Qur’an teaches us, through the models it cited in its verses, that this is through repentance, a feeling of remorse, and a determination to leave mistakes, and quit disobedience and sins, etc., and all this is done through constructive criticism, and at the same time, one must realize his strengths. , in order to succeed in preserving it and employing it in the right path that pleases God, His Messenger, himself and his society. This has been explained through an introduction, two topics and a conclusion, and God is t

This paper study two stratified quantile regression models of the marginal and the conditional varieties. We estimate the quantile functions of these models by using two nonparametric methods of smoothing spline (B-spline) and kernel regression (Nadaraya-Watson). The estimates can be obtained by solve nonparametric quantile regression problem which means minimizing the quantile regression objective functions and using the approach of varying coefficient models. The main goal is discussing the comparison between the estimators of the two nonparametric methods and adopting the best one between them

This paper presents a grey model GM(1,1) of the first rank and a variable one and is the basis of the grey system theory , This research dealt  properties of grey model and a set of methods to estimate parameters of the grey model GM(1,1)  is the least square Method (LS) , weighted least square method (WLS), total least square method (TLS) and gradient descent method  (DS). These methods were compared based on two types of standards: Mean square error (MSE), mean absolute percentage error (MAPE), and after comparison using simulation the best method was applied to real data represented by the rate of consumption of the two types of oils a Heavy fuel (HFO) and diesel fuel (D.O) and has been applied several tests to

This paper presents a newly developed method with new algorithms to find the numerical solution of nth-order state-space equations (SSE) of linear continuous-time control system by using block method. The algorithms have been written in Matlab language. The state-space equation is the modern representation to the analysis of continuous-time system. It was treated numerically to the single-input-single-output (SISO) systems as well as multiple-input-multiple-output (MIMO) systems by using fourth-order-six-steps block method. We show that it is possible to find the output values of the state-space method using block method. Comparison between the numerical and exact results has been given for some numerical examples for solving different type

     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.

Abstract

     Travel Time estimation and reliability measurement is an important issues for improving operation efficiency and safety of traffic roads networks. The aim of this research is the estimation of total travel time and distribution analysis for three selected links in Palestine Arterial Street in Baghdad city. Buffer time index results in worse reliability conditions. Link (2) from Bab Al Mutham intersection to Al-Sakara intersection produced a buffer index of about 36%  and 26 % for Link (1) Al-Mawall intersection to Bab Al- Mutham intersection and finally for link (3) which presented a 24% buffer index. These illustrated that the reliability get worst for link

The research took the spatial autoregressive model: SAR and spatial error model: SEM  in an attempt to provide practical evidence that proves the importance of spatial analysis, with a particular focus on the importance of using regression models spatial and that includes all of the spatial dependence, which we can test its presence or not by using Moran test. While ignoring this dependency may lead to the loss of important information about the phenomenon under research is reflected in the end on the strength of the statistical estimation power, as these models are the link between the usual regression models with time-series models. The spatial analysis had been applied to Iraq Household Socio-Economic Survey: IHS