Mathematical Theory and Modeling
http://www.iiste.org/Journals/index.php/MTM
<p><span id="internal-source-marker_0.04939836589619517"><span id="internal-source-marker_0.04939836589619517">Mathematical Theory and Modeling </span>is a peer reviewed journal published by IISTE. The journal publishes original papers at the forefront of mathematical theories, modelings, and applications. The journal is published in both printed and online versions. The online version is free access and download.</span></p><p><span>IISTE is member of <a href="http://www.crossref.org/01company/17crossref_members.html">CrossRef</a>.<br /></span></p>en-USMathematical Theory and Modeling2224-5804An Alternative Solution to Multi Objective Linear Fractional Programming Problem by Using Geometric Programming Technique
http://www.iiste.org/Journals/index.php/MTM/article/view/30420
<p>In this study, we have proposed an alternative solution to the multi objective linear fractional programming problems. This method deals with every objective of multi objective linear fractional programming problems gradually by using geometric programming technique to find the pareto optimal solution. The proposed solution procedure has been used in numeric examples and results have been compared with the real solution values.</p> <p><strong>Keywords: </strong>multi objective, fractional programming, geometric programming</p>Ersoy OZSelcuk AlpNuran Guzel6Assessing Univariate and Multivariate Homogeneity of Variance: A Guide For Practitioners
http://www.iiste.org/Journals/index.php/MTM/article/view/30421
<p>Most statistical methods assume constant variance and the validity of result from some of the methods highly rely on constant variance. However, a very high number of practitioners and researchers publications do not check the constant variance assumptions and hence the results are very prone to error. With aim of reducing this, both graphical and formal methods of assessing constant variance assumption are presented and illustrated in this paper. In univariate data several methods have been proposed. The graphical methods of assessing constancy of variance include plot of residuals against the fitted values, residuals against the fitted value square, and residual versus predictor variable are widely used. In addition, formal tests of assessing this assumption are <em>Bartlett’s, Levene’s</em><em>, </em>Breusch-Pagan, Brown and Forsythe<em>, </em>O’Brien’s, White’s<em> <em>and Fligner-Killeen are commonly used and also applicable in most of statistical software. For multivariate data, the two common tests in practice are Box’s M teste and Bartlett’s. Finally, when the constancy of variance assumption not satisfied, it is very important to </em></em>find a variance-stabilizing transformation.</p> <p><strong>Keywords: </strong>Homogeneity of variance, <em>Bartlett’s test, </em>Breusch-Pagan test, Brown and Forsythe test, <em>Levene’s test</em><em>.</em></p>Kassu Mehari Beyene6The Convergence of Expansion Method of Chebyshev Polynomials
http://www.iiste.org/Journals/index.php/MTM/article/view/30422
<p>In this paper, the weakly singular linear and nonlinear integro-differential equations are solved by using expansion method of Chebyshev polynomials of the first kind .The approximation solution of this equation is calculated in the form of a series which its components are computed easily .The existence and uniqueness of the solution and the convergence of the proposed method are proved. Numerical examples are studied to demonstrate the accuracy of the presented method.</p> <p><strong>Keywords: </strong>China insurance industry, Volterra integral equations, Fredholm integral equations, Integro-differential equations, Singular integral equations, Chebyshev polynomials method.</p>Eman Ali HussainNabaa Najdi HassanWafaa Abd Ibrahim6On Minimal Semi neat Subgroups
http://www.iiste.org/Journals/index.php/MTM/article/view/30423
<p>In [1] Abdulla Hattem gave some new results of minimal neat subgroups of Abelian G . 'L. Fuchs '' poses the problem of characterizing the subgroups of an Aealian group G which are intersections of finitely many pure subgroups of G (problem 13, p. 134 ) . This problem has been solved by ''Khalid Benabdallah'' and John Irwin (see[2]) . In this paper we shall give the generalization of the problem solved by Khalid Benabdallah . Firstly we shall give the definition of such subgroups which are called almost almostdense in G .</p>Hattem. M. A AbdullahAtifa J. S AbdullahRasha Hassen Ibraheem6On The Class Of Factored Arrangements
http://www.iiste.org/Journals/index.php/MTM/article/view/30424
<p>The first main objective of the work was to create a combinatorial answer to an essential question; "How Terao generalization of the class of supersolvable arrangements preserved the tensor factorization of the O-S algebra?", by finding a relation among several bases of the O-S algebra. This was achieved in two parts. First, the class of factored arrangements was classified in two subclasses, the subclass of completely factored arrangements and the subclass of factored arrangement that not completely factored. Our classification criteria was, "the existence of an ordering on the hyperplanes of a factored arrangement such that the set of all monomials that related to the sections of a factorization on forms an NBC basis of the O-S algebra as a free module". The second part was, a comparison among the structures of the O-S complex, the NBC complex and the partition complex. In spite of, our classification criteria was failed of the second subclass of factored arrangement that not completely factored, the existence of a one to one correspondence between the set of all NBC bases of and the set of all sections of a factorization on , provides a tensor factorization fashion to the O-S algebra.</p> <p>The second main aim of the work was to prove that our classification is compatible with the product construction for arrangements, by constructing the O-S complex, the NBC complex and the partition complex of the reducible factored arrangements. Finally, several illustrations and applications were indicated.</p> <p><strong>Keywords: </strong>Hyperplane arrangement, Supersolvable arrangement, factored (Nice) arrangement, Orlik-Solomon algebra, NBC module and Partition tensor module.</p> <p> </p>Hana' M. AliHawra'a H. Abd-Kareem6On the Global Existence of Solutions to a System of Second – Order Nonlinear Differential Equations
http://www.iiste.org/Journals/index.php/MTM/article/view/30425
<p>Solutions of second – order nonlinear differential system is investigated. A sufficient condition for every solution of the system to exist globally is obtained. Sufficient conditions are placed on the functions in the system that guarantee global existence of solutions to the system and these conditions are put into a theorem which is proved.</p>Faniran Taye Samuel6Other Distributions for a Continuous Response Aside the Normal Distribution in a Linear Regression Model.
http://www.iiste.org/Journals/index.php/MTM/article/view/30426
<p>In many instances, when one encounters a continuous response in model building, the normal distribution is often the preferred choice for the distribution of the response given the predictors. In particular, to some statisticians, the normal distribution is seen as the only distribution for a continuous response. Even when the assumption of normality is not met, various transformations are applied on the data so that it appears to be more nearly normal. This is sometimes not pleasant since, the model may no longer apply directly to the original scale of measurement, which is in most cases of interest. Likewise, in doing so, one tries to force the model framework and distributional assumption that may not be best for the data at hand. Aside transformations, other distributions exist and can equally (or even better) be used for a continuous response in a linear regression model. The theory in GLM extends the linear regression theory such that, a much broader family of distributions can be used for the error terms other than the normal distribution. In this paper, other continuous distributions are used to illustrate how they outperform the normal distribution in some instances. It is also shown that, occasionally (for a continuous response), the normal distribution does not seem to be a choice unless transformations are applied. As a tool for assessing which of the distributions provides the best fit, both AIC and BIC are used.</p> <p>To fit a GLM in SAS, the GENMOD procedure is used. In R, this can be accomplished by using the <em>glm</em> function. With these tools, only a handful of distributions can be used for the error terms. However, with the GAMLSS package in R, a number of distributions can be utilized. In using GAMLSS, the distribution of the response variable does not necessarily have to belong to the exponential family.</p> <p><strong>Keywords:</strong> GLM, Exponential Family, AIC, BIC, GAMLSS.</p>Felix Boakye Oppong6A Fixed Point Theorem In 2-Banach Space For Banach Contraction Principle
http://www.iiste.org/Journals/index.php/MTM/article/view/30427
<p>In This Paper we prove An Extension of Banach contraction principle through rational expression in 2-Banach space satisfying Three continuous mappings . Some result with S. banach (1922). And discuss about fixed point theory in 2-Banach space also established a fixed point theorem in 2-Banach space which generalized the result of many mathematician.</p> <p><strong>Mathematics Subject classification:</strong> 47H10,54H25</p> <p><strong>Keywords:</strong> Banach Space, Common Fixed point, Triangle inequality , Normed space, 2- Normed space, 2-Banach space.</p>Geeta Modi Priyanka Tyagi6Bayesian Analysis for Generalized Rayleigh Distribution
http://www.iiste.org/Journals/index.php/MTM/article/view/30428
<p>The generalized Rayleigh distribution (GRD) is considered to be a very useful life distribution. In this paper, we obtain Bayesian estimation of the shape parameter of the two-parameter Generalized Rayleigh distribution using single and double priors. A simulation study is conducted in R software to compare the different priors.</p> <p><strong>Key Words:</strong> Bayes estimation, double prior, hyper parameter, posterior distribution, posterior predictive distribution.</p>Saima Naqash6Using Fractional Series for Solving Fractional Burger's Equation
http://www.iiste.org/Journals/index.php/MTM/article/view/30429
<p>In this paper we study Fractional Burger's Equation of the form =0, Saad N. AL- AzzawiWurood Riyadh Abd AL- Hussein6ON JORDAN GENERALIZED HIGHER BI-DERIVATIONS ON PRIME GAMMA RINGS
http://www.iiste.org/Journals/index.php/MTM/article/view/30430
<p>In this study , we define the concepts of a generalized higher bi-derivation , Jordan generalized higher bi-derivation and Jordan triple generalized higher bi-derivation on Г-rings and show that a Jordan generalized higher bi-derivation on 2-torsion free prime Г-ring is a generalized higher bi-derivation .</p>Salah M. SalihAhmed M. Marir6On The CW Complex of the Complement of A Hypersolvable Graphic Arrangement
http://www.iiste.org/Journals/index.php/MTM/article/view/30431
<p>This paper interested in studying a CW complex for the complement of a hypersolvable graphic arrangement that related to a hypersolvable graph , by comparing it with the minimal CW complex for the complement of Jambu's-Papadima's deformed supersolvable arrangement . Motivated by our aim, a dimension of the first non-vanishing higher homotopy group for was calculated and a fashion of the cohomological ring of the complement was considered, just by using the hypersolvable partition analogue on . Moreover, an algorithm to deform any hypersolvable graph into a supersolvable graph was stated. Key-words: connected simple graph, graphic arrangement, hypersolvable (supersolvable) graph, Orlik-Solomon algebra, no broken circuit module, CW complex....</p>Hana' M. Ali6Different methods of estimation for generalized inverse Lindley distribution
http://www.iiste.org/Journals/index.php/MTM/article/view/30432
In this paper, we have considered different methods of estimation of the unknown param- eters of GILD. First we briefly describe different methods of estimations, namely maximum likelihood estimators, moments estimators, least squares estimators, weighted least squares, maximum product spacing estimates, methods of minimum distances, method of Cramer- von-Misses and methods of Anderson-Darling and compare them using extensive numerical simulations.Arber QoshjaFatmir Hoxha6An Alternative Solution to Multi Objective Linear Fractional Programming Problem by Using Geometric Programming Technique
http://www.iiste.org/Journals/index.php/MTM/article/view/30680
<p>In this study, we have proposed an alternative solution to the multi objective linear fractional programming problems. This method deals with every objective of multi objective linear fractional programming problems gradually by using geometric programming technique to find the pareto optimal solution. The proposed solution procedure has been used in numeric examples and results have been compared with the real solution values.</p> <p><strong>Keywords: </strong>multi objective, fractional programming, geometric programming</p>Ersoy OZSelcuk AlpNuran Guzel6