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 Modeling2224-5804Analytic approximate solutions of Volterra’s population and some scientific models by power series method
http://www.iiste.org/Journals/index.php/MTM/article/view/16372
In this paper, we have implement an analytic approximate method based on power series method (PSM) to obtain asolutions for Volterra’s population model of population growth of a species in a closed system. The numerical solution isobtained by combining the PSM and Pad´e technique. The Pad´e approximation that often show superior performance overseries approximation are effectively used in the analysis to capture essential behavior of the population u(t) of identicalindividuals. The results demonstrate that the method has many merits such as being derivative-free, overcome the difficultyarising in calculating Adomian polynomials to handle the nonlinear terms in Adomian Decomposition Method (ADM).It does not require to calculate Lagrange multiplier as in Variational Iteration Method (VIM) and no needs to construct ahomotopy and solve the corresponding algebraic equations as in Homotopy Perturbation Method (HPM). Moreover, weused this method to solve some scientific models, namely, the hybrid selection model, the Riccati model and the logisticmodel to provide the analytic solutions. The obtained analytic approximate solutions of applying the PSM is in fullagreement with the results obtained with those methods available in the literature. The software used for the calculationsin this study was MATHEMATICAr 8.0.M. A. AL-JawaryF. S. AhmedFadhel S. F.4A Study of Derivations on Lattices
http://www.iiste.org/Journals/index.php/MTM/article/view/16370
In this paper we introduce the notion...................Funmilola Balogun4Bayes Estimators for the Shape Parameter of Pareto Type I Distribution under Generalized Square Error Loss Function
http://www.iiste.org/Journals/index.php/MTM/article/view/16373
<p>In this paper, we obtained Basyian estimators of the shape parameter of the Pareto type I distribution using Bayian method under Generalized square error loss function and Quadratic loss function. In order to get better understanding of our Bayesian analysis we consider non-informative prior for the shape parameter Using Jeffery prior Information as well as informative prior density represented by Exponential distribution. These Bayes estimators of the shape parameter of the Pareto type I distribution are compared with some classical estimators such as, the Maximum likelihood estimator (MLE), the Uniformly minimum variance unbiased estimator (UMVUE), and the Minimum mean squared error (MinMSE) estimator according to Monte-Carlo simulation study. The performance of these estimators is compared by employing the mean square errors (MSE’s).</p> <p><strong>Key words:</strong> Pareto distribution; Maximum likelihood estimator; Uniformly minimum variance unbiased estimator; Minimum mean squared error; Bayes estimator; Generalized square error loss function; Quadratic loss function; Jeffery prior; Exponential prior.</p>Huda A. RasheedNajam A. Aleawy Al-Gazi4Constructing a MUSA Model to Determine Priority Factor of a SERVPERF Model.
http://www.iiste.org/Journals/index.php/MTM/article/view/16374
<p>The study aimed to determine the priority factor among the factors in a <em>SERVPERF</em> Model. The <em>SERVPERF</em> Model explains the students’ satisfaction towards the quality of service provided by their hostel management. Priority factor is the factor that is considered important by the customers, but they are not satisfied with the service provided for that factor. A Multi-criteria Satisfaction Analysis (<em>MUSA</em>) Model is built based on ordinal regression with linear programming approach. However, study found that the <em>MUSA</em> Model built is not stable and could not interpret the data set used. This finding is consistent with the fact that <em>MUSA</em> Model does not always give out an interpretable results..</p> <p><strong>Keywords: </strong>Multi-criteria Satisfaction Analysis (<em>MUSA</em>), Modified SERVPERF Model, Priority Factor, Ordinal Regression, Linear Programming Approach.</p>Sabri AhmadLoshini Thiruchelvam4Enhancing Students’ Mathematical Creative Problem Solving Ability Through Situation-Based Learning
http://www.iiste.org/Journals/index.php/MTM/article/view/16376
<p>Learning activities which emphasize more on answering questions than presenting questions have caused students’ lack awareness to encounter some problems. The situation of the students’ weak problem finding competence leads to their weak idea finding and problem solving. As a result, Creative Problem Solving (CPS) ability necessarily has to be developed in learning mathematics. There are six aspects of CPS competence as parts of thinking process stages, namely: objective finding, fact finding, problem finding, idea finding, solution finding, and acceptance finding. In this case, to learn mathematics is about to explore the ability to present and to solve the problems emerged by the students themselves, applying Situation-Based Learning (SBL). This research used quasi-experimental design with experimented and controlled groups. The experimented group was examined using SBL learning while the controlled one using conventional learning. Based on the research result, it can be concluded that the enhancement of students’ mathematical CPS ability who were taught under SBL learning is higher than those who were taught under conventional learning. Fact finding is the highest aspect of the students’ mathematical CPS ability, and the lowest aspect is acceptance finding.</p> <p><strong>Keywords: </strong>Mathematical situation, Mathematical problems, Mathematical creative problem solving, Situation-based learning</p>Isrok’atun .Tiurlina .4Forecasting Precipitation Using SARIMA Model: A Case Study of Mt. Kenya Region
http://www.iiste.org/Journals/index.php/MTM/article/view/16377
<p>Precipitation estimates are an important component of water resources applications, example, in designing drainage system and irrigation. The amount of rainfall in Kenya fluctuates from year to year causing it to be very hard to predict it through empirical observations of the atmosphere alone. Our objective was to determine the forecasted values of precipitation in Mt. Kenya region and also to determine the accuracy of the SARIMA model in forecasting precipitation in the same region. This research considers a univariate time series model to forecast precipitation in Mt. Kenya region. We fitted the SARIMA model to our data and we picked the model which exhibited the least AIC and BIC values. Finally, we forecasted our data after following the three Box-Jenkins methodologies, that is, model identification, estimation of parameters and diagnostic check. Having three tentative models, the best model had two highly significant variables, a constant and with p-values< 0.01 respectively<sup>.</sup> This model passed residual normality test and the forecasting evaluation statistics shows ME= -0.0053687, MSE=0.96794, RMSE=0.98384 and MAE= 0.75197. Indeed, SARIMA model is a good model for forecasting precipitation in Mt. Kenya region<strong> </strong></p> <p><strong>Keywords: </strong>SARIMA, Precipitation, Forecast, Mt. Kenya, AIC and BIC</p>Hellen W. KibunjaJohn M. KihoroGeorge O. OrwaWalter O. Yodah4Some Results on the Integral Means of the Derivative of a Univalent Function
http://www.iiste.org/Journals/index.php/MTM/article/view/16378
<p>The purpose of this research paper to show all the possible values of the pth- power of the integrable function which make the integral means of the derivative of univalent function exists and ?nite.</p> <p><strong>Keywords: </strong>univalent function, Integral means, self conformal maps.</p>Shatha S. Alhily4Explicit upper bound for the function of sum of divisors
http://www.iiste.org/Journals/index.php/MTM/article/view/16380
we developed the result proved by A.Eviwhere he proved the following theoremSaad A. BaddaiKhulood M. Hussein4Analysis Of Single Server Queueing System With Batch Service Under Multiple Vacations With Loss And Feedback
http://www.iiste.org/Journals/index.php/MTM/article/view/16382
<p>Consider a single server queueing system with foxed batch service under multiple vacations with loss and feedback in which the arrival rate ? follows a Poisson process and the service time follows an exponential distribution with parameter ?. Assume that the system initially contain k customers when the server enters the system and starts the service in batch. The concept of feedback is incorporated in this model (i.e) after completion of the service, if this batch of customers dissatisfied then this batch may join the queue with probability q and with probability (1-q) leaves the system. This q is called a feedback probability. After completion of the service if he finds more than k customers in the queue then the first k customers will be taken for service and service will be given as a batch of size k and if he finds less than k customers in the queue then he leaves for a multiple vacation of exponential length ?. The impatient behaviour of customer is also studied in this model (i.e) the arriving customer may join the queue with probability p when the server is busy or in vacation. This probability p is called loss probability. This model is completely solved by constructing the generating function and Rouche’s theorem is applied and we have derived the closed form solutions for probability of number of customers in the queue during the server busy and in vacation. Further we are providing the analytical solution for mean number of customers and variance of the system. Numerical studies have been done for analysis of mean and variance for various values of ?, µ, ?, p, q and k and also various particular cases of this model have been discussed.</p> <p><strong>Keywords : </strong>Single Server , Batch Service, Loss and Feedback, Multiple vacations, Steady state distribution.</p>G. AyyappanG. DevipriyaA. Muthu Ganapathi Subramanian4Modeling the SBC Tanzania Production-Distribution Logistics Network
http://www.iiste.org/Journals/index.php/MTM/article/view/16385
<p>The increase in customer expectation in terms of cost and services rendered, coupled with competitive business environment and uncertainty in cost of raw materials have posed challenges on effective supply chain engineering making it essential to do cost-benefit analysis before making final decisions on production-distribution logistics. This paper provides a conceptual model that provide guidance in supply chain decision making for business expansion. It presents a mathematical model for production-distribution of an integrated supply chain derived from current operations of SBC Tanzania Ltd which is a major supply chain that manages products' distribution in whole of Tanzania. In addition to finding the optimal cost, we also carried out a sensitivity analysis on the model so as to find ways in which the company can expand at optimal cost, while meeting customers' demands. Genetic algorithms is used to run the simulation for their efficient in solving combinatorial problems.</p> <p><strong>Key words:</strong> Business environment, supply chain engineering, production-distribution, genetic algorithms, optimal cost.</p>Nelson Christopher DzupireYaw Nkansah-GyekyeSilas Steven Mirau4Numerical Solution of Poisson Equation Using Fuzzy Data by finite Difference
http://www.iiste.org/Journals/index.php/MTM/article/view/16386
<p>In this paper, we have discussed fuzzification of elliptic partial differential equation taking Poisson Equation in two dimensions are discussed. The interval of fuzzy interval can be determined. Finite difference method applied of two different grids using five points, first for initial values and the second to solve Poisson equation numerically.</p> <p><strong>Keywords: </strong>Fuzzy membership function (f.m.f.), interval of confidence, triangular fuzzy number (t.f.n.), cuts, five points finite difference, Poisson Equation.</p>Mhassin A. A.4Presentation of Conjugacy Classes in the Partial Order - Preserving Transformation Semigroup with the aid of graph
http://www.iiste.org/Journals/index.php/MTM/article/view/16388
<p>Let denote the set of all partial transformation semigroup in a finite set 3, .., n} that is the set of all mapping from . The aim of this paper is to study the elements of partial order - - preserving transformation semigroup and arranged the elements in their respective conjugacy classes with the aids of unlabelled graph.</p> <p><strong>Keywords: </strong>Semigroup, transformation semigroup, conjugacy, conjugacy classes, graph, partial order – preserving transformation semigroup.</p>Mogbonju M. MGwary T. MOjeniyi A. B4Asymptotic Properties of Bayes Factor in One- Way Repeated Measurements Model
http://www.iiste.org/Journals/index.php/MTM/article/view/16391
<p class="Default">In this paper, we consider the linear one- way repeated measurements model which has only one within units factor and one between units factor incorporating univariate random effects as well as the experimental error term. In this model, we investigate the consistency property of Bayes factor for testing the fixed effects linear one- way repeated measurements model against the mixed one- way repeated measurements alternative model. Under some conditions on the prior and design matrix, we identify the analytic form of the Bayes factor and show that the Bayes factor is consistent.</p> <p class="Default"><strong>Keywords</strong>: One- Way Repeated Measurements Model, ANOVA, Mixed model, Prior Distribution, Posterior Distribution, covariance matrix, Bayes Factor, Consistent.</p> <p class="Default"> </p>Ameera Jaber MohaisenKhawla Abdul Razzaq Swadi4A Structural Equation Model of Tertiary Academic Achievement and Individual Private Returns
http://www.iiste.org/Journals/index.php/MTM/article/view/16392
<p>The primary objective of this study was to estimate individual private returns to tertiary academic achievement based on the classical human capital model. Using non-random sampling method, a structured questionnaire was used to collect data from relevant participants. A reduced form Structural Equation Model (SEM) in STATA 12 was applied to estimate individual private returns to tertiary academic achievement. The computed results show that both tertiary academic achievement and college ranking have sizable effects on individual incomes; while tertiary academic achievement further has a significant impact on employment prospects. Congruently, employment prospects and individual incomes exhibit substantial endogenous positive impacts on tertiary academic achievement. The reduced form estimates of the SEM show that grade point average (GPA) and college ranking have significant positive impacts on tertiary academic achievement, employment prospects and individual incomes. <strong></strong></p> <p><strong>Keywords</strong>: tertiary, academic, achievement, private returns, Structural Equation Model</p>Allexander Muzenda4An Improved Tabular Technique for Presenting the Various Algorithms for Finding Initial Basic Feasible Solutions to Transportation Problems
http://www.iiste.org/Journals/index.php/MTM/article/view/16393
<p>The special structure of the transportation problem allows securing a non-artificial starting basic solution using one of the three methods: Northwest-corner Method, Least-cost Method and Vogel Approximation Method. The difference among the three methods is the “quality” of the starting basic solution they produce, in the sense that a good starting solution yields an optimal solution in a fewer number of iterations. In general, the Vogel Approximation Method yields the best starting basic solution, and the Northwest-corner Method yields the worst. However, the Northwest-corner Method involves the least computations. Extensive and critical examination regarding the usage and improvement of these methods abound in several publications with trivial consideration given to the development of a near-ideal technique for presenting these algorithms. This paper develops and implements an all-encompassing tabular technique for presenting the algorithms for these three methods.</p> <p><strong>Keywords: </strong>Transportation problem, Improved Tabular Technique, Initial Basic Feasible Solution</p>John Usen EffiongNkereuwem Ikpang Ikpang4Robust Method for Testing the Significance of Bivariate Correlation of Ordinal Data
http://www.iiste.org/Journals/index.php/MTM/article/view/16394
<p>The Tau’s statistics were introduced to solve the problems of tied data but its effect on shape of table cannot be ascertained. This study compares the non parametric approaches for testing the significance of bivariate correlation for ordinal data based on table shape (square and rectangular table). The bootstrap method was used to compare the magnitude of the correlation values and the associated standard error of the values of tau’s -b, c and Gamma over a square and rectangular table. The Gamma was found to be the most robust statistic for computing the correlation of ordinal data<strong></strong></p> <p><strong>Keywords:</strong> Tau statistics, Gamma, ordinal correlation, Bivariate correlation</p>Odimientimi D. AgbedeyiAmechi H Igweze4On Z- generalized closed sets in topology
http://www.iiste.org/Journals/index.php/MTM/article/view/16395
<p>In this paper, we introduce and study the notion of generalized Z-closed sets. Also, the notion of generalized Z-open sets and some of its basic properties are introduced discussed. Further, we introduce the notion of generalized Z-closed functions. Moreover, some characterizations and properties of it are investigated.<em></em></p> <p><strong>Keywords</strong>: gZ-closed sets, Z-T<sub>1/2</sub>-spaces, gZ-continuous and ZgZ-continuous functions.</p>A. ZaghdaniA. I. EL-MaghrabiM. Ezzat MohamedA. M. Mubarki4Oscillations of Third Order Nonlinear Neutral Differential Equations with Positive and Negative Coefficients
http://www.iiste.org/Journals/index.php/MTM/article/view/16396
<p>In this paper oscillation criterion is investigated for all solutions of the third-order non linear neutral differential equations with positive and negative coefficients:</p>Hussain Ali MohamadBushra Mohammed Shehab4Trends in Transitive p-Groups and Their Defining Relations
http://www.iiste.org/Journals/index.php/MTM/article/view/16398
<p>In this paper unless otherwise stated the letter represents a fixed prime number. The concept of p- groups is fundamental in the theory of groups. Sylow theorems will be assumed known in this paper. In classifying finite groups we know in the Abelian case that the number of groups of order n is influenced largely by the character of the prime factorization of n, and not by the size of n alone. Any finite group G contains the so called Sylow p-subgroups which are p-groups and are closely linked to the structure of G. Recent developments in theory of finite simple groups have brought insights on p-groups and have suggested investigations in diverse areas. In this paper, however, we shall present some of the most basic results on transitive p-groups and their defining relations.</p> <p><strong> </strong></p> <p><strong>Keywords: </strong>transitive -groups, isomorphism, classification</p>Apine, EJelten, B. N4