The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some s

This paper considers approximate solution of the hyperbolic one-dimensional wave equation with nonlocal mixed boundary conditions by improved methods based on the assumption that the solution is a double power series based on orthogonal polynomials, such as Bernstein, Legendre, and Chebyshev. The solution is ultimately compared with the original method that is based on standard polynomials by calculating the absolute error to verify the validity and accuracy of the performance.

In this paper, we made comparison among different parametric ,nonparametric and semiparametric estimators for partial linear regression model users parametric represented by ols and nonparametric methods represented by cubic smoothing spline estimator and Nadaraya-Watson estimator, we study three nonparametric regression models and samples sizes  n=40,60,100,variances used σ²=0.5,1,1.5 the results  for the first model show that N.W estimator for partial linear regression model(PLM) is the best followed the cubic smoothing spline estimator for (PLM),and the results of the second and the third model show that the best estimator is C.S.S.followed by N.W estimator for (PLM) ,the

In high-dimensional semiparametric regression, balancing accuracy and interpretability often requires combining dimension reduction with variable selection. This study intro- duces two novel methods for dimension reduction in additive partial linear models: (i) minimum average variance estimation (MAVE) combined with the adaptive least abso- lute shrinkage and selection operator (MAVE-ALASSO) and (ii) MAVE with smoothly clipped absolute deviation (MAVE-SCAD). These methods leverage the flexibility of MAVE for sufficient dimension reduction while incorporating adaptive penalties to en- sure sparse and interpretable models. The performance of both methods is evaluated through simulations using the mean squared error and variable selection cri

The military presence in the Gulf region after the British withdrawal from it in 1971 was one of the most important pillars of the American strategy to climb the ladder of global leadership, as the geostrategic features that the region enjoyed provided factors of controlling energy sources and global trade routes. The United States of America guarantees Western Europe and Japan the process of access to energy sources and the exclusion of its opponents from the region, especially the Soviet Union, and the growing American military presence in the Gulf after the invasion of Iraq in 2003. On the other hand, the region experiences many contradictions, some of which threaten its security, such as the exacerbation of disputes between its count

        In this paper, the Magnetohydrodynamic (MHD) for Williamson fluid with varying temperature and concentration in an inclined channel with variable viscosity has been examined. The perturbation technique in terms of the Weissenberg number  to obtain explicit forms for the velocity field has been used. All the solutions of physical parameters of the Darcy parameter , Reynolds number , Peclet number  and Magnetic parameter  are discussed under the different values as shown in plots.

Variable selection is an essential and necessary task in the statistical modeling field. Several studies have triedto develop and standardize the process of variable selection, but it isdifficultto do so. The first question a researcher needs to ask himself/herself what are the most significant variables that should be used to describe a given dataset’s response. In thispaper, a new method for variable selection using Gibbs sampler techniqueshas beendeveloped.First, the model is defined, and the posterior distributions for all the parameters are derived.The new variable selection methodis tested usingfour simulation datasets. The new approachiscompared with some existingtechniques: Ordinary Least Squared (OLS), Least Absolute Shrinkage

To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was ‎proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the ‎exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the ‎modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact ‎solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which ‎shows the reliability and applicability of the proposed approach. ‎

  This research is interested in studying the constant and the variable within the signing reality in Iraqi Kurdistan region, and the researcher tries to tackle the importance of this topic within a search that serves the Kurdish culture, and contribute to its intellectual settlement, and introducing it to centers concerned with studying singing and music science in any civilized environment, whether inside or outside the territory of Kurdistan region. We see that this research which dealt with the topic (the constant and the variable in the Kurdish signing between the past and the present) deserves research and investigation for all its causes, being one of the academic necessities that contribute in identifying the historic artist