Document Sample

٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ International conference of mathematics and its applications 1-3 March 2011 Under the slogan ((By Mathematics sciences progress and nations develop)) The conference is promoted by "The two Mathematics Departments at the colleges of Science and Education" University of Basrah. 1 ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ ١١٠٢ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Contents Sponsors 3 Welcome 4 Word of Dean of the College of 5 Education Committees 6 Abstracts 8 Keynote Speakers 06 Participants 16 2 ﺍﳌﺆﲤﺮ ﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ ١١٠٢ ional confere of mathe Internati ence its ons hematics and i applicatio ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ــــــــــــــــــــ ــــــــــــــــــــ ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Sponsors • Ministry o higher Education and Sci M of esearch ientific Re • Basra Uni B iversity • College of Educatio C f on • Internation Conf I nal ference in Mathema atics and its Applic )CMA cations(IC 3 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Welcome A big welcome to all the participants. We are pleased to hold the International Conference of Mathematics and its Application at the Department of Mathematics-College of Education /Basrah University; with the co-operation of the Department of Mathematics /College of Sciences. This conference will feature the recent research developments in: Topology, Numerical Analysis and Differential Equations, Statistics, Optimization, Algebra, Functional Analysis , Mathematical Analysis and other applications in the science of Mathematics. It will bring together experts in these fields in the hope of promoting scientific exchange and discussing possibilities for further co-operation for all participants. The participants will present their results and discuss further new developments concerning applicable methods in their fields. The conference will feature lectures by the invited and keynote prominent mathematicians and will illustrate or provide the opportunity for regional researchers to present their latest work. It is hoped that a refereed proceeding will be published after the conference in the journal of Basrah Research (Section of Sciences).This will be subject to the usual rigorous refereeing process of the journal. We hope you will gain much from this conference and will find your involvement meaningful and worthwhile. If you have come from overseas or from other cities in Iraq we wish you a pleasant and enjoyable stay in Basrah-IRAQ. Thanks for all; thanks for your co-operation and encouraging to the conference. Organizing Committee 4 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ The 1St International Conference on Mathematics and It's Application Compassionate In the name of Allah, The Beneficent, the Merciful. 1. The Beneficent. 2. Hath made known the Quran. 3. He hath taught him utterance. 4. The sun and the moon are made punctual. The BENEFICIENT. Mathematics and language are the most important of human mind innovations since the emergence of human civilization. They represent communication means of the highest significance among individual, communities and peoples at large. This is evidenced by what is used in our daily life, beginning from the concepts of point, straight line, areas, volumes, motions and dealings in our livable linear world or of multidimensional worlds. Advancement of nations and their perspective of life and the universe reflects advances in mathematics and its applications. However, mathematics has many advantages over languages by being more precise and not constrained by national or geographic borders. Thus, making it more communicable among all disciplines especially in sciences, engineering, economy and medicine. Despite its utmost significance, education circles at all levels in Iraq have not given it proportionate consideration. We can notice refrainment from the subject matter of mathematics among students at pre university education and at its outset. Such response of dislikeness indicates our failure in presenting the subject matter in a way that is interactive enough to create a feeling of likeness up to understanding. On the other hand, contextual constraints, social and economic considerations set aside the best, high school graduates with the highest scores moving toward medical and engineering colleges. Eventually, we end up with students enrolling in Mathematic departments either against their wishes or of low scores; and consequently teachers or graduates of quality less than what is needed to carry out fine teaching or research. It is teaching of low quality for learning. As a result, many families resort to sending their kids to private education delineating privileged and unprivileged peoples in the same society. What we hope to achieve in this conference and upcoming ones beside scientific gains is to come out with viable and workable suggestions and recommendation, to address this problem. In other words, recommendations that can be transformed into appropriate curricula and teaching methods utilising advances in teaching technology that can stimulate students minds and vitalize their brains to be mathematically oriented in one way or another. Moreover, we have to think of providing some incentive measures by granting scholarships to college students to encourage secondary school graduates with high scores to enroll in departments of mathematics. In essence, we ought to embark on a national program for improving and upgrading mathematical learning taking into consideration successful experiments abroad. Finally, colleges of education and science and directorate general of education should play a crucial role in this respect. Wishing all of you success and fine stay in Basrah with Allah blessing. Prof. Amin A. Al-Sulami Dean college of education Basra university 5 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Supervisory committee Prof. Dr. Saleh E. Nejim (chairman) Prof. Dr. Amin A. Abdullah (member) Assist. Prof. Dr. Falih H. Al-Khudair (member) Assist. Prof. Dr. Abdul-Sattar J. Al-Saif (member) Organizing Committee Assist. prof. Dr.Abdul-Sattar J. Al-Saif (chairman) Assist. prof. Dr. Saeed A. Taban (vice chairman) Assist. prof. Dr. Habeeb M.Abood (secretary) Assist. prof. Dr. Abdul Hussen S. Al-Mouel (member) Assist. prof. Dr. Yehea H.Saleem (member) Assist. prof. Dr. Housam L. Saad (member) Assist. prof. Dr. Ali J. Mohammad (member) Assist. prof. Amira Jaber (member) Assist. prof. Ban M. Saleem (member) Lecturer Dr. Ayad R.Kudair (member) Lecturer Khaled A. Abdul-Zahera (member) Lecturer Ali Abdul-Amir Alwan (member) Lecturer Jasim Mohammed Ali (member) Lecturer Ali Hussain Reson (member) Lecturer Ansam Ahmed Abdul-Rahman (member) International Committee of ICMA Prof. Dr. Saleem H. Al-Kutubi (Iraq) – Chairman Prof. Dr. Abdul-Adhim M. Al-Sudani (New Zealand) –1st -Vice Chairman Prof. Dr. Mohamed A. Al-Lawati (Oman) –2nd-Vice Chairman Members Prof. Dr. Tariq S.Abdul-Razaq Iraq Prof. Dr. Ahad Rahimi Iran Prof. Dr. Mohammad Taghi Darvishi Iran Prof. Dr. Dhwyia Salman Hassun Iraq Prof.Dr.Abdul-Rahman H.Majeed Iraq Assist. Prof. Dr.Noori F. Al- mayahi Iraq Assist. Prof. Dr.Abdul-Sattar J. Al-Saif Iraq Assist.Prof. Dr. Nemat Nyamoradi Iran Assist.Prof. Dr. Ali Farajzadeh Iran Assist. Prof. Dr.Fadhel S.Fadhel Iraq Assist. Prof. Dr. Radhi A. Zboon Iraq 6 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ International Advisory Board Prof. Dr. Abdul-Adhim M. Al-sudani (New Zealand) Prof. Dr. Ahad Rahimi (Iran) Prof. Dr. Mohamed A. Al-Lawati (Oman) Prof. Dr. R.R. Bhargava (India) Prof. Dr. Abdul-Maqsod A. Suleaman (Egypt) Assist.Prof. Dr. Kamal H. Yasier (Iraq) Assist.Prof. Dr. Ali Farajzadeh (Iran) National Advisory Board Dr. Tariq S. Abdul-Razaq (Al-Mustansiriya Univ.) Dr. Abdul-Rahman H. Majeed (Baghdad Univ.) Dr. Abdul-Hussein Saber (Basrah Univ.) Dr. Abdul –Nabi I. Ibrahem (Basrah Univ.) Dr. Mohmmed J. Mohmmed (Thi-Qar Univ.) Dr. Ra’ad Saleh Mahdi (Basrah Univ.) Dr. Baseem N. Abood (Technology Univ.) Dr. Osama H. Mohammed (Al-Nahrain Univ.) Dr. Abba s K. Al Khafaji (Basrah Univ.) Dr. Mudher A. Abdul-Hussien (Basrah Univ.) Dr. Fuad K. Hameed (Basrah Univ.) Dr. Hanna M. Ali (Basrah Univ.) 7 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Simulating the Markov Renewal Process Abdul – Kareem I. Sheet Remote Sensing Center, University of Mosul –Iraq. Nadia Adeel Saeed Department of Physics- College of Sciences- University of Mosul-Iraq. , Sawsan Jawad Kadhum Department of Mathematics, College of Education - Ibn Al-Haitham , University of Baghdad-Iraq. Abstract The simulation technique is one of the common computational tools used to imitate and follow up complex real life systems and their development with time. Variables of a disease problem were defined and the mathematical model for this problem was constructed. The numerical solution of this model was compared with the computational simulation of Markov Renewal Process of the type '' Birth and Death .The results we obtained show the efficiency of the simulation technique and through out the extended time period's episodes. Single machine scheduling to minimize three criteria hierarchically Haidar younis kawi Department of Math. College of Computer Science, Al_Qadisiya University-Iraq. Email: hadirkawi@yahoo.com Tariq Salih Abdul-Razaq Department of Math, College of Science and Mathematics, AL-Mustansiriya University-Iraq. Abstract In this paper, to minimize a function of three cost criteria for scheduling n jobs on a single machine , the problem is discussed : {Minimizing a function of three criteria Tmax ,Emax and ∑Ci2 in hierarchical method }. A set of n independent jobs has to be scheduled on a single machine that is continuously available from time zero onwards and that can handle no more than one job at a time. Job Jj(j=1, . . . , n) requires processing during a given positive uninterrupted time pj, without loss of generality, we assume pj to be integral. For the problem we proposed some algorithms and procedure to find the exact and best possible solutions for three criteria Tmax ,Emax and ∑Ci2 in hierarchical case. 8 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Innovative Strategies to Teach Statistics Nazera Khalil Mathematics Department, College of Mathematics and Computer Sciences, University of Kufa-Iraq. Abstract This research is mainly concerned with novel methods to teach statistics. It looks into the relevance understanding some properties of the average (the arithmetic mean) to students’ general education in order to access its importance and place in curriculum design and to assess the effects of different teaching methods, materials and media of presentation on student’s understanding of that concept. Teaching materials were designed and put into practice with a group of students. One of the two groups followed the teaching materials that were taught by us, using innovatory and various other teaching strategies. The other group was taught by their usual teacher using standard teaching methods. We compared the learning outcome of both methods, and evaluated teaching methods and materials. On Solution of Two Point Second Order Boundary Value Problems using Semi-Analytic Method Luma. N. M.Tawfiq Department of Mathematics, College of Education-Ibn Al-Haitham, University of Baghdad-Iraq. Khalid. M. M. Al-Abrahemee Department of Mathematics, College of Education, Al-Qadissiya University-Iraq. Abstract In this paper a new method is proposed for the solution of two-point second order boundary- value problems( TPBVP ) ,that is, we are concerned with constructing polynomial solutions to two point second order boundary value problems for ordinary differential equation. A semi-analytic technique using two-point osculatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0,1] is compared with conventional methods via a series of examples and is shown to be that it seems to converge faster and more accurately than the conventional methods and generally superior, particularly for problems involving nonlinear equations and/or boundary conditions. Also we introduce some general observations about control of a residual and control of the true error and we prove, there is a more useful connection between scaled residual and true error. 9 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Improving Gradient Descent method For Training Feed Forward Neural Networks Luma. N. M.Tawfiq Department of Mathematics, College of Education-Ibn Al-Haitham, University of Baghdad-Iraq. Alaa. K. J. AL-Mosawi Department of Mathematics, College of Education, Al-Qadissiya University-Iraq. Abstract In this paper, many modified and new algorithms have been proposed for training feed forward neural networks, many of them having a very fast convergence rate for reasonable size networks. In all of these algorithms we use the gradient of the performance function (energy function, error function) to determine how to adjust the weights such that the performance function is minimized, where the back propagation algorithm has been used to increase the speed of training. The above algorithms have a variety of different computation and thus different type of form of search direction and storage requirements, and all the above algorithms applied in approximation problem. On Coconvex Approximation In , , ∞ Habeeb A.Kadhim Department of Mathematics ,College of Computer and Mathematics Science ,Thi- Qar University , Iraq. Abstract Let a function , which changes convexity finitely many times at by peicewise polynomial and dividing differences for the interpolating polynomial which are Coconvex with it. In this paper we discuss the estimate of the degree of approximation of by using the divided difference and weighted D.T. modulus of smoothness. 10 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Essentially Prime Modules and Related Modules Inaam Mohammed Ali Department of Mathematics, College of Education-Ibn Al-Haitham, University of Baghdad-Iraq. Tha'ar Younis Ghawi Department of Mathematics , College of Education University of AL-Qadissiya-Iraq. E-mail: tharali_1988@yahoo.com & tthhaaaarr@yahoo.com Abstract Let R be a commutative ring with unity . An R-module M is called prime if, annR M = annR N for each nonzero submodules N of M . In this paper we introduce and study the concept of essentially prime module as a generalization of p 7-decomposition matrix for the spin characters of the symmetric group Saeed A.Taban and J. A. Resen Mathematic Department, College of Since, University of Basrah-Iraq. Abstract The main objective of this paper is to determine the decomposition matrix for the spin characters of the symmetric group for 7. Decomposition Matrix of the Projective Characters of S 16 Modules 5 Saeed Abdul- Ameer Taban and Najla'a Sadiq Abduallah Department of Mathematics, College of Science , Basrah University; Iraq. Abstract The main purpose of this paper is to compute the decomposition matrix of the projective characters of the symmetric group S 16 modulo 5, by using the method of ( r , r ) - inducing. The work is complete except one column remaining undetermined. 11 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ The Homotopy Perturbation Method for Solving K(2,2) Equation Abdul-Sattar J. Al-Saif and Dhifaf A. Abood Department of Mathematics, College of Education, University of Basrah, Basrah, Iraq. Abstract In this paper, we present homotopy perturbation method (HPM) for solving the Korteweg-de Vries (KdV) equation and convergence study of homotopy perturbation method for nonlinear K(2,2) equation. We compared our solution with the exact solution and homotopy analysis method (HAM). The results show that the HPM is an appropriate method in solving the nonlinear equation. The Solution of Diffusion And Exothermic Zero By Using Newton – Kantorovich Method Eman Ali Hussan Department of Mathematics, College of science ,AL-Mustansiriyah University, Iraq Muntaha K. Abbas Foundation Technical Education, Technical College Management ,Iraq Abstract This paper included a solution of a diffusion and exothermic using Newton- Kantorovich method. The Newton- Kantorovich method is used to convert the nonlinear two points boundary value problem into linear boundary value problem , and then using a numerical method to solve the linear boundary value problem. The numerical method is suitable based on a finite – difference method, the central-difference scheme was considered herein since it gave a good results and thus obtaining small error . The central difference method is preferable over backward or forward difference scheme. Finally ,some numerical examples followed in this paper show that the proposed methods , and the results have a good agreement compared with that of the exact solution .The use of finite- difference method produced a system of linear algebraic equations which are solved by using the MATLAB computer software. 12 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ COMPUTATION OF ODD MAGIC SQUARE USING A NEW APPROACH WITH SOME PROPERTIES Shatha A. Salman, Nuha A. Rejab, Fuad A. Al-Heety Department of Applied Sciences, University of Technology, Iraq. Shatha.alnajar@yahoo.com Nuha1900@yahoo.com FuadHeety@yahoo.com Abstract Several aspects of magic square studies fall within the computation of all universes.Some of the experimental computations as reverted patterns, have lead to analytic insight. With the aid of arithmetic modular and its property , we get magic squares. Also, we use the algebraic operation of matrices which include addition, subtraction, multiplication, transpose, rotation, and re°ection, then we discuss the results that are obtained. The eigenvalue of this magic squares is also computed and we get some magic squares with the same eigenvalues, the inverse of the matrices are also found. An example with order 3 of magic square is given to explain our obtained results. A CLASS OF UNIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS DEFINED BY HADAMARED PRODUCT WITH ((RAFID – OPERATOR)) BY APPLYING A NEW FRACTIONAL CALCULUS Rafid Habib Buti and Salah Mahdi Ali Department of Mathematics, College of Computer Science and Mathematics, University of Al- Qadissiya- Iraq Rafidhb@yahoo.com Salah_x9@yahoo.com Abstract In the present paper , we have studied a class of univalent functions by applying a new fractional calculus , we obtain distortion theorem , wighted mean , arithmetic mean and some other results . 13 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ TWO-WAY MRM ANCOVA MODEL WITH TWO COVARIATES Abdul-Hussein Saber Al-Mouel and Atyaf S. Fakhir Department of Mathematics, College of Education, University of Basrah , Iraq. Abstract This research is devoted to study the two-way Multivariate repeated measurements analysis of covariance model (MRM ANCOVA), which contains two between-unites factors (factor A and factor B), two within-units factors (Time and Day) and two covariates , .For this model the two covariates are time-independent, that is measured only once. The test statistics of various hypotheses on between-unites factors, within-units factors and the interaction between them is given, including its application to study the effect of some internal and external factors on blood parameters, which is available in the experiment during one year through nine months. The initial Fuzzy Semi-Normed ( Normed ) Vector Space I Noori Farhan AL-Mayahi and Salah Mahdi Ali Department of Mathematics, College of Computer Science and Mathematics, Al-Qadisiya University ,Iraq. Abstract In this paper, we introduce a new definition of the initial fuzzy vector topology , the initial fuzzy semi-normed ( normed ) vector space and we proved that the initial fuzzy vector topology has a base at zero. 14 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ The transformations induced on hypersurfaces of almost Hermitian manifolds Anna V. Nikiforova and Lia A. Ignatochkina Department of Topology and Geometry, College of Mathematics, Moscow State Pedagogical University Moscow-Russia Abstract In this paper the authors study the transformations on hypersurfaces of almost Hermitian manifolds. It’s known that the almost contact metric structure is defined on hypersurfaces of almost Hermitian manifolds. The holomorphic projective transformations of almost Hermitian manifolds induce the transformations of the almost contact metric structure. These transformations were called the contact projective transformations. The main result of this paper is that each holomorphic almost geodesic is not invariant under contact projective transformations. The transformations induced by conformal transformations on T 1 - bundle. Lia A. Ignatochkina and Pavel B. Morozov Department of Topology and Geometry, College of Mathematics, Moscow State Pedagogical University Moscow-Russia Abstract The paper studies the transformations on T 1 - bundle. The almost Hermitian structure is defined on T 1 - bundle’s base. The conformal transformations of this almost Hermitian structure induce the transformations of T 1 - bundle’s almost contact metric structure. The correlations between adjoined G − structures of T 1 - bundle’s almost contact metric structure and transformed almost contact metric structure were obtained. The conditions of invariance for some almost contact metric structures were obtained. 15 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ DIFFERENTIAL TRANSFORM METHOD FOR SOLVING FUZZY FRACTIONAL INITIAL VALUE PROBLEMS Osama H. Mohammed Fadhel S. Fadhel Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Iraq. Fajer A. Abdul-Khaleq Department of Computer Science,Dijlah University College, Iraq. Abstract In this paper we present an approximate analytical solution for fuzzy fractional initial value problems (FFIVP's) of the form: y(q)(x) = f(x, y(x)), p − 1 < q ≤ p, p ∈ Ν y(j)(a) = y ja , j = 0, 1, …, p −1 where the fuzzyness appeared in the initial conditions, to be fuzzy numbers, using the differential transform method. The solution of our model equations is calculated in the form of convergent series with easily computable components. Some examples are solved as illustrations using symbolic computation. The numerical results show that the followed approach is easy to implement and accurate when applied to fractional fuzzy initial value problems. Cancellation and Weakly Cancellation Fuzzy Modules Inaam, M.A.Hadi and Maysounm , A. Hamil Department of Mathematics, Ibn – Al-Haithm college of Education ,Baghdad University ,Iraq. Abstract In this paper , we introduce and study (cancellation, weakly cancellation) fuzzy modules as a generalization of notations cancellation, weakly cancellation modules . We give many basic properties about both concepts. 16 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ The Use of Reduced Differential Transform Method for Solving Partial Differential Equations with Variable Coefficients Bushra A.Taha Department of Mathematics; College of Science; University of Basrah ,Basrah, Iraq. Abstract In this paper, we apply the Reduced Differential Transform Method (RDTM) for solving partial differential equations in different dimensions with variable coefficients, which did not use the method previously. The results show that this method is very effective and simple . Review of Continued Fractions Solutions of Riccati Equations And Integrable Lattice Equations Salah Taha Hafez Aly Higher Technological Institute, 6th October branch. Egypt Abstract Continued fraction solutions to the matrix Riccati equation are discussed. The relation between the elements of the continued fraction and the coefficients of the matrix Riccati equation is used to generate a class of well known non-linear lattice equations. It is demonstrated that the relation between the elements of the continued fraction and the power series was used to construct a new approach for linearising these equations. This method of linearisation is extended to other lattice equations solvable in the framework of the discrete A.K.N.S. system if a boundary condition is imposed at the finite end. A connection with this discrete A.K.N.S. system is found. Other non-linear lattice equations obtained as the compatibility condition between two linear systems are linearised and solutions of these lattice equations are obtained. This new approach of linearisation illustrates the important role played by the boundary condition at the finite end of the lattice. 17 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ A three species ratio-dependent food web model dynamics Raid Kamel Naji and Alaa Jabbar Badai Department of Mathematics;College of Science; University of Baghdad;Iraq Abstract In this paper, a three species ratio-dependent food web model consisting of a prey, specialist predator and generalist predator is proposed and analyzed. The dynamical behavior of all possible subsystems is carried out. The stability analysis of all nonnegative equilibrium points is investigated. The persistence conditions for the proposed food web model are established. Finally, the local as well as global stability of the positive equilibrium point of the food web model are discussed. It is proved that the proposed food web model is persistence and globally asymptotically stable under some appropriate conditions. A NEW SUBCLASS OF ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS ABDUL RAHMAN S. JUMA Department of Mathematics, College of Science, Al-Anbar University, Iraq S. R. KULKARNI Department of Mathematics, Fergusson College, Pune - 411004, India Abstract In this paper we have introduced and investigated a new subclass of analytic functions in the unit disc. We derived various properties and characteristics for functions belonging to this class. 18 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Farctional Calculus Operators of A New Class of Uniformly Convex Functions Waggas Galib Atshan and Hesham Rehman Mohamad Department of Mathematics, College of Computer Science and Mathematics, University of AL- Qadisiya Diwaniya – Iraq Abstract In the present paper, we study a new class of analytic and univalent functions with negative coefficients defined by using a certain fractional differential and fractional integral operators. We obtain good results, like, The characterization property, Growth and Distortion theorem and results involving modified Hadamard product. We also study the integral transform of the class WAGG( µ , γ ,η , θ , α , l ). On approximate observability of strongly stable linear perturbed SlyvesTer system Samir Kasim Hassan Department of Mathematics; College of Education; Al-Mustansirya University; Iraq. Abstract The Jacob and Zwart test is sufficient for approximate observability if the system is strongly stable . In this paper we show by means of an example that this statement hold for generalized strongly stable linear perturbed slyvester systems even if the system is modeled by a contraction perturbed Composite semigroup . 19 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ The Cyclic Decomposition of The Factor Group cf(Dnh×C2,Z)/R(Dnh×C2) When n is an Odd Number Hussien Hadi Abass Department of Mathematics, College of Education for Girls, AL-Kufa University,Iraq Kareem Abass AL-Ghurabi Department of Mathematics, College of Education, Babylon University,Iraq Abstract Let Dn be the dihedral group , C2 be the cyclic group of order 2 and Dnh is the direct product group of Dn and C2 (i.e. Dnh=Dn×C2) . Let cf(Dnh×C2,Z) be the abelian group of Z-valued class functions of the group Dnh×C2 . The intersection cf(Dnh×C2,Z) with the group of all generalized characters of Dnh×C2 which is denoted by R (Dnh×C2) , is a normal subgroup of cf(Dnh×C2,Z) denoted by R (Dnh×C2) , then factor group cf(Dnh×C2,Z)/ R (Dnh×C2) is a finite abelian group denoted by K(Dnh×C2) . The problem of determining the cyclic decomposition of the group K(Dnh×C2) seem to be untouched .The aim of this paper is to find the cyclic decomposition of this group . To do this work we use some concepts of linear algebra to find 1. The rational valued characters table of the group Dnh×C2 when n is an odd number . 2. The invariant factors matrix of the group Dnh×C2 when n is an odd number . 3. The cyclic decomposition of the factor group K(Dnh×C2) . m We find that when n is an odd number such that n = ∏ p iα i , where all pi ' s are distinct i =1 ⎡ ⎡ ⎤ ⎤ ⎢ m ⎥ ⎥ (α1+1)⋅(α2+1)⋅........⋅(αm+1)+2 2(α1+1)⋅(α2+1)⋅........⋅(αm+1)+1 ( ( )) ⎢m (αj +1)⎥time⎥ 4 ∑ ∑ α primes , then: K(Dnh×C2)= ⊕⎢⊕ ⊕ K Cpii i =1 ⎢∏ ⊕ i =1 C4 ⊕ i= 1 C2 ⊕ C 8 . ⎢ i =1 j ≠i ⎢ j =1 ⎥ ⎥ ⎣ ⎣ ⎦ ⎦ S-COPRIME MODULES Inaam A. M. and Rasha K. I. Department of mathematics, College of Education Ibn-Al-Haitham, University of Baghdad,Iraq Abstract Let R be a commutative ring with unity, M an R-Module. M is called coprime if ann M ann = Μ Ν R R for each proper submodule N of M. In this paper we introduce the notion of s-coprime as a generalization of coprime modules by restricting the above definition to small submodules of M. 20 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Counter Example for Solving Systems of Differential Equations by Repeated Eigen Values Saad Naji Al-Azawi Department of Mathematics; College of Sciences for women; Baghdad University;Iraq Abstract In this paper we give a counter example to show that the construction of n linearly independent solutions of when an eigenvalue has multiplicity n is not true in general because it leads to the contradiction that a zero vector is an eigenvector Estimate Survival Function for the Brain Cancer Disease by Using Three Parameters Weibull Distribution Iden Hassan Al – Kanani and Shaima Abbass Jasim Department of Mathematics;College of Sciences for women; Baghdad University;Iraq Abstract In this research we derive and find the survival probability function , hazard probability function and failure (death) probability function for three – parameters Weibull distribution of the brain cancer in complete data. To satisfy and estimate all parameters (shape, scale and location) we use two classical methods (MLE method and OLS method) to find the survival function. We depend on a sample from real data which describes the duration of survivor for patients who suffer from the brain cancer based on diagnosis of disease or the enter of patients in a hospital for the period 1/1/2009 until 31/12/2009 .We calculate and estimate all previous probabilities functions , then compare the numerical results by using the mean squares error measure to survival probability function, reaching that the survival function for the brain cancer by using maximum likelihood method is the best. 21 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Solving a Tri-Diagonal System of Size N Equations by Stair-Diagonal Approach Anwar Ja'afar Mohammed Jawad Faculty of Electrical Engineering, University of Technology, Iraq Abstract The proposed program deals with solving a set of simultaneous linear algebraic tri-diagonal system of equations of order (N×N). The tri-diagonal system of equations is represented as a tri- diagonal matrix with even or odd numbers of equations N. The tri-diagonal matrix is eliminated and converted to a stair-diagonal matrix by four steps. A flow chart is designed to implement the proposed algorithm. Two numerical examples for odd and even numbers of equations are presented to apply the proposal algorithm. Results showed that the proposed algorithm is efficient and can be used as a subroutine program to solve the tri-diagonal system of equations of order (N×N). Newton-Kantorovich method for non-linear Sturm-Liouville problems Hussien Ali Hussien, Renna D. Abdul-Wahab and Mohammed Ali Ibraheem Department of Mathematics, College of Science, University of Basrah ,Iraq Abstract In this work the Newton-Kantorovich method is applied to the non-linear Sturm-Liouville problems subject to linear homogeneous boundary conditions. And we compare the result of this method with the result of the series solution of Adomian’s decomposition method at a specified eigenvalue parameter. Parallel Algorithm To Solve The Mathematical Model To Fight The Armed Gangs Sadiq A. Mehdi Department of Computer Science, College of Education, Al-Mustansiriya University ,Iraq Abstract Aim of this paper, constructing a mathematical model to fight the armed gangs, including a set of differential equations , and being based on Parallel Algorithm we solved this model by using a Mathematical program. 22 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Tri- Cofibration and Tri- Hurewicz Cofibration Daher Waly Freh Department of Mathematics, College of Science, University of Wassit ,Iraq Abstract In this paper we study a new concept namely Tri- cofibration (T-cofibration) and Tri- Hurewicz cofibration (T-Hurewicz cofibration). Most of the theorem which are valid for cofibration will be also valid for (T-cofibration) the others will be valid if we add an extra condition .Among the result we obtain are: 1-A product of two Tri- Cofibration(Tri- Hurewicz cofibration) is also a Tri- Cofibration(Tri- Hurewicz cofibration) 2- The M-pullback of Tri- Cofibration(Tri- Hurewicz cofibration)is also Tri- Cofibration(Tri– Hurewicz cofibration) FREE ACTIONS ON PRIME AND SEMIPRIME RINGS Fatin A. Fadhil Department of Mathematics, College of Science, University of Baghdad, IRAQ e-mail:fatinalsaadymath@yahoo.com A.H.Majeed Department of Mathematics, College of Science, University of Baghdad, IRAQ e-mail:ahmajeed@yahoo.com Abstract Let R be an associative ring with center Z(R). We identify some situations where mappings related to left reverse-centralizer, derivations are free actions on prime and semiprime rings. We show that for a left reverse - centralizer of a semiprime ring R the mapping :R→R defined by ψ x T x , x , for all x R is a free action. We also show that for a generalized derivation F of a semiprime ring R , if a R is a dependent element of F, then a Z(R). Furthermore, we prove that for a left reverse-centralizer T and a derivation d of a prime ring R, ψ T d is free action. 23 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Three Modes Bifurcation Solutions of Nonlinear Fourth order Differential Equation Ahmed K. Shanan and Mudhir A. Abdul Hussain Department of Mathematics , College of Education , University of Basrah , Basrah, IRAQ. Abstract In this paper, we are interested in the study of three modes bifurcation solutions of nonlinear wave equation of elastic beams located on elastic foundations by using the local method of Lyapunov -Schmidt. We showed that the bifurcation equation corresponding to the elastic beams equation is given by a nonlinear system of three quadratic equations. Also, we determined the bifurcation diagram of the specified problem. Tanh Method for Solutions of Nonlinear Evolution Equations Anwar Ja'afar Muhammad-Jawad Electrical Engineering, Department, University of Technology, Baghdad, Iraq. Abstract This paper applied the tanh method for analytic study for the nonlinear coupled KdV systems of PDEs. Compared with existing sophisticated approaches, the proposed method gives more general exact traveling wave solutions without much extra effort. Two applications from a literature of nonlinear systems of PDEs were solved by the method. The calculations demonstrate the effectiveness and convenience of the method for nonlinear system of PDEs. FINITELY HOLLOW-LIFTING MODULES Ali A. Hassan and Bahar H. AL-Bahraany Department of Mathematics,College of Science, University of Baghdad, Iraq Abstract Let R be any ring and let M be any left R-module. We say that M is called a finitely hollow-lifting module (or briefly f-hollow lifting) if every finitely generated submodule N of M with hollow, has a coessential submodule in that is a direct summand of M. The main purpose of this paper is to develop the properties of f-hollow-lifting modules. Also, we study the relation between the projectivity and f-hollow-lifting modules. We prove that for a projective module P, P is f-hollow- lifting module if and only if for every submodule A of P with hollow, has a projective cover. 24 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ EXTENSIBILITY OF GRAPHS Akram B. Attar Department of Mathematics, Faculty of Education,University of Thi-Qar,Iraq Abstract In this paper, the concepts of extension of a graph(digraph) and the extensible class of graphs(digraphs) have been introduced. The class of connected graphs as well as the class of Hamiltonian graphs which are extensible classes have also been proved. The classes of regular, eulerian, bipartite and trees graphs which are not extensible classes have also been proved. The concept of extensibility number has been introduced as well as the characterization of regular graphs(digraphs) which have extensibility number k . Also the extensibility number of eulerian graphs(digraphs) has been characterized. Equivalence between the category of Cat¹-complexes and the category of crossed modules of complexes Ra'ad S. Mahdi and Ihssan A. Fadhel. Department of Mathematic , College of Science, University of Basrah, Iraq Abstract In this paper, we introduce the notion of cat¹-complexes as a suitable generalization of the cat¹- groups through embedding the category of cat¹- groups in the category of Cat¹-complexes as a subcategory ( via isomorphism of categories). It was shown that the category of Cat¹-complexes is equivalent to the category of crossed modules of complexes as well as the couple of two covariant functors used to show the equivalence between these two categories are represent an adjoint pair of functors. 25 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Explicit Runge-Kutta Methods for Solving Stochastic Differential Equations Fadhel S. Fadhel and Ali Amjed Abdul-Ameer Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University Abstract The main objective of this paper is to derive explicit Runge-Kutta methods for solving stochastic ordinary differential equations numerically using a modified approach for the derivation of the explicit Runge-Kutta method. This derivation is based on using stochastic Taylor series expansion for the deterministic and stochastic parts of the stochastic differential equation. Stable Extending Modules Mehdi Sadik Abbas and Saad Abdulkadhim Al-Saadi Department of Mathematics, College of Science, Al- Mustansiriyah University, Iraq E-mail: amsaj59@yahoo.com E-mail: saadalsaadi08@yahoo.com Abstract Let R be a ring and M be an R-module. Recall that M is extends if, every submodule of M is essential in a direct summand of M. Since 1980s, the developments of modules with the extending property have been a major area in ring and module theory. In this paper, we introduce and study a proper generalization of extending modules. We call an R-module M a stable extending if every stable submodule of M is essential in a direct summand of M. Many characterizations and properties of stable extending modules are given. Moreover, it is well known that a direct sum of extending modules need not be extending. Unlike extending modules, we assert that a direct sum of stable extending modules is a stable extending. On Pairwise Semi – P - Connectedness Narjis Abdual Jabbar Dawood and Nadia Faiq Mohammed Department of Mathematics , Ibn – AL-Haitham College of Education, BaghdadUniversity,Iraq Abstract In this paper we study a new kind of connectedness,namely'Pairwise Semi – P -Connectedness'.Also we study the relationships among this type of connectedness and the other kind of connectedness like pairwise connectedness and pairwise pre– connectedness . 26 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Extension of Gosper’s algorithm and Greatest Factorial Factorization Mohammed Kh. Abdullah Department of Mathematics, College of Science, Basrah University, Basrah, Iraq. Abstract In this paper we extend Gosper’s algorithm [4], by using “Greatest Factorial Factorization” (GFF), introduced by Paule [5], and “greatest common divisor” (gcd) concepts to find the value of the summation ∑ · . On bg- Generalized Closed Sets and Their Relationships A.K. Hussein Department of Mathematics, College of Basic Education, Al- Mustansiriyah University,Iraq E- mail: aalobiadi@yahoo.com Abstract In [11], M. Ganster and M. Steiner introduced many relations between some known types of generalized closed sets and b- generalized closed sets. In this paper we investigate more relationships. Also we obtain some characterizations of extremely disconnected, Tgs spaces and sg- submaximal spaces. Paired Bootstrapping procedure in Gamma Regression Model using R Zakariya Y. Algamal and Khairy B. Rasheed Departmennt of Statistics and Informatics , College of Computer Science and Mathematics, University of Mosul,Iraq zak.sm_stat@yahoo.com Khairy_line@yahoo.com Abstract This paper attempts to introduce the concept of the gamma regression model, in which the dependent variable has the gamma distribution, and the use of the paired bootstrapping resampling associated with the "boot" package in R program. Three confidence intervals were computed. 27 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Some probability characteristics function of the solution of stochastic Fredholm integral equation contains a known Sine wave function Mohammad Wahdan Muflih and Huda Hammoodi Imran Department of Mathematics, College of Ed. Ibn AL-Haitham, University of Baghdad,Iraq Abstract In this paper, some probability functions (probability density, characteristic, correlation and special density) are found depending upon the smallest variance of the analytical solution of random non-linear Fredholm integral equation (RFIE) of the second kind contained a known sine wave equation.The solution of RFIE is found by Adomian decomposition method (A.D.M). New modification on Homotopy Analysis Method Mohanad Riyadh Saad Department of Mathematics, College of Science, University of Basrah,Iraq Abstract In this paper, a new modification of homotopy analysis method (HAM) is discussed. This modification is based on a new formula for Adomain polynomails introduced by Ibrahim L.El Kalla[4]. Test problem is given to verify the reliability and efficiency of this modification. On (k,n;f)-arcs of type (n-5,n) in PG(2,5) F.K. Hmeed , Mustafa Hussein, Mohammed Y. Abbas Department of Mathematics, College of Education,University of Basrah.Iraq. Abstract In this paper we proved that the existence of (k,n;f)-arcs of type (n-5,n) in the projective plane of order q; when the points of weight 0 is equal 13. For this purpose we used of the technique in reference [1] and we deduced the example (18,9;f)-arc of type (4,9) in PG(2,5) when the points of weight 0 from a (13,4)-arc of type (3,18,6,0,4). 28 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Semi-Primary Fuzzy Submodules Layla Salman Mahmood and Shrooq Bahjat Semeein Department of Mathematics , Ibn – AL-Haitham college of Education, BaghdadUniversity,Iraq Abstract In this paper, we shall introduce the concept of semi– primary fuzzy submodule as a generalization of the ordinary concept of semi – primary Submodules , also we shall establish some basic properties of this type of submodules . We study the elationship between semi- primary fuzzy submodules and certain types of fuzzy submodules such as fuzzy prime Fuzzy primary and fuzzy quasi – prime submodules. On b-Covering Dimension Raad Aziz Hussain Al-Abdulla and Sema Kadhim Gaber Department of Mathematic, College of Mathematics and computer Science , Al-Qadissiya University ,Iraq. Abstract We study some properties of -open set in topological space and we study the covering dimension by using -open set which is called -dim. On a general class of hybrid weakly picard mappings Amal M. Hashim and Zeinab Sami Department of Mathematics, College of Science, University of Basrah, Basrah- Iraq amalmhashim@yhoo.com Abstract The concept of weak contraction from the case of multi-valued maps is extended to hybrid pair of single valued maps and multi-valued maps and then the corresponding convergence theorems for Picard iteration associated to a hybrid weak contraction are obtained. Our work extends and improves recent results due to Daffer et al .(1995) ,Berinde (2004) and Berinde et al.(2007) . 29 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Oscillations of First Order Linear Delay Differential Equations with positive and negative coefficients Hussain Ali Mohamad, Intisar Haitham Qasem, and Zainab Hhmed Abullah Department of Mathematics, College of science for women, University of Baghdad,Iraq Abstract Oscillation criteria are obtained for all solutions of first-order linear delay differential equations with positive and negative coefficients. Our results extend and improve some well known results in the literature. Some examples are considered to illustrate our main results. A new estimator by generalized modified jackknife ridge regression estimator Feras Sh. M. Batah Department of Mathematics, College of science Al-Anber Unversity , Iraq Abstract Multicollinearity is an important problem in regression which produces undesirable effects on the least squares estimator. Ridge regression is one of the well known solution to the multicollinearity problem. Specifically, the generalized ridge regression (GRR) estimation leads to a reduction in the sampling variance where as jackknifed ridge regression (JRR) estimation leads to a reducation in the bias. Batah etal. [1]proposed a modified jackknife ridge regression estimator (GJR) by generalzing the MJR. We showed that a new proposed estimator (GJR) is superior in mean square error (MSE) sense to the LASSO estimator Generalized Ridge regression estimator jackknifed Ridge regression estimator and modified jackknifed Ridge regression estimator. The Cyclic Decomposition of Module Where is Prime Malik Saad Al-Muhja Department of Mathematics Computer Application, College of Sciences, University of Al- Muthana,Iraq Alaa H. Mohamed Department of Mathematics, College of Education, University of Al-Qadisiya, Iraq Abstract In 2010 [1], introduced a paper about the cyclic decomposition of the finite abelian factor group , / , in this paper we discuss the determination with matrix module on the cyclic decomposition formula by the addition of two modules on the factor module / , i.e. , the module of all 1, 1 , valued generalized characters of a module over the module of induced unit characters from all cyclic subgroup of a module . 30 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ On complete (k,3)-arcs in PG(2,8) Salam A. Falih Department of Mathematics,University of Basrah, Iraq Email: salamkader2006@yahoo.com Abstract In this paper, the classification of the (k,3)-arcs in PG(2,8) with respect to the type of their lines has been obtained as well as the group of projectivities of the projectively distinct (k,3)-arcs are found. Furthermore, all the complete (k,3)-arcs in PG(2,8) are investigated. Also it was shown that PG(2,8) has no maximum arc. A new class of multivalent functions with hypergeometric function Hussein jaber Abdul hussein and Rafied habib buti Department of Mathematics ,College Of Science, University of Al-Muthanna, Iraq Abstract In this paper we introduce a new class M of multivalent functions with hypergeometric function in the unit disk U. We obtain coefficient estimates and some theorems. New Third and Sixth Order Iterative Methods for Solving Nonlinear Equations Ahlam J.Kaleel Department Of Mathematics and Computer Application , College of Science , Al-Nahrain University,Iraq Huda H. Omran Department Of Mathematics , College of Education ,Ibn Al-Haitham University of Baghdad,Iraq Salam J.Majeed Department Of Physics , College of Science , University of Thi-Qar,Iraq Abstract Finding the zero of a nonlinear equation f (x) = 0 , is a classical problem which has nice applications in various branches of science and engineering . In this paper , we introduce two iterative methods which are based on the Modified Simpson's approximations to definite integral in Newton theorem. It is proved that first method have cubic convergence and second method have six convergence . In order to demonstrate the convergence properties of the introduced methods, several numerical examples are given. 31 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Bifurcation solution of Nonlinear fourth order differential Equation of elastic beams Murtada J. Mohammed Department of Mathematics, College of Education, University of Basrah, Iraq Abstract In this paper , the bifurcation solutions of elastic beams equation was studied by using Lypaunov-Schmidt method. The bifurcation equation corresponding to the elastic beams equation has been found as a finite system of two equations. Also, the discriminant set (bifurcation set) of the elastic beams equation has been found for some values of parameters. A New Method for Finding a General Solution for the Differential Equations Using Laplace Transformations Adel M.Hassan and Ahmed Wady Shehab Department of Mathematics,college of Mathematics and Computer Sciences,Kufa University,Iraq adelramahi@gmail.com ahmed71@gawab.com Abstract In this paper ,a proposed method was introduced to find the exact general solution of the differential equations using Laplace transformations without the need for initial conditions . 32 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Dependent Elements of Semiprime Rings Mehsin Jabel Atteya Department of Mathematics, College of Education, Al-Mustansiriyah University,Iraq. E-mail: mehsinatteya@yahoo.com Abstract In this paper we study and investigate concerning a dependent elements of semiprime rings and prume rings R by using generalized derivation and inner derivation,when R admsit to satisfy some conditions,we give some results about that. Some researchers have studied the notion of free action on operator algebras,Murray and von Neumann [1] and von Neumann [2] introduced the notion of free action on abelian von Neumann algebras and used it for the construction of certain factors.Throughout,R will stand for associative ring with center Z(R).As usual,the commutator xy−yx will be denoted by [x,y].We shall use the basic commutator identities[xy,z]= [x,z]y+x[y,z] and [x,yz]=[x,y]z+y[x,z].A ring R is said to be n-torsion free, where n≠o is an integer,if whenever nx=0,with x ∈ R,then x=.Recall that a ring R is prime if aRb=(0) implies that either a=0 or b=0,and is semiprime if aRa= (0) implies a=0.A prime ring is semiprime but the converse is not true in general,a ring R is 2-torsion free in case 2x = o implies that x = o for any x ∈ R. An additive mapping d:R → R is called a derivation provided d(xy)=d(x)y+xd(y) holds for all pairs x,y ∈ R.Let a ∈ R,then the mapping d:R → R given by d(x)=[a,x] is a derivation on R.It is called inner derivation on R.An additive mapping D:R → R is called a generalized derivation on R if there exists a derivation d:R→R such that D(xy)=D(x)y+xd(y) holds for all x,y ∈ R.However,generalized derivation covers the concept of derivation.Also with d=o,a generalized derivation covers the concept of left multiplier (left centralizer) that is,an additive mapping D satisfying D(xy) = D(x)y for all x,y ∈ R. We mention some results which are obtained in our paper Implementation of a new approach of steganography using (PN) sequence cipher system Mahmuod H. Al-Muifraje , Saad M. Khalifa and Asmaell Abdulsattar Jabar Computer Science Department, College of Sciences, University of Al-Mustamsiriyah,Iraq Abstract Steganography is the science of hiding secret information inside the cover color image. Least- significant-bit (LSB) insertion is one of the techniques in steganography to hide Data inside the image. One bit of the secret information is inserted in one byte of the cover image. This paper proposed using PN sequences (pesedo-noise-sequences) as a ciphering for the hiding information before employing steganograhy.The work used the random bit sequence generated by linear feedback shift register (LFSR) to hide two bits of the secret information in each byte of the color cover image. Implementation of the proposed approach is presented in this work. The results showed that the suggested approach is robust enough to prevent the detection of a secret image or text. Also, the system is conceptually simple and straight forward to implement in a software. 33 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Performance Evaluation of Speech Scrambling Methods Based on Statistical Approach Sattar B. Sadkhan and Nidaa A. Abbas, University of Babylon, Member, IEEE Abstract Speech scrambling plays a great role in many important communication systems, such as a military communication and a banks communication systems. There are many traditional scrambling methods used in single dimension such as time or frequency domain scrambling. This paper propose a comparison between speech scrambler methods using methods based on statistical metrics called Independent Component Analysis (ICA) and Principal Component Analysis (PCA). For ICA method, Approximate Diagonalization of Eigen-matrices (JADE) algorithm was implemented while for PCA , traditional PCA algorithm was implemented. The paper takes into consideration the testability of many input speech signals in English in two types of bits 8 bits and 16 bits. The objective test using Linear Predictive Coding (LPC), Signal-to-Noise Ratio (SNR) were applied to evaluate the scrambling systems under consideration. A proposed Developed Theorems for Mathematical Analysis of Elliptic Curve Discrete Logarithm Problem (ECDLP) Sattar B. Sadkhan University of Babylon – E-mail: drengsattar@ieee.org Ammar A. Neamah University of Babylon,Iraq Abstract One of the problems that have found great a popularity in cryptography is the problem of discrete logarithms in a subgroup of order n of an elliptic curve over the finite field used for authentication and secrecy systems. This paper presents proposed developed theorems and corollaries that relate to the computation of the Elliptic Curve Discrete Logarithm Problem (ECDLP). These theorems are the results of mathematical analysis and investigation of the published literatures of the well known methods used to treat the attacks problems of ECDLP, especially following the Polared Rho Method. 34 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Complexity Evaluation of Knapsack Crypto System using a Fuzzy Set Sattar B. Sadkhan Babylon University- E-mail: drengsattar@ieee.org Azhar H.Nasef AL-Mustansiryia University- E-mail: alazhar1999@yahoo.com Sabiha F.Jawad AL-Mustansiryia University- E-mail: sabiha_fj@yahoo.com Abstract It is well known that the knapsack cryptosystem is a type of public key cryptosystems. It is based on the well known mathematical concept, i.e., the choosing of one way function. Many Knapsack cryptosystems were invented in the last 20 years, and many attacking methods were invented as counterattacks against the developed knapsack cryptosystems. All the attacking methods aim towards breaking the security of the considered system. But, sometimes, the designer needs to know the level of security ( complexity ) of the new designed knapsack cryptosystem, or she / he needs to know what the advantage given by any development performed on any known knapsack cryptosystem. Hence she / he must look for an evaluation criteria that can be used as an evaluation method or ( procedure) . Till now, the field of security evaluation is considered as a new field. Most of the interested experts consider it as a part of cryptanalysis. Four years ago, Fuzzy logic evaluator was used for the first time as a complexity evaluator for stream cipher system. This paper considers the Fuzzy logic evaluation method against another type of cryptosystem , that is knapsack cryptosystems. Two input variables are taken into consideration, and according to them the complexity evaluator based on Fuzzy logic was designed and simulated. Many knapsack cryptosystems were tested by this evaluator like (Luli system, Chor Rivest, Traditional and Advance Adina Diparto Systems). The results were promising . Distal in Transformation Group Rewayda R. Mohsin Department of Mathematics, College of Mathematics and Computer Science, University of Kufa, Najaf, Iraq. Enas Y. Abdullah Department of Mathematics, College of Education, University of Kufa, Najaf, Iraq Abstract In this paper we define distal in transformation group and continuous map as well as some of his property is studied. 35 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ On invertible spaces Hadi Jabber Mustafa and Adel M.Hassan Department of Mathematics,college of Mathematics and Computer Sciences,Kufa University,Iraq Abstract In this paper , we study invertible spaces seveval properties of invertible spaces among these ideas: 1) The property of being invertible is property 2) Let x be an invertible spaces of more than two points .let u be a proper open subset of x . If u is Hausdorff , then x is also Hausdorff 3) Let x be an invertible space . if x contains a nonempty open subset u whose clousure is compact then x is compact . A Topological Interpretation for Vanishing of Higher Homotopy Groups of a Hypersolvable Arrangements Abid Ali Al-Ta'ai Ministry of Higher Education of Iraq. Hana' M. Ali University of Basrah, Collage of Science, Department of Mathematics. Abstract In this paper we constructed a minimal CW complex for the complement of a supersolvable arrangement induced from the structure of its fundamental group as iterated semi direct product of finitely generated groups, in order to give a topological interpretation for vanishing of higher homotopy groups of the complement of a hypersolvable r -arrangement A , when we deformed it by Jambu's and Papadima's deformation method into a one parameter family of fiber-type ~ arrangements { At }t∈C . 36 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ ON THE GEOMETRY OF CONHARMONIC CURVTUAR TENSOR OF NEARLY KAHLER MANIFOLD Ali A. Shihab Moscow State Pedagogical University, Moscow- Russia. Abstract In this paper we investigated the conharmonic curvature tensor of nearly Kahle manifold. We proved that, any four-dimensional NK- manifold is conharmonic-parakähler manifold if and only if, it is manifold of zero scalar curvature. Also it has been proved that, NK- manifold of dimension greater than four is conharmonic-parakähler manifold if and only if, it is Ricci-flat Kahler manifold. Finally, we proved that NK- manifold of dimension greater than four is conharmonic flat if and only if, it is locally holomorphically isometric to the complex space supplied with standard Kahler structure. Under symmetric loss function Comparison of MINQUE and Simple estimator in general Gauss -Markov Model Nadia Abud Habeeb AL-Mousaway Department of Mathematics,College of Science of computer and Mathematics,University of Thi- Qar,Iraq Abstract Under the general Gauss-Markov model {Y , Xβ , σ 2V } comparison of MINQUE and so called " simple estimator" ( 1 )Y T (1 − XX + )Y with k = rank( x Mv) − rank(v) f or σ 2 it is considered under k the symmetric loss function. 37 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ APPROXIMATION BY A NEW MODIFICATION OF SZÃSZ-MIRAKYAN TYPE OPERATORS ALI J. MOHAMMED University of Basrah, College of Education, Department of Mathematics, Basrah, IRAQ. HASAN A. NASER University of Thi-Qar, College of Education, Department of Mathematics, Thi-Qar, IRAQ. Abstract In this paper, we define and consider modified Szãsz-Mirakyan type operators to approximate a class of functions integrable on the interval 0, ∞ and study some direct results in simultaneous approximation for this operator which is denoted by , ; . First, we study the convergence for the operators , ; ; 0,1,2, … , ∞ and we prove a Voronovskaja- type asymptotic formula for our operators. Finally, we obtain an error estimate in terms of modulus of continuity of the function being approximated. Comparison Study for some Local Search Methods for Multiple Objective Function in a Single Machine Scheduling Problem Al Zuwaini M. K. Department of Mathematics, Collage of Mathematics and Computer science Thi-qar University, Iraq Abdul Razaq , T. S. Saidy , S. K. Math. Dep. College of Science University of Al- Mustansiriyah, Iraq Abstract In this paper we considered a multiple objective function on single machine scheduling ∑ n problem. The aim is solving the problem i =1 (α i Ei + β iTi + γ iCi ) , minimizing the weighted sum of earliness, tardiness and completion time. As this problem is strongly NP- hard, so we used local search methods, genetic algorithm and we suggested a hybrid method to find approximate solutions. The results are cooperated with the optimal solution in [1] and [2] in case n (no. of jobs) less than or equal to 35 jobs, and in case n greater than 35 jobs, the results are compared with these obtained from the above methods. We note that the hybrid method is the best, as it is illustrated in the tables and figures. 38 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ The Separation Axioms In Tritopological Spaces Luay Al- Sweedy Department of Mathematics, College of Education, Babyloon University,Iraq. Asmahan Flieh Hassan Department of Mathematics, College of Education for girls, Kufa University,Iraq. Abstract In this research we recall the separation axioms in tritopological space and we study the relation among them and give some examples and theorems . δ** - continuous function in tritopological space Luay Al- Sweedy Department of Mathematics, College of Education, Babyloon University,Iraq. Asmahan Flieh Hassan Department of Mathematics, College of Education for girls, Kufa University,Iraq. Abstract In this work , we introduce a new definition of the continuous function in tritopological space . Also, we study the separattion axioms that we can translate by a continuos function and the nature condition that we need to satisfy the translation . Pairwise Completely Regular in Double Topological Spaces Rewayda R. Mohsin Math-Dep. Coll. of Math. and Com. Sci. University of Kufa, Najaf, Iraq Enas Y. Abdullah Math-Dep. College of Edu. University of Kufa, Najaf, Iraq Abstract The concept of intuitionistic topological space was introduced by Çoker. The aim of this paper is to generalize notions between bitopological spaces and double topological spaces and also give a notion of pairwise completely regular for double-topological spaces. 39 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Suggesting a New Method to Find The approximately optimal stratum boundaries Abdulsattar Ali Hussien Department of Mathematics ,Education college of woman. University of Anbar ,Iraq Abstract 25 A new approximate method has been studied in this paper, that is ( cum.f 26 ) which is used for calculating the approximate normal boundaries using the Proportional allocation in case of studying the heterogeneous sample classes .Then the new method was compared with the most efficient 5 approximate method, that is, (cum.f 6 ) . It has been concluded that the new method is more efficient than the old one in case of uniform distribution for all (d) values, while in normal distribution, the efficiency of the new method depends on( σ )value. If (σ< 0.229) , the old method will be better .If ( σ =0.229) both methods are equal in efficiency .But when (σ > 0.229 ) , the new method will be better and more efficient than the old method .In case of exponential distribution, the new method becomes better and more efficient in spec ific intervals depending on (λ) value .If (λ < 3.0491 ) , the new method will be more efficient while when (λ > 3.0491 ) the old method will be more efficient .If (λ = 3.0491 ) both methods will be same in efficiency. The Moment Generating Function of a Poisson Exponential Joint Distribution Kareema A. Makrib Al-Khafaji and Ali H. Mahmood Al-Obaidi Department of Mathematics, College of Education Ibn- Hayyan,University of Babylon,Iraq Abstract In this work, the researcher derives the moment generating a function of the joint probability distribution of random vector , where is defined as max and , ,…, is a random sample of size from exponential distribution with parameter 0. Also, be a Poisson random variable with parameter 0, such that be an independent of , , … , . This idea has wide areas in probability applications, especially in wait time distribution of Poisson process which is a special case from birth and death processes. 40 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Generalization of Newton-Kantorovich method to solve higher order Non-linear Systems of partial differential equations Abdul Nabi I.Ibrahem Afrah A.Ahmed Department of Mathematics,college of Science,University of Basrah,Iraq. Abstract In this paper we generalize Newton-Kantorovich method to solve system of nonlinear third order partial differential equations and then discuss the convergence analysis of this method. We solve the coupled KdV (Korteweg-de Vries ) equations . The obtained numerical solutions are compared with the corresponding exact solutions. We deduce that our results are fairly good approximations to the exact solution. Bifurcation Periodic Solutions of Nonlinear Fourth Order Differential Equation Ahmed Abbas Mezaal Department of Mathematics, College of Computer Science and Mathematics, University of Thi-Qar , Iraq. Mudhir A. Abdul Hussain Department of Mathematics , College of Education , University of Basrah , Basrah, IRAQ. Abstract In this paper, we are interested in the study of bifurcation periodic solutions of nonlinear wave equation of elastic beams located on elastic foundations with small perturbation by using the local method of Lyapunov-Schmidt. We showed that the bifurcation equation corresponding to the elastic beams equation is given by the nonlinear system of two cubic equations. 41 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Homotopy Analysis Method for Solving System of Fractional Integro Differential Equations of Fractional Integrals Osama H. Mohamed , Dept. of Mathematics and Computer Applications, College of Science, Al-Nahrian University,Iraq. Omar I. Khaleel Department of Computer and Continuous Education, Al-Nahrian University, Baghdad, Iraq. lam A. Ahmed Department of Biotechnology, College of Science, Al-Nahrian University, Baghdad, Iraq. Abstract In this paper we study Homotopy Analysis Method (HAM), as a well-known method for solving functional equations, which has been employed to solve the system of linear and nonlinear fractional integro-differential equations of the form: α D* i = gi ( x ) + J αi fi 1 (u1 ) + J αi fi 2 (u2 ) + ... + J αi fi n (un ); i = 1, 2,..., n …….(1) α With initial conditions ui (0) = ui 0 , i = 1,2,..., n where D* i represents the caputo fractional α derivative of order αi and J i is the Riemann-Liouville fractional integral operator of order αi ≥ 0 .The technique is tested for some examples and the results demonstrate reliability and efficiency of proposed method. Stability of Dynamic Systems of Stochastic Differential Equations Zainab R. Shaker and Fadhel S. Fadhel Dept. of Mathematics and Computer Applications, College of Science, Al-Nahrian University,Iraq Abstract In this paper, dynamical systems of stochastic differential equations have been studied in detail, as well as some of their basic properties. Then, the stability of such type of systems was introduced using the direct method of Lyaponuv, namely, the variable gradient method, where two examples are considered as an illustration. 42 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ On Generalaized Derivations with Commutativity of Semiprime Rings Mehsin Jabel Atteya and Dalal Ibraheem Resan Al-Mustansiriyah University-College of Education-Department of Mathematics –Iraq. E-mail: mehsinatteya@yahoo.com E-mail: dalalresan@yahoo.com Abstract The main purpose of this paper is to study and investigate some results concerning generalized derivation D on semiprime ring R, we obtain R which contains a non-zero central ideal and when D=0,then R is commutative. This research has been motivated by the work of M.Ashraf [1]and M.A.Quadri,M.Shadab Khan and N.Rehman[10].Throughout this paper,R will represent an associative ring with the center Z(R).We recall that R is semiprime if xRx = (o) implies x=o and it is prime if xRy=(o) implies x=o or y=o.A prime ring is semiprime but the converse is not true in general.A ring R is 2-torsion free in case 2x = o implies that x=o for any x ∈ R .An additive mapping d:R → R is called a derivation if d(xy) = d(x)y + xd(y) holds for all x,y ∈ R.A mapping d is called centralizing if [d(x),x] ∈ Z(R) for all x ∈ R, in particular , if [d(x),x] = o for all x ∈ R, then it is called commuting,and is called central if d(x) ∈ Z(R) for all x ∈ R.Every central mapping is obviously commuting but not conversely in general . Following Bresar [3] an additive mapping D: R → R is called a generalized derivation on R if there exists a derivation d:R→R such that D(xy) = D(x)y+ xd(y) holds for all x,y ∈ R.However , a generalized derivation covers the concept of derivation . Also with d=o,a generalized derivation covers the concept of left multiplier (left centralizer) that is,an additive mapping D satisfying D(xy) = D(x)y for all x,y ∈ R.As usual,we write [x,y] for xy –yx and make use of the commutator identities [xy,z]=x[y,z]+[x,z]y and [x,yz]=y[x,z]+ [x,y]z. Pairwise Separation Axioms and Compact Topological Spaces Rewayda R. Mohsin Department of Mathematics, College of Mathematics and computer Science,University of Kufa, Najaf, Iraq. Enas Y. Abdullah and Ahmed M. Rajab Department of Mathematics, College of Education, University of Kufa, Najaf, Iraq. Abstract The concept of intuitionistic topological space was introduced by Çoker. The aim of this paper is to generalize bitopological notions of separation to intuitionistic topological spaces and give a notion of pairwise compact for double topological spaces and some separation axioms. 43 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Pairwise Regular Double-Topological Spaces Rewayda R. Mohsin Department of Mathematics, College of Mathematics and Computer Science, University of Kufa, Najaf, Iraq Enas Y. Abdullah Department of Mathematics, College of Education, University of Kufa, Najaf, Iraq Abstract The concept of intuitionistic topological space was introduced by Çoker. The aim of this paper is to generalize notions between bitopological spaces and double topological spaces and also give a notion of pairwise regular for double-topological spaces. Another Type of Separation Axioms Anmar Hashim Jasim and Hatim Kareem Khudhair Department of Mathematics, College of Science, Al-Mustansiriyah University ,Iraq Abstract In this paper we have introduced another kind of separation axioms which we call θg-separation axioms, where we got the following results: 1- θg-separation axioms give g-separation axioms. Besides , we give examples to show that the converse may not be true. 2- We have proved some theorems and have given examples to discuss the property of the separation axioms which we have introduced. On (α,β)-semi continuous Ali A. Kasim Department Of Statistics, College of Administration and Economics, Baghdad University ,Iraq E-mail: ali661971@yahoo.com Abstract In this paper we show that Remark 4 in (Rosas,2002) is not true ,in general, but if we add some conditions it will be true. Some relations among (α,β)-semi continuous function and other classes of continuous function are explained. 44 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Some Topological Dynamical Properties of Cellular Automata Hussein Jaber Abdul Hussein College of Sciences, Al-Muthana University , Al-Samawa, Iraq Abstract Cellular Automata denoted by (CA) are dynamical system with very rich and diversified behavior. They are often used in physics and sciences as models of complicated behavior. We study properties of one dimensional CA as topological dynamical systems and we generalize some of these properties to the two dimensional CA ANALYSIS OF THEGENERALIZED NESTED REPEATED MEASURES MODEL Sami D. Gabbara Department of Mathematics, College of Science, Salahaddin University- Erbil – Iraq s_gabbara@yahoo.com Abstract Gabbara (1985) developed a general method to analyze a nested repeated measures model when the covariance matrix has a certain pattern. In this paper a weaker assumption is used when the covariance matrix is arbitrary (i.e., unpatterned). Let Yi = (Yi11 , L , Yidr )′ be the vector of observations on the i th individual. It is assumed that the Yi are independently normally distributed with mean µ i and the common arbitrary covariance matrix Σ > 0 . We want to test hypotheses about µ i . Two techniques are used, the first is based on the multivariate one sample model when each individual receives the same treatments and hence has the same mean vector. The second is based on the multivariate linear model when different individuals receive different treatments and hence have different mean vectors. For each technique a uniformly most powerful (UMP) invariant size α test is found. Operator connected Hadi J. Mustafa Department of Mathematics, College of Mathematics and Computer Science ,Kufah Universty,Iraq Ali A. Kasim Department Of Statistics, College of Administration and Economics, Baghdad University ,Iraq Abstract In this paper we studied the concept of (α,β)-semi connected and (α,β)-connected by using the operator associated with a topology. Several relations are discussed by using some classes of continuous functions . 45 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ More on the topology of ω-open sets Asaad M.A. Al-hosaini Department of Mathematics, College of Education Ibn Hayan,University of Babylon,Iraq Abstract In view of the concept of ω-open set, three new concepts will be discussed in this paper ; the ω- maximal topology on a set, ω- space and ω-equivalence relation on the family of all topologies on one set. For each of these concepts some results are obtained and counter examples are discussed. GENERALIZED b- CLOSED SETS AND THEIR RELATIONSHIPS ADEA K. AL- OBIADI and ALI SAADI Department of Mathematics, College of Basic Education, Al- Mustansiriyah Univ,Iraq E-mail: aalobiadi@yahoo.com Abstract In [11], M. Ganster and M. Steiner introduced many relations between some known types of generalized closed sets and b- generalized closed sets. In this paper we investigate more relations. Also we obtain some characterizations of extremely disconnected, Tgs and sg- submaximal spaces. On Minimal L(θC)-Spaces Saheb K. Al-Saidy and Haider J. Ali Department of Mathematics,/College of Science, Al-Mustansiriya University,Iraq Abstract In the present paper we introduce a new concept namely minimal L(θC)-spaces which is a strong form of L(θC)-spaces. We study the properties of this concept and its relationships with L(θC)-spaces. Several examples are given to illustrate our results 46 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Single sampling plan when the truncated life test follows inverse Gaussian data Dhwyia Salman Hassan and Saad Ahmed Abdulrahman Al-Naimi Department of Statistics,College of Administration and Economics, University of Baghdad,Iraq Waleed A. Arhema AL-Elaiwe Department of Informative technology,Technical College of Management,Foundation of technical Education Abstract The term sampling inspection is used when the quality of the product is evaluated by sample ,rather than by total inspection ,where the time and cost of inspection can be saved through sampling. In this paper we provide an algorithm to establish the sampling plan(n , c) which represents the sampling size (n)and accepting number (c ) .Tables are provided for purposed sampling plan, considering consumer risk and producer risk, and operating characteristic curve, and truncated life test ,where the quality variables the lifetime of an item ,and we would like to know whether the lifetimes of items reach our standardized ones or not. The test can be performed without waiting until all test items fail, and then the test time can be reduced significantly Another Types of L(θc) Spaces Abd Ali H. Al-Taai and Haider J. Ali Department of Mathematics, College of Science, Al-Mustansiryh University,Baghdad,Iraq. Abstract The aim of this work is to extend the notion of L(θc)- spaces, these are the spaces whose Lindelof subsets are θ-closed. We will consider four weaker forms of this concept namely θLi, where i=1,2,3,4 and investigate their relationships with L(θc)-spaces as well as among themselves. δ * * -continuous on ( δ * -open , δ * -closed , δ * -interior, δ * -closure ) in tritopological space Asmahan Flieh Hassan , Nieran Taher Abd Al-Ameer and Nabaa Mery Qassim Department of Mathematics, College of Education for girls, Kufa University,Iraq. Abstract In this research we define a new continuous function in tritopological space and bitopological space , and we study the specification of this continuous function , with some examples and theorems. 47 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ O-Spaces Abed Al-Hamza Mahdi Hamza Department of Mathematics College of Mathematics and Computer Sciences,University of Kufa,Iraq Abstract In this paper a new topological concept will be given and it is called o- spaces. We have proved that: 1) An o-space is a property. 2) An o -space is not a hereditary property. 3) An o- space is connected but the converse is not true. 4) The continuous image of an o- space need not be an o- space. On non linear chaotic dynamic control system design problems with application Zainab R. Shaker and Dept. of Mathematics and Computer Applications, College of Science, Al-Nahrian University,Iraq Radhi A. Zaboon Department of Mathematics, College of Science, Al-Mustansiryh University,Baghdad,Iraq. Abstract In this paper, a new scheme and procedure for nonlinear dynamical control system are developed supported by the necessary mathematical justifications. Some nonlinear chaotic dynamic systems are considered, and their non-linear feedback controllers are also designed to overcome the problem of undesirable chaos in their systems. The simulation of some real life chaotic dynamic system before / after controlling depending on the suggested scheme, are presented. On Some Properties of Separation Axioms for β − open sets in Bitopological Spaces Alaa Erees Abdul-Rauof Department of Mathematics, College of Mathematics and Computer Sciences,Kufa University,Iraq Abstract In this paper ,we introduce a definition for β − open set in bitopological space ,so we give the basic specification for the definition above ,and we will state some properties of separation axioms T2 , T 1 , T3 , T 1 , T4 and T5 . 2 3 2 2 48 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Approximation by spline interpolation for solving fifth order Initial value problems Dhuha.M.Alyassiri and Faraidun K.Hama Salih Department of Mathematics, College of Education Science, University of Sulaimania, Iraq Abstract Some difference schemes for the initial value problems are derived using spline interpolation. These schemes are fifth order accurate by the six degree spline function with interpolates by the function. Also , it was shown that by making use of the continuity of the first and fourth derivatives of the spline function ,the resulting for two spline differences scheme give a new type which can be solved efficiently by the well known algorithm to the fourth order initial value problem. In our paper we give a brief description of the method. The derivation of the difference schemes spline function has been shown also, and the second order accuracy method and convergence analysis are studied. We have solved some numerical examples whose their solution is given as exact solution. The numerical examples are given in support of the theoretical results. Complete controllability of Non-linear Sylvester Stochastic Dynamic Control System in the presence of Brownian motion uncertainty Radhi A. Zaboon Department of Mathematics, College of Sciences, Al-Mustanseryia University, Baghdad, Iraq. radhi_maths@yahoo.com Auras K. Hameed Department of Computer, College of Science for Women, University of Baghdad, Baghdad, Iraq. E‐mail: oras_hameed@yahoo.com. Jehad R. Khider Department of Applied Sciences, University of Technology, Baghdad, Iraq. Abstract The problem of getting a complete controllability of some classes of a non-linear stochastic dynamic control system with Sylvester type equation as its linear part has been considered. The complete controllability of this stochastic dynamic system in the presence of the Brownian motion uncertainty is proved by using the Banach contraction principle, in suitable Banach spaces. An algorithm based on the proposed theoretical result supported by an illustration has been given with discussion. 49 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ On the Design of the Best Resilient Boolean Functions used in Secret Key Generation of Stream Cipher System Sattar B. Sadkhan University of Babylon ,Iraq E-mail: drengsattar@ieee.org Abstract Boolean Functions play an important role in block ciphers and stream ciphers. The nonlinearity of a Boolean function f(x1, ……, xn) is defined as a distance between f and the set of affine functions {a0 + a1x1 + a2x2 + …anxn}. The Nonlinearity Nf should be large enough to resist the linear attack. The relationship between resiliency and nonlinearity of Boolean function is an important aspect in the design of a stream cipher. Hence it is required to offer a construction of Resilient Boolean functions with high nonlinearity. Such a construction leads to the problem of finding a set of linear codes with a fixed maximum distance. This paper offers a developed approach to consider a suitable way of getting best the Resilient Boolean function that can be used in the design of a stream cipher with a suitable nonlinearity. A modification of Newton 's method with third-order convergence Husnia Mohamed Eldanfour Department of Mathematics- Faculty of Science- Mistruth University – PO Box 966 Mistruth - Libya Abstract In this paper, We present an improvement to the Newton ’s method and obtain a new method with third-order convergence for solving non-linear equations. A general error analysis providing the higher order of convergence is given. Per iteration of the new method requires two evaluations of function and one evaluation of its first derivative. Numerical examples are also included in the performance of the new method. Fixed point theory in cone metric spaces Ali Farajzadeh Department of Mathematics, Razi University ,Kermanshah , 67149, Iran Abstract In this paper, a cone metric is introduced. Then, some fixed point theorems for generalized contractions in cone metric spaces are proved. These theorems extend some results in Suzuki (2008) [T. Suzuki. A generalized Banach contraction principle that characterizes metric completeness,Proc. Amer. Math. Soc., 136(5) (2008), 1861-1869] and Kikkawa and Suzuki (2008) [M. Kikkawa and T. Suzuki. Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69(9) (2008), 2942-2949.]. 50 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ APPLICATION OF THE GENERALIZED PURCELL METHOD FOR THE COMPLEX EIGENVALUE PROBLEM M. RAHMANI Technology Development Institute, ACECR, Tehran, Iran. rahmanimr@yahoo.com S. H. MOMENI-MASULEH Department of Mathematics, Shahed University, Tehran, P.O. Box:18151-159, Iran. Abstract Let be the set of row vectors of an arbitrary matrix and = be the normal basis of the vector space . For j > 1 let = , ,…, , ,…, and set for k = j+1, … , n and a suitable we construct , such that the new vectors , be orthogonal to . The set , for j = 1,…, n are a basis of and A = R where R is an upper triangular matrix. Let r = rank(A). Then every vector on is an independent solution of Ax = 0 [1]. Based on relations for complex eigenvalues of a matrix A, i.e. we have the following homogenous linear system of equations (1) 0. For initial values of _0 and _0 the new generalized Purcell iterative method(GIP) is proposed for solving Eq. (1), from and , 0,1,2, … ,. Theorems, lemmas, related discussions and new deation method based on GPmethod are presented to obtain other eigenvalues of the Matrix A. For accel-erating the convergence of the iterative method, also, a new version of Aitkin'sacceleration for complex series is proposed. The method in comparison with the QR method shows reliable results [2]. In order to elucidate the accuracy of the proposed method, we have considered the matrices FS1836(n = 183) and STEAM1(n = 240) that are obtained from Matrix Market [3]. 51 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Parameter Estimation of Communication Systems Using Two Accelerated EM Algorithm H. Saleh Estahbanati, S. H. Momeni-Masuleh, B. Zarpak Department of Mathematics and Computer Sciences, Shahed University, Tehran, P. O. Box: 18151-159, Iran. H.R. Bakhshi Department of Electrical Engineering, Shahed University, Tehran, P. O. Box: 18151-159,Iran Abstract In this paper, we offer an effective hybrid algorithm to estimate the parameters of communication systems that include missing data. The communication systems have some parameters such as channel coefficients and carrier frequency offset that we should estimate with sufficient accuracy to obtain the receiver performance in the information detection and data analysis. When information is sent by trasmitter to receiver, some of these data are incomplete downloads due to noise in the environment. The EM algorithm is employed to estimate the incomplete data and unknown parameters. Our fundamental problem in EM algorithm is the slow convergence and selection of initial points. To accelerate the rate of convergence of EM algorithm we combined EM algorithm with Aitken and Louis method. Also we use the improvement of the initial point selection by Rayleigh distribution. This method is used for MIMO OFDMA system. Comparison with available literature shows a high accuracy of the results. Study of The Effect of Age On The Otitis Media Infection By Using a Mathematical Model Syoof Khowman AL-Ramahi / Biomathematics unit, College of Computer Sciences and Mathematics, University of AL- Qadisiyah,Iraq ddssnn2004@yahoo.com Abstract The present study entailed a collection of 293 swabs from patients at the E. N. T section of AL-Diwaniya Teaching hospital . The study was carried out during the period from the first of October, 2009, until the first of August , and it aimed at investigating the effect of age on the otitis media infection. The mathematical result by using SIR Model indicated that the percentage of otitis media differ according to age group. 52 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Interpretation for the Vanishing Higher Homotopy Groups of A Hypersolvable Arrangement Abd Ali H. Al-Ta'ai Ministry of Higher Education of Iraq Hana' M. Ali Department of Mathematics, College of Science, University of Basrah ,Iraq. Abstract A hypersolvable class is introduced by Jambu and Papadima as a generalization of a fiber type (supersolvable) class. They defined a vertical deformation method which deformed a ~ ~ hypersolvable r -arrangement A with s -singularity into supersolvable l -arrangement A = A1 by ~ one-parameter family of arrangements { A t } t ∈ C in C × C = C l with preserving all the r s collinear relations of A (i.e. this method preserves the lattice intersection pattern up to codimension ~ two l 2 ( A) ≈ l 2 ( A) ). Our aim in this paper is to give an interpretation according to the deformation r ~ l method. Why, when we deform A in C to At in C , all the non-vanishing higher homotopy groups of the complement πn (M(A)), n ≥ p(A) are vanished (killed). Analytical and Numerical Solutions of a Second-order Linear Hyperbolic Problems Idris A. Masoud Abdulhamid Department, of Mathematics ,College of Education University of Omar Al-Mukhtar , Libya edreesatea@yahoo.com Abstract This paper examines some types of analytical and numerical solutions for the linear hyperbolic problems of second order with Cauchy boundary conditions .Experiments are conducted to conﬁrm the numerical solutions observed by other researchers for many boundary conditions . The work mainly concentrates on the case of the homogeneous linear hyperbolic equation, which depends on the "separation of variable" method. Finally the analytical and numerical solutions of the second order linear hyperbolic equation are compared in one and two dimension, with special types of initial conditions . 53 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Study of The Overlapping Relation Between Levels of Education of Iraq and Some of Economic and Sociality Index Mohammed A. Mohammed Al- Diwanya Technical Institute, Iraq. Fadel Hameed Hadi College of Administration and economic,Al-Qadisiya University, Iraq Abstract The operation of education of Iraq suffers from many problems ,despite serious treatment by the Iraqi governments . Most of these problems were caused by wars and economics impasse. These problems lead to the decline operation of education .To develop education in Iraq we must study all the effect difficulty ,then find a solution . In this paper we attempt to study the relation between levels of education in Iraq and some economic and sociality indexes by the use of the Canonical correlation and we determine the important variables which effect and order this variable according importance . Nonassociative Grassmann Algebra Saad Salman Ahmad Section of mathematics, Department of Computing and Mathematics,Higher College of Technology AL-KHWAIR 133, Box 74, Muscat, Oman Abstract One of the main sources of algebraic structure is theoretical physics that illustrates basic concepts of modern algebra. There are many well-known algebraic structures used in theatrical Physics as the rotation groups, lie groups and “Algebra of color” proposed by G.Domokos as a candidate for the algebra obeyed by quantized field describing quark and leptons. Z.OZIEWIOZ and C.SITARCZYK in (a non-published paper) investigate the non associative Grassmann algebra by Combining the exterior and interior products for the Grassmann and symmetric algebra in one product on the Z-graded vector space (with no positive graduation). As a result, we get the non- associative Gassmann and symmetric algebra which incorporate the full set of the creation and annihilation operators for both particles and anti-particles.A new table of multiplication for this algebra was derived and the complete tables of multiplication in dimension 7 and 15 were given. 54 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ fuzzy distance function and its applications on fuzzy due dates and cost function Hanan Ali Al-Ta’ai Department of Mathematics, College of Sciences, University of Al-Mustamsiriyah,Iraq hanan_altaai@yahoo.com Hussam Abd Ali Department of Mathematics, College of Science, Karbla University,Iraq hussammath@yahoo.comhgfvd Fiaria Ali Al-Ta’ai Department of Mathematics, College of Sciences, University of Al-Mustamsiriyah,Iraq fiaria_altaai@yahoo.com Abstract The objective of this paper is to test the feasibility of using fuzzy distance function concepts which are introduced by Lam and cai to solve single machine scheduling multi objective functions one of them is nonlinear lateness and we develop, compare and test different local search methods ( Tabu search (Ts), Particle Swarm Optimization (PSO)and Honey Bee colony algorithms ) computational experience 1000 jobs with reasonable time. THE DEFINITION OF ENTROPY Saleem H. Al-Kutobi Alaa Hussein Hamadi Department Mathematics, College of Mathematics and Computer Science, Al-Qadysia University,Iraq Abstract In this paper we introduce a new definition for entropy via n- block maps while the classical way adopts the definition for entropy via n-blocks 55 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Flat Bochner curvature tensor of Locally Conformal Kahler manifold Jassim M. Jawad Department of Mathematic, Education College, Basrah University- Iraq Lamees K. Ali Department of Mathematic ,Education College, Thiqar University - Iraq Abstract In this paper we investigated the Bochner tensor of the class Locally Conformal Kahler manifold. The components of the Bochner tensor of this class have been found. We studied the special class of an almost Hermatian manifold, namely 2 and we proved that, if is Locally Conformal Kahler manifold with flat Bochner tensor, then is a manifold of class 2 if and only if, is flat Ricci tensor. Finally we proved that, if is Locally Conformal Kahler manifold with flat Bochner and Ricci tensors, then is Kahler manifold . Algorithms to Solve Multicriteria Scheduling Problems on Single Machine Tariq S. Abdul-Razaq Ali M. Delphi Department of Mathematics, college of science Al-Mustansiriya University, Iraq dr.tariqsalih@yahoo.com alimathdelphi@yahoo.com Abstract In this paper, we consider the multicriteria scheduling problem with release dates on single machine to minimize three criteria: maximum cost function, noted γ max ∈{Cmax , Tmax } and the sum of completion times, noted ∑C i . This problem, which is known to be NP-hard, is important in practice. We propose three new algorithms to solve this problem. Two of these algorithms dealing with hierarchical minimization problem case to find the best possible solution for each of the following two problems 1 / ri / Lex(C max , Tmax , ∑ C i ) and 1 / ri / Lex(C max , ∑ C i , Tmax ) . The third one is constructive algorithm based on branch and bound method (BAB) to find some of the efficient solutions when all the three criteria Cmax ,Tmax and ∑ Ci are of simultaneous interest for the general problem 1/ ri / F (Cmax , Tmax , ∑Ci ) . Our experimental results indicate that the third proposed algorithm enumerates the set of efficient solutions for the three criteria optimality. 56 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ THE SOLVABILITY, CONTROLLABILITY AND OBSERVABILITY OF INFINITE DIMENSIONAL NONLINEAR CONTROL SYSTEM USING SEMIGROUP THEORY Radhi Ali Zboon Department of Mathematics, College of Sciences, University of Al-mustamsiriyah,Iraq Manaf Adnan Salah Mathematics & Computer Applications Department, University of AL-Nahrain / Baghdad, Iraq . Abstract In this paper, the theoretical results of the solvability, controllability and observability of the mild solution to the following nonlinear dynamic control system d ⎛ ⎞ ⎛ s=t ⎛ τ=s ⎞ ⎞ ⎜ E uw (t) ⎟ = A uw ( t ) + F ⎜ t, uw ( t ) , ∫ G ⎜ t,s, uw ( s ) , ∫ K ( s, τ , uw ( τ ) ) dτ ⎟ ds ⎟ + P ( t, uw ( t ) ) + Bw ( t ) dt ⎝ ⎠ ⎜ ⎟ ⎝ s=0 ⎝ τ=0 ⎠ ⎠ uw ( 0 ) = u 0 , yw = C uw have been discussed and proved via Banach fixed point theorem and strongly continuous semigroup theory. Uniform Relative Reciprocal Velocity in Lorentz -Einstein Transformations F.A.Al-Bassam Laser Physics Department-College of Science for Women Babylon Univ.,Iraq E-mail:albassam1799@yahoo.co.uk Abstract The relative dimension velocity were converted to the relative time velocity in all equations by using the reciprocal of the velocity that equal to the negative of time velocity. The equations of the relative time velocity of two moving particles are in the same and opposite direction. The resultant of time velocity of two moving particles travel with right and less right angle ,while the resultant of time velocity in three- components. The relative uniform translational and rotational time velocities are derived from the known dimension velocity equations. The Lorentz- Einstein transformations are converted by the principle formula(reciprocal ). In addition to, the classical relative of elapsed time was produced in a different directions of two moving particles, so that the time values was postulate to verify the time of moving one particle or more. The new relative reciprocal equations give an obvious and complementary idea about the classical relative motion, whenever the special relativity of moving particles with very high time velocities are also verified. 57 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Principles of math (DNA) philosophy Mohanned saad abd karkosh Baghdad, Iraq Abstract The biological (DNA) is composed from four nitrogenic bases which are A, T, C and G as shown on the shape, they bond to each other by various sequences and repetitions to form various types of (DNA) tape and in various lengths. Every single tape from (DNA) biological tapes is connected to it's complementary counterpart, but the complementary tape is holding the same bases that existed in the original (DNA) tape in opposite sequence. By examining the (DNA) double tape, we can figure out the genetic characteristics of the living cell. Accordingly, I managed to form arithmetical mechanism which so far takes after (DNA) biological mechanism, metaphorically, and this mechanism is working on arithmetical functions. A genetic algorithm for measuring the teaching services efficiency of a scientific department Khulood Moosa Omran Arab Gulf Studies Center , Basrah University, Iraq Abstract In this research a system has been designed depending on the optimization intelligence programming problems using the integer genetic algorithm in order to measure the collage efficiency in performing the teaching services. A genetic module has been designed for measuring the college efficiency following two styles: the first one is the integer genetic algorithm for solving directly integer constrained linear optimization style through transforming the problem from a complex formula into a simple one indirectly and hence through the latter, a new technology has been used in the crossover process which is the zigzag crossover method. Also the mutation function was used. It was obvious that the second style is more efficient than the first style by comparing the results of both. 58 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Optimal Design for Electronic Circuits Alauldin Noori Ahmed Ahmed Ayyoub Yousif Ranen Z.Ahmood Department of Mathematic and Computer Applications , College of Science , AL-Nahrain University , Iraq Abstract In this paper , the non- linear mathematical model is constructed to design the hybrid circuit , based on partial differential equations , in which the optimum components locations for hybrid circuit is determiner , by minimizing the total thermal distribution subject to conditions that no component , are overlap . Hook and Jeeve'e optimization technique has been used for solving this mathematical module , to show the efficiency of our model building. MATHEMATICAL MODEL FOR OPTIMIZING DRAIN SPACING FORMULAE FOR STEADY STATE AND TRANSIENT CONDITIONS Dr. Hasan Naima Northern Virginia Community College, Woodbridge, VA 22191 ,USA Abstract A computer model has been developed to optimize design of subsurface agricultural drainage systems in humid or irrigated areas. To choose the optimal layout for a closed system, the model evaluates the trade-off between spacing and depth by optimizing steady state and transient drainage spacing formulae. The optimal design is defined as the drain spacing and depth combination which give the least cost drain layout. For a given allowable depth to the water table, a least cost drain layout is determined by minimizing a cost function subjected to equality constraints which specify approximate relationships between the drain spacing, depth and size required to result in the specified minimum depth to water. Input data required by the model includes soil properties, costs, irrigation schedules, water table position, drainage quantities and cropping intensity. Output information includes optimal drain depth, spacing, diameter of the drain and the collector, and the optimal cost. 59 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Keynote Speakers 1- Prof. Dr. Saleem H. Al-Kutubi "Illuminations of Dynamic", Iraq 2- Prof. Dr Abid Ali H. Al-Ta'ai" Mathematical Structures", Iraq 3-Dr. Nasser Said Al-Salti "A three-dimensional stationary MHD model for magnetic reconnection" , Sultan Qapos university. Oman 4-Prof. Dr. Mahmood Khalid Jasim " Numerical Simulation of changed fluid Spheres", Universty of Nizwa,Oman 5- Prof Dr. Giovanni Fasano Univ. Ci Foscar, "On Optimization" , Venice Optimization France 6- Baha Alzalg "Chance-Constrained second order cone programming" Washihgton State University , USA 7- Assist. Prof.Dr. Ahmad Zainy Hussain Al Yasry " NOTES IN KHOVANOV HOMOLOGY FOR KNOTS AND GRAPHS", Iraq 8- Assist. Prof. Dr.Ibrahim O.Hamad " Introduction to nonstandard analysis via IST approach" Iraq 9- Prof Dr. Ahad Raimi "Local cohomology of bigraded modules" , Iran 10- Habeeb M. Abood "Complex Structure On Finite Dimentional Space", Iraq 11- Ali Farajzadeh" Fixed point theory in cone metric spaces", Iran 12- Prof. Dr. Abdul-Adhim M. Al-Sudani "Theory of Metrizbale Manifold" , New Zealand 13- Prof. Dr. R. R. Bhargava "Mathematical Modeling of Smart materials with applications" India 14- Prof. Dr.Saad Salman Ahmad" NONASSOCIATIVE GRASSMANN ALGEBRA" ,Oman 15- Prof. Dr. Mohamed A. Abdullah "Numerical Methods for Advection-diffusion equations" 60 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Participants Abdul – Kareem I. Sheet Habeeb A.Kadhim Remote Sensing Center University of Department of Mathematics ,College of Mosul –Iraq. Computer and Mathematics Science, Thi- Qar University ,Iraq. Nadia Adeel Saeed Department of Physics – College of Sciences , Inaam Mohammed Ali University of Mosul, Iraq Department of Mathematics, College of Education-Ibn Al-Haitham, University of Baghdad, Iraq Sawsan Jawad Kadhum Department of Mathematics , College of Tha'ar Younis Ghawi Education , Ibn Al-Haitham University of Department of Mathematics , College of Education University of AL-Qadisiya Baghdad ,Iraq E-mail: tharali_1988@yahoo.com Haidar younis kawi Saeed A.Taban Department of math. College of computer Mathematic Department, College of Since, science, Al_Qadisiya university, Iraq University of Basrah, Iraq Email: hadirkawi@yahoo.com J. A. Resen Tariq Salih Abdul-Razaq Mathematic Department, College of Since, Department of Math., College of science and University of Basrah, Iraq mathematics, AL-Mustansiriya university, Iraq Saeed Abdul- Ameer Taban Nazera Khalil Department of Mathematics, College of Science, Basrah University ,Iraq. Mathematics Department, College of Mathematics and Computer Sciences, University of Kufa, Iraq Najla'a Sadiq Abduallah Luma. N. M.Tawfiq Department of Mathematics, College of Department of Mathematics, College of Science, Basrah University, Iraq. Education-Ibn Al-Haitham, University of Baghdad Abdul-Sattar J. Al-Saif Khalid. M. M. Al-Abrahemee Department of Mathematics, College of Department of Mathematics, College of Education, University of Basrah, Basrah, Education, Al-Qadisiya University, Iraq Iraq. 61 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Luma. N. M.Tawfiq Dhifaf A. Abood Department of Mathematics, College of Department of Mathematics, College of Education-Ibn Al-Haitham, University of Education, University of Basrah, Basrah, Baghdad, Iraq Iraq. Alaa. K. J. AL-Mosawi Eman Ali Hussan Department of Mathematics, College of Department of Mathematics, College of Education, Al_Qadisiya University, Iraq science ,AL-Mustansiriyah University, Iraq Muntaha K. Abbas Shatha A. Salman Foundation Technical Education, Technical Department of Applied Sciences, University College Management, Iraq of Technology, Iraq Shatha.alnajar@yahoo.com Nuha A. Rejab Fuad A. Al-Heety Department of Applied Sciences, University of Department of Applied Sciences, University Technology, Iraq of Technology, Iraq Nuha1900@yahoo.com FuadHeety@yahoo.com Rafid Habib Buti Salah Mahdi Ali Department of Mathematics, College of Department of Mathematics, College of Computer Science and Mathematics,University Computer Science and of Al-Qadissiya, Iraq Mathematics,University of Al-Qadissiya, Rafidhb@yahoo.com Iraq Salah_x9@yahoo.com Abdul-Hussein Saber Al-Mouel Atyaf S. Fakhir Department of Mathematics, College of Department of Mathematics, College of Education, University of Basrah , Iraq Education, University of Basrah , Iraq Noori Farhan AL-Mayahi Salah Mahdi Ali Department of Mathematics, College of Department of Mathematics, College of Computer Science and Mathematics, Al- Computer Science and Mathematics, Al- Qadisiya University ,Iraq Qadisiya University ,Iraq Anna V. Nikiforova Lia A. Ignatochkina Department of Topology and Geometry, Department of Topology and Geometry, College of Mathematics, Moscow State College of Mathematics, Moscow State Pedagogical University Moscow-Russia Pedagogical University Moscow-Russia Pavel B. Morozov Osama H. Mohammed Department of Topology and Geometry, Department of Mathematics and Computer College of Mathematics, Moscow State Applications, College of Science, Al- Pedagogical University Moscow-Russia Nahrain University , Iraq 62 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Fadhel S. Fadhel Fajer A. Abdul-Khaleq Department of Mathematics and Computer Department of Computer Science ,Dijlah Applications, College of Science, Al-Nahrain University College, Iraq University, Iraq Maysounm , A. Hamil Salah Taha Hafez Aly Department of Mathematics, Ibn – Al- Higher Technological Institute, 6th October Haithm college of Education, Baghdad branch. Egypt University, Iraq Bushra A.Taha Raid Kamel Naji Department of Mathematics; College of Department of Mathematics, College of Science; University of Basrah ,Basrah, Iraq. Science, University of Baghdad, Iraq Alaa Jabbar Badai ABDUL RAHMAN S. JUMA Department of Mathematics, College of Department of Mathematics, College of Science, University of Baghdad, Iraq Science, Al-Anbar University, Iraq S. R. KULKARNI Waggas Galib Atshan Department of Mathematics, Fergusson Department of Mathematics, College of College, Pune - 411004, India Computer Science and Mathematics, University of AL-Qadisiya Diwaniya , Iraq Hesham Rehman Mohamad Department of Mathematics, College of Samir Kasim Hassan Computer Science and Mathematics, University Department of Mathematics , College of of AL-Qadisiya Diwaniya , Iraq Education, Al-Mustansirya University ,Iraq. Hussien Hadi Abass Department of Mathematics, College of Kareem Abass AL-Ghurabi Education for Girls, AL-Kufa University ,Iraq Department of Mathematics, College of Education, Babylon University ,Iraq Rasha K. I. Department of mathematics, College of Saad Naji Al-Azawi Education Ibn-Al-Haitham, University of Department of Mathematics; College of Baghdad ,Iraq Sciences for women; Baghdad University , Iraq Iden Hassan Al – Kanani Department of Mathematics, College of Shaima Abbass Jasim Sciences for women, Baghdad University, Iraq Department of Mathematics, College of Sciences for women, Baghdad University, Iraq Anwar Ja'afar Mohammed Jawad Faculty of Electrical Engineering, University of Hussien Ali Hussien Technology, Iraq Department of Mathematics, College of science, University of Basrah ,Iraq 63 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Renna D. Abdul-Wahab Mohammed Ali Ibraheem Department of Mathematics, College of Department of Mathematics, College of science, University of Basrah ,Iraq science, University of Basrah ,Iraq Sadiq A. Mehdi Daher Waly Freh Department of Computer Science, College of Department of Mathematics, College of Education, Al-Mustansiriya University ,Iraq Science, University of Wassit ,Iraq Fatin A. Fadhil A.H.Majeed Department of Mathematics, College of Department of Mathematics, College Science, University of Baghdad, Iraq of Science, University of Baghdad, e-mail:fatinalsaadymath@yahoo.com Iraq e-mail:ahmajeed@yahoo.com Ahmed K. Shanan Department of Mathematics , College of Mudhir A. Abdul Hussain Education , University of Basrah , Basrah, Department of Mathematics , College of Iraq. Education , University of Basrah , Basrah, Iraq Ali A. Hassan Department of Mathematics,College of Science, Bahar H. AL-Bahraany University of Baghdad, Iraq Department of Mathematics,College of Science, University of Baghdad, Iraq Akram B. Attar Department of Mathematics, Faculty of Ra'ad S. Mahdi Education ,University of Thi-Qar ,Iraq Department of Mathematic , College of Science, University of Basrah, Iraq Ihssan A. Fadhel. Department of Mathematic , College of Abdulamear A. A. scince, University of Basrah, Iraq Department of Mathematics and Computer Applications, College of Science, Al- Nahrain University- Iraq Saad Abdulkadhim Al-Saadi Department, of Mathematics, College of Narjis Abdual Jabbar Dawood Science, Al- Mustansiriyah University, Iraq Department of Mathematics , Ibn – AL- E-mail: saadalsaadi08@yahoo.com Haitham College of Education, Baghdad University ,Iraq Nadia Faiq Mohammed Mohammed Kh. Abdullah Department of Mathematics , Ibn – AL- Department of Mathematics,college Haitham College of Education, Baghdad of Science, Basrah University, University ,Iraq Basrah, Iraq. 64 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ A.K. Hussein Zakariya Y. Algamal Department of Mathematics, College of Department of Statistics and Informatics , College of Computer Science and Basic Education, Al- Mustansiriyah Mathematics, University of Mosul ,Iraq University ,Iraq zak.sm_stat@yahoo.com E- mail: aalobiadi@yahoo.com Khairy B. Rasheed Mohammad Wahdan Muflih Department of Statistics and Informatics , Department of Mathematics, College of College of Computer Science and Ed. Ibn AL-Haitham, University of Mathematics, University of Mosul ,Iraq Baghdad ,Iraq Khairy_line@yahoo.com Huda Hammoodi Imran Mohanad Riyadh Saad Department of Mathematics, College of Ed. Department of Mathematics, College of Ibn AL-Haitham, University of Baghdad ,Iraq Science, University of Basrah, Iraq F.K. Hmeed Mustafa Hussein Department of Mathematics, College of Educat Department of Mathematics, College of ,University of Basrah. Iraq Education, University of Basrah., Iraq Mohammed Y. Abbas Layla Salman Mahmood Department of Mathematics, College of Educat Department of Mathematics , Ibn – AL- University of Basrah. Iraq Haitham college of Education, Baghdad University, Iraq Shrooq Bahjat Semeein Department of Mathematics , Ibn – AL- Raad Aziz Hussain Al-Abdulla Haitham college of Education, Baghdad Department of Mathematic, College of University ,Iraq Mathematics and computer Science , Al- Qadissiya University ,Iraq. Sema Kadhim Gaber Department of Mathematic, College of Amal M. Hashim Mathematics and computer Science , Al- Department of Mathematics, College of Qadissiya University ,Iraq Science, University of Basrah, Basrah- Iraq amalmhashim@yhoo.com Zeinab Sami Hussain Ali Mohamad Department of Mathematics, College of Department of Mathematics, College of Science, University of Basrah, Basrah- Iraq Science for Women, University of Baghdad ,Iraq Intisar Haitham Qasem Department of Mathematics, College of science Zainab Hhmed Abullah for women, University of Baghdad,Iraq Department of Mathematics, College of science for women, University of Baghdad,Iraq 65 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Feras Sh. M. Batah Malik Saad Al-Muhja Al-Anber Unversity , Iraq Department of Mathematics Computer Application, College of Sciences, University of Al-Muthana,Iraq Alaa, H. Mohamed Department of Mathematics, College of Salam A. Falih Education, University of Al-Qadisiya, Iraq Department of Mathematics,University of Basrah , Iraq Email: salamkader2006@yahoo.com Hussein jaber Abdul Hussein University of almuthanna, Iraq Ahlam J.Kaleel Department Of Mathematics and Computer Application , College of Science , Al- Nahrain University,Iraq Salam J.Majeed Department Of Physics , College of Science , Murtada J. Mohammed University of Thi-Qar,Iraq Department of Mathematics, College of Education, University of basrah, Iraq Adel M.Hassan Department of Mathematics,college of Ahmed Wady Shehab Mathematics and Computer Sciences ,Kufa Department of Mathematics,college of University ,Iraq Mathematics and Computer Sciences, Kufa adelramahi@gmail.com University ,Iraq ahmed71@gawab.com Mehsin Jabel Atteya Department of Mathematics, College of Mahmuod H. Al-Muifraje Education, Al-Mustansiriyah University,Iraq. Computer Science Department, E-mail: mehsinatteya@yahoo.com College of Sciences, University of Al- mustamsiriyah,Iraq Saad M. Khalifa Computer Science Department, College Asmaell Abdulsattar Jabar of Sciences, University of Al- Computer Science Department, mustamsiriyah,Iraq College of Sciences, University of Al- mustamsiriyah,Iraq Sattar B. Sadkhan University of Babylon, Member, IEEE, Nidaa A. Abbas, Iraq University of Babylon, Member, IEEE , E-mail: drengsattar@ieee.org Iraq Azhar H.Nasef Ammar A. Neamah AL-Mustansiryia University , Iraq University of Babylon,Iraq E-mail: alazhar1999@yahoo.com 66 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Sabiha F.Jawad Rewayda R. Mohsin AL-Mustansiryia University, Iraq E-mail: Department of Mathematics, College of sabiha_fj@yahoo.com Mathematics and Computer Science, University of Kufa, Najaf, Iraq Enas Y. Abdullah Hadi Jabber Mustafa Department of Mathematics, College of Department of Mathematics,college of Education, University of Kufa, Najaf, Iraq Mathematics and Computer Sciences ,Kufa University ,Iraq Dr. Abid Ali Al-Ta'ai Ministry of Higher Education of Iraq. Dr. Hana' M. Ali Department of Mathematics, Collage of Science, University of Basrah, Iraq Ali A. Shihab Moscow State Pedagogical University Moscow- Nadia Abud Habeeb AL-Mousaway Russia Department of Mathematics ,College of Science of Computer and Mathematics ,University of Thi-Qar ,Iraq ALI J. MOHAMMED University of Basrah, College of Education, HASAN A. NASER Department of Mathematics, Basrah, Iraq. University of Thi-Qar, College of Education, Department of Mathematics, Thi-Qar, Iraq Al Zuwaini M. K. Department of Mathematics, Collage of Mathematics Abdul Razaq , T. S. and Computer science Thi-qar University, Iraq Math. Dep. College of Science University of Al- Mustansiriyah, Iraq Saidy , S. K. Luay Al- Sweedy Math. Dep. College of Science University of Al- Department of Mathematics, College of Mustansiriyah, Iraq Education, Babyloon University,Iraq. Asmahan Flieh Hassan Abdulsattar Ali Hussien Department of Mathematics, College of Department of Mathematics ,Education Education for girls, Kufa University,Iraq. College of Woman, University of Anbar, Iraq Kareema A. Makrib Al-Khafaji Ali H. Mahmood Al-Obaidi Department of Mathematics, College of Department of Mathematics, College of Education Ibn- Hayyan,University of Education Ibn- Hayyan,University of Babylon,Iraq Babylon,Iraq Abdul Nabi I.Ibrahem Afrah A.Ahmed Department of Mathematics,college of Department of Mathematics,college of Science,University of Basrah,Iraq. Science,University of Basrah,Iraq. 67 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Ahmed Abbas Mezaal Omar I. Khaleel Department of Mathematics, College of Department of Computer and Continuous Computer Science and Mathematics, Education, Al-Nahrian University, University of Thi-Qar,Iraq. Baghdad, Iraq. lam A. Ahmed Zainab R. Shaker Department of Biotechnology, College of Science, Al-Nahrian University, Baghdad, Dept. of Mathematics and Computer Iraq. Applications, College of Science, Al- Nahrian University ,Iraq Dalal Ibraheem Resan Al-Mustansiriyah University-College of Ahmed M. Rajab Education-Department of Mathematics, Iraq. Department of Mathematics, College of E-mail: dalalresan@yahoo.com Education, University of Kufa, Najaf, Iraq Ali A. Kasim Anmar Hashim Jasim Department Of Statistics, College of Department of Mathematics, College of Administration and Economics, Baghdad Science, Al-Mustansiriyah University ,Iraq University ,Iraq E‐mail: ali661971@yahoo.com Sami D. Gabbara Hatim Kareem Khudhair Department of Mathematics, College of Department of Mathematics, College of Science, Salahaddin University- Erbil , Science, Al-Mustansiriyah University ,Iraq Iraq s_gabbara@yahoo.com Asaad M.A. Al-hosaini Department of Mathematics, College of ADEA K. AL- OBIADI Education Ibn Hayan,University of Department of Mathematics, College of Babylon,Iraq Basic Education, Al- Mustansiriyah Univ,Iraq E-mail: aalobiadi@yahoo.com ALI SAADI Department of Mathematics, College of Basic Saheb K. Al-Saidy Education, Al- Mustansiriyah Univ,Iraq Department of Mathematics,/College of Science, Al-Mustansiriya University,Iraq Haider J. Ali Department of Mathematics,/College of Dhwyia Salman Hassan Science, Al-Mustansiriya University,Iraq Department of Statistics,College of Administration and Economics, University of Baghdad ,Iraq Saad Ahmed Abdulrahman Al-Naimi Department of Statistics,College of Waleed A. Arhema AL-Elaiwe Administration and Economics, University of Department of Informative Baghdad, Iraq technology,Technical College of Management,Foundation of technical Education , Iraq 68 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Nieran Taher Abd Al-Ameer Nabaa Mery Qassim Department of Mathematics, College of Department of Mathematics, College of Education for girls, Kufa University, Iraq. Education for girls, Kufa University,Iraq. Abed Al-Hamza Mahdi Hamza Radhi A. Zaboon Department of Mathematics College of Department of Mathematics, College of Mathematics and Computer Science, Al-Mustansiryh University, Sciences,University of Kufa,Iraq Baghdad , Iraq Alaa Erees Abdul-Rauof Dhuha.M.Alyassiri Department of Mathematics, College of Department of Mathematics, College of Mathematics and Computer Sciences, Kufa Education Science, University of University, Iraq Sulaimania, Iraq Faraidun K.Hama Salih Jehad R. Khider Department of Mathematics, College of Department of applied sciences, university Education Science, University of Sulaimania, of technology, Baghdad, IRAQ Iraq Husnia Mohamed Eldanfour M. RAHMANI Department of Mathematics- Faculty of Technology Development Institute, ACECR, Science- Mistruth University – PO Box 966 Tehran, Iran. Mistruth – Libya rahmanimr@yahoo.com S. H. MOMENI-MASULEH Ali Farajzadeh Department of Mathematics, Shahed Department of Mathematics, Razi University University, Tehran, P.O. Box:18151-159, ,Kermanshah , 67149, Iran Iran H. Saleh Estahbanati B. Zarpak Department of Mathematics Department Mathematics of and and Computer Sciences, Computer Sciences, Shahed University, Shahed University, Tehran, Tehran, P. O. Box: 18151-159, Iran. P. O. Box: 18151-159, Iran. Syoof Khowman AL-Ramahi H.R. Bakhshi / Biomathematics unit, College of Computer Department of Electrical Engineering, Sciences and Mathematics, University of AL- Shahed University, Tehran, P. , Iran Qadisiyah,Iraq ddssnn2004@yahoo.com Mohammed A. Mohammed Idris A. Masoud Abdulhamid Al- Diwanya Technical Institute- University of Omar Al-Mukhtar,College of Iraq Education , Mathematics Department, Libya edreesatea@yahoo.com 69 ٢٠١١ ﺍﳌﺆﲤﺮ ﺍﻟﺪﻭﱄ ﻟﻠﺮﻳﺎﺿﻴﺎﺕ ﻭﺗﻄﺒﻴﻘﺎﺗﻬﺎ ١-٣ ﺁﺫﺍﺭ International conference of mathematics and its applications ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ Fadel Hameed Hadi Saad Salman Ahmad College of Administration and Section of mathematics, Department of economic,Al-Qadisiya University- Iraq Computing and Mathematics,Higher College of Technology AL-KHWAIR 133, Box 74, Muscat, Oman Hanan Ali Al-Ta’ai Department of Mathematics, College of Hussam Abd Ali Sciences, University of Al-mustamsiriyah,Iraq Department of Mathematics, College of hanan_altaai@yahoo.com Science, Karbla University,Iraq hussammath@yahoo.comhgfvd Fiaria Ali Al-Ta’ai Department of Mathematics, College of Saleem H. Al-Kutobi Sciences, University of Al-mustamsiriyah,Iraq Department Mathematics, College of fiaria_altaai@yahoo.com Mathematics and Computer Science, Kufa University, Iraq Alaa Hussein Hamadi Jassim M. Jawad Department Mathematics, College of Education College Mathematics and Computer Science, Al- Basrah University- Iraq Qadysia University,Iraq Ali M. Delphi Lamees K. Ali Department of Mathematics, college of Education College science Al-Mustansiriya University, Iraq Thiqar University - Iraq alimathdelphi@yahoo.com Mohanned saad abd karkosh Khulood Moosa Omran Baghdad, Iraq Arab Gulf Studies Center , Basrah University, Iraq Alauldin Noori Ahmed Department of Mathematic and Ahmed Ayyoub Yousif Computer Applications , College of Science , Department of Mathematic and AL-Nahrain University , Iraq Computer Applications , College of Science AL-Nahrain University , Iraq Ranen Z.Ahmood Department of Mathematic and Fadel A.Al-Bassam Computer Applications , College of Science Laser Physics Department-College of AL-Nahrain University , Iraq Science for Women Babylon Univ.,Iraq E-mail:albassam1799@yahoo.co.uk Dr. Hasan Naima Northern Virginia Community College, Woodbridge, VA 22191 ,USA 70

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 395 |

posted: | 8/9/2011 |

language: | Arabic |

pages: | 70 |

OTHER DOCS BY xiangpeng

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.