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 Modeling2224-5804HLLY'S Theorem in Banach Lattice With order continuous norm in term of a double sequence
http://www.iiste.org/Journals/index.php/MTM/article/view/24138
<p><strong> </strong>In this paper, we introduce Helly and Helly -Bray theorems in term double sequence in the context of Riesz space with order continuous norm, and we review some of the results that are needed to prove our theorems. <strong></strong></p> <p>We state some definitions, like as the moment double sequence and complete moment. Later we prove the corresponding generalized moment theorem and representation in term of double sequence of positive operators.</p> <p>2010 Mathematics Subject Classification primary 46B42.</p> <p><strong>Keywords: </strong>vector lattice, Moment sequence, completely moment sequence, positive operator.</p>Ali Hussein BattorEman Samir BhayaSaja Fadhil Abed5On Pairwise #pi-g-s - Closed maps in Bitopological Spaces
http://www.iiste.org/Journals/index.php/MTM/article/view/24139
<p class="Default">In this paper we introduce the class of closed sets namely (1, 2)* - generalized<strong><sup>(1, 2)*-</sup></strong> <sup>πgb</sup> semi -closed sets (briefly(1,2)*- #πgs closed sets) and discuss some of their properties in bitopological spaces.Further, we define and study a new class of generalized maps called (1,2)* generalized<strong><sup>(1, 2)*-</sup></strong> <sup>πgb</sup> semi-closed maps(briefly(1,2)*-#πgs- closed maps). Also, we give some characterizations and applications of it.</p> <p><strong> </strong></p>Bushra Jaralla Tawfeeqd5Data Based Mechanistic modelling optimal utilisation of raingauge data for rainfall-riverflow modelling of sparsely gauged tropical basin in Ghana
http://www.iiste.org/Journals/index.php/MTM/article/view/24140
<p>Data-Based Mechanistic (DBM) modelling is a Transfer Function (TF) modelling approach, whereby the data defines the model. The DBM approach, unlike physics-based distributed and conceptual models that fit existing laws to data-series, uses the data to identify the model structure in an objective statistical manner. The approach is parsimonious, in that it requires few spatially-distributed data and is, therefore, suitable for data limited regions like West Africa. Multiple Input Single Output (MISO) rainfall to riverflow modelling approach is the utilization of multiple rainfall time-series as separate input in parallel into a model to simulate a single riverflow time-series in a large scale. The approach is capable of simulating the effects of each rain gauge on a lumped riverflow response.</p> <p> </p> <p>Within this paper we present the application of DBM-MISO modelling approach to 20778 km<sup>2</sup> humid tropical rain forest basin in Ghana. The approach makes use of the Bedford Ouse modelling technique to evaluate the non-linear behaviour of the catchment with the input of the model integrated in different ways including into new single-input time-series for subsequent Single Input Single Output (SISO) modelling. The identified MISO models were able to improve the efficiency and understanding of the rainfall-riverflow behaviour within the study catchment. The paper illustrates the potential benefits of the methodology in modelling large catchments with sparse network of rainfall stations.</p> <p><strong>Keywords: </strong>Ghana, DBM model, Rainfall, MISO, Transfer function,</p> <p><strong> </strong></p>Boateng AmpaduNick A. ChappellWlodek Tych5Best Approximation in Space L_(p,α) [I] α>0 .0<p<1, I=[a,b] By Means of Modulus of Smoothness.
http://www.iiste.org/Journals/index.php/MTM/article/view/24141
The aim of this work is to estimate the degree of best approximation for unbounded function.............Abdulsattar A. AL-DulaimiSaheb K. Al-SaidyHussein A. AL-Juboori5An Improved Algorithm for the Solution of Nonlinear Partial Differential Equations
http://www.iiste.org/Journals/index.php/MTM/article/view/24142
<p>In this paper, an improved algorithm for the solution of Generalized Burger-Fisher’s Equation is presented. A Maple code is generated for the algorithm and simulated. It was observed that the algorithm gives the solution with less computation.</p> <p><strong>Keyword</strong>: Algorithm, Pde, MVIM, Generalized Burger-Fisher’s Equation</p>Olayiwola, M. O.5Study of the Geographically Weighted Regression Application on Climate Data
http://www.iiste.org/Journals/index.php/MTM/article/view/24143
<p>This study used Geographical Weighted Regression (GWR) technique to find spatial relationship between Elevation and climate (Rainfall, Temperature) in Northern Nigeria using climate (Rainfall, Temperature) data from weather stations from 1980 – 2010 obtained from Nigerian Meteorological Agency (Nimet). From the results of the analysis it was shown that there is significant relationship between the elevation and climate variables (Rainfall, Tmax and Tmin). The study also shows that GWR has smaller residual sum of square than OLS in analysing the relationship between Elevation and Climate data. This may be due to the consideration of the spatial variation of the relationship over the study region. When mapping the results of GWR model it was observed that the effect of Elevation on climate variables appears to vary geographically</p> <p><strong>Keyword</strong>: Geographical Weighted Regression (GWR), Ordinary Least square (OLS),</p>U. UsmanAliyu M. L.Aminu M. K.5Genetic Algorithm and Statistical Applications in Mines for Radiation Safety Requirements
http://www.iiste.org/Journals/index.php/MTM/article/view/24144
<p>Genetic algorithm and statistical probability distributions can give a good result for estimating the radon airborne levels into underground mines. The computer-aided algorithm for a regional mines controlling plan is presented. The mines are modeled and analyzed with the use of genetic algorithm and the total population will be distributed rationally according to the result to reach optimal values. Thus, offering an effective approach for regional radon condition improvement and pollutants control. Probability distributions are used for reducing the error rate of the radon prediction model. This is done by developing and converting the multiple regression model to probability multiple regression model using Cumulative Distribution Function (CDF) of suitable probability distributions. The CDF is used to convert the actual values to probability values for creating the probability model. Then the predicted probability values are converted to the original values using the inverse CDF (quantile function). The optimal results obtained from Genetic Algorithm have been used in the probability multiple regression model for estimating the radon levels in the entire mines. Accuracy measurements are calculated to evaluate the two investigated models. The results show that the probability multiple regression model diminishes the error rate nearly by 50% to 70%. The results give accurate prediction for determining the radon levels in mines.</p> <p><strong>Keywords: </strong>Radon level, genetic algorithm, multiple regression model, probability distributions</p>Ghada I. El-shanshouryEman Sarwat5The Modified Double Weighted Exponential Distribution with Properties
http://www.iiste.org/Journals/index.php/MTM/article/view/24145
<p>The weighted distributions are widely used in many real life fields such as medicine, ecology, reliability, etc., for the development of proper statistical model. The concept of double weighted distribution was introduced by Al-khadim and Hantoosh (2013) and later has been studied by other researchers. In his article, has been considered as suitable weight for efficient modeling of double weight exponential distribution. The statistical properties of the modified double weighted exponential distribution (MDWED) are explored. The Kolmogorov- Smirnov test has been used to choose a better fitted probability model. The result of this testshown that (MDWED) is more suitable distribution to fit rainfall data then (DWED) proposed by Al-khadim and Hantoosh (2013).</p> <div><p><strong><em>Keywords:</em></strong>Weighted distribution, Exponential distribution, Moment Generating Function, Fisher information.</p></div>Amir SaghirMuhammad SaleemAneeqa KhadimSadaf Tazeem5MODELLING EXCHANGE RATE VOLATILITY OF THE GHANA CEDI TO THE US DOLLAR USING GARCH MODELS.
http://www.iiste.org/Journals/index.php/MTM/article/view/24146
<p>The study examines exchange rate volatility with GARCH models using monthly exchange rate data from January 1990 to November 2013. Simple rate of returns is employed to model the exchange rate volatility of Ghana Cedi-United States Dollar. The models included both symmetric and asymmetric models that capture the most common stylized facts about returns such as volatility persistence and leverage effect. The result identified EGARCH (2, 2) as the overall best fitted model. This model has the least AIC of -6.28 and SIC of -6.16. Diagnostic test of the models residuals with the Ljung-Box test, the ARCH-LM test and the ACF plots revealed that the models are free from higher order autocorrelation and conditional heteroscedasticity separately. Our results also revealed persistence of volatility and the non-existence of leverage effects as shown by the asymmetric models.</p> <p><strong>Keywords</strong>: Leptokurtic, volatility persistence, leverage effect.</p>Albert LuguterahRobert Adombire AkumbobeElizabeth Awo Yaan5ON THE EXISTENCE OF A STOCHASTIC MODEL OF TYPHOID FEVER
http://www.iiste.org/Journals/index.php/MTM/article/view/24147
<p>In this work a stochastic model is developed and analyzed for the dynamics of Typhoid fever. The model includes susceptible, vaccinated, infected, carrier and recovered individuals. The model used in this work is based on a deterministic model. The deterministic model is transformed into a stochastic model and solved numerically using MATLAB. It is shown that the model satisfies the conditions for existence and uniqueness of solution. The simulation result also shows that increased vaccination rate will lead to Typhoid fever reduction and possible extinction. <strong></strong></p> <p><strong>Keywords and phrases</strong>: Stochastic model, typhoid fever, transition probability, Wiener process, vaccination.</p>Andrew OmameReuben Andrew UmanaNneka Onyinyechi IheonuSimeon Chioma Inyama5Robustness of the Job – Finding, Job Loss (JFJL) Model in Modeling the Employment and Unemployment Rates of Ghana
http://www.iiste.org/Journals/index.php/MTM/article/view/24148
<p>The issues of employment and unemployment have become major macroeconomic factors that determine growth patterns of the modern Ghanaian economy. Periods of economic boom or growth of output can be associated with high rates of employment while recession periods correlate positively with woeful rates of unemployment. This undoubtedly suggests an inverse association between high rates of employment and recession; and high rates of unemployment and economic boom. This paper evaluates the robustness of the Job – Finding, Job Loss (JFJL) model in modeling the employment and unemployment rates in Ghana. It uses the job – finding and separation parameters as bases to model the employment and unemployment rates of Ghana in the form of simple Non – Homogenous First Order Ordinary Differential Equations. The resulting model is obtained by solving the differential equations via the Method of Variation of Constants (MVC). The JFJL model suggests an environment in which labour force is allowed to vary with time. It assumes a stable state equilibrium condition of the labour market which assisted in obtaining the same expressions as those for the natural rates of employment and unemployment. The predictive ability of the models is ascertained with real data obtained from the Ministry of Labour and Employment, which served as the inputs of simple input/output functions written in Microsoft Excel. The data cover labour force, employment, employment rates, unemployment and unemployment rates from the year 2000 through to 2014. The results evince the closeness of the predicted values or rates to the actual values or rates of employment and unemployment. In fact, at certain points in time especially getting to the end of the period (2013, 2014 and 2015), the model predicted approximately the same values and rates as the actual values and rates of employment and unemployment. Thus, the robustness of the JFJL model in predicting the employment and unemployment rates in the Ghanaian economy is established.</p> <p><strong>Keywords: </strong>Employment and unemployment rates, Job – Loss, Job Finding model, Non – homogeneous first order ordinary differential equations, Method of variation of constants, Ministry of Labour and Employment and Stable state equilibrium of the labour market</p>John Awuah AddorDaniel Yeboah – ForsonAbigail Padi5Separation Axioms via α^m-Kernel Set associated with α^m-Closed Set
http://www.iiste.org/Journals/index.php/MTM/article/view/24149
<p>In this paper, we introduce a new class of sets called <em>-</em>kernel set and study their basic properties in topological spaces. We introduce and investigate some separation axioms by using <em>-</em>kernel set and the <em>-</em>closed set. Further, we also introduce topological <em>-</em> <em>-</em>space.</p> <p><strong>Mathematics Subject Classification (2010):</strong> 54A05, 54C10, 54D10, 54D15.</p> <p><strong>Keywords:</strong> <em>-</em>closed set, <em>-</em>kernel set, <em>-</em> <em>-</em>space, and <em>-</em> <em>-</em>space, .</p> <p> </p>Qays Hatem Imran5Shortest Transportation Route Network in Nigeria Using Floyd-Warshall’s Algorithm
http://www.iiste.org/Journals/index.php/MTM/article/view/24150
<p>This study presents the application of Floyd – Warshall algorithm, which is an all pairs shortest path algorithm in finding the shortest route network for major cities in Nigeria. Twenty one (21) city route networks in Nigeria showing distances (km) are considered with Calabar, Cross River State as the origin node and Kaduna, Kaduna State as the sink node. Distance and precedence matrices are computed for all iterations to obtain the weight between nodes in the network and the shortest route respectively. The optimal route for all pairs in the network and the total distance travelled from one node to another are obtained respectively from the precedence and distance matrices of the final iteration. Detailed results showed that the algorithm is efficient. The designed route network shows the shortest route for all pairs of nodes in the network and also exposes hidden shortest routes. These routes are recommended for inter-city transportation in Nigeria.</p> <p><strong>Keywords:</strong> Floyd-Warshall algorithm, optimal shortest path, shortest distances, route determination</p>Esuabana, Ita MicahIkpang, Ikpang NkereuwemOkon, Ekom-obong Jackson5Quadra-Statistical Modeling Of Corrosion Penetration Rate (CPR) Of Martensitic and Annealed Stainless Steel in H2SO4 and HCl.
http://www.iiste.org/Journals/index.php/MTM/article/view/24151
A lucid quadratic model graphs and equations has been successfully generated after corrosion characterization behavior analysis of cast stainless steel (70.90% Fe, 19% Cr 10%Ni, 0.08% C) alloys in (0.25M- 0.5M) H<sub>2</sub>SO<sub>4</sub> and (0.25M- 0.5M) HCl using SPSS computer software. The cast stainless steel specimen were sectioned into three sets labeled M, A, U and machined to the same cross sectional area. M and A were subjected to a temperature of 900<sup>o</sup>C (1173K or 1652<sup>o</sup>F) where the grains formed austenitic phase which was further heat-treated to form martensitic stainless steel (M) and annealed stainless steel (A) test coupons respectively. Then, (U) was left untreated as a control test coupon sample. These pre-weighed test coupon samples were immersed in 0.25M and 0.5M simulated tetraoxosulphate (vi) acid (H<sub>2</sub>SO<sub>4</sub>) and Hydrochloric acid (HCl) respectively. The........Oshionwu Lucky C.,Idenyi N.EUgwu Emmanuel I.5STOCK MARKET EFFICIENCY, NON-LINEARITY AND THIN TRADING EFFECTS IN SOME SELECTED COMPANIES IN GHANA
http://www.iiste.org/Journals/index.php/MTM/article/view/24152
<p>This paper investigates market efficiency, non-linearity and thin trading effects in the returns of two companies listed on the Ghana Stock Exchange, namely Ghana Commercial Bank (GCB) and Transol. The Jarque-Bera and Runs tests showed that the returns of both companies deviate from normality and randomness, respectively. The returns are also non-linearly dependent using Ljung-Box and BDS tests. ARCH effects were found in the return series’ of both companies. An ARMA-GARCH model was adopted for the linearity modeling of the stock returns of GCB. The sum of the parameter estimate, Wiredu SampsonAtopeo Apuri BenjaminAllotey Robert Nii Ampah5Fixed Point Theorem in Intuitionistic Fuzzy Metric Space by Using Occasionally Weakly Compatible Maps in Rational Form
http://www.iiste.org/Journals/index.php/MTM/article/view/24153
<p>In this paper we have generalized the result of Kamal Wadhwa and Hariom Dubey by using occasionally weakly compatible maps using intuitionistic fuzzy metric space. The concept of compatible maps introduced by Kramosil and Michalek and weakly compatible maps in fuzzy metric space is generalized by A. Al. Thagafi and Nasser Shahzad by introducing the concept of occasionally weakly compatible mappings.</p> <p><strong>Keywords: </strong>Fixed point, intuitionistic fuzzy metric space, compatible mappings.<strong> </strong></p>Anupama Gupta, Arvind Gupta5How differential equations influence the tumor growth via mathematical models
http://www.iiste.org/Journals/index.php/MTM/article/view/24154
<p>This work demonstrates the importance of differential equations to develop mathematical model of tumor growth. Since the malignant tumor (cancer) grows voraciously, the scientists and mathematicians have tried to better understand how it grows. In view of mathematics, the modeling for tumour growth can be divided into two different categories: probabilistic and deterministic. Probabilistic model describes a set of measurement to evaluate the behaviour of individual cells, and deterministic model explains the behaviour of large populations of cells and their growth by changing the state in the transition from an active reproducing cell to a cell that is not reproducing. In this survey, we first answer the question: How ordinary and partial differential equations (ODE \ PDE) help to provide mathematical models in tumor growth? Secondly, how to use deterministic models and involve the ODE and PDE with some basic aspects of tumor growth to fit any mathematical model. Finally, we provide a relatively comprehensive list of existing models in this area and discuss other representative models in detail together with some possible future developments of mathematical modeling of cancerous cells.</p> <p><strong>Key</strong><strong>words: </strong>Cancerous cells, differential equations (ODE/PDE), immunotherapy, mathematical models, tumors.<strong></strong></p>Moharram A. Khan Sirazul Haq5The effect of joule heating, thermal radiation on the MHD convective Heat and Mass Transfer flow of a variable electrically conducting micro polar fluid.
http://www.iiste.org/Journals/index.php/MTM/article/view/24155
<p>The magneto-hydrodynamic (MHD) and effect of Joule heating, thermal radiation, chemical reaction and dissipation on the convective heat and mass transfer flow of a micro polar fluid past a stretching sheet with variable electric conductivity in the presence of a magnetic field. The non-linear equations governing the flow, heat and mass transfer have been solved numerically by employing fourth order Runge – Kutta shooting method. Results are obtained for a range of Eckert number (Ec), magnetic, Joule heating, micro rotation parameter, heat source parameter, thermal radiation parameter and chemical reaction parameter. The sheet is assumed to be non-isothermal with prescribed heat flux varying with length.<strong></strong></p> <p><strong>Keywords:</strong> Joule heating, magnetic field, micro polar fluid, stretching sheet.</p>C. Sulochana K. Gnanaprasunamba5Investigating Trend in Defined Pension Contribution Based on Trend Projection Model
http://www.iiste.org/Journals/index.php/MTM/article/view/24156
<p>Forecast is simply predicting the future based on current information. Pension forecast help to predict the future with respect to some expected or proposed changes. This short note is designed to investigate trend in defined contribution (DC)/ defined benefit (DB) with regard to age falsification. The causes and effects of trends are investigated using trend projection model. The analysis is based on time series data to build and validate the model. SAS/IML software is used to program the projection model and the MATLAB software is used for the graphical analysis. Statistical summary and margin of error are computed to advice management on strategic future plans and expenditure. The duty of the analyst is to advice management based on the output of the simulation.</p> <p> </p>F. Z. Okwonu5Comparison between Conventional and Adjusted Mean Probability of Correct Classification for Two Groups Problem: A Preliminary Study
http://www.iiste.org/Journals/index.php/MTM/article/view/24157
<p>This paper describes a new approach to determine classification performance based on the computation and application of margin of error. This procedure revealed that as the proportion of contamination increases, the misclassification rate and the margin of error also increases. On the other hand, if the mean probability of correct classification is approaching the mean of the optimal probability, the margin of error tends to reduce maximally. The upper and lower classification limits enable us to determine the performance of the technique of interest. If the computed mean probability exceed the upper classification limit this indicates that the rate of misclassification is high. In a general note, we are confident of the classification result based on this approach. This new technique was applied to investigate the performance of the Fisher linear classification analysis, Fisher’s approach based on the minimum covariance determinant and the probability based classification technique. In general, the performance analysis revealed that as the proportion of contamination increases, the misclassification rate increases thereby producing large margin of error. The implication of large margin of error to classification rule is that the adjusted mean probability based on the margin of error will overshot the upper classification limit which indicates high misclassification rate or possibly highly contaminated data set.</p> <p><strong>Keywords</strong>: Classification, Robust, Mean probability, Margin of error</p> <p>2010 Mathematics Subject Classification:62H99,62M20</p>F. Z. Okwonu5Modeling MSMEs Financing and Economic Growth: Evidence from Nigeria
http://www.iiste.org/Journals/index.php/MTM/article/view/24158
<p>MSMEs constitute the driving force in the attainment of industrial growth and development. Several previous studies have examined the relationship between MSMEs financing and economic growth in Nigeria but the results of these studies are still mixed. Therefore, this paper examines the causality between MSMEs financing and economic growth in Nigeria during the periods 1992 to 2013. However, the analysis technique of this study differs from the previous studies as the approaches of the previous studies are not adequate in obtaining robust estimates and drawing meaningful inference given the potential impact of MSMEs financing on economic growth. Unlike previous studies that totally relied on traditional methods for unit root testing, co-integration analysis, and causality test, our study relies on the ultra-modern econometric methods such as; the Ng-Perron modified unit root test, Autoregressive Distributed Lag (ARDL) Bound testing approach to co-integration, parsimonious ECM version of ARDL model, and the Toda – Yamamoto causality procedure. The empirical results indicate evidence of a stable long – run relationship among the chosen variables. The Toda – Yamamoto causality test show evidence of a unidirectional causality running from MSMEs financing to MSMEs output, a bi-directional causality between MSMEs output and economic growth, as well as, a unidirectional causality running from MSMEs financing to economic growth in Nigeria during the periods covered. The study therefore recommends that the government through the monetary authority (CBN) should energize the MSMEs by instituting a programme that will adequately promote the financing of MSMEs with relatively low interest rate for sustainable economic growth.</p> <p><strong>Keywords: </strong>MSMEs financing, economic growth, Ng- Perron, ARDL, Toda– Yamamoto</p>Kalu, Chris UUzonwanne, Maria COkeyika, Kene.O,Maduka, Olisaemeka, D5Derivation of an Implicit Runge – Kutta Method for First Order Initial Value Problem in Ordinary Differential Equation using Hermite, Laguerre and Legendre Polynomials.
http://www.iiste.org/Journals/index.php/MTM/article/view/24227
<p>In this paper, three Implicit Runge – Kutta methods are derived using Hermite, Laguerre and Legendre polynomials for the direct solution of general first order initial value problems of ordinary differential equations with constant step size. The analysis of the properties of the developed methods were investigated and found to be consistent, convergent and A – stable. The efficiency of the methods were tested on some numerical examples and are found to give better approximations than the existing methods.</p> <p><strong>Keywords:</strong> Implicit Runge – Kutta shemes, Collocation, Interpolation, canonical polynomial and A – stable.</p>Taparki R.Shika’a S.Shallom D.5A Mathematical Model to Study the Dynamics of Hazardous Substances in E-Waste on Ecosystem in Developing Countries
http://www.iiste.org/Journals/index.php/MTM/article/view/24228
<p>Environmental pollution has become a global concern several decades ago due to human activities particularly industrialization. Many pollutants have immediate effects while most pollutants like greenhouse gases, radioactive substances and other heavy metals for instance, have a generational consequence. It is against this background that, this research uses mathematical formulations and analysis to simulate the dynamics of hazardous substances in electronic and medical wastes. The system is compartmentalized in to five units namely: terrestrial habitats, aquatic habitats, terrestrial living organisms, aquatic living organisms and the human population. The system has an equilibrium point which is found uniformly and asymptotically stable</p> <p> </p>Shikaa S.Taparki R.Waniyos H. U.5Numerical analysis of the Taylor Galerkin Pressure Correction (TGPC) finite element method for Newtonian fluid
http://www.iiste.org/Journals/index.php/MTM/article/view/24367
<p>In this study, a time stepping Taylor Galerkin Pressure Correction finite element scheme (TGPC) is investigated on the basis of incompressible Newtonian flows. Naiver-Stoke partial differential equations have been used to describe the motion of the fluid. The equations consist of a time-dependent continuity equation for conservation of mass and time-dependent conservation of momentum equations. Examples considered include a start-up of Poiseuille flow in a rectangular channel for the Newtonian fluid. In that context, three different meshes 2×2, 5×5 and 10×10 are implemented to investigate the effect mesh refinements on the accuracy of the solution. In addition, the behaviour of velocity and pressure are reported in this study.</p> <p><strong>Keywords:</strong> Finite element methods, Taylor expansion, Naiver-Stoke equations, Newtonian fluid, Galerkin method</p>Alaa H. Al-MuslimawiSahar D. Shakir5