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Stokes flow before plane boundary with mixed stick-slip boundary conditions

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Applied Mathematics and Mechanics(English Edition) 2011年第6期32卷 795-804页

作者： N.AKHTAR G.A.H.CHOWDHURY S.K.SEN Department of Mathematics Shahjalal University of Science and Technology Research centre for mathematical and Physical sciences University of Chittagong

A general theorem for the Stokes flow over a plane boundary with mixed stick-slip boundary conditions is established. This is done by using a representation for the velocity and pressure fields in the three-dimensional Stokes flow in terms of a biharmonic function and a harmonic function. The earlier theorem for the Stokes flow due to fundamental singularities before a no-slip plane boundary is shown to be a special case of the present theorem. Furthermore, in terms of the Stokes stream function, a corollary of the theorem is also derived, providing a solution to the problem of the axisymmetric Stokes flow along a rigid plane with stick-slip boundary conditions. The formulae for the drag and torque exerted by the fluid on the boundary are established. An illustrative example is given.

关键词： Stokes flow Stokes stream function stick-slip boundary conditions,harmonic function biharmonic function

Modeling and investigating malaria *** and *** infections:Application to Djibouti data

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Infectious Disease Modelling 2024年第4期9卷 1095-1116页

作者： Yahyeh Souleiman Liban Ismail Raluca Eftimie centre de Recherche en Mathematiques et Numerique(CRMN) University of the DjiboutiCampus BalbalaDjibouti Laboratoire Mathematiques de Besançon(LMB) University of Bourgogne Franche-ComteBesanconFrance

Malaria is an infectious and communicable disease,caused by one or more species of Plasmodium *** are five species of parasites responsible for malaria in humans,of which two,Plasmodium Falciparum and Plasmodium Vivax,are the most *** Djibouti,the two species of Plasmodium are present in different proportions in the infected population:77%of *** and 33%of *** this study we present a new mathematical model describing the temporal dynamics of Plasmodium Falciparum and Plasmodium Vivax *** focus briefly on the well posedness of this model and on the calculation of the basic reproductive numbers for the infections with each Plasmodium species that help us understand the long-term dynamics of this model(i.e.,existence and stability of various eqiuilibria).Then we use computational approaches to:(a)identify model parameters using real data on malaria infections in Djibouti;(b)illustrate the influence of different estimated parameters on the basic reproduction numbers;(c)perform global sensitivity and uncertainty analysis for the impact of various model parameters on the transient dynamics of infectious mosquitoes and infected humans,for infections with each of the Plasmodium *** originality of this research stems from employing the FAST method and the LHS method to identify the key factors influencing the progression of the disease within the population of *** addition,sensitivity analysis identified the most influential parameter for Falciparium and Vivax reproduction ***,the uncertainty analysis enabled us to understand the variability of certain parameters on the infected compartments.

关键词： Falciparum and vivax models Reproduction number Stability analysis Sensitivity analysis FAST method LHS method Djibouti data

The topology of Julia sets for polynomials

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Science China Mathematics 2002年第8期45卷 1020-1024页

作者：尹永成 centre of mathematical sciences Zhejiang University Hangzhou China

We prove that wandering components of the Julia set of a polynomial are singletons provided each critical point in a wandering Julia component is non-recurrent. This means a conjecture of Branner-Hubbard is true for t... 详细信息

关键词： critical point, non-recurrent, Julia set.

Reflected BSDEs with Random Default Time and Related Mixed Optimal Stopping-control Problems

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Acta Mathematicae Applicatae Sinica 2013年第1期29卷 165-178页

作者： Dong-mei Guo Xiao-ming Xu School of Economics Central University of Finance and Economics Academy of Mathematics and Systems Science Chinese Academy of Sciences Institute of Mathematics School of Mathematical Sciences Nanjing Normal University

In this paper we study the one-dimensional reflected backward stochastic differential equations which are driven by Brownian motion as well as a mutually independent martingale appearing in a defaultable setting. Using a penalization method, we prove the existence and uniqueness of the solutions to these equations. As an application, we show that under proper assumptions the solution of the reflected equation is the value of the related mixed optimal stopping-control problem.

关键词： backward stochastic differential equation random default time mixed optimal stopping-controlproblem

The impact of age structure and vaccine prioritization on COVID-19 in West Africa

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Infectious Disease Modelling 2022年第4期7卷 709-727页

作者： Hemaho B.Taboe Michael Asare-Baah Afsana Yesmin Calistus N.Ngonghala Department of Mathematics University of FloridaGainesvilleFL32611USA Laboratoire de Biomathematiques et d’Estimations Forestieres University of Abomey-CalaviCotonouBenin Department of Epidemiology University of Florida2004 Mowry RoadGainesvilleFL32610USA Emerging Pathogens Institute University of FloridaGainesvilleFL32610USA

The ongoing COVID-19 pandemic has been a major global health challenge since its emergence in *** to early predictions that sub-Saharan Africa(SSA)would bear a disproportionate share of the burden of COVID-19 due to the region's vulnerability to other infectious diseases,weak healthcare systems,and socioeconomic conditions,the pandemic's effects in SSA have been very mild in comparison to other ***,the number of cases,hospitalizations,and disease-induced deaths in SSA remain low,despite the loose implementation of non-pharmaceutical interventions(NPIs)and the low availability and administration of *** explanations for this low burden include epidemiological disparities,under-reporting(due to limited testing),climatic factors,population structure,and government policy *** this study,we formulate a model framework consisting of a basic model(in which only susceptible individuals are vaccinated),a vaccine-structured model,and a hybrid vaccine-age-structured model to assess the dynamics of COVID-19 in West Africa(WA).The framework is trained with a portion of the confirmed daily COVID-19 case data for 16 West African countries,validated with the remaining portion of the data,and used to(i)assess the effect of age structure on the incidence of COVID-19 in WA,(ii)evaluate the impact of vaccination and vaccine prioritization based on age brackets on the burden of COVID-19 in the sub-region,and(iii)explore plausible reasons for the low burden of COVID-19 in WA compared to other parts of the *** of the model parameters and global sensitivity analysis show that asymptomatic youths are the primary drivers of the pandemic in ***,the basic and control reproduction numbers of the hybrid vaccine-age-structured model are smaller than those of the other two models indicating that the disease burden is overestimated in the models which do not account for *** result is confirmed through the vaccine-d

关键词： Vaccine prioritization SARS-CoV-2 Omicron variant AVAT Reproduction number Herd immunity

The Bulk-Surface Virtual Element Method for Reaction-Diffusion PDEs:Analysis and Applications

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Communications in Computational Physics 2023年第3期33卷 733-763页

作者： Massimo Frittelli Anotida Madzvamuse Ivonne Sgura Department of Mathematics and Physics“E.De Giorgi” University of SalentoVia per Arnesano73100 LecceItaly Department of Mathematics University of British Columbia1984 Mathematics RoadVancouverBC V6T 1Z2Canada Department of Mathematics School of Mathematical and Physical SciencesUniversity of SussexBrightonBN19QHUK Department of Mathematics and Applied Mathematics University of PretoriaPrivate Bag x 20Hatfield0028South Africa.

Bulk-surface partial differential equations(BS-PDEs)are prevalent in manyapplications such as cellular,developmental and plant biology as well as in engineeringand material *** numerical methods for BS-PDEs in three space dimensions(3D)are *** this work,we present a bulk-surface virtual elementmethod(BS-VEM)for bulk-surface reaction-diffusion systems,a form of semilinearparabolic BS-PDEs in *** previous studies in two space dimensions(2D),the3D bulk is approximated with general polyhedra,whose outer faces constitute a flatpolygonal approximation of the *** this reason,the method is restricted tothe lowest order case where the geometric error is not *** BS-VEM guaranteesall the advantages of polyhedral methods such as easy mesh generation andfast matrix assembly on general *** advantages are much more relevantthan in *** allowing for general polyhedra,general nonlinear reaction kineticsand general surface curvature,the method only relies on nodal values without needingadditional evaluations usually associated with the quadrature of general *** latter is particularly costly in *** BS-VEM as implemented in thisstudy retains optimal convergence of second order in space.

关键词： Bulk-surface PDEs bulk-surface reaction-diffusion systems polyhedral meshes bulksurface virtual element method convergence.

Spatial distribution of leprosy in India:an ecological study

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Infectious Diseases of Poverty 2018年第1期7卷 206-214页

作者： Kyra H.Grantz Winnie Chabaari Ramolotja Kagiso Samuel Buri Gershom Laura Blum Lee Worden Sarah Ackley Fengchen Liu Thomas M.Lietman Alison P.Galvani Lalitha Prajna Travis C.Porco Department of Biology University of FloridaGainesvilleFLUSA Emerging Pathogens Institute University of FloridaGainesvilleFLUSA DST/NRF Center for Excellence in Epidemiological Modeling and Analysis(SACEMA) StellenboschSouth Africa Stellenbosch University StellenboschSouth Africa African Institute of mathematical sciences MuizenbergSouth Africa University of California BerkeleyCAUSA Francis I.Proctor Foundation for Research in Ophthalmology University of CaliforniaSan FranciscoCAUSA Department of Ophthalmology University of CaliforniaSan FranciscoCAUSA Department of Epidemiology and Biostatistics University of CaliforniaSan FranciscoCAUSA Yale University New HavenCTUSA Aravind Eye Hospital MaduraiTamil NaduIndia

Background:As leprosy elimination becomes an increasingly realistic goal,it is essential to determine the factors that contribute to its *** evaluate social and economic factors as predictors of leprosy annual new case detection rates within India,where the majority of leprosy cases ***:We used correlation and linear mixed effect regressions to assess whether poverty,illiteracy,nighttime satellite radiance(an index of development),and other covariates can explain district-wise annual new case detection rate and Grade 2 disability ***:We find only weak evidence of an association between poverty and annual new case detection rates at the district level,though illiteracy and satellite radiance are statistically significant predictors of leprosy at the district *** find no evidence of rapid decline over the period 2008-2015 in either new case detection or new Grade 2 ***:Our findings suggest a somewhat higher rate of leprosy detection,on average,in poorer districts;the overall effect is *** divide between leprosy case detection and true incidence of clinical leprosy complicates these results,particularly given that the detection rate is likely disproportionately lower in impoverished *** information is needed to distinguish the determinants of leprosy case detection and transmission during the elimination epoch.

关键词： Leprosy Hansen’s disease India Poverty Spatial

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