Mathematical Modelling and Applications最新文献

{"title":"Mathematical Model for Thermo-Electrical Instabilities in Semiconductors","authors":"Mukaddas Arzikulova","doi":"10.11648/j.mma.20240902.11","DOIUrl":"https://doi.org/10.11648/j.mma.20240902.11","url":null,"abstract":"Crystalline semiconductors under specific conditions, with an applied electric field, switch or oscillate between two conductive states, thus producing low frequency oscillations of electric current flowing through the sample and as a result of Joule heating oscillations of sample temperature. These phenomena are recognized to be thermo - electrical instabilities. Although current oscillations can be detected and registered experimentally, there is no device that can detect, register and allow us to study the sample temperature change in time. The purpose of this study is to learn about the relationship of electric current and sample temperature coupled with deep traps that play an important part in supporting the phenomenon. This can be done only by setting up a mathematical model that describes the phenomenon in detail. The equations that make up the model are continuity equations for free electron and deep traps carrier populations, as well as a heat conduction equation – a set of ordinary nonlinear inhomogeneous differential equations. The system is transformed into a so called “canonical form” as a result of linearization of the system at isolated equilibrium. It is achieved by expansion of the right hand sides of the equations into two variable Taylor series at isolated equilibrium involving linear non-singular transformation. The mathematical model for thermo-electrical instabilities in an n-type semiconductor with non-degenerate electron statistics has been studied as 3D dynamical system. The system of differential equations is broken down into component planar systems, each of them being tested for existence of limit cycles on a determined phase plane, followed by quantitative investigation of their local behavior at isolated equilibrium and at points on individual trajectories on phase plane dependant on single parameter T₀. Solutions of sets of initial value problems as time series of the variables: free electron concentration; sample temperature; deep trap population is presented. The investigation results show that oscillations of sample temperature follow those of current. Change in T₀ forces the system to adjust to new thermodynamical state by changing frequency and amplitude of the oscillations as well as dynamics of deep trap population.\u0000","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":" 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141126825","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":"On the Performance of Some Estimation Methods in Models with Heteroscedasticity and Autocorrelated Disturbances (A Monte-Carlo Approach)","authors":"O. Ayansola, A. Adejumo","doi":"10.11648/j.mma.20240901.13","DOIUrl":"https://doi.org/10.11648/j.mma.20240901.13","url":null,"abstract":"The proliferation of panel data studies has been greatly motivated by the availability of data and capacity for modelling the complexity of human behaviour than a single cross-section or time series data and these led to the rise of challenging methodologies for estimating the data set. It is pertinent that, in practice, panel data are bound to exhibit autocorrelation or heteroscedasticity or both. In view of the fact that the presence of heteroscedasticity and autocorrelated errors in panel data models biases the standard errors and leads to less efficient results. This study deemed it fit to search for estimator that can handle the presence of these twin problems when they co- exists in panel data. Therefore, robust inference in the presence of these problems needs to be simultaneously addressed. The Monte-Carlo simulation method was designed to investigate the finite sample properties of five estimation methods: Between Estimator (BE), Feasible Generalized Least Square (FGLS), Maximum Estimator (ME) and Modified Maximum Estimator (MME), including a new Proposed Estimator (PE) in the simulated data infected with heteroscedasticity and autocorrelated errors. The results of the root mean square error and absolute bias criteria, revealed that Proposed Estimator in the presence of these problems is asymptotically more efficient and consistent than other estimators in the class of the estimators in the study. This is experienced in all combinatorial level of autocorrelated errors in remainder error and fixed heteroscedastic individual effects. For this reason, PE has better performance among other estimators.","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"82 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140754772","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":"Complexity of Some Types of Cyclic Snake Graphs","authors":"Basma Mohamed, Mohamed Amin","doi":"10.11648/j.mma.20240901.12","DOIUrl":"https://doi.org/10.11648/j.mma.20240901.12","url":null,"abstract":"The number of spanning trees in graphs (networks) is a crucial invariant, and it is also an important measure of the reliability of a network. Spanning trees are special subgraphs of a graph that have several important properties. First, <I>T</I> must span <I>G</I>, which means it must contain every vertex in graph <I>G</I>, if <I>T</I> is a spanning tree of graph <I>G</I>. <I>T</I> needs to be a subgraph of <I>G</I>, second. Stated differently, any edge present in <I>T</I> needs to be present in <I>G </I>as well. Third, <I>G</I> is the same as <I>T</I> if each edge in <I>T</I> is likewise present in <I>G</I>. In path-finding algorithms like Dijkstra's shortest path algorithm and A* search algorithm, spanning trees play an essential part. In those approaches, spanning trees are computed as component components. Protocols for network routing also take advantage of it. In numerous techniques and applications, minimum spanning trees are highly beneficial. Computer networks, electrical grids, and water networks all frequently use them. They are also utilized in significant algorithms like the min-cut max-flow algorithm and in graph issues like the travelling salesperson problem. In this paper, we use matrix analysis and linear algebra techniques to obtain simple formulas for the number of spanning trees of certain kinds of cyclic snake graphs.","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"720 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140446432","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 Modelling and Simulation of the Factors Associated with Targeted Cells, Virus-Producing Cells, and Infected Cells","authors":"Kubugha Wilcox Bunonyo, L. Ebiwareme","doi":"10.11648/j.mma.20230801.12","DOIUrl":"https://doi.org/10.11648/j.mma.20230801.12","url":null,"abstract":"","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121278555","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":"Time Series Analysis and Forecasting of Household Products’ Prices (A Case Study of Nyeri County)","authors":"Muriuki Brian Muriithi, Waiguru Samuel","doi":"10.11648/j.mma.20220702.11","DOIUrl":"https://doi.org/10.11648/j.mma.20220702.11","url":null,"abstract":"","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122022168","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":"Numerical Modelling of the Slope: A Case Study of Dounia Park (North Algeria)","authors":"T. Abderrahmane, Cheriet Fayssal, A. Naas, Abdellaoui Merouane","doi":"10.11648/J.MMA.20210603.12","DOIUrl":"https://doi.org/10.11648/J.MMA.20210603.12","url":null,"abstract":"In this study, we describe the landslide of Dounia Park, Northen the capital Algiers, exactly in the city of Dely Ibrahim, near the Mercedes house. It is regarded as a huge park with games, and the green lungs of Algiers. This study is based on the configuration of the slope, mechanical properties and soil class, geology intervenes in the relief geomorphology and stratification, water, and earthquake shaking, etc…, the field observation has revealed the existence of land instabilities, cracks, and types of landslides (translation, rotation), in order to examine the landslides of Dounia Park, numerical modeling by the finite element limit analysis is employed to investigate this slope. The results obtained in this article show numerous points. During the site visit, it was observed that the area of Dounia Park is affected by many types of instabilities. Also, this paper show adequately give out the morphology of the slope instability observed on the site.","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131061459","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":"Modelling the Dynamics of Endemic Malaria Disease with Imperfect Quarantine and Optimal Control","authors":"D. Edossa, Alemu Geleta Wedajo, P. Koya","doi":"10.11648/J.MMA.20210602.12","DOIUrl":"https://doi.org/10.11648/J.MMA.20210602.12","url":null,"abstract":"Malaria is an infectious disease caused by Plasmodium parasite and it is transmitted among humans through bites of female Anopheles mosquitoes. In this paper, a new deterministic mathematical model for the endemic malaria disease transmission that incorporates imperfect quarantine and optimal control is proposed. Impact of various intervention strategies in the community with varying population at time t are analyzed using mathematical techniques. Further, the model is analyzed using stability theory of differential equations and the basic reproduction number is obtained from the largest eigenvalue of the next-generation matrix. Conditions for local and global stability of disease free, local stability of endemic equilibria and bifurcations are determined in terms of the basic reproduction number. The Center manifold theory is used to analyze the bifurcation of the model. It is shown that the model exhibit both a backward and a forward bifurcation. Reducing the biting rate of the quarantined people is advice able to minimize the spread of endemic malaria disease. The optimal control is designed by applying Pontryagins’s Maximum Principle (PMP) with four control strategies namely, insecticide treated nets, screening, treatment and indoor residual spray. The best strategy to control endemic malaria disease is the combination that incorporated all four control strategies.","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126993751","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":"32 Factorial Design and Model for the Spread of COVID-19 in West Africa","authors":"Richard Ayamah, Samuel Kwarteng, A. Obeng, Patrick Kwame Babah","doi":"10.11648/J.MMA.20210602.11","DOIUrl":"https://doi.org/10.11648/J.MMA.20210602.11","url":null,"abstract":"The coronavirus diseases 2019 (COVID-19) is a worldwide pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-COV-2). This research is therefore aimed at using experimental design to derive a model for the spread of COVID-19 in West Africa. In effect, 32 factorial design with mixed factors was used to design the data layout with country as the random factor and status of COVID-19 patient as the fixed factor. Under country, Nigeria, Senegal and Ghana were randomly selected as the three levels from the seventeen West African countries while under status of COVID-19 patient, recovery, death and active cases were the three fixed levels used. The data for the study were collected based on the monthly recorded number of the various COVID-19 cases (i.e. recovery cases, death cases and active cases out of the total confirmed cases) for the period from February to September, 2020. The data were retrieved from the reports on COVID-19 given by the respective country’s health authorities and published on their various websites. In effect, a mixed effect model was derived through formulation processes for the prediction of the various COVID-19 cases across West Africa. Also, different residual analyses were conducted for the model adequacy checking and it proved that the model was adequate in the estimation of the various COVID-19 cases in the West African Sub-region. This therefore makes it the first time experimental design and analysis has successfully been used for a study of this nature on the spread of COVID-19 in West Africa.","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114701191","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":"COVID-19 vaccination hesitancy model: The impact of vaccine education on controlling the outbreak in the United States","authors":"B. Oduro, A. Miloua, O. Apenteng, P. P. Osei","doi":"10.1101/2021.05.21.21257612","DOIUrl":"https://doi.org/10.1101/2021.05.21.21257612","url":null,"abstract":"The coronavirus outbreak continues to pose a significant challenge to human lives globally. Many efforts have been made to develop vaccines to combat this virus. However, with the arrival of the COVID-19 vaccine, there is hesitancy and a mixed reaction toward getting the vaccine. We develop a mathematical model to analyze and investigate the impacts of education on individuals hesitant to get vaccinated. The findings indicate that vaccine education can substantially minimize the daily cumulative cases and deaths of COVID-19 in the United States. The results also show that vaccine education significantly increases the number of willing susceptible individuals, and with a high vaccination rate and vaccine effectiveness, the outbreak can be controlled in the US.","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129806869","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, Design and Development of Light-Weight Polyvinyl Chloride (PVC) Pipe Based Quadrotor for Monitoring an Outdoor Environment","authors":"Khan Muhammad, Naveed Sheikh, A. Rehman","doi":"10.11648/J.MMA.20210601.12","DOIUrl":"https://doi.org/10.11648/J.MMA.20210601.12","url":null,"abstract":"The quadcopter, also known as an unmanned aerial vehicle (UAV), is a revolutionary innovation that has a great deal of potential. Modern quadrotors are transforming into small, powerful, light-weight, and agile vehicles. For the study, a variety of multirotor configurations were created before settling on a quadcopter structure. Our current focus is on mounting and designing a new polyvinyl chloride (PVC) pipe-based outdoor quadrotor setup. The quadcopter's controller is built based on the estimated mass output by decomposing the mathematical model, selecting the required motors, and using coherent electronic modules to track the outdoor environment. Quadrotor will take-off without generating any torque in the body casing. Rotors attached with motors generate thrust in the upward direction entirely based on the shape and dimension of the rotors. The proposed algorithm has strengthened the theory of nonlinear system output feedback control. The output control of a nonlinear system with parametric and functional uncertainties, as well as the input delay, is the most significant problem the configuration's materials were solely based on mass and forces acting on them. In this research we proposed a delayed roll and pitch angle reaction with standard specifications, and the faster roll and pitch angle reaction with appropriate parameters Quadrotor serves as the central body, tracking all controllable functions. Test results are then presented in order to show balanced flight performance.","PeriodicalId":340874,"journal":{"name":"Mathematical Modelling and Applications","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125395772","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}