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 Modeling2224-5804Parameter Estimation of Weighted Erlang Distribution Using R Software
http://www.iiste.org/Journals/index.php/MTM/article/view/37685
<p>The Erlang distribution belongs to a group of continuous probability distributions with universal relevance primarily due to its relation to the exponential and Gamma distributions. If the time period of individual telephone calls is exponentially distributed, then the duration of the successive calls follows the Erlang distribution. In this paper, we take into account the weighted version of Erlang distribution known as weighted Erlang distribution. We obtain the posterior mean and posterior variance of the model. Maximum likelihood method of estimation is discussed. Bayes estimates of the scale parameter of Weighted Erlang distribution is offered for consideration under Squared Error Loss Function (SELF), Quadratic Loss Function (QLF) and entropy Loss Function (ELF) using Jeffrey`s, extension of Jeffrey`s and Quasi priors.</p> <p><strong>Keywords: </strong>Erlang distribution, Weighted Erlang distribution, Loss function, Bayesian estimation.</p>Sofi MudasirS.P Ahmad7Calibration Estimators by Penalty Function Method
http://www.iiste.org/Journals/index.php/MTM/article/view/37686
<p>Estimation of finite population total using calibration has been considered by several authors. A distance measure is minimized subject to some calibration constraints, usually by way of introducing langrage equation whose solution gives the design weights used in estimation of population total. Sometimes a solution to the langrage constants does not exist. In this paper, we have considered the calibration problem as a nonlinear constrained minimization problem, which we transform to an unconstrained optimization problem using penalty functions. The design weights are obtained iteratively in a numerical manner. We show that the resulting estimator is more accurate than the popular Horvitz Thompson design estimator</p> <p><strong>Keywords: </strong>calibration, interior penalty function, exterior penalty function</p>Pius Nderitu Kihara7Axiomatic Probability Theory and Dimensional Probability Spaces
http://www.iiste.org/Journals/index.php/MTM/article/view/37687
<p>The aim of this research is to evaluate the main occurrences that blossoms in mathematics especially in the field of probability. To abstract the whole course generated in this context of both dimensional probability space and axiomatic probability theories then some few cases are discussed in it. These are the ways and the modes in which we can approach these core subjects of probability. Everything that pertain these two subjects is included in order to help in learning about these two prospective probability issues. <strong></strong></p> <p><strong>Keywords: </strong>axiomatic, axiomatic probability, axiomatic probability theories, dimensional probability</p>Moudhi sameer alshelahi7Comparative Analysis of WAEC and NECO Senior Secondary School Mathematics Examination
http://www.iiste.org/Journals/index.php/MTM/article/view/37688
<p>The main objective of this study was to compare the senior secondary school Mathematics examination questions set by the West African Examinations Council (WAEC) and the National Examinations Council (NECO) to ascertain how much the questions were distributed across the cognitive domain, the themes and topics in their syllabi. To this effect, the objective and essay question papers set by WAEC and NECO in Mathematics in 2008, 2009, 2010, 2011 and 2012 were obtained. A total of 917 Mathematics questions were set by the two examination bodies. The number of candidates that took both the Mathematics examinations conducted by WAEC and NECO in those years was 135, 712. A sample of 2000 was selected for the study using a purposive sampling technique. The questions were analysed in terms of how many of them fell under the various levels of the cognitive domain, the themes and topics in the syllabi of the examination bodies. Six research questions were stated were formulated and tested using the chi-square and t-test analyses at .05 level of significance. The results showed that for both examination bodies most of the questions came from application level, number and numeration theme and statistics topics. Based on academic performance on the candidates there was significant difference among the urban and rural candidates and likewise among the public and the private school candidates. The conclusion therefore is that, taking the distribution of questions across the level of the cognitive domain, the themes and the topics in the syllabi into consideration, WAEC and NECO were similar. It was recommended that the teachers should endeavour to teach to cover all the topics in the syllabi of the examination bodies so that the students would not found wanting when answering the examination questions.</p> <p><strong>Keywords</strong>: WAEC, NECO, Mathematic Syllabus, SSCE, Test Development.</p>Nsikak-Abasi UdofiaKenneth Isaac Udoh7Turbulent Natural Convection in an Enclosure at Varying Aspect Ratio
http://www.iiste.org/Journals/index.php/MTM/article/view/37689
<p>Energy transfer mechanism in most technical flows is through turbulent natural convection due to low viscosity of the fluids used in technical applications. Consequently, there is need to establish the parameters that influence the flow field of turbulent flow regime in order to enhance the energy-efficacy of many thermal applications. In order to establish the influence of the geometrical configuration of the flow domain on the flow field, we obtain and analyze the distribution of the velocity and temperature fields of a Boussinesq buoyancy-driven turbulent flow field in a locally heated and cooled enclosure for while maintaining the Rayleigh number of the flow at . To filter out the enormous turbulent scales inherent in the turbulent flow regime, we decompose the flow variables present in the instantaneous equations governing a viscous Boussinesq buoyant flow and subject the resulting equations to the Reynolds averaging process to obtain equations that governs the turbulent flow field. We resolve the turbulent quantities emanating from this process using the turbulence model coupled with the Boussinesq approximation. To ensure the satisfaction of the conservation laws at the discrete level and over the entire solution domain, the non-dimensionalized equations are discretized using the robust finite volume method. The method possesses the ability to adapt a grid structure that captures the local features of the flow domain and imposes the integral form of the governing equations to each finite volume of the discretized solution domain so that the final mathematical formulation has an intimate connection to the actual physical situation. Since the equations are coupled, a segregated pressure-based iterative method is used to obtain the solution. The results revealed that the velocity and temperature fields are non-uniformly distributed in the enclosure and their magnitude and distribution significantly depend on the Aspect ratio of the enclosure. The results are consistent with the experimental results of Markatos and Pericleous (Markatos & Pericleous, 1984).</p> <p><strong><em>Keywords</em></strong>: Aspect Ratio, Boussinesq, Buoyancy, Natural Convection, Reynolds Stresses, Turbulent heat flux.</p>Stephen KaranjaJohana SigeyFrancis GatheriEustace Kirima7Practical Implementation of Unconstrained Optimization Methods Tested on Quadratic Functions
http://www.iiste.org/Journals/index.php/MTM/article/view/37690
In this work we give a detailed look to the Practical implementation of unconstrained optimization tested on quadratic functions. Section (1) speak about the theory of optimization problems, introduce definitions and theorems of linear programming problems , definitions and theorems of quadratic programming problems . Section (2) introduce some methods of unconstrained optimization. In section(3) we look at methods for approximating solutions to equations, solving unconstrained optimization problems . Section(4) gives practical implementation of some method s using Matlab programs.Awatif M. A. El Siddieg7On Higher Derivations of Lattices
http://www.iiste.org/Journals/index.php/MTM/article/view/37691
<p>In this paper, as a generalization of derivation on a lattice, the notion of higher derivation is introduced and some fundamental properties are investigated for the higher derivation on a lattice. Furthermore it is shown that the image of an ideal and the set of fixed points under higher derivation are ideals under certain conditions.</p> <p><strong>Keywords: </strong>derivation, higher derivation, lattice</p>Yilmaz Ceven7Optimal Control Strategies and Cost Effectiveness Analysis of a Malaria Transmission Model
http://www.iiste.org/Journals/index.php/MTM/article/view/37692
<p>In this paper, a non-linear model with three control parameters for household of malaria has been study. The disease free equilibrium is obtained and the basic reproduction number is computed using the next generation matrix. We carry out cost evaluation of the model to optimize the cost of the intervention in the objective functional using Pontryagins’s Maximum Principle (PMP). We apply the optimal control strategy to investigate and analyze the optimal cost for controlling the transmission of malaria using treated bednets, treatment and indoor residual spray as parameters. Numerical simulation has been carry out using Runge-Kutta of order four to calculate the incremental cost effectiveness ratio () for the implementation of various combinations of the parameters to determine the most cost effective strategy that check the spread of the disease. Our findings show that the most cost-effective strategy to check the spread of malaria is strategy F (the combination of treatment of infected individuals and indoor residual spray parameters).</p> <p>Keywords: Optimal Control, Malaria Transmission, Cost-Effectiveness, Treated Bednets, Treatment, Indoor Spray</p>A. AlhassanA. A. MomohA. S. AbdullahiM. T. Y. Kadzai7Multivariate Assessment of Industrial Attachment by Students of Tertiary Institutions in Ghana
http://www.iiste.org/Journals/index.php/MTM/article/view/37693
<p>The paper examines the latent benefits as well as the challenges that are associated with industrial attachment exercise undertaken by tertiary institution students in Ghana. It makes use of exploratory factor analysis of high-dimensional datasets generated on likert scale using a total of forty-eight indicators of the usefulness and challenges of the exercise along various dimensions. The results show a general acceptance of the usefulness of the exercise. However, there is equally a general acceptance of challenges. Specific dimensions of these challenges are issues related to distance that students and supervisors have to cover to access attachment centres; lack of monitoring and supervision; and lack of suitability of training programmes. Using factor scores, the results further show that the extent of usefulness and challenges associated with industrial attachment are almost equally experienced by all students irrespective of sex and programme of study.</p> <p><strong>KEYWORDS: </strong>Industrial Attachment, Graduate Unemployment, Training Programme</p>M. FrempongH. NkansahB. K. Nkansah7Transmuted Inverse Loglogistic Model: Properties and Application in Medical Sciences and Engineering
http://www.iiste.org/Journals/index.php/MTM/article/view/37694
<p>In this article, we introduced a two parameter Transmuted model of Inverse Log-logistic Distribution (TILLD) using the quadratic rank transmutation map technique studied by Shaw and Buckley [1]. We provide a comprehensive description of the statistical properties of the TILLD. Robust measures of skewness and kurtosis of the proposed model have also been derived along with the moment generating function, characteristic function, reliability function and hazard rate function of the said model. The estimation of the model parameters is performed by maximum likelihood method followed by a Monte Carlo simulation procedure. The applicability of this distribution to modeling real life data is illustrated by two real life examples and the results of comparison to base distribution in modeling the data are also exhibited.</p> <p> </p> <p><strong>Key Words: </strong>Transmuted Inverse Log-logistic Distribution (TILLD), Survival Analysis, Robust measures, Monte Carlo Simulation.</p>B.A. ParaT. R. Jan7Application of Sobolev inequalities for higher order fractional derivatives
http://www.iiste.org/Journals/index.php/MTM/article/view/37695
in this paper we study the general uncertainty principal , we obtain the best constant as application of Sobolev inequalities for higher order fractional derivatives .Ali Hassan Abbaker Abd alla7