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 Modeling2224-5804Rice Production Forecasting in Bangladesh: An Application Of Box-Jenkins ARIMA Model
http://www.iiste.org/Journals/index.php/MTM/article/view/11738
<p>The study was undertaken to fit the best Auto-Regressive Integrated Moving Average (ARIMA) model that could be used to forecast the rice productions of Bangladesh such as in Aus, Boro, Aman season covering the whole country. This data for the present study is available in the Bangladesh Agricultural Ministry’s websites www.moa.gov.bd. The best selected ARIMA model for Aus productions is ARIMA (2,1,2), for Aman it is ARIMA (2,1,2) and, for Boro it is ARIMA (1,1,3). In this study, it was tried to make a comparison between the original series and forecasted series which also shows the same manner indicating fitted model are statistically well behaved to forecast rice productions in Bangladesh. It is found from the analysis that ARIMA model gives good forecasting for short term analysis.</p> <p><strong>KEYWORDS:</strong> Rice production, ARIMA, Forecasting, Bangladesh.</p>Mohammed Amir Hamjah4Measuring Climatic and Hydrological Effects on Cereal crop Production in Bangladesh using Multiple Regression and Measuring Efficiency using Stochastic Frontier Model
http://www.iiste.org/Journals/index.php/MTM/article/view/11739
<p>The objective of this study is to develop a Multiple Regression model to measure the climatic and hydrological effects on cereal crop productions in Bangladesh and Stochastic Frontier model for measuring the production efficiency due to climate and hydrology. The month October, November, December, January and February are taken as “dry season” and March, April, May, June, July, August, September as a “summer season” considering the weather and climatic conditions of Bangladesh. From Multiple Regression model, it is found that the Multiple R-squared for maize, barley and wheat production model are 0.9447, 0.8995 and 0.7674 respectively, which are implied to a good model to measure the climatic and hydrological effects on cereal production; and Global test implies that these models are valid linear model. Again, from Stochastic Frontier model, it is found that there is a huge opportunity to increase barley and maize production; and wheat achieves maximum production due to climates and Hydrology in the Bangladesh.</p> <p><strong>Keywords:</strong> Cereal Production, Multiple Regression Model, Efficiency, Stochastic Frontier Model.<strong></strong></p>Mohammed Amir Hamjah4A New (Proposed) Formula for Interpolation and Comparison with Existing Formula of Interpolation
http://www.iiste.org/Journals/index.php/MTM/article/view/11740
<p>The word “interpolation” originates from the Latin verb interpolare, a contraction of “inter,” meaning “between,” and “polare,” meaning “to polish.” That is to say, to smooth in between given pieces of information. A number of different methods have been developed to construct useful interpolation formulas for evenly and unevenly spaced points. The aim of this paper is to develop a central difference interpolation formula which is derived from Gauss’s Backward Formula and another formula in which we retreat the subscripts in Gauss’s Forward Formula by one unit and replacing <strong></strong>by . Also, we make the comparisons of the developed interpolation formula with the existing interpolation formulas based on differences. Results show that the new formula is very efficient and posses good accuracy for evaluating functional values between given data.</p> <p><strong>Keywords: </strong>Interpolation, Central Difference, Gauss’s Formula.</p>Faruq AbdullaMd. Moyazem HossainMd. Mahabubur Rahman4A Simple Proof of the Generalization of the Binomial Theorem Using Differential Calculus
http://www.iiste.org/Journals/index.php/MTM/article/view/11741
<p>The binomial theorem is a simple and important mathematical result, and it is of substantial interest to statisticalscientists in particular. Its proof and applications appear quite often in textbooks of probability and mathematicalstatistics. In this article, a new and very simple proof of multinomial theorem is presented. The new proof isbased on a direct computation involving partial derivatives.</p><p><strong>Key Words</strong>: Binomial distribution; Combinatorial Analysis; Mathematical Induction; Multinomial theorem;Partial derivatives.</p>Olusegun Ayodele ADELODUN4Analysis of Head Loss in Pipe System Components: Quasi-one-Dimensional Nozzle Flow
http://www.iiste.org/Journals/index.php/MTM/article/view/11742
<p>The problem under investigation is to determine the flow-field variables that is the total head which is the sum total of Elevation head, velocity head and pressure head instantaneous distributions as a function of distance through the nozzle up to “steady-state” solution that is, when the result approach the stage where the flow-field variables are not materially changing any more. The finite difference method is used to arrive at the results. Effects of temperature and density on velocity and pressure are analyzed with the help of a graph and table. It is found that the total head loss needed to accelerate the fluid through the constriction/the nozzle throat causes fluid velocity to increase.</p> <p><strong>Keywords: </strong>Quasi-one-dimensional flow, Head loss, Incompressible flow, Steady state flow.</p>Charles Ndambuki Muli4Ranking Function Methods For Solving Fuzzy Linear Programming Problems
http://www.iiste.org/Journals/index.php/MTM/article/view/11743
<p>In this paper, we concentrate on linear programming problems in which the coefficients of objective function are fuzzy numbers, the right-hand side are fuzzy numbers too, and both the coefficients of objective function as well as right-hand side are fuzzy numbers. Then solving these fuzzy linear programming problems by using many linear ranking functions. After that develop six numerical examples to illustrates the steps of solutions for all these type of linear programming problems which studying in this paper.</p> <p><strong>Keywords: </strong>Fuzzy set theory, fuzzy linear programming, linear ranking function, trapezoidal membership.<strong></strong></p>Iden Hassan AIkananiFarrah Alaa Adnan4Application of Markov Chain Model in Studying progression Of Secondary School Students by Sex During The Free Secondary Education: A Case Study of Kisii Central District
http://www.iiste.org/Journals/index.php/MTM/article/view/11744
<p>Enrollment forecasting is an essential element in budgeting, resource allocation, and the overall planning for the growth of education sector. This paper demonstrates the use of Markov chain techniques in studying progression of secondary school students from the time of entry/enrollment in form one to graduation after the expected four years in Kenya’s secondary school level of education. The target population included all the secondary school students in Kisii Central District. The model was used to determine the district’s secondary school completion/dropout rate, retention rate and the expected duration of schooling by sex. It was established that completion rates for male students was higher than that of female students and dropout rates for female students was higher than that of male students. In the long run, it was established that the completion and dropout rates were the absorbing rates. Female students had lower expectation of schooling compared to male students in Kisii Central District. The model is only appropriate in making short period projections.</p> <p><strong>Keywords: </strong>Absorbing States, Absorbing Markov Chain, Transition Rates, Dropout Rates, Completion Rates, Fundamental Matrix</p>Mose Job NyandwakiOdhiambo E AkeloOjunga O SamsonOnyango Fredrick4On The Comparative Analysis Of Beta And Kumaraswamy Priors Using Stigmatized Attributes
http://www.iiste.org/Journals/index.php/MTM/article/view/11745
<p>Hussain et al 2011 compared bayes estimator of population proportion of a stigmatized attribute with the Maximum Likelihood Estimator (MLE) but this paper compares two priors: beta and kumaraswamy in the Bayesian analysis using various values of n, x, p1 and p2 and it was<strong> </strong>observed that across the sample sizes considered over different values of x’s, p1 and p2 using R package software for simulation, the mean square error and bias of the Kumaraswamy prior are smaller than that of Beta prior when the proportion of stigmatized attribute increases from 0.1 to 0.4</p> <p><strong>Keyword</strong>: Prior, Beta, kumaraswamy, Stigmatized, Attribute</p>Tijani, I. A.Adewara A. A.4On Best One-Sided Approximation By Interpolation Polynomials In Space Lp.w(X)
http://www.iiste.org/Journals/index.php/MTM/article/view/11746
The aim of this article is to obtain the order of convergence of weighted space by interpolation polynomials on [-pi, pi]. More details can be found in the full paper.S.K. JassimAlaa.A. Auad4Stability Analysis of Infectious Diseases with Media Coverage and Poverty
http://www.iiste.org/Journals/index.php/MTM/article/view/11747
<p>In this paper ,the effect of poverty along with media coverage on the stability dynamics of infectious disease has been checked . The incorporation of the factor, poverty along with media coverage makes our model more closer to the real life situations. Using stability theory, the analysis of the model has been done by finding out all the equilibrium points of the system. Numerical simulation of the model is also performed to check the effect of key parameters on the spread of the disease.</p> <p><strong>Keywords :</strong> Poverty, Equilibrium points, Media coverage, Stability.</p>Rajinder Sharma4Studying the Scientific State Of Students Using the Adjusted Residuals
http://www.iiste.org/Journals/index.php/MTM/article/view/11748
<p class="IJOPCMAbstract"><span lang="EN-US">The aim of this article is to apply the adjusted residuals to analysis of (two-way) contingency tables to determine the cells which affected to the significance of chi-square statistic</span></p> <p class="IJOPCMAbstract"><span lang="EN-US">Keywords</span><span lang="EN-US">:</span><span lang="EN-US"> </span><span lang="EN-US">adjusted residuals, contingency tables ,significance, chi-square</span></p>SAMEERA ABDULSALAM OTHMANSHELAN SAIED ISMAEEL4Arterial Pulse Waveform under the watch of Left Ventricular Ejection time: A physiological outlook
http://www.iiste.org/Journals/index.php/MTM/article/view/11749
<p>The behavior of arterial pulse waves was studied in connection with time interval at different phases of propagation. The essence of the study was to have a clue about the incidence of the time of pulse wave propagation on cardio-vascular parameters. Model analysis shows that arterial waveforms behave like solitons. It was seen, from the soliton solution of the arterial pulse waveform, that time interval between the phases of propagation, which corresponds with left ventricular ejection time (LVET), could supply some information about apparent pathogenesis.</p> <p><strong>Keywords: </strong>pressure; waveform; soliton; incompressible; mathematical; physiology.</p>Nzerem Francis EgentiUgorji Hycinth Chimezie4Some Chaotic Properties of Ikeda Map
http://www.iiste.org/Journals/index.php/MTM/article/view/11750
<p>We study the dynamical system of Ikeda map on three dimension, we find some the general properties, and we show some chaotic properties of it. We prove the Lypaunov exponent of Ikeda map is positive and Ikeda map has sensitivity dependence to initial condition. Finally we use the Matlab program to draw the sensitivity of Ikeda map.</p>Iftichar M.T. AL-Shara'aWafaa H. Al-Hilli4Semi Compatibility and Fixed Points For Expansion Mappings In 2-Metric Space
http://www.iiste.org/Journals/index.php/MTM/article/view/11751
<p>This paper introduces the notion of semi-compatible self- maps in 2- metric spaces and establishes a fixed point theorem for six self maps, satisfying an implicit relation through semi-compatibility of a pair of self-maps.</p> <p><strong>Key words</strong>: semi-compatibility, metric space, 2- metric space,</p>Shweta Maheshwari4An Application Of Extreme Value Theory In Modelling Electricity Production In Kenya
http://www.iiste.org/Journals/index.php/MTM/article/view/12055
<p>Extreme Value Theory provides a well-established statistical model for the computation of extreme risk measure which includes, Value at Risk and Expected Shortfall. In this paper we apply Univariate Extreme Value Theory to model extreme production for the Kenyan Electricity. We demonstrate that Extreme value theory can successfully be applied in predicting future Value at Risk to the electricity production. This will provide solutions to the problems faced by producers and consumers in the electricity market. In this paper Value at Risk is estimated using a Peak Over Threshold method. This technique models the distribution of exceedances over a high threshold rather than the individual observations. It concentrates on observation that exceeds central limits, focusing on the tail of the distribution. Extreme value theory is also applied to compute the tail risk measures at given confidence interval. An overview of the Extreme Value Theory and Peaks Over Threshold Method are also given. These methods are applied to electricity production in Kenya and the data exhibit some trend and modeled as a Gumbel distribution since the shape parameter is not significantly different from zero.</p> <p><strong>Keywords</strong>: Risk Modeling, Value at Risk, Extreme Value Theory.<strong></strong></p>Apudo, B. O.Mwita, P. N.Mbugua, L. N.Machuke, G.W.Kiche, J.4