In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the  traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms wit

This paper deals with a method called Statistical Energy Analysis that can be applied to the mechanical and acoustical systems like buildings, bridges and aircrafts …etc. S.E.A as a tool can be applied to the resonant systems in the circumstances of high frequency or/and complex structure». The parameters of S.E.A such as coupling loss factor, internal loss factor, modal density and input power are clarified in this work ; coupled plate sub-systems and explanations are presented for these parameters. The developed system is assumed to be resonant, conservative, linear and there is an equipartition of energy between all the resonant modes within a given frequency band in a given sub-system. The aim of th

An innovative two-step noncatalytic esterifcation technique was proposed to synthesize alkyl esters from free fatty acids simulated in waste cooking oil, as a pretreatment process for biodiesel production, without adding any catalyst under normal conditions of pressure and temperature. The efect of methanol:oil molar ratio, reaction time, mixing rate, and reaction temperature were investigated. The results confrmed that the conversion of the reaction was increased when increasing the methanol molar ratio and decreased in prolonged reaction temperature. High conversion (94.545%) was successfully achieved at optimized conditions of 115:1, 65:1 methanol:oil molar ratio in the frst step and second step, respectively, other conditions i

The local resolving neighborhood  of a pair of vertices  for  and  is if there is a vertex  in a connected graph  where the distance from  to  is not equal to the distance from  to , or defined by . A local resolving function  of  is a real valued function   such that  for  and . The local fractional metric dimension of graph  denoted by , defined by  In this research, the author discusses about the local fractional metric dimension of comb product are two graphs, namely graph  and graph , where graph  is a connected graphs and graph  is a complate graph &

Correlation equations for expressing the boiling temperature as direct function of liquid composition have been tested successfully and applied for predicting azeotropic behavior of multicomponent mixtures and the kind of azeotrope (minimum, maximum and saddle type) using modified correlation of Gibbs-Konovalov theorem. Also, the binary and ternary azeotropic point have been detected experimentally using graphical determination on the basis of experimental binary and ternary vapor-liquid equilibrium data.

            In this study, isobaric vapor-liquid equilibrium for two ternary systems: “1-Propanol – Hexane – Benzene” and its binaries “1-Propanol –

Abstract

The Classical Normal Linear Regression Model Based on Several hypotheses, one of them is Heteroscedasticity as it is known that the wing of least squares method (OLS), under the existence of these two problems make the estimators, lose their desirable properties, in addition the statistical inference becomes unaccepted table. According that we put tow alternative,  the first one is  (Generalized Least Square) Which is denoted by (GLS), and the second alternative is to (Robust covariance matrix estimation) the estimated parameters method(OLS), and that the way (GLS) method neat and certified, if the capabilities (Efficient) and the statistical inference Thread on the basis of an acceptable

The development of information systems in recent years has contributed to various methods of gathering information to evaluate IS performance. The most common approach used to collect information is called the survey system. This method, however, suffers one major drawback. The decision makers consume considerable time to transform data from survey sheets to analytical programs. As such, this paper proposes a method called ‘survey algorithm based on R programming language’ or SABR, for data transformation from the survey sheets inside R environments by treating the arrangement of data as a relational format. R and Relational data format provide excellent opportunity to manage and analyse the accumulated data. Moreover, a survey syste

The aim of this study is to know the effect of different percentages of chitosan added to drinking water on the weight and quality of quail meat, physical anatomy in terms of (the body of the long carcass, the girth of the chest, the length of the thigh bones, the thigh racket, the fullness of the chest), chemical analysis (protein, moisture, fat and ash) and sensory evaluation of quail meat. It was purchased 320 Iraqi-origin birds of quail and one day old. Chicks were randomly distributed to three equal groups' treatments and treated with chitosan and added to the drinking water: the first treatment (0.1 gm./L water only as a control treatment), the second treatment (0.2 gm./L of chitosan was added to the drinking water) and the