In this paper we shall generalize fifth explicit Runge-Kutta Feldberg(ERKF(5)) and Continuous explicit Runge-Kutta (CERK) method using shooting method to solve second order boundary value problem  which can be reduced to order one.These methods we shall call them as shooting Continuous Explicit Runge-Kutta method, the results are computed using matlab program.

The legal security has become a principle and necessity in the state of law, based on the fact that the legal basis must be based on legal security, Since the Council of State has become the backbone of the legal base as long as we cannot talk about the value of the rule of law only in view of the degree of stability and the extent of the realization of rights and legal conditions and the consequent to achieve the confidence of individuals in the legal system as a whole.

     That means stabilizing the rules governing the affairs of individuals and nations and keeping them away from factors that lead to instability. This ensures the rights of individuals and states as well, since the individual cannot obtain h

In this paper, the rotation curve of the Milky Way galaxy has been determined using the observed HI emission line at a wavelength of 21 cm. Particularly, the Tangent Point Method was used in order to measure the rotational velocity and the distance to the center of the Milky Way. The measured rotation curve showed that the rotational velocity remains approximately constant at large distances from the center of the Galaxy. This is actually an evidence for the existence of dark matter in the halo of the Milky Way. If all the matter in the Milky Way is visible, then the behavior of the rotation curve of the galaxy should experience a Keplerian decline. The mass of the Milky Way within a radius of 15 kpc was also estimated to be ~ 1.65 × 10

In this paper, the continuous classical boundary optimal control problem (CCBOCP) for triple linear partial differential equations of parabolic type (TLPDEPAR) with initial and boundary conditions (ICs & BCs) is studied. The Galerkin method (GM) is used to prove the existence and uniqueness theorem of the state vector solution (SVS) for given continuous classical boundary control vector (CCBCV). The proof of the existence theorem of a continuous classical boundary optimal control vector (CCBOCV) associated with the TLPDEPAR is proved. The derivation of the Fréchet derivative (FrD) for the cost function (CoF) is obtained. At the end, the theorem of the necessary conditions for optimality (NCsThOP) of this problem is stated and prov

In this paper Hermite interpolation method is used for solving linear and non-linear second order singular multi point boundary value problems with nonlocal condition. The approximate solution is found in the form of a rapidly convergent polynomial. We discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems. The examples to demonstrate the applicability and efficiency of the method have been given.

In this research we study a variance component model, Which is the one of the most important models widely used in the analysis of the data, this model is one type of a multilevel models, and it is considered as linear models , there are three types of linear variance component models ,Fixed effect of linear variance component model, Random effect of linear variance component model and Mixed effect of linear variance component model . In this paper we will examine the model of mixed effect of linear variance component model with one –way random effect ,and the mixed model is a mixture of fixed effect and random effect in the same model, where it contains the parameter (μ) and treatment effect (τ_i ) which  has

     This investigation aims to determine whether it is feasible to use the limestone rocks found in the Al-Samawa stone quarry in southern Iraq as the stationary phase in column chromatography separation. Together with the chromatographic application, the physical and chemical characteristics of the rocks are examined. SiO₂, SO₄, PO₄, NO₃, and Cl are the negative ions, while Ca, Mg, Na, K, and Li are the positive ions. The limestone samples are characterized via chromatographic analysis. The results suggest that limestone samples could be used as an adsorbent material for chromatographic separation techniques. Additionally, samples from the Nasiriyah refinery's crude oil can be used to sep

Abstract

In this research we been estimated the survival function for data suffer from the disturbances and confusion of  Iraq Household Socio-Economic Survey: IHSES II 2012 , to data from a five-year age groups follow the distribution of the Generalized Gamma: GG. It had been used two methods for the purposes of estimating and fitting which is the way the Principle of Maximizing Entropy: POME, and method of booting to nonparametric smoothing function for Kernel, to overcome the mathematical problems plaguing integrals contained in this distribution in particular of the integration of the incomplete gamma function, along with the use of traditional way in which is the Maximum Likelihood: ML. Where the comparison on t

In this research we been estimated the survival function for data suffer from the disturbances and confusion of Iraq Household Socio-Economic Survey: IHSES II 2012 , to data from a five-year age groups follow the distribution of the Generalized Gamma: GG. It had been used two methods for the purposes of estimating and fitting which is the way the Principle of Maximizing Entropy: POME, and method of booting to nonparametric smoothing function for Kernel, to overcome the mathematical problems plaguing integrals contained in this distribution in particular of the integration of the incomplete gamma function, along with the use of traditional way in which is the Maximum Likelihood: ML. Where the comparison on the basis of the method of the Cen