Volume 34, Issue 3, Autumn 2016, Page 1-211

Algorithms for Multicriteria Scheduling Problems

Tariq S. Abdul-Razaq and Karar F. Abdul-Razaq

basrah journal of science, Volume 34, Issue 3, Pages 1-12

In this paper, we consider the multicriteria scheduling problem on single machine to minimize two criteria: maximum cost function, denoted by maximum late work (Vmax) and maximum earliness (Emax). We propose several algorithms based on types of objectives function to be optimized. The solutions of the proposed procedures are compared with that of the optimal solutions and Pareto optimal solutions for the smaller instance size, these algorithms dealing with hierarchical minimization problem as well as simultaneous minimization problem with and without weight. Computational results show the usefulness of these procedures.

Obtaining the suitable for cycles

Shuker Mahmood Khalil

basrah journal of science, Volume 34, Issue 3, Pages 13-18

We show that, if is odd. Then the -cycles form a single ambivalent conjugacy class in the alternating group for all . This generalize to the following result, if , then 3-cycles form a single conjugacy class in [see, (1)].

Parameters estimation for modified weibull distribution based on singly type one censored samples

and Dhfifaf Fadhil Majeed; Iden H. AL-Kanani

basrah journal of science, Volume 34, Issue 3, Pages 19-32

The three parameters distribution called modified Weibull distribution (MWD) introduced by sarhan and zaindin (2009). In this paper, we deal with point estimation to estimate the parameters of modified Weibull distribution based on complete data, using maximum likelihood method Ordinary least squares estimator method and rank set sampling estimator method to obtain the estimate parameters for modified Weibull distribution, then estimate the death function , survival function and hazard function obtained these estimate functions by applied on set of real data which taken for Leukemia disease in the Baghdad general hospital.

On Generalization of Beta Operators

Rihab R. Abdul-Rezaq; Ali J. Mohammad; and

basrah journal of science, Volume 34, Issue 3, Pages 33-44

In this present paper, we introduce a generalization definition to Beta weight functions depend on a non-negative integer r called r-Beta. This definition restricts to the classical Lupas and to the classical Beta weight functions whenever r=0,1 respectively. In addition, we used these weight functions to define two operators of summation and of summation-integral types. Surly, these operators restrict to the classical Lupas operators and to the classical Beta operators of both summation and summation-integral types whenever r=0,1 respectively. In addition, we can get the mixed operators of Lupas-Beta and Beta-Lupas for a suitable chose of integer values. Furthermore, we derive a Voronovaskaja-type asymptotic formula for the new operators from which we can get the similar formulas for many operators of summation and summation-integral types of mixed Lupas-Beta (or Beta-Lupas) weight functions and more.

Double weighted distribution

Kareema Abed AL; Kadim

basrah journal of science, Volume 34, Issue 3, Pages 51-63

In this paper, we present the Double Weighted Inverse Weibull (DWIW) using different weight functions. In particular, we derive the pdf, cdf, reliability, hazard and reverse hazard functions.

Variable Order Two Steps Runge – Kutta Method for Solving Stochastic Ordinary Differential Equation

and Mustafa M. Subhi; Fadhel S. Fadhel

basrah journal of science, Volume 34, Issue 3, Pages 64-73

In this paper, the variable order method in connection with two steps Runge – Kutta method for solving stochastic ordinary differential equations have been proposed in order to improve the accuracy of the obtained results by increasing the order of convergence of the numerical schemes. The proposed approach has been introduced for Stratonovich type stochastic differential equation.

On Riesz’s Theorem on Intuitionistic Fuzzy Measure

Mohammed J. Mohammed; Amneh Kareem Yousif

basrah journal of science, Volume 34, Issue 3, Pages 74-86

In this paper, the concepts of the property(S), property(PS) and the converse autocontinuity from below of an intuitionistic fuzzy measure on an intuitionistic fuzzy σ-algebra of an intuitionistic fuzzy sets will be introduced, and we proved Riesz’s Theorem and three forms of Riesz’sTheorem for a sequence of measurable functions on an intuitionistic fuzzy σ-algebra.

Alternating Direction Implicit Formulation of the Cosine-based DQM for Solving Navier-Stokes Equation

Mohammed J. Al-Kanani

basrah journal of science, Volume 34, Issue 3, Pages 87-93

In this article, we have discussed a new application of alternating direction implicit formulation of the differential quadrature method (ADI-DQM) (Al-Saif A.S.J. et al. 2011,2012) (1, 2) on Navier-Stokes equations . the weighting coefficient computing by Cosine expansion based. Numerical results of one example, show that the present method has been high accuracy ,good convergence comparing with using weighting coefficients is Lagrange interpolation polynomial.

Approximation by q- Bernstein Schurer-SzaszMirakyan Operators for Functions in Two Variables

Ali J. Mohammad and Rafah Fouad

basrah journal of science, Volume 34, Issue 3, Pages 94-103

In this paper, we define operators of summation-integral q-type of BernsteinSchurer – SzaszMirakyan operators F_n in two dimensional space. Firstly we restrict the operators in BernsteinSchurer operators and study the restrictionQ_n, then we discuss the convergence for the operators and then we prove a Voronovskaya- type asymptotic formula for this operators.

A Reliable Algorithm of Homotopy Analysis Method for Solving Fuzzy Integral Equations of Fractional Order

Salam A. Ahmed

basrah journal of science, Volume 34, Issue 3, Pages 104-119

In this paper, we based on the homotopy analysis method (HAM), a powerful algorithm is developed for the solution of linear and nonlinear fuzzy integral equations of fractional order. The proposed algorithm presents the procedure of constructing the set of base functions and gives the high-order deformation equation in a simple form. This method different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter h. The fractional derivative is described in the Caputo sense and the fractional integration is described in the Riemann-Liouville formula. The analysis is accompanied by some numerical examples to show the accuracy and validity of this approach.

Blocks of defect zero for the symmetric group

Najlaa Sadeq Abdullah

basrah journal of science, Volume 34, Issue 3, Pages 137-144

The main result of this paper is to find (if exist) the spin blocks of defect zero to thedecomposition matrix ofthe spin characters of the symmetric group S_non a field with characteristic p=3, also to find the general formula of the spin blocks of defect zero (if exist) to the decomposition matrices of the spin characters of the symmetric group S_n on fields with characteristic p=5,7.

Minimax arc of kind ( 0, δ ) with weighted points

Mohammed Yousif Abass

basrah journal of science, Volume 34, Issue 3, Pages 145-156

In this paper we proved that the existence of ( k, s; f ) – arcs of type ( r, s ) in PG( 2, q ); whenq=nt+1, derived from a minimax arc Cof kind ( 0, δ ), that is a ((n – 1)q+1,n) – arc. We find these ( k, s; f ) – arcswhens – r = q, as in the table below. We denote by MIN for minimal, MAX for maximal and X for neither minimal nor maximal.

On Projective Plane Over A Finite Field of Order Seventeen and its Application to Error-Correcting Codes

J.W.P. Hirschfeld; Najm A.M. Al-seraji; and

basrah journal of science, Volume 34, Issue 3, Pages 157-169

The aim of the paper is to classify certain geometric structures, called arcs. The main computing tool is the mathematical programming language GAP. In the plane PG(2,17), the important arcs are called complete and are those that cannot be increased to a larger arc. So far, all arcs up to and including size eight have been classified, as have complete 10-arcs, 11-arcs, 12-arcs, 13-arcs and 14-arcs. In the plane of order seventeen, the maximum size is eighteen. Each of these arcs gives rise to an error-correcting code that corrects the maximum possible number of errors for its length.

The primal element in integral domain

Sinan O. Al-Salihi

basrah journal of science, Volume 34, Issue 3, Pages 170-181

An element x of an integral domain R is called primal if whenever x divides a product a1a2 with a1 , a2∈ R, x can be written as x = x1x2 such that xi divides ai ,i =1,2.We study whenin X2 primal in A + X B[X] or A + X B[[X]], when A ⊆ B be an extension of domains. Also we show that if A is an integral domain and S ⊆ A a splitting multiplicative system, then A+XAS[X] is a semirigid GCD-domain if and only if A is a semirigid GCD-domain and for each two elements of S, one of them divides the other.

Robust Hotelling's Statistic for Test A Hypothesis of Mean Multivariate Population Based on RMCD

Abdullah A. Ameen; Mohand N. Abdul - Seid

basrah journal of science, Volume 34, Issue 3, Pages 182-195

Hotelling’s statistic is an important to test a hypothesis about the mean of a multivariate normal population with location and scale parameters (with the proposition that the scale parameter is unknown positive definite matrix ) . However, hypothesis test based on this statistic can be adversely affected by outliers. In this paper, an alternative technique is proposed based on a statistic which uses the reweighted minimum covariance determinant (RMCD) estimators instead of the classical mean vector and covariance matrix . A simulation technique has been used as a technique to make a comparison between the classical and the proposed statistic by generating the data that have a contaminated multivariate normal distribution from one side and from two sides . The results have shown that, the proposed robust statistic is almost better than the classical statistic depending on the rates of type I error and the power test.

Classification of The Projective Line of Order Nineteen and its Application to Error-Correcting Codes

Emad Bakr Al-Zangana; and James Hirschfeld

basrah journal of science, Volume 34, Issue 3, Pages 196-211

In this paper, the -sets in the projective line of order nineteen up to are classified and their stabilizer groups also computed. Also, the projective line spilt into five tetrads of type harmonic, equianharmonic and neither harmonic nor equianharmonic. Finally, the applications of these sets into error-correcting codes are given.