Real life scheduling problems require the decision maker to consider a number of criteria before arriving at any decision. In this paper, we consider the multi-criteria scheduling problem of n jobs on single machine to minimize a function of five criteria denoted by total completion times (∑), total tardiness (∑), total earliness (∑), maximum tardiness () and maximum earliness (). The single machine total tardiness problem and total earliness problem are already NP-hard, so the considered problem is strongly NP-hard.

We apply two local search algorithms (LSAs) descent method (DM) and simulated annealing method (SM) for the 1// (∑∑∑

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

       Canonical correlation analysis is one of the common methods for analyzing data and know the relationship between two sets of variables under study, as it depends on the process of analyzing the variance matrix or the correlation matrix. Researchers resort to the use of many methods to estimate canonical correlation (CC); some are biased for outliers, and others are resistant to those values; in addition, there are standards that check the efficiency of estimation methods.

In our research, we dealt with robust estimation methods that depend on the correlation matrix in the analysis process to obtain a robust canonical correlation coefficient, which is the method of Biwe

In this study, we investigate about the estimation improvement for Autoregressive model of the third order, by using Levinson-Durbin Recurrence (LDR) and Weighted Least Squares Error ( WLSE ).By generating time series from AR(3) model when the error term for AR(3) is normally and Non normally distributed and when the error term has ARCH(q) model with order q=1,2.We used different samples sizes and the results are obtained by using simulation. In general, we concluded that the estimation improvement for Autoregressive model for both estimation methods (LDR&WLSE), would be by increasing sample size, for all distributions which are considered for the error term , except the lognormal distribution. Also we see that the estimation improve

Rutting is one of the major distresses in pavement. The objective of this paper is to develop an improved asphalt binder grading system for Iraq based on the principal of Superpave system, and increasing performance grade of product asphalt binder in Iraq using polymers without raising the viscosity of the binder. Two types of polymers are used, Plastomers, Functionalized Polyethylene (PE) which is developed by asphalt research group in Wisconsin University in the USA, and Elastomers, Styrene Butadiene Styrene (SBS) with and without cross linker. Mastercurve are drown for these modified binders, Rolling thin film aged, to show effects on rheological properties at high temperature for complex modulus (G*) and phas

Finding orthogonal matrices in different sizes is very complex and important because it can be used in different applications like image processing and communications (eg CDMA and OFDM). In this paper we introduce a new method to find orthogonal matrices by using tensor products between two or more orthogonal matrices of real and imaginary numbers with applying it in images and communication signals processing. The output matrices will be orthogonal matrices too and the processing by our new method is very easy compared to other classical methods those use basic proofs. The results are normal and acceptable in communication signals and images but it needs more research works.

Abstract: The aim of the research identify the effect of using the five-finger strategy in learning a movement chain on the balance beam apparatus for students in the third stage in the College of Physical Education and Sports Science, as well as to identify which groups (experimental and controlling) are better in learning the kinematic chain on the balance beam device, has been used The experimental approach is to design the experimental and control groups with pre-and post-test. The research sample was represented by third-graders, as the third division (j) was chosen by lot to represent the experimental group, and a division Third (i) to represent the control group, after which (10) students from each division were tested by lot to repr

The research aims to identify the impact of using the electronic participatory learning strategy according to internet programs in learning some basic basketball skills for middle first graders according to the curricular course, and the sample of research was selected in the deliberate way of students The first stage of intermediate school.As for the problem of research, the researchers said that there is a weakness in the levels of school students in terms of teaching basketball skills, which prompted the researchers to create appropriate solutions by using a participatory learning strategy.The researchers imposed statistically significant differences between pre and post-test tests, in favor of the post tests individually and in favor of

Boltzmann mach ine neural network bas been used to recognize the Arabic speech.  Fast Fourier transl(>lmation algorithm has been used t() extract speciral 'features from an a caustic signal .

The  spectral  feature size is reduced by series of operations in

order to make it salable as input for a neural network which is used as a recogni zer by Boltzmann Machine Neural  network which has been used as a recognizer for phonemes . A training set consist of a number of Arabic phoneme repesentations, is used to train lhe neuntl network.

The neural network recognized Arabic. After Boltzmann Machine Neura l    network   training  the  system   with