In this paper, the bi-criteria machine scheduling problems (BMSP) are solved, where the discussed problem is represented by the sum of completion and the sum of late work times  simultaneously. In order to solve the suggested BMSP, some metaheurisitc methods are suggested which produce good results. The suggested local search methods are simulated annulling and bees algorithm. The results of the new metaheurisitc methods are compared with the complete enumeration method, which is considered an exact method, then compared results of the heuristics with each other to obtain the most efficient method.

TI1e Web service securi ty challenge is to understand  and  assess the risk  involved  in securing  a web-based  service  today, based on our existing security technology, and at the same time tmck emerging standards and  understand  how they will be used  to offset the risk in

new web services. Any  security model must  i llustrate  how data  can

now  through   an  application   and   network   topology  to  meet  the

requirements  defined  by the busi ness  wi thout exposing  the data  to undue  risk.  In this paper  we propose &n

The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.

In this paper, cubic trigonometric spline is used to solve nonlinear Volterra integral equations of second kind. Examples are illustrated to show the presented method’s efficiency and convenience.

     In this paper, we built a mathematical model for convection and thermal radiation heat transfer of fluid flowing through a vertical channel with porous medium under effects of horizontal magnetic field (MF) at the channel. This model represents a 2-dimensional system of non-linear partial differential equations. Then, we solved this system numerically by finite difference methods using Alternating Direction Implicit (ADI) Scheme in two phases (steady state and unsteady state). Moreover, we found the distribution and behaviour of the heat temperature inside the channel and studied the effects of Brinkman number, Reynolds number, and Boltzmann number on the heat temperature behaviour. We solved the system by buildi

Is in this research review of the way minimum absolute deviations values ​​based on linear programming method to estimate the parameters of simple linear regression model and give an overview of this model. We were modeling method deviations of the absolute values ​​proposed using a scale of dispersion and composition of a simple linear regression model based on the proposed measure. Object of the work is to find the capabilities of not affected by abnormal values by using numerical method and at the lowest possible recurrence.

Separation of Trigonelline, the major alkaloid in fenugreek seeds, is difficult because the extract of these seeds usually contains Trigonelline, choline, mucilage, and steroidal saponins, in addition to some other substances. This study amis to isolate the quaternary ammonium alkaloid (Trigonelline) and choline from fenugreek seeds (Trigonella-foenum graecum L.) which have similar physiochemical properties by modifying of the classical method. Seeds were defatted and then extracted with methanol. The presence of alkaloids was detected by using Mayer's and Dragendorff's reagents. In this work, trigonilline was isolated with traces of choline by subsequent processes of purification using analytical and preparative TLC techniques.

This paper presents a newly developed method with new algorithms to find the numerical solution of nth-order state-space equations (SSE) of linear continuous-time control system by using block method. The algorithms have been written in Matlab language. The state-space equation is the modern representation to the analysis of continuous-time system. It was treated numerically to the single-input-single-output (SISO) systems as well as multiple-input-multiple-output (MIMO) systems by using fourth-order-six-steps block method. We show that it is possible to find the output values of the state-space method using block method. Comparison between the numerical and exact results has been given for some numerical examples for solving different type

In this paper, a least squares group finite element method for solving coupled Burgers' problem in   2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved.  The theoretical results  show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the effic