Mathematical Theory and Modeling最新文献

{"title":"Numerical Modeling for Transmission Dynamics of Hepatitis B Virus Disease","authors":"Anmole Razzaq","doi":"10.7176/mtm/9-1-04","DOIUrl":"https://doi.org/10.7176/mtm/9-1-04","url":null,"abstract":"Numerical modeling of communicable disease is a device to appreciate the instrument in what way syndrome pushovers and in what way stately. we have studied numerically the dynamics of HBV. We frame an entirely constant Non-Standard Finite Difference (NSFD) structure for a mathematical model of HBV. The introduce numerical array is bounded, dynamically designate and contain the positivity of the solution, which is one of the important requirements when modeling a prevalent contagious. The comparison between the innovative Non-Standard Finite Alteration structure, Euler method and Runge-Kutta scheme of order four (RK-4) displays the usefulness of the suggested Non-Standard Finite Alteration scheme. NSFD scheme shows convergence to the exact equilibrium facts of the model for any time steps used but Euler and RK-4 fail for large time steps. Keywords: Hepatitis B Disease, Dynamical System, Numerical Modeling, Convergence. DOI : 10.7176/MTM/9-1-04","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"203 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126075562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hypothesis Testing for the Association Between Categorical Variables: Empirical Application of Chi square Test","authors":"Basil Msuha, T. Mdendemi","doi":"10.7176/mtm/9-2-02","DOIUrl":"https://doi.org/10.7176/mtm/9-2-02","url":null,"abstract":"Chi-square test and the logic of hypothesis testing were developed by Karl Pearson. In this article we demonstrate theoretically and empirically the hypothesis testing for the association between categorical variables using Chi‑square Test. In research, there are studies which often collect data on categorical variables that can be summarized as a series of counts. These counts are commonly arranged in a tabular format known as a contingency table. We show in this paper how the chi-square test statistic can be used to evaluate whether there is an association between the rows and columns in a contingency table. We describes in detail what is a chi-square test, on which type of data it is used and the assumptions associated with its application. We consider both theoretical and empirical cases. On empirical case we use the data from the study which was conducted between September 2017 and March, 2018 in two municipalities of Dodoma and Morogoro, Tanzania. We conclude in this article that the Chi-square test,  only tells us the probability of independence of a distribution of data or in simple terms it does only test that whether two categorical variables are associated with each other or not. It does not tell us that how closely they are associated. Therefore, once we got to know that there is a relation between these two variables, we need to explore other methods to calculate the amount of association between them. Key words: Contingency table , categorical data analysis, Chi-square test, hypothesis testing DOI : 10.7176/MTM/9-2-02","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124441575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"AN EXPLORATORY STUDY OF THE THREE PHASES ANALYSIS OF FACTOR","authors":"O. ChineduK., G. A. Osuji, C. K. Onyekwere, Chukwuemeka B. Iwe","doi":"10.7176/mtm/11-3-01","DOIUrl":"https://doi.org/10.7176/mtm/11-3-01","url":null,"abstract":"In this study, we examine factor analysis as a multivariate statistical tool, starting from the origin of factor analysis with regards to Spearman’s approach of 1904 to the three phases of factor analysis. This is done with a view of determining the similarities and individual contributions of each of the three phases of factor analysis. This was achieved by examining the algorithms used in parameter estimations of the three phases of factor analysis. By inputting data into the algorithms and examining their outcomes and proffering recommendations based on the respective findings.","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129127989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Application of Simplex Lattice Design in Maize Fodder Production","authors":"J. Cheruiyot, J. Koske, J. Mutiso","doi":"10.7176/mtm/9-7-05","DOIUrl":"https://doi.org/10.7176/mtm/9-7-05","url":null,"abstract":"This study involved mixture experiment using simplex lattice design approach in cultivation of Maize crop with the view of optimizing the fertilizer components (dependent variables) on the output parameter (maize fodder). The objective of this study was to evaluate optimal sets of mixture of fertilizer components that could maximize the response variables of interest. Di-Ammonium Phosphate (DAP), Poultry manure, Sheep manure, and Farmyard manure components mixed in various proportions in accordance with simplex lattice design were applied in planting hybrid maize seeds. With the application of the special cubic statistical model formulated, it was found that farmyard manure and poultry manure produced the optimal fertilizer condition. However, the this study further provided specific optimal fertilizer blend for maize fodder production as 8.0 tons ha -1 of farmyard manure mixed with 1.212 tons ha -1 of poultry manure. Under these conditions, a maximum outputs 42 tons ha -1 of maize fodder were realized. The study concluded that the formulation of statistical model for crop production could be useful for prediction and evaluation of the effects of experimental factors. KEY WORDS : Maize fodder; Fertilizer components; Model; Mixture experiment; Simplex Lattice Design; DOI : 10.7176/MTM/9-7-05 Publication date : July 31 st 2019","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122757947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Backward Bifurcation and the Endemic Equilibrium for an HIV/AIDS - Tuberculosis Co infection Model","authors":"M. O. Okongo","doi":"10.7176/mtm/9-4-05","DOIUrl":"https://doi.org/10.7176/mtm/9-4-05","url":null,"abstract":"This study proposes a model that describes the dynamics of HIV/AIDS Co infection with Tuberculosis (TB) using systems of nonlinear ordinary differential equations. A characteristic of nonlinear oscillating systems is the sudden change in behavior which occurs as a parameter passes through a critical value called a bifurcation point. A bifurcation point is a point in parameter space where the number of equilibrium points, or their stability properties, or both, change. The results of the study shows that the Co infection model  has a diseases-free equilibrium (DFE) which is globally asymptotically unstable implying that the stable  endemic state co-exists with the DFE. Numerical simulations are carried out to illustrate the b ackward bifurcation phenomenon. Keywords: Backward bifurcation,  Equilibria, Co-infection, Stability . DOI : 10.7176/MTM/9-4-05 Publication date : April 30 th 2019.","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126056565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"IMPACT OF SIGNAL RADIATION LEAKAGE ON POWER LINE COMMUNICATION SYSTEMS","authors":"G. Ajenikoko, Ezekiel Olusegun Ojekunle","doi":"10.7176/mtm/9-8-02","DOIUrl":"https://doi.org/10.7176/mtm/9-8-02","url":null,"abstract":"Power Line Communication (PLC) is the usage of electrical power supply networks as a transmission medium for the transfer of various telecommunication services. However, PLC associated with the major cause of harmful interference (radiation leakage) to other users in transmission of information affects the full development and success of PLC. There is the need to develop a proper standard and regulations that will eliminate this problem globally. This study therefore, studies the impact of signal radiation leakage on Power Line Communication systems using Numerical Electromagnetic Code (NEC) method and field measurement to measure spacing along the power line and for measuring distance between the system frequencies in the power line. The result shows that the spacing between the wires on the power lines has effect on the radiation leakage. As wire spacing increases and external cancellation degrades, radiation escapes similar to those of long wire antennas. The result also shows that the frequencies of  power line operation lies between 444 kHz and 482 kHz. In general the PLC electric field along and near the power line decay with distance from the device but in at least one case, the electric field actually increased with increasing distance from the PLC device. Therefore, high levels of radiation suppression can be achieved only if the wires are very close together in terms of wavelength and balanced signals. Keywords : Power Line Communication(PLC) , Numerical Electromagnetic Code (NEC), Field Measurement, Electrical Power Network, Radiation Leakage, Frequency. DOI : 10.7176/MTM/9-8-02 Publication date : August 31st 2019","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"124 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128471284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Application of Lagrange Polynomial for Interpolating Income Generation from Certain Students’ Fee Structure","authors":"Justine Kira","doi":"10.7176/mtm/9-5-05","DOIUrl":"https://doi.org/10.7176/mtm/9-5-05","url":null,"abstract":"This paper presents the findings of the study that aimed to examine the changing aspects of income generation from certain students’ fee structure. It used an empirical example of Higher learning institution from Tanzania to determine whether Lagrange interpolation method would emerge a useful tool for interpolating and extrapolating enrolments of undergraduate students. The functional values evaluated at all nodes on the given data set accurately match the enrolments records of each respective academic year, though with nonconformities at the additional interior nodes. The function obtained from polynomial curve fitting using Excel spreadsheet at replaced the Lagrange polynomial to compute the rate of income generated from undergraduate students’ fees for academic years 2012/2013 to 2018/2019. The relative errors committed by range from the number at the node  to the number at the node . Enrolments trend however is not stable, as it fluctuates basing on the particular academic year that causes the rate of income generated from undergraduate students’ fees to act wildly. Being the cause therefore oscillatory behaviour perhaps lax if enrolments grew continuously in the successive academic years, however, this would mark progressive manner if there will be reciprocal efforts to improve physical and electronic resources imbued by human resources capacity. Higher learning institutions could diversify their income generation strategies from multiplicity sources of incomes by using various techniques, including rising students’ fees and downhill expenses without compromising quality of services and products, reducing dependency on Government subsidies, and strengthening the rate of students’ retention in higher learning. They may also utilize to the maximum the unobserved multiplicity sources of incomes for instance; consultation fees, project funds, and new competitive learning programs to support realization of their strategic objectives in coherence with their missions and visions. Keywords: Enrolment, Generation, Income, Interpolation, Lagrange, Polynomial DOI : 10.7176/MTM/9-5-05 Publication date :May 31 st 2019","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126344412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Invasive Species Population Status Modeling Using Stage Based Matrix: Mount Elgon Ecosystem","authors":"Samson Okoth Ojunga, J. Nyakinda, E. Okuto, J. Mullah","doi":"10.7176/mtm/9-2-04","DOIUrl":"https://doi.org/10.7176/mtm/9-2-04","url":null,"abstract":"The matrix models have been applied to evaluate the impacts and management of tree species. Modeling of invasive species using stage based matrix methods has not been exploited to understand the population structure of the invasive species. The study simulated using stage-structured Lefkovitch models to assess the population structure and impacts of invasive population growth within Mount Elgon Ecosystem. The survey data were used to calculate the transition probabilities and the growth rate ( Kiptogot","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126789665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The “Difficulties” in Fermat's Original Discourse on the Indecomposability of Powers Greater Than a Square: A Retrospect","authors":"G. Dedenko","doi":"10.7176/mtm/9-7-04","DOIUrl":"https://doi.org/10.7176/mtm/9-7-04","url":null,"abstract":"A possible version has been identified of the original proof of the decomposability of whole degrees above the square which Pierre Fermat spoke of. This reconstructed evidence is discussed with some extra conclusions drawn from it. Keywords: number theory, Fermat’s Big Theorem/Last Theorem DOI : 10.7176/MTM/9-7-04 Publication date : July 31 st 2019","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129521280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Minimization of Transportation Cost Problems","authors":"S. S. Kpanja, Atama Alhamdu Madaki","doi":"10.7176/mtm/9-3-03","DOIUrl":"https://doi.org/10.7176/mtm/9-3-03","url":null,"abstract":"The research is financed by Tertiary Education Trust Fund (TETFund). No. 6 Zambezi Crescent, Maitama, Abuja, Nigeria. Abstract This paper present seven initial methods of solving transportation problems. These methods were compared on a balanced transportation model of Dangote’s Cement Factories and the result shows that the Vogel’s method yields the best starting solution and gives an initial solution as the optimal with zero number of iteration. The North-West Corner Method although fast in obtaining the initial solution is not very efficient and accurate enough in finding initial solution as it pays no attention to the unit cost particularly as the solution is far from the optional. The objective value for the initial basic feasible solutions obtained from Russel’s and Row-Minimum Method are in perfect agreement. Keywords: Linear Programming, Transportation, Initial Solution, Minimization. DOI : 10.7176/MTM/9-3-03 Publication date : March 31 st 2019","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"418 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132485796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}