Mathematical Theory and Modeling最新文献

{"title":"Comments on the paper “’Concentration-dependent viscosity and thermal radiation effects on MHD peristaltic motion of Synovial Nanofluid: Applications to rheumatoid arthritis treatment’ by M. G. Ibrahim, W. M. Hasona, and A. A. El-Shekhipy, Computer Method","authors":"M. A. Elogail","doi":"10.7176/mtm/9-10-02","DOIUrl":"https://doi.org/10.7176/mtm/9-10-02","url":null,"abstract":"This comment has been prepared from the perspective point of view that the readers of the above mentioned paper may not be aware of the several serious flawed analysis and typographical errors throughout the whole work. In the next few pages I will focus on most of these mistakes/typos, clarifying that the obtained results should be reported as fabricated results that no one can rely upon. Suggested corrections for these numerous errors will be offered to correct the literature and ensure its integrity. Keywords: Peristaltic motion, Synovial nanofluid, Magnetohydrodynamics (MHD), Thermal radiation. DOI : 10.7176/MTM/9-10-02 Publication date : October 31 st 2019","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"107 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":"133257126","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":"Fixed Point Result with Soft Cone Metric Space with Examples","authors":"Sneha A. Khandait, R. Bhardwaj, Chitra Singh","doi":"10.7176/mtm/9-4-07","DOIUrl":"https://doi.org/10.7176/mtm/9-4-07","url":null,"abstract":"In the present paper, some fixed point and communal fixed point theorems are established for new contractive mapping in soft cone metric spaces. The generalized many previous well known results. Keywords: soft cone metric space, communal fixed point theorem. DOI : 10.7176/MTM/9-4-07 Publication date : April 30 th 2019.","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"48 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":"114069611","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":"Cycle Index Formulas for Dn Acting on Unordered Pairs","authors":"Geoffrey Muthoka, I. Kamuti, Hussein Lao, Patrick Kimani","doi":"10.21275/v5i4.nov162995","DOIUrl":"https://doi.org/10.21275/v5i4.nov162995","url":null,"abstract":"The concept of the cycle index was discovered by Polya (See [2]) and he gave it its present name. He used the cycle index to count graphs and chemical compounds via the Polya’s Enumeration Theorem. More current cycle index formulas include the cycle index of the reduced ordered triples groups (See [3]) which was further extended by Kamuti and Njuguna to cycle index of the reduced ordered r-group (See [4]). The Cycle Index of Internal Direct Product Groups was done in 2012 (See [5]).","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"29 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":"127127321","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":"Ornstein-Uhlenbeck Process via Conflated Drive of Brownian Motion and Lévy Process and its Application","authors":"R. O. Olanrewaju, Thierno Souleymane Barry, Abdi Hassan Muse, Alex Habineza","doi":"10.7176/mtm/11-3-02","DOIUrl":"https://doi.org/10.7176/mtm/11-3-02","url":null,"abstract":"Non-linear time series and linear models were not designed to detect probabilistic process that are depict by velocity and drift associated to returns the way Ornstein-Uhlenbeck stochastic process describes diffusion and velocity associated to series or waves influenced by Brownian motion or Levy process.  In this research, Brownian motion and Levy process were conflated as driving force for Ornstein-Uhlenbeck process with its solution applied to Naira-Dollar exchange rates from 2009-2019.The drift and diffusion estimates for the Ornstein-Uhlenbeck process driven by Brownian motion and Levy process are realization of AR (1) with 2.991 and 0.1672 respectively. The AR(1) realization for the Ornstein-Uhlenbeck process was stationary with estimate  that lies outside the unit circle. The AIC, BIC, RMSE, and MSE for the Ornstein-Uhlenbeck process were estimated to be 483.7572, 483.4782, 0.00101, and 8.395 respectively, compare to estimates of the same indexes for AR (1) of 767.5, 634.09, 0.3819, and 23.48. The criterion via the residuals from the Ornstein-Uhlenbeck process was smaller, which connotes that the errors approximated in using drift, Brownian motion and to estimate  is relatively small via the Ornstein-Uhlenbeck process. Keywords: Brownian motion; Drift; Diffusion; Levy process; Ornstein-Uhlenbeck Process DOI: 10.7176/MTM/11-3-02 Publication date: May 31 st 2021","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"37 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":"132335150","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":"Dynamics of 2014 Ebola Epidemic in West Africa","authors":"Mutuguta John, Rotich Titusy, Chepkwony Isaac","doi":"10.7176/mtm/9-2-05","DOIUrl":"https://doi.org/10.7176/mtm/9-2-05","url":null,"abstract":"Ebola virus disease is transmitted from human to human through physi- cal contact of body uid of infected or dead case. It can also be transmitted indirectly through contact with contaminated surfaces. This risk is however low and can be minimised through cleaning the surfaces by the use of disin- fectants. In this paper we investigate the transmission dynamics of the 2014 Ebola virus disease in west Africa. We use a four compartmental network of Susceptible individuals (S), Exposed individuals (E), Infectious individuals (I) and the Removed individuals (R) without demographic factors. The re- moved compartment is further split into two compartments i.e the recovered individuals (R) and the dead and buried individuals (D). We give the math- ematical model that describe the transmission dynamics of the 2014 Ebola virus disease in West Africa. The results of the model analysis indicate that the threshold value for the transmission dynamics equals the relative removal rate. It is shown that provided that the susceptible ratio is kept below the relative removal rate then the epidemic will not occur. Keywords ; Ebola virus disease, basic reproduction number, epidemic threshold Mathematics subject classi cation: 97M60, 00A71, 46N70 DOI: 10.7176/MTM/9-2-05","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":"129066642","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":"Mathematical Model of Infectious Disease with Multistage Vaccine","authors":"Assefa Erba Bikila","doi":"10.7176/mtm/9-10-04","DOIUrl":"https://doi.org/10.7176/mtm/9-10-04","url":null,"abstract":"Many diseases, such as the seasonal influenza, tetanus, and smallpox, can be vaccinated against with a single dose of a vaccine. However, some diseases require multiple doses of a vaccine for immunity. Diseases requiring a multistage vaccine such as Hepatitis B can have extra complications with its vaccination program, as some who start the doses may forget to complete the program or could become infected before completing the program. This thesis concerns the setup and analysis of a model for developing a mathematical model to describe the dynamics of an infectious disease with a multistage vaccine. In this thesis, we considered Susceptible-Infected-Removed (SIR) epidemic models and discussed the mathematical analysis and simulation study is conducted. We discuss an epidemic model which represents the direct transmission of infectious disease. The model assumes that individuals are equally likely to be infected by the infectious individuals in a case of contact except those who are immune. We formulated SIR epidemiological model to determine the transmission disease by using compartmental model approach to using a system of nonlinear differential equations. We study about basic reproduction number and equilibrium point for compartmental mathematical models of infectious disease transmission. The basic reproduction number R 0 , which is a threshold quantity for the stability of equilibrium point is calculated. If R 0 1 then an endemic equilibrium point appears which is locally asymptotically stable. Keywords : Equilibrium Stability, SIR, Multistage Vaccine and Basic Reproduction Number DOI : 10.7176/MTM/9-10-04 Publication date : October 31 st 2019","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"41 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":"124823344","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":"OPTIMAL ALLOCATION OF BISCUIT INGREDIENT IN THE PRODUCTION PROCESS - AN INVARIANT PROPERTY BASED ALGORITHM APPROACH","authors":"E. S. Udofia, I. Etukudo","doi":"10.7176/mtm/9-4-06","DOIUrl":"https://doi.org/10.7176/mtm/9-4-06","url":null,"abstract":"For the achievement of optimal ingredient allocation and mixing, this work proposes a mathematical model of efficient allocation of these ingredients. The problem of this allocation in the production of biscuit is modeled as a linear programming problem and analyzed using an invariant property based algorithm approach. An Optdesolver, a computer program was used to obtain the optimal solution to this problem. This solution revealed that in order to have a maximum profit of N3,404,010.27, the allocations to shortcake, petit, marie and gem should respectively be N270.50, N267.50, N268.20 and N268.80. Keywords: Biscuit, Optimal Allocation, Production Process, Invariant, Approach. DOI : 10.7176/MTM/9-4-06 Publication date : April 30 th 2019.","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"18 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":"122514504","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":"Exponentiated Exponential Lomax Distribution and its Properties","authors":"M. Adeleke","doi":"10.7176/mtm/9-1-01","DOIUrl":"https://doi.org/10.7176/mtm/9-1-01","url":null,"abstract":"This research study the generalization of exponentiated version of Exponential lomax Distribution (ELD) called Exponentiated exponential lomax distribution (EEPD) through its  distribution function and mathematical derivation of their moment, reliability, cumulative distribution function, Renyi Entropy and hazard rate function, Median, Quartile and Quantile Function. The distribution was found to generalize some known distributions thereby providing a great flexibility in modeling heavy tailed, skewed and bimodal distributions . Keywords: Exponentiated-exponential Lomax Distribution (EELD), Moment generating function, Hazard Function, Entropy, Median, Quartile, Quantile Function . DOI: 10.7176/MTM/9-1-01","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"33 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":"122678677","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":"Mathematical Modeling and Stability Analyses of Lassa Fever Disease with the Introduction of the Carrier Compartment","authors":"M. O. Akinade, A. Afolabi, M. Kimathi","doi":"10.7176/mtm/9-6-04","DOIUrl":"https://doi.org/10.7176/mtm/9-6-04","url":null,"abstract":"In this paper, a new mathematical model which takes into account the human and vector populations together with their interactions during Lassa fever disease transmission was developed. This transmission process is denoted by a seven mutually exclusive compartments for the human and vector populations. The proposed model is used to introduce the incubation period of the disease, a period in which an infected individual is yet to be symptomatic but infectious however, as denoted by the carrier human compartment. This carrier compartment was critically examined for its short and long term effects on the spread and control of the disease. Local and global stability analyses of the equilibrium points of the model was carried out using the first generation matrix approach and the direct Lyapunov method respectively. These analyses showed that the disease free equilibrium point of the developed model is locally asymptotically stable but not globally asymptotically stable. It was also observed that, although, there exist a unique endemic equilibria for the disease, this equilibria however is not stable. Numerical simulations of the model were carried out by implementing the MATLAB ODE45 algorithm for solving non-stiff ordinary differential equations. The results of these simulations are the effects of the various model parameters on each compartment of the developed model. Based on the findings of this research, necessary recommendations were made for the applications of the model to an endemic area. Keywords: Mathematical Model, Stability Analyses, Lassa Fever, Equilibrium Points, Numerical Simulation. DOI : 10.7176/MTM/9-6-04 Publication date : June 30 th 2019","PeriodicalId":394772,"journal":{"name":"Mathematical Theory and Modeling","volume":"21 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":"122390165","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 Impact of Using Rubrics as Assessment Tools on Pupils’ Academic Performance in Senior Secondary Mathematics: A case of Malela Secondary School, Copperbelt Province, Zambia.","authors":"Fridah Chileshe, H. Jacob","doi":"10.7176/mtm/9-7-02","DOIUrl":"https://doi.org/10.7176/mtm/9-7-02","url":null,"abstract":"This study was conducted to show whether or not using rubrics as an assessment tool has an impact on pupils’ academic performance in Mathematics at senior secondary school level. The problem of poor performance of Grade 12 pupils in Mathematics has been a matter of concern, especially at Malela secondary school.  In this study, a rubric served as an assessment tool to gather information about pupils’ achievement levels in demonstrating both knowledge and skills. The study sample population included two (2) grade 12 classes, were one class was the experimental group (N=55) and the other one was a control group (N=55) and Six (6) teachers of Mathematics. The two (2) grades twelve (12) classes were selected from the target population of the five (5) grade twelve classes using simple random sampling, and the six (6) teachers were selected purporsively.The study was based on three (3) research questions and two hypotheses. The research method used was a mixed approach and the research design was a quasi-experimental design. Three topics were taught to both the experimental and control groups which included probability, geometrical transformations and linear programing using problem based learning strategies. The experimental group was assessed using rubrics while the control group was assessed using conventional forms of assessment. The two groups were subjected to a pre-test, end of topic tests and a post-test. Data was also collected using teacher questionnaires and classroom observations. Quantitative data was analyzed using SPSS version 20, where an independent sample t-test was conducted at alpha (α) = 0.05 significance level and qualitative data was analyzed by categorizing, describing and explaining. The study revealed that using rubrics for assessment was found to have a positive impact on pupils’ academic performance as the experimental group outperformed the control group. The study also revealed that Mathematics teachers had a limited way of assessing pupils in class. Hence the reason to recommend that alternative assessment tools (rubrics) should be made mandatory to teachers of Mathematics at senior secondary school level. Keywords: Rubric, Assessment, Assessment tools, Conventional forms of assessment, academic performance. DOI : 10.7176/MTM/9-7-02 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":"129785902","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}