Lagrangian Dynamical Systems with Three Para-complex Structures
Ibrahim Yousif Ibrahim Abad Alrhman
Issue:
Volume 4, Issue 4, December 2019
Pages:
47-52
Received:
21 March 2019
Accepted:
16 May 2019
Published:
17 January 2020
Abstract: This paper aims to present Lagrangian Dynamical systems formalism for mechanical systems using Three Para- Complex Structures, which represent an interesting multidisciplinary field of research. As a result of this study, partial differential equations will be obtained for movement of objects in space and solutions of these equations. In this study, some geometrical, relativistic, mechanical, and physical results related to Three Para- Complex Structures mechanical systems broad applications in mathematical physics, geometrical optics, classical mechanics, analytical mechanics, mechanical systems, thermodynamics, geometric quantization and applied mathematics such as control theory.
Abstract: This paper aims to present Lagrangian Dynamical systems formalism for mechanical systems using Three Para- Complex Structures, which represent an interesting multidisciplinary field of research. As a result of this study, partial differential equations will be obtained for movement of objects in space and solutions of these equations. In this study...
Show More
B-spline Speckman Estimator of Partially Linear Model
Sayed Meshaal El-sayed,
Mohamed Reda Abonazel,
Mohamed Metwally Seliem
Issue:
Volume 4, Issue 4, December 2019
Pages:
53-59
Received:
25 August 2019
Accepted:
31 December 2019
Published:
3 February 2020
Abstract: The partially linear model (PLM) is one of semiparametric regression models; since it has both parametric (more than one) and nonparametric (only one) components in the same model, so this model is more flexible than the linear regression models containing only parametric components. In the literature, there are several estimators are proposed for this model; where the main difference between these estimators is the estimation method used to estimate the nonparametric component, since the parametric component is estimated by least squares method mostly. The Speckman estimator is one of the commonly used for estimating the parameters of the PLM, this estimator based on kernel smoothing approach to estimate nonparametric component in the model. According to the papers in nonparametric regression, in general, the spline smoothing approach is more efficient than kernel smoothing approach. Therefore, we suggested, in this paper, using the basis spline (B-spline) smoothing approach to estimate nonparametric component in the model instead of the kernel smoothing approach. To study the performance of the new estimator and compare it with other estimators, we conducted a Monte Carlo simulation study. The results of our simulation study confirmed that the proposed estimator was the best, because it has the lowest mean squared error.
Abstract: The partially linear model (PLM) is one of semiparametric regression models; since it has both parametric (more than one) and nonparametric (only one) components in the same model, so this model is more flexible than the linear regression models containing only parametric components. In the literature, there are several estimators are proposed for ...
Show More
