Global dynamics of a mathematical model for HTLV-I infection of CD4 T cells with delayed CTL response

Human T-cell leukaemia virus type I (HTLV-I) preferentially infects the CD4⁺ T cells. The HTLV-I infection causes a strong HTLV-I specific immune response from CD8⁺ cytotoxic T cells (CTLs). The persistent cytotoxicity of the CTL is believed to contribute to the development of a progressive neurologic disease, HTLV-I associated myelopathy/tropical spastic paraparesis (HAM/TSP). We investigate the global dynamics of a mathematical model for the CTL response to HTLV-I infection in vivo. To account for a series of immunological events leading to the CTL response, we incorporate a time delay in the response term. Our mathematical analysis establishes that the global dynamics are determined by two threshold parameters R₀ and R₁, basic reproduction numbers for viral infection and for CTL response, respectively. If R₀≤1, the infection-free equilibrium P₀ is globally asymptotically stable, and the HTLV-I viruses are cleared. If R₁≤1<R₀, the asymptomatic-carrier equilibrium P₁ is globally asymptotically stable, and the HTLV-I infection becomes chronic but with no persistent CTL response. If R₁>1, a unique HAM/TSP equilibrium P₂ exists, at which the HTLV-I infection is chronic with a persistent CTL response. We show that the time delay can destabilize the HAM/TSP equilibrium, leading to Hopf bifurcations and stable periodic oscillations. Implications of our results to the pathogenesis of HTLV-I infection and HAM/TSP development are discussed.     

The art and the science of British algebra: A study in the perception of mathematical truth

This paper investigates the origins of the concept of mathematical truth by focusing on the development of algebra in England in the early 19th century. In particular, it investigates the reasons why the English, despite their attention to the elements of abstract algebra, never produced a system comparable to modern algebra. Special consideration is given to the works of George Peacock, Augustus DeMorgan, William Whewell, and John Herschel. It is argued that what separated the early development of English algebra from modern algebra is a fundamental difference between 19th- and 20th-century views of truth.     

A mathematical modeling approach to the formation of urban and rural areas: Convergence of global solutions of the mixed problem for the master equation in sociodynamics

Urban and rural areas are formed by human migration from thinly populated areas to densely populated areas. It is known in sociodynamics that human migration is described by a nonlinear integro-partial differential equation whose unknown function denotes the population density. This equation is called the master equation. The master equation has its origin in statistical physics, and is regarded as one of the most fundamental equations in natural sciences, as its name suggests. We describe the formation of urban and rural areas by making use of global solutions of the mixed problem for this equation. In this paper we prove sufficient conditions for the mixed problem to have a unique global solution that converges to a two-tier step function as the time variable tends to infinity. This step function is a stationary solution of the master equation, and the higher (lower, respectively) step represents a stationary urban (rural, respectively) area. This result mathematically describes the formation of urban and rural areas in the real world.     

Steady-state skill levels of workers in learning and forgetting environments: A dynamical system analysis

This article presents a study on the long-term (i.e., steady-state, convergence) characteristics of workers’ skill levels under learning and forgetting in processing units in a manufacturing environment, in which products are produced in batches. Assuming that all workers already have the basic knowledge to execute the jobs, workers learn (accumulate their skill) while producing units within a batch, forget during interruptions in production, and relearn when production resumes. The convergence properties in the paper are examined under assumptions of an infinite time horizon, a constant demand rate, and a fixed lot size. Our work extends the steady-state results of Teyarachakul, Chand, and Ward (2008) to the learning and forgetting functions that belong to a large class of functions possessing some differentiability conditions. We also discuss circumstances of manufacturing environments where our results would provide useful managerial information and other potential applications.     

Participation of V. S. Vladimirov in work on the USSR atomic project: A significant milestone in the development of the foundations of mathematical modeling of the processes of neutron physics

This paper is dedicated to the 90th anniversary of the birth of a leading Soviet and Russian scientist and a member of the USSR Academy of Sciences: Academician Vasilii Sergeevich Vladimirov. Vladimirov, one of the strongest contemporary mathematicians, worked from 1951 through 1955 at KB-11 (today, the Russian Federal Nuclear Center — All-Russian Scientific Research Institute for Experimental Physics), the “secret facility” where development of atomic weaponry was conducted. We present the main results of Vladimirov’s scientific activity connected with his work on the USSR atomic project.     

A regularity result for a minimum problem in orlicz-sobolev spaces with applications in the study of the dirichlet problem for the operator of hencky-nadai theory

The existence and uniqueness of the solution to the problem of minimum for functionals generated by N- functions are obtained in Orlicz-Sobolev spaces. Applications for some functionals dealing with Hencky theory are given.     

A simulation study of the fleet sizing problem arising in offshore anchor handling operations

A fleet sizing problem arising in anchor handling operations related to movement of offshore mobile units is presented in this paper. Typically, the intensity of these operations is unevenly spread throughout the year. The operations are performed by dedicated vessels, which can be hired either on the long-term basis or on the spot market. Spot rates are frequently a magnitude higher than long-term rates, and vessels are hired on the spot market if there is a shortage of long-term vessels to cover the ongoing anchor handling operations. Deciding the cost-optimal fleet of vessels on the long-term hire to cover future operations is a problem facing offshore oil and gas operators. This decision has a heavy economic impact as anchor handling vessels are among the most expensive ones. The problem is highly stochastic because durations of anchor handling operations vary and depend on uncertain weather conditions. Moreover, future spot rates for anchor handling vessels are extremely volatile. The objective of this paper is to describe a simulation model for the fleet sizing problem. The study was initiated by the largest Norwegian offshore oil and gas operator and has received considerable acceptance among the planners.