Studying some approaches to estimate the smoothing parameter for the nonparametric regression model

Several previous studies have addressed various topics in regression analysis and estimation of the appropriate regression equation. It assumes that there is a known and pre-defined function relationship between variables. The studied variables are known for distribution using some known methods of estimation, such as the ordinary least squares method (OLS) and the maximum likelihood method (MLE). The parameter model can be estimated due to problems arising from the application of the parameter model, because the theoretical assumptions of the model application are not met. Here, we adopted another method of estimating the regression equation using non-parametric methods. It proved its efficiency and ability to analyze data without the need for prior assumptions on the model. Based on the adopted data, it determines the functional shape of the studied population. Therefore, the aim of this research is to use non-parametric smoothing methods to approximate the non-parametric regression function to the real regression function. This is done by using some non-parametric smoothing methods such as Kernel methods by Nadaraya-Watson and the method of the nearest neighbor (K-Nearest-Neighbor) depending on the bandwidth (h).The study uses the experimental method of simulation on two test functions. Three sizes of sample data (n = 15, n = 50, n = 75) and three values for random error variance (σ^2=0.5),(σ^2=1),(σ^2=2) are assumed. Kernel methods based on Nadaraya-Watson Smoothed Cross Validation are the best choice for the bandwidth of the first test function. On the other hand, Least Squared Cross Validation method for the forensic crossing is the best choice for the bandwidth of the second test function. The second one was better than the neighbor method closest to the first test function

Substrate Temperature Effect on the Optical Properties of ZrO2 Films Prepared by Thermal Evaporation

The pure substance of Zirconium oxide  (ZrO2) was deposited on substrate of glass with various substrate temperatures using thermal evaporation under the pressure of (2×10-5 bar) and with a deposition rate of (0.5 nm/S) with an average thickness of (300 nm). The optical properties of these prepared films were concentrated as a function of the substrate temperature. It was found that the values ​​of each of the refractive index, packing density, together with the extinction coefficient increased with the increase in the substrate temperature of the prepared films

Spherically Symmetric Solutions in M\o ller's Tetrad Theory of Gravitation

The general solution of M\o ller's field equations in case of spherical symmetry is derived. The previously obtained solutions are verified as special cases of the general solution.Comment: LaTeX2e with AMS-LaTeX 1.2, 8 page

Late Miocene karst system at Sheikh Abdallah, between Bahariya and Farafra, Western Desert, Egypt : Implications for palaeoclimate and geomorphology

The extensive spelean deposits in the Western Desert of Egypt at Crystal Mountain (Gebel Bellorat) are considered to be 11-10 Ma, confirming the 'Vallesian' estimate made by Heissig (1982). Several new faunal elements have been discovered including anurans, snakes, soricids, bats, galagids, hystricids and glirids. This fauna indicates that the region was appreciably more humid 11-10 Ma than it is today, with at least 750 mm and possibly as much as 1,200 mm mean annual rainfall. The role of karst processes in the development of the oases of the Western Desert that may have been underestimated by previous researchers is emphasized

New Path Equations in Absolute Parallelism Geometry

The Bazanski approach, for deriving the geodesic equations in Riemannian geometry, is generalized in the absolute parallelism geometry. As a consequence of this generalization three path equations are obtained. A striking feature in the derived equations is the appearance of a torsion term with a numerical coefficients that jumps by a step of one half from equation to another. This is tempting to speculate that the paths in absolute parallelism geometry might admit a quantum feature.Comment: 4 pages Latex file Journal Reference: Astrophysics and space science 228, 273, (1995

Cosmological applications in Kaluza-Klein theory

The field equations of Kaluza-Klein (KK) theory have been applied in the domain of cosmology. These equations are solved for a flat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor's expansion of cosmological function, $\Lambda(t)$, up to the first order of the time $t$. The cosmological parameters are calculated and some cosmological problems are discussed.Comment: 14 pages Latex, 5 figures, one table. arXiv admin note: text overlap with arXiv:gr-qc/9805018 and arXiv:astro-ph/980526

On Finslerized Absolute Parallelism spaces

The aim of the present paper is to construct and investigate a Finsler structure within the framework of a Generalized Absolute Parallelism space (GAP-space). The Finsler structure is obtained from the vector fields forming the parallelization of the GAP-space. The resulting space, which we refer to as a Finslerized Parallelizable space, combines within its geometric structure the simplicity of GAP-geometry and the richness of Finsler geometry, hence is potentially more suitable for applications and especially for describing physical phenomena. A study of the geometry of the two structures and their interrelation is carried out. Five connections are introduced and their torsion and curvature tensors derived. Some special Finslerized Parallelizable spaces are singled out. One of the main reasons to introduce this new space is that both Absolute Parallelism and Finsler geometries have proved effective in the formulation of physical theories, so it is worthy to try to build a more general geometric structure that would share the benefits of both geometries.Comment: Some references added and others removed, PACS2010, Typos corrected, Amendemrnts and revisions performe

Inhomogeneities in dusty universe - a possible alternative to dark energy?

There have been of late renewed debates on the role of inhomogeneities to explain the observed late acceleration of the universe. We have looked into the problem analytically with the help of the well known spherically symmetric but inhomogeneous Lemaitre-Tolman-Bondi(LTB) model generalised to higher dimensions. It is observed that in contrast to the claim made by Kolb et al the presence of inhomogeneities as well as extra dimensions can not reverse the signature of the deceleration parameter if the matter field obeys the energy conditions. The well known Raychaudhuri equation also points to the same result. Without solving the field equations explicitly it can, however, be shown that although the total deceleration is positive everywhere nevertheless it does not exclude the possibility of having radial acceleration, even in the pure dust universe, if the angular scale factor is decelerating fast enough and vice versa. Moreover it is found that introduction of extra dimensions can not reverse the scenario. To the contrary it actually helps the decelerating process.Comment: 14 pages, 4 figure

Energy-Momentum Complex in M\o ller's Tetrad Theory of Gravitation

M\o ller's Tetrad Theory of Gravitation is examined with regard to the energy-momentum complex. The energy-momentum complex as well as the superpotential associated with M\o ller's theory are derived. M\o ller's field equations are solved in the case of spherical symmetry. Two different solutions, giving rise to the same metric, are obtained. The energy associated with one solution is found to be twice the energy associated with the other. Some suggestions to get out of this inconsistency are discussed at the end of the paper.Comment: LaTeX2e with AMS-LaTeX 1.2, 13 page