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 Modeling2224-5804Effect of heat transfer on the peristaltic transport of MHD with couple-stress fluid through a porous medium with slip effect
http://www.iiste.org/Journals/index.php/MTM/article/view/13704
<p>This paper concern with the Peristaltic transport of MHD Newtonian fluid in asymmetric two dimensional channel with couple –stress through a porous medium under the influence of heat transfer analysis. For the formulation of the problem long wave length and low Reynold number assumption is taken into account. An exact solution is presented for velocity field and the temperature field through solving a non-homogenies partial differential equation that described the flow field. Effects of different physical parameters, reflecting couple-stress parameter, permeability parameter, slip parameter, Hartman number, constant heat radiation factor and Grashof number, as well as amplitude ration on pumping characteristics and frictional force, stream lines pattern and trapping of peristaltic flow pattern studied with particular emphasis. This study are discussed through graphs.</p> <p><strong>Keywords</strong>: Peristaltic Transport, Couple-Stress, Magnetic Field, Newtonian Fluid, Porous Medium, Reynolds Number, Heat transfer.</p>Lika Z. HummadyAhmed M. Abdulhadi4Effectiveness of Progressive Learning Approach toward Enhancement of Students’ Competency on Mathematics Journal Writing and Mathematical Proof
http://www.iiste.org/Journals/index.php/MTM/article/view/13705
<p>This is quasi-experimental research of two different groups of 41 and 46 mathematics students. This research was conducted at Haluoleo University of Kendari South-East Sulawesi Indonesia. Progressive learning approach was applied to group of 41 students as an experimental group and conventional learning approach was applied to the other group of 46 students as conventional group. The students were also categorized by their grade point average (GPA) into higher, medium, and lower levels. Mathematical journal writing and mathematics proof competencies were measured by pre-test and post-test on both areas. Scores of these tests were analised with Anacova test, two-way Anova, t-test, and Mann-Whitney U test. In this reaseach students were expected to have mathematics journal writing and mathematical proof competencies. The results of the research are (1) students’ mathematics journal writing competency and students’ increment at mathematics journal writing competency of progressive learning approach is better than that of conventional one; (2) students’ mathematical proof competency and students’ increment at mathematical proof competency of progressive learning approach is better than that of conventional one, but students’ increment of mathematical proof competency at lower level of GPA is not significantly different.</p> <p><strong>Key</strong><strong>w</strong><strong>ords</strong>: progressive learning approach, mathematics journal writing competency, mathematical proof competency</p>Kodirun .Yaya S. KusumahJozua SabandarDarhim .4Estimation of Irrigation Water Demand in Rice Production Tanzania
http://www.iiste.org/Journals/index.php/MTM/article/view/13706
<p>The agriculture sector is one of the major users of water resource for irrigation activities. In Tanzania irrigation water demand for rice is still increasing due to the area being irrigated continues to expand while the amount of water for irrigation is decreasing. The purpose of this paper was to develop the demand function for estimation of irrigation water in rice production in Tanzania. The secondary data were collected from various sources such as the Ministry of Agriculture, Food Security and Cooperatives at Statistics Unit, and relevant basin authorities and zonal irrigation units. A demand function was estimated after carrying out the relevant statistical tests. The Breush and Pagan Lagrangian Multiplier Test were used to select whether to use the Pool or Panel Data approaches. The Panel model was verified to be more suitable than the Pool model. The fixed effect and random effect were compared in the Hausman’s specification test. The price elasticity of irrigation water demand and other elasticity were also estimated using Ordinary Least Squares facilitated by STATA 11. A panel data of 16 regions of Tanzania in the period of 2007 - 2012 were used. The estimated average water demand found to be 8000m<sup>3</sup>/ha whereas water productivity in rice cultivation found to be 0.3kg/m<sup>3</sup>.</p> <p><strong>Keywords:</strong> Water demand function, Water productivity, Panel data, Rice, Irrigation water</p>Amos MichaelDmitry KuznetsovSilas Mirau4Study On Feebly Lambda – Functions
http://www.iiste.org/Journals/index.php/MTM/article/view/13707
<p>In this research we study a several characterization of feebly Lambda-functions and investigate the relationship between such functions.</p>Yiezi Al-Talkany4An Extension of Peano Axioms for the Natural Number System
http://www.iiste.org/Journals/index.php/MTM/article/view/13708
<p>As a fundamental requirement, a natural number system must necessarily satisfy Peano axioms. These axioms altogether justify whether or not a number system is a natural number system. In this paper, a set of axioms have been proposed and established to augment and extend the existing Peano axioms for the natural number system.</p> <p><strong>Key Words:</strong> Natural numbers, Rational numbers, Peano axioms, Pearson correlation coefficient, Even and Odd partitions.</p>Stephen Sebastine AkpanJohn UsenThomas Adidaumbe Ugbe4Modeling the Effect of Screening and Treatment on the Transmission of Tuberculosis Infections
http://www.iiste.org/Journals/index.php/MTM/article/view/13710
<p>Tuberculosis (TB) is a chronic airborne disease caused mainly by Mycobacterium tuberculosis and has caused many deaths globally and Tanzania in particular due to failure or delayed intervention. In this paper, a deterministic mathematical model for transmission dynamics of TB with vaccination and screening the population for the purpose of identifying those for immediate treatment is formulated. The effective reproduction number is computed in order to measure the relative impact for individual or combined intervention for effective disease control. Numerical simulations of the basic reproduction number shows that, the combination of vaccination, screening and treatment is the most effective intervention for minimizing the transmission of TB in a population.</p> <p><strong>Key words</strong>: Tuberculosis, Modeling, Screening, Treatment.</p>N. NyerereL. S. LuboobiY. Nkansah-Gyekye4Some Estimation Methods for the Shape Parameter and Reliability Function of Burr Type XII Distribution / Comparison Study
http://www.iiste.org/Journals/index.php/MTM/article/view/13712
<p>Burr type XII distribution plays an important role in reliability modeling, risk analyzing and process capability estimation. The choice of the best estimation method is one of the goals in estimating parameters of the distribution. The main aim of this paper is to obtain and compare the classical "maximum likelihood and uniformly minimum variance unbiased" estimators and the Bayesian estimators of the shape parameter, ???? and reliability function based on a complete sample when the other shape parameter, ? known. The Bayes estimators are obtained under non-informative priors "Jeffrey’s prior, modified and extension of Jeffrey’s prior" as well as under informative gamma prior based on different symmetric and asymmetric loss functions "squared error, quadratic, LINEX, precautionary and entropy". The Monte Carlo experiment was performed under a wide range of cases and sample size. The estimates of the unknown shape parameter were compared by employing the mean square errors and the estimates of reliability function were compared by employing the <a title="Mean integrated squared error" href="http://en.wikipedia.org/wiki/Mean_integrated_squared_error">integrated mean squared error</a>.</p> <p> </p> <p><strong><span style="text-decoration: underline;">Keywords:</span></strong><strong> </strong>Burr type XII distribution; Maximum likelihood estimator; Uniformly Minimum Variance Unbiased estimator; Bayes estimators; non-informative Prior; informative Prior; Squared error loss function; quadratic loss function; LINEX loss function; Precautionary loss function; Entropy Loss function; Mean squared error; <a title="Mean integrated squared error" href="http://en.wikipedia.org/wiki/Mean_integrated_squared_error">integrated mean squared error</a>.</p>Nadia H. Al-NoorHuda A. Abd Al-Ameer4Fixed point theorems through rational expression in Altering distance functions
http://www.iiste.org/Journals/index.php/MTM/article/view/13714
<p>In this paper we proves a generalised results of J.R. Morales , E.M.Rojas , B.K.Dasand, S.Gupta .Also the results given by B.Samet and H.Yazid using altering distance functions and property P for the contraction mappings.</p> <p><strong>Keywords:</strong>Fixed point, Altering distance functions, Complete metric space.</p> <p><strong>Mathematical Subject Classification</strong>: 45H10, 54H25.</p>Renu Praveen PathakRashmi TiwariRamakant Bhardwaj4State-Dependent Model for the Analysis of Inflationary Rates
http://www.iiste.org/Journals/index.php/MTM/article/view/13715
<p>In this study, an extension of the class of state-dependent model (SDM) for which optimal forecasts may be computed using a recursive examination procedure referred to as the Kalman filter is developed for the analysis of Inflationary rates in Nigeria. The SDM formulation yields a practical means of estimation for the complex time varying dynamical process and provided a generic flexible framework for inflationary rate modelling and inference. A straight forward implementation was achieved in the study by the use of R software package.</p> <p>Key words: Dynamical systems, Non-Linear time series models, State space model, Kalman filter,</p>AGWUEGBO, S.O.NADEWOLE, A.POLAYIWOLA, O.MAPANTAKU. F. S.4Common Fixed Point of Weakly Compatible Maps on Intuitionistic Fuzzy Metric Spaces
http://www.iiste.org/Journals/index.php/MTM/article/view/13718
<p>In this paper, we introduce the concept of - chainable intuitionistic fuzzy metric space askin to the notion of - chainable fuzzy metric space and prove a common fixed point theorem for weakly compatible mappings in this newly defined space.</p> <p> </p> <p><strong>2010 Mathematics Subject Classification:</strong> 47H10, 54H25.<strong> </strong></p>Rasik M. PatelRashmi TiwariRamakant Bhardwaj4The new class of L-stable hybrid method based on super-future point, for numerical solution of stiff ODEs
http://www.iiste.org/Journals/index.php/MTM/article/view/13719
<p>In this paper, we present a class of super-future hybrid method for the numerical solution of first-order stiff ordinary differential equations. In order to obtain higher order L-stable methods, we have used second derivative of the solution, off-step point and one future point. The accuracy and stability analysis are discussed. An appropriate choice of the coefficients allows us to derive L-stable schemes of order 5. A good comparison between the results of the new class and the results due to others, show that the new class is suitable for stiff ODEs.</p> <div><p><strong>Keywords:</strong> Stiff initial value problems, Super-future, Off-step point, Stability aspects.</p></div>M. Mehdizadeh Khalsaraei4Bioeconomic Model for Tilapia – Nile Perch Fishery in Polluted Environment with Constant Harvesting Efforts in Tanzanian Waters of Lake Victoria
http://www.iiste.org/Journals/index.php/MTM/article/view/13722
<p>In this paper, bioeconomic model for Tilapia (Oreochromis niloticus) – Nile perch (Lates niloticus) fishery in polluted environment with the constant harvesting efforts is developed. The model analysed to get maximum sustainable yield (MSY) points and the corresponding conditions for existence established. The equilibrium points of the model found and the conditions for their existence established. The stability analysis of the interior equilibrium point is investigated by using Jacobian matrix method. Later, numerical simulations and their corresponding graphs revealed that water pollution has significant effects on the maximum sustainable yields of both Tilapia and Nile perch produces. These effects also manifests the rapid changes of species population at the interior equilibrium point.</p> <p><strong>Keywords: </strong>bioeconomic model, fishery, Tilapia, Nile perch, harvesting and water pollution.<strong></strong></p>Maranya Makuru MayengoLivingstone S. LuboobiDmitry Kuznetsov4Effects of Flow Parameters on Flow Variables of a Newtonian Fluid through a Cylindrical Collapsible Tube
http://www.iiste.org/Journals/index.php/MTM/article/view/13725
<p>The dynamics of fluid flow in collapsible tube are vital in understanding the behavior and analysis of flow phenomenon in veins, arteries, airways, urethra, etc. These fluid-conveying vessels in human body are highly flexible and collapsible, and accommodate deformation that result to a highly noncircular cross sectional area. This research aimed at determining the effects of various flow parameters on the flow variables of a Newtonian fluid flowing through a cylindrical collapsible tube. The tube is considered collapsible in the transverse direction, taken to be perpendicular to the main flow direction. The mathematical model in this study can be employed to simulate biological fluid flows such as blood flow in the arteries and veins. The equations governing the flow i.e. the continuity equation, the momentum equation and the tube law have been discussed. The results are presented in form of graphs. The results show that the flow parameters considered are directly proportional to both the cross sectional area and internal pressure and inversely proportional to the flow velocity</p> <p> </p> <p><strong>Keywords:</strong> collapsible tube, flow parameters, flow variables, transverse direction</p>Caroline KanyiriKang’ethe GiterereMathew Kinyajui4New Proposed Length-Biased Weighted Exponential and Rayleigh Distribution with Application
http://www.iiste.org/Journals/index.php/MTM/article/view/13729
<p>The concept of length-biased distribution can be employed in development of proper models for lifetime data. Length-biased distribution is a special case of the more general form known as weighted distribution. In this paper we introduce a new class of length-biased of weighted exponential and Rayleigh distributions(LBW<sub>1</sub>E<sub>1</sub>D), (LBWRD).This paper surveys some of the possible uses of Length - biased distribution We study the some of its statistical properties<strong> </strong>with application of these new distribution<strong>.</strong></p> <p><strong> </strong></p> <p><strong>Keywords</strong>: length- biased weighted Rayleigh distribution, length- biased weighted exponential distribution, maximum likelihood estimation.</p>Kareema Abed Al-kadimNabeel Ali Hussein4Use of Dummy Variable Regression Techniques in Estimating Joint and Marginal Values of an Outcome
http://www.iiste.org/Journals/index.php/MTM/article/view/13732
<p>This paper proposes a statistical method for estimating the values, including the joint and marginal values of an outcome variable, using dummy variable multiple regression techniques. Estimates are also provided for the direct and indirect effects of a parent independent variable on a dependent variable through its representative dummy variables in the presence of other independent variables in the model. The proposed method is illustrated with some data.</p> <p><strong>Keywords:</strong> Dummy Variables, Total Effect, Direct Effect, Indirect Effect, Parent Variables, Mediation Model, Joint Value, Marginal Value.</p>Nwankwo Chike HOyeka, I.C.A.4Comparison Of Survival Models And Estimation Of Their Parameters With Respect To Mortality in a Given Population .
http://www.iiste.org/Journals/index.php/MTM/article/view/13734
<p>In this research, we consider three different survival models under the assumption of Gompertz model as the baseline distribution. We compare the fitting results of the Exponential distribution , the Gompertz distribution and the Gompertz - Makeham model in a given population. As the human lifespan decreases, more and more people are becoming interested in mortality rates at higher ages. The aim of this study is to estimate the robust and reliable estimates of level and trend in mortality in Homa-Bay county , Kenya . The purpose of this study is to find out if the population of Homa-Bay area in Nyanza Province fits the Gompertz model and also to compare different survival models parametrically in a population. And also to determine the relationship between death rate and age in the area. . Akaike Information Criterion (AIC) is used to identify the best model. The expected output is that the preferred model is the one which satisfies the characteristics of the given population.</p> <p><strong>Keywords</strong>: Gompertz distribution, Gompertz-Makeham Model , Expected life time, Force of mortality, AIC, Stochastic process.</p>Kiche JAduda J.Athiany K.H.OApudo. B.OWanjoya A.4Common Fixed Point Theorems for Countable Faintly Compatible Mappings in Fuzzy Metric Space
http://www.iiste.org/Journals/index.php/MTM/article/view/13736
<p>In the present paper, we prove some fixed point theorems for countable faintly compatible mappings in fuzzy metric space. Our results extend and generalized the result of S. Manro and A. Tomar [Faintly compatible maps and existence of common fixed points in fuzzy metric space, Anal. of Fuzzy Math. and Informatics, 10 (2014), 1-8].</p> <p><strong>Keywords:</strong> Fuzzy Metric Spaces, non-compatible mappings, faintly compatible mappings and reciprocally continuous mappings.</p>Kamal WadhwaVed Prakash Bhardwaj4Logistic Regression Model for Determining the Sex of a Child Using Age of the Mother and Month of Conception
http://www.iiste.org/Journals/index.php/MTM/article/view/13740
<p>The issue of sex determination (before conception) is beyond the study of Science. Though current studies have developed means to determine gender, it is not until the baby has been conceived. After conception, scientific methods can be used to determine whether the baby will be a boy or a girl. This study seeks to use the age of the mother and the month in which she conceives to predict the gender of the baby, using appropriate statistical methods. The data used for this study was extracted from the delivery books of the Maternity Department of Achimota Hospital in the Amasaman District of Greater Accra Region in Ghana from 2000-2004. Logistic regression was used to analyze the data since the dependent variable has only two possible values (Male or Female). The results reveal that the odds of estimating correctly the gender of a baby improves by only 0.4% if one knows the age of the mother and by 1.1% if one knows the month within which the child was conceived.</p> <p><strong>Keywords: </strong>Sex Determination, Logistic Regression, Age, Month of Conception.</p>Ben Apau-DadsonIddrisu Wahab AbdulMartin Owusu AmoamahJoseph Dadzie4