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 Modeling2224-5804Effects of Culture Conditions on Growth of Kefir Grains using Milk for Nutrition and Health: An Application of Response Surface Methodoly with Box-behnken Design.
http://www.iiste.org/Journals/index.php/MTM/article/view/41802
<div><p class="Els-Abstract-head">This combined process was successfully modeled by response surface methodology method with a Box–Behnken design. In this work, Box-Behnken Design of response surface methodology was used to investigate the effects of fat content in milk, incubation time and the number of rotations or shaking as culture conditions to for growing kefir grains using milk as culture liquid. The implementation of first order factorial experiment was based on a 3<sup>k </sup>Box- Benhnken experimental factorial design with one replicate. Response surface methodology was adopted to express the output parameter (Size of the kefir grain) that is decided by the input parameters (Number of rotations, Time and milk fat content) which yielded the response surface models. The effects of the culture conditions on growth of kefir grains using milk was studied by use of first order model. The adequacy of the first order model was examined by use residual analysis, the normal plot, the main affects plots, the contour plot, and ANOVA statistics F-test, t-test, R<sup>2</sup>, and the adjusted R. The optimization of culture conditions was achieved by the help of the steepest ascent method to locate the optimal domain and direction of growth of kefir grains. The first order model was predicted using a D-optimal criterion which was used to evaluate the growth of kefir grains. The confidence level to check the growth of kefir grain was at 95%. The data was analyzed using R statistical software and excel. Data was presented using tables and graphs. Milk fat content and number of rotations per minute had a positive effects while time had a negative effects on the growth of kefir grains using milk.</p></div> <p class="Els-Abstract-Copyright"><strong><em>Keywords:</em></strong> Kefir grains; Response Surface Methodology; Box-behnken design; Culture conditions</p>Edwine B. AtitwaJoseph.K. KoskeJohn M. Muindi8Modified Approach on Similarity Properties of Triangles and Trapezoids
http://www.iiste.org/Journals/index.php/MTM/article/view/41803
<p>The objective of this note is to provide presumably new technique to explain similarity properties in both triangles and trapezoids respectively. The author presented very short form of general conditions on similarity properties of triangles as well as trapezoids in a very elementary way.</p> <p><strong>Key words:</strong> similarity, triangles, trapezoids</p> <p><em>2010 Mathematics Subject Classifications: 51A15, 51M20, 51M30</em><strong></strong></p>Getachew Abiye Salilew8DISTRIBUTION OF ERRORS OF MISCLASSIFICATION FOR THE LINEAR DISCRIMINANT FUNCTION (A CASE OF EDGEWORTH SERIES NON NORMAL DISTRIBUTION)
http://www.iiste.org/Journals/index.php/MTM/article/view/41804
<p><em>In this paper, the discrimination and classification problem associated with the persistent non normal distribution has been studied. Sampling from non normal distribution is assessed through the distribution of errors of misclassification in respect of Edgeworth Series Distribution (ESD) which is restricted to asymmetry. The effects of applying a normal classificatory rule (ND) when the distribution is ESD by empirical approach is examined by comparing the errors of misclassication for ESD with ND using small sample sizes at every level of skewness factor. The empirical results obtained show that the normal procedure is sturdy against departure from normality. This is evident from the total probabilities of misclassification that are not greatly affected by the skewness factor.</em></p> <p><strong>Keywords: </strong> Normal Distribution, Classificatory Rules, Apparent Probability of Misclassification,</p> <p>Skewness Factor and Optimum Probabilities of Classification.</p>Awogbemi, C.A.Onyeagu, S.I.8Approach to Two-Phase Flow in Gas Transmission Pipeline Network System
http://www.iiste.org/Journals/index.php/MTM/article/view/41805
<p>Flow of natural gas in a gas pipeline is not entirely single phase flow situation. Even from the well or treatment plant the gas stream might carry along with it appreciable amount of dirts, debris, water or corrosion products from the walls of the pipes, resulting in two or three phase flow situation [1]. Oftentimes the gas might be transported above or below the earth surface or below the sea bed through places of diverse temperature gradients, giving rise to certain undesirable problems. Condensates and hydrates formation are such problems. The condensates so formed accumulate at low points in the pipes, thereby obstructing flow of gas. Hydrates do form around valves resulting in total blockage or freeze up of the valves. A worst case situation is total obstruction of flow. The end result is increased pressure drop along the pipeline. The approach in the two-phase flow analysis in gas transmission line is to separate the liquid phase from the dry gas phase and develop or deduce the governing expressions for friction factor. The friction factor for two phases so deduced can be injected into any appropriate flow equations to determine the various pressure drop components, overall pressure drop, line throughput or any other flow variables of interest. Two-phase flow analysis approach in this work has enabled the deduction of mathematical models that would be more precise and accurate in predicting flow situations.</p> <p><strong>Keywords: </strong>Mean Flow Velocity; Compressibility Factor; Friction Factor; Liquid Holdup; Gas Holdup; Liquid Velocity Gradient; Gas Velocity Gradient; Liquid and Gas Acceleration Gradient; No Slip; Equivalent length; Two Phase; Pipeline Efficiency; Equilibrium Constant.</p>Mathew, Shadrack UzomaTobinson A. Briggs8Model Formulation for the Exact Position of Dew Point along a Gas Pipeline
http://www.iiste.org/Journals/index.php/MTM/article/view/41806
<p>Natural gas piping network are often laid under the sea bed, under or above earth surface through places of diverse temperature gradients. In such environments, if the temperature of the flowing stream of gas is below the water or hydrocarbons dew points temperatures condensation occurs. The condensates so formed accumulate at low points in the pipes thereby obstructing flow of gas. Flow obstruction leads to pressure drop along the line. Hydrates can also be formed if there is excessive cooling of the gas due to pressure drop. The end result of this is obstruction of flow or freeze up of the valves, a worst case situation leading to total obstruction of flow. This necessitates the need to find at what point along a pipeline at which condensation will commence after attainment of dew point for natural gas gaseous mixtures. The mathematical models so generated help to determine the dew point of such hydrocarbons mixtures and the extent of the length from the upstream end of the pipeline at which dew point will be attained. To prolong the pipe length or stop attainment of dew point temperature, the pipe is covered with a layer of insulating materials of low thermal conductivity.</p> <p><strong> </strong></p> <p><strong>Keywords: </strong>Mass Flowrate; Specific Heat Capacity; Burial Depth; Convective Heat Transfer; Thermal Conductivity; Residual Heat; Dew Point Temperature; Flow Resident Time.</p>Mathew, Shadrack UzomaTobinson A. Briggs8PROPOSING A SOLUTION FOR THE PROBLEM OF CHOOSING ORTHOGONAL CONTRASTS FOR EQUAL SAMPLE SIZES
http://www.iiste.org/Journals/index.php/MTM/article/view/41807
<p>Many scholars as it is stated in the literature faced the problem of finding a suitable solution for finding and selecting orthogonal contrasts with (k-1) number, in terms of having groups (samples, types and treatments) with (k) number, where (contrasts=treatments-1). These are based on independence and orthogonalization as two conditions for selecting significant differences between (averages) treatments, and for identifying which one is responsible for these differences. The researchers solve this problem by proposing a method for selecting orthogonal contrasts in terms of equal observations, where independence and orthogonalization exist simply ,to let the experimenter to test all averages with no need to test these two conditions if more averages are formulated or added.</p> <p><strong>Keywords: </strong>ANOVA, F-Test, Independence, p value, Stock Exchange, Orthogonal, Contrasts, Treatments, Trading, Rainfall, Annual.</p> <p><strong><span style="text-decoration: underline;">Contribution/Orginality</span></strong></p> <p>The proposed method for simply selecting orthogonal contrasts in terms of equal observations where independence and othogonalization exist is important; especially it is concerned with (k) of averages and treatment. The application of this method is useful in experimental design since it is applied before experimenting, and consequently new results and conclusions may be revealed.</p>Mohammed Qadoury AbedAhmed Alwan SalehAbbas Lafta Kneehr8Mathematical Model of the Transmission Dynamics of Genital Elephantiasis (Lymphatic Filariasis)
http://www.iiste.org/Journals/index.php/MTM/article/view/41808
<p>This thesis presents a deterministic compartmental model, developed and analyzed to investigate the dynamics of lymphatic filariasis disease, through mosquito-borne infection. The model is in eight compartments: five for the human population and three for the mosquito population based on the microfilariae and antibody levels. The existence of the invariant region where the model is epidemiologically feasible and the positivity of the solution were established. The existence of Disease-free equilibrium (DFE) and the Endemic equilibrium (EE) were determined. Stability analysis of the disease-free equilibrium was investigated via the threshold parameter (reproduction number R<sub>o</sub>) obtained using the next generation matrix technique. The model was found to be locally asymptotically stable when the basic reproduction number is less than unity for both special and non special case. It was also revealed that the disease is endemic when R<sub>o</sub> > 1. It was proved through Lyapunov method that the DFE and EE are globally asymptotically stable. Simulation analysis was also carried out and it was shown that even when all lymphatic filariasis cases displaying elephantiasis symptoms are put on treatment it will not be able to eradicate the disease. This result suggests that effective control of lymphatic filariasis may lie in treatment for those displaying symptoms. It was also shown that if on the long run as the biting rate of the Mosquitoes increases, the infected population increases. Then as biting rate decreases, then the chronic infected individuals are completely eradicated from the population while the highly infected humans are reduced. The simulation also showed the impact of the effectiveness of treatment on the chronic infected humans, where we see that the population reduces rigorously until we get to a period of 70 days and then begins to increase again. This shows that the treatment strategies are not effective or perfect. Hence there are chances of fail in treatment. Furthermore our analysis shows that on a long run the trend continues indefinitely.</p> <p><strong>Key words: </strong>Genital Elephantiasis, Mathematical Modeling, Lymphatic filariasis, Endemic Equilibrium (EE)</p>Nwadibia, Anthoney IfeanyiEze, FranklineInyama, Simeon ChiomaNse, Celestine AOmame, AndrewMbachu, Hope Ifeyinwa8APPLICATION OF RCBD IN DETERMINING DEVIATION OF PRICES OF BASKET COMMODITIES IN SUPERMARKETS IN MOMBASA COUNTY
http://www.iiste.org/Journals/index.php/MTM/article/view/41809
<p>This study reveals the significant deviation, correlation and statistical significance and variance on the prices of the commodities charged by the four supermarkets in Mombasa County. A statistical model, Randomized Completely Block Design has been used to ascertain the significance deviation with the sample size taken as twenty five basket commodities of each category, selected from four leading supermarkets in Mombasa. Coefficient of determination for drinks and beverages, food-stuff and non-foodstuff was: 50.3%, 78.2% and 84% respectively. Null hypothesis was rejected at 95% C.I, correlation coefficient was 0.987** at 99%, this showed significance in correlation and statistical significance. <strong></strong></p> <p><strong>Key words:</strong> Analysis of Variance, coefficient of determination, Randomized Complete Block design AND Confidence of Interval</p>Otulo Wandera CyrilusOtugeh CharlesVictor Nyawanga8GENERALISED OPTIMAL STOPPING STRATEGIES WITH APPLICATIONS TO FINANCE
http://www.iiste.org/Journals/index.php/MTM/article/view/41810
<p>In this paper we examine the problem of determining the best time to sell an asset, where the stock price is modelled by a hybrid process. In this paper hybrid variable is a mathematical concept that is used to describe a situation in which randomness and fuzziness simultaneously appear in a system or phenomenon. Based on this concept, a hybrid stopping time problem is formulated and investigated. A verification theorem is derived and proved. We illustrate the application of the verification theorem through a practical example in mathematics of finance. A power function with exponent , is used as the utility function in the example. This study is extending the model from Oksendal [12] by including the fuzzy component since market value of assets is usually described using vague human language. The theory of hybrid variables provides a more realistic description of the evolution of price processes of financial assets.</p> <p><strong>Keywords: </strong>Randomness, fuzziness, Fuzzy variable, fuzzy process, hybrid variable, hybrid process, stopping time.</p>Nicholas MwareyaEriyoti ChikodzaMemory Mandiudza8Finite Time Stability Criteria for Nonlinear Fractional Order Dynamical System
http://www.iiste.org/Journals/index.php/MTM/article/view/41811
<p>In this paper finite time stability criteria for a class of nonlinear fractional order delayed system is addressed. By using the generalized and classical Bellman-Gronwall’s approach sufficient conditions that guarantees system trajectories to stay within the a priori given set is obtained.</p> <p><strong>Keywords</strong>: Nonlinear system, multiple time delays, Finite time stability, fractional order system</p>Prebo Clifford Jackreece8Effects of Some Coding Techniques On Multicolinearity and Model Statistics
http://www.iiste.org/Journals/index.php/MTM/article/view/42314
<p>Two known methods of coding data for analyses in the presence of multicollinearity and evaluation of model performance viz: Dummy coding and Effect coding which are alternatives to each other were considered. Efforts were made to improve on their performances by modifying them as modified Dummy coding and modified Effect coding respectively and their performances of the now coding methods compared in this paper. The results show that all coding methods significantly reduced the effect of multicollinearity. The effect coding was found to be the best coding method in remedying multicollinearity while closely followed by the dummy coding. However, the proposed modified dummy coding gave the best R-squared values as well as F-values while still reducing the effect of multicollinearity to a great extent and closely followed by modified effect coding. The dummy and effect coding methods proved very efficient in remedying multicollinearity as their observed variance inflation factor (VIF) were all close to unity.</p> <p><strong>Keywords: </strong>Dummy coding, effect coding, multicollinearity, variance inflation factor.</p>Eze Francis CNwankwo Chike HNwosu Lazarus OIgweze Amechi. H8Modeling and Estimation of Market Risk Using Extreme Value Theory
http://www.iiste.org/Journals/index.php/MTM/article/view/42315
<p>Most commercial airline agencies have suffered losses due to extreme conditions like climatic conditions, price fluctuations and airline problems. One of these airline agencies that have experienced large losses is the Kenya Airways. This study assesses the market risk in the Kenyan stock market using Kenya Airways (KQ) share prices. This paper helps an investor to weigh whether to invest in the company at a particular time or not. Due to the fluctuations and variations of share prices, the Extreme Value Theory has been used to capture the extreme and rare events. Extreme Value Theory provides a well-established statistical model for the computation of extreme risk measures which include; Value at Risk and Expected Shortfall. In this paper, Univariate Extreme Value Theory is applied to model extreme prices of shares for the Kenya airways in Kenyan market. This paper demonstrates how successful Extreme value theory can be applied in predicting future Value at Risk to the share prices. This provides solutions to the problems faced by the investors and the owners of the commercial agency in the market. This paper concentrates on the Peak over Threshold (POT) as the method of estimating Value at Risk. This technique models the distribution of extremes and the distribution of exceedances over a certain high threshold rather than the individual observations. It concentrates on observations that exceed 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. This paper also shows that POT is the best method since the modeling the exceedances, they follow a generalized pareto distribution (GPD) which fits the sample losses very well. This technique of extreme value theory helps us to model and estimate the stock market risk of the Kenya airways since it helps us to assess the goodness of fit of the series and detect the outliers and also in estimation of the extreme quantiles.This study used the stock data which was obtained from the Nairobi stock exchange (NSE). With Generalized Pareto Distribution the estimates of value at risk and the expected shortfall for share prices indicate that with probability 5% the daily loss for the stock market prices exceeds 2.5105%, for 1% the daily loss exceeds 2.5330, for 0.5% the daily loss exceeds 2.5358 and for 0.1% the daily loss exceeds 2.5380%. These results can be used to estimate risk measures in the stock market as well as providing insights to the managers of the airline and also as a reference for actual or potential investors in the airline industry.</p> <p><strong>Keywords: </strong>Extreme Value Theory, Peak -Over Threshold (POT), Generalized Pareto Distribution (GPD), Value at Risk (VaR), Expected Shortfall (ES).</p> <p> </p>Sheillah WanjalaGeorge OrwaJoel KoimaJoyce Jeptoo8