Multiple linear regressions are concerned with studying and analyzing the relationship between the dependent variable and a set of explanatory variables. From this relationship the values of variables are predicted. In this paper the multiple linear regression model and three covariates were studied in the presence of the problem of auto-correlation of errors when the random error distributed the distribution of exponential. Three methods were compared (general least squares, M robust, and Laplace robust method). We have employed the simulation studies and calculated the statistical standard mean squares error with sample sizes (15, 30, 60, 100). Further we applied the best method on the real experiment data representing the varieties of

This paper aims to find new analytical closed-forms to the  solutions of the nonhomogeneous functional differential equations of the n^th order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability

􀀑􀀃Pure Cu (CZTSe) and Ag dopant CZTSe (CAZTSe) thin films with Ag content of 0.1 and 0.2 were fabricated on coring glass substrate at R.T with thickness of 800nm by thermal evaporation method. Comparison between the optical characteristics of pure Cu and Ag alloying thin films was done by measuring and analyzing the absorbance and transmittance spectra in the range of (400-1100)nm. Also, the effect of annealing temperature at 373K and 473K on these characteristics was studied. The results indicated that all films had high absorbance and low transmittance in visible region, and the direct bang gap of films decreases with increasing Ag content and annealing temperature. Optical parameters like extinction coefficientrefractive index, and

Abstract Background: The hip joint and lumbar spine are both anatomically and functionally closely related as had shown by many authors. So the abnormality in one area can affect the other e.g. hip joint osteoarthritis can cause lumbar sagittal malalignment and backache. Objectives: is to see if there is significant improvement in backache after total hip replacement? And which degree of backache improvement is associated with significant changes in lumbar lordosis? Methods and patients: a prospective open trial study was performed on 30 patients who had severe hip osteoarthritis and chronic low back pain. Total hip replacement was performed to all patients. Backache and lumbar lordosis were measured by visual analogue scale and Cobb’s a

     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