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

     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

Proxy-based sliding mode control PSMC is an improved version of PID control that combines the features of PID and sliding mode control SMC with continuously dynamic behaviour. However, the stability of the control architecture maybe not well addressed. Consequently, this work is focused on modification of the original version of the proxy-based sliding mode control PSMC by adding an adaptive approximation compensator AAC term for vibration control of an Euler-Bernoulli beam. The role of the AAC term is to compensate for unmodelled dynamics and make the stability proof more easily. The stability of the proposed control algorithm is systematically proved using Lyapunov theory. Multi-modal equation of motion is derived using the Galerkin metho

Artificial Intelligence Algorithms have been used in recent years in many scientific fields. We suggest employing flower pollination algorithm in the environmental field to find the best estimate of the semi-parametric regression function with measurement errors in the explanatory variables and the dependent variable, where measurement errors appear frequently in fields such as chemistry, biological sciences, medicine, and epidemiological studies, rather than an exact measurement. We estimate the regression function of the semi-parametric model by estimating the parametric model and estimating the non-parametric model, the parametric model is estimated by using an instrumental variables method (Wald method, Bartlett’s method, and Durbin

The amount of protein in the serum depends on the balance between the rate of its synthesis, and that of its catabolism or loss. Abnormal metabolism may result from nutritional deficiency, enzyme deficiency, abnormal secretion of hormones, or the actions of drugs and toxins. Renal cancer is the third most common malignancy of the genitourinary system, and accounts for 3% of adult malignancies globally. Total serum proteins were measured in malignant kidney tumor, benign kidney tumors, and non tumoral kidney diseases patient groups, as well as in healthy individuals. A significant decrease (p< 0.001) of total serum protein levels in patients with malignant kidney tumors when compared with those of benign tumors, non tumoral diseases, and hea

This paper introduces a non-conventional approach with multi-dimensional random sampling to solve a cocaine abuse model with statistical probability. The mean Latin hypercube finite difference (MLHFD) method is proposed for the first time via hybrid integration of the classical numerical finite difference (FD) formula with Latin hypercube sampling (LHS) technique to create a random distribution for the model parameters which are dependent on time [Formula: see text]. The LHS technique gives advantage to MLHFD method to produce fast variation of the parameters’ values via number of multidimensional simulations (100, 1000 and 5000). The generated Latin hypercube sample which is random or non-deterministic in nature is further integ