Mixture experiments are response variables based on the proportions of component for this mixture. In our research we will compare the scheffʼe model with the kronecker model for the mixture experiments, especially when the experimental area is restricted.

     Because of the experience of the mixture of high correlation problem and the problem of multicollinearity between the explanatory variables, which has an effect on the calculation of the Fisher information matrix of the regression model.

     to estimate the parameters of the mixture model, we used the (generalized inverse ) And the Stepwise Regression procedure

Flexible job-shop scheduling problem (FJSP) is one of the instances in flexible manufacturing systems. It is considered as a very complex to control. Hence generating a control system for this problem domain is difficult. FJSP inherits the job-shop scheduling problem characteristics. It has an additional decision level to the sequencing one which allows the operations to be processed on any machine among a set of available machines at a facility. In this article, we present Artificial Fish Swarm Algorithm with Harmony Search for solving the flexible job shop scheduling problem. It is based on the new harmony improvised from results obtained by artificial fish swarm algorithm. This improvised solution is sent to comparison to an overall best

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

The objective of an Optimal Power Flow (OPF) algorithm is to find steady state operation point which minimizes generation cost, loss etc. while maintaining an acceptable system performance in terms of limits on generators real and reactive powers, line flow limits etc. The OPF solution includes an objective function. A common objective function concerns the active power generation cost. A Linear programming method is proposed to solve the OPF problem. The Linear Programming (LP) approach transforms the nonlinear optimization problem into an iterative algorithm that in each iteration solves a linear optimization problem resulting from linearization both the objective function and constrains. A computer program, written in MATLAB environme

Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

The aim of the present study was to develop theophylline (TP) inhalable sustained delivery system by preparing solid lipid microparticles using glyceryl behenate (GB) and poloxamer 188 (PX) as a lipid carrier and a surfactant respectively. The method involves loading TP nanoparticles into the lipid using high shear homogenization – ultrasonication technique followed by lyophilization. The compositional variations and interactions were evaluated using response surface methodology, a Box – Behnken design of experiment (DOE). The DOE constructed using TP (X₁), GB (X₂) and PX (X₃) levels as independent factors. Responses measured were the entrapment efficiency (% EE) (Y₁), mass median