一类高阶非线性中立型时滞差分方程正解的存在性定理

研究了一类高阶非线性中立型时滞差分方程正解的存在性,给出了该类方程存在有界最终正解的一个充要条件。     

Global stability in a delayed partial differential equation describing cellular replication

Here we consider the dynamics of a population of cells that are capable of simultaneous proliferation and maturation. The equations describing the cellular population numbers are first order partial differential equations (transport equations) in which there is an explicit temporal retardation as well as a nonlocal dependence in the maturation variable due to cell replication. The behavior of this system may be considered along the characteristics, and a global stability condition is proved.     

种间竞争的一个新的数学模型—对经典的Lotka—Vol—terra竞争方程的扩充

本文根据营养动力学理论,建立了一类种间竞争的新的数学模型:它是单种群增长的Cui-Lawson模型,在种间竞争上的推广。新的种间竞争模型克服了经典的种间竞争的Lotka-Volteira方程的局限与不足,具有更广泛和复杂的行为,并在特殊条件下以Lotka-Volterra竞争方程为其特例。因此,新的种间竞争的数学模型是更一般的解释性模型,是对经典的Lotka-Voterra竞争方程的扩充。     

Effects of ambient temperature steps on thermal comfort requirements

The purpose of this study was to determine the thermal comfort requirements for steps in temperature. Thirty male subjects were exposed for 50 min to a 34 or 37°C condition, and then quickly transferred to a cooler environment of 31, 28, 25, and 22°C for 50 min. Mean skin temperature was continuously measured, and the subjects reported their thermal sensation and comfort sensation every 2 min. Just after the step changes, the mean skin temperature immediately decreased, while the thermal sensation overshot and gradually rose again. Both the skin temperature and the thermal sensation seemed to reach a constant level within about 20 min. However, there were differences in the mean skin temperature and the neutral temperature derived from the correlation between the ambient temperature and the thermal sensation even 50 min after the steps, due to the thermal environmental condition before the changes of temperature. The change in the neutral temperature with time was expressed as two attenuating equations. These equations indicate that there is an obvious difference between the neutral temperatures due to the thermal condition before step changes, and that it takes >50 min after the step changes to reach the steady state. It is expected that these equations predict in quantitative terms the thermal comfort requirements within a given experimental condition.     

Periodic solutions of population models in a periodically fluctuating environment.

A periodically fluctuating environment is assumed in a population-modeling process that generates nonautonomous difference equations. The existence and uniqueness of periodic solutions are studied. A sufficient condition for existence and a necessary condition for uniqueness are obtained. Stability of the periodic solutions is investigated. Several numerical examples are given to illustrate the basic results, and a brief discussion is presented.     

A Statistical Approach to the Definition of Bacterial Species

A statistical method is proposed for recognition of a bacterial species or for differentiation of two groups of bacterial strains. Comparison between two groups is done by the “t”-test. When the mean S-values (similarity value) of two groups are A and B, and the mean S-value for all possible combinations between strains of both groups is S, a condition necessary for defining the two groups as different species is to demonstrate the existence of equations A > S and B > S. Unless this condition is fulfilled, the two groups should be considered unseparable. The condition necessary for recognition of two groups as one species is to demonstrate the existence of equations A:= S and B = S. A few examples of the test were shown using the mycobacteria, and it was suggested that this statistical method is useful in the recognition of a species.     

Solitary wave and spatially locked solitary pattern in a chemical reaction system

We investigate the behavior of a one-dimensional two component dynamical system. The dynamical equations are obtained by extracting an essence out of equations which describe the behavior of a biochemical reaction catalyzed by an allosteric protein. The obtained dynamical equations are similar to van der Pol equations. The dynamical equations are solved numerically. In the continuous system, a solitary wave is found to occur in certain ranges of the parameter space. The condition of occurrence of the solitary wave is investigated. The solitary wave can be induced by various initial perturbations, including rectangular ones with space-wise length longer than a certain critical value. The property of the solitary wave is similar to that of the impulses in nervous systems. In the discrete system, a spatially locked solitary pattern is found to occur in certain ranges of the parameter space.     

Kinetics of the trypsinogen activation by enterokinase and trypsin

A global kinetic analysis of the mechanisms of the trypsinogen activation by enterokinase and trypsin is presented. The kinetic equations of both the transient-phase and the steady-state of these mechanisms are presented. In addition, we here derive the corresponding kinetic equations for the case in which the condition of rapid equilibrium prevails and we propose a kinetic data analysis. The significance of this approach to the treatment of other zymogen activation processes is discussed.     

The structure of steady-state enzyme kinetic equations: a graph-theoretical algorithm for obtaining conditions for reduction in degree by common-factor cancellation

Many enzyme kinetic steady-state equations are so complicated that analysis of their predictions, preferably by graph-theoretical methods, without deriving the equations is desirable. An example of such a method is given here. It is a graph-theoretical algorithm for determining non-trivial relations between the rate constants of a mechanism that cause the numerator and denominator of its rate expression have a common factor so permitting the degree of the expression to be reduced. An algorithm for writing the several different forms of the reduced rate equation is also given. The algorithm is applied to some standard simple enzymic mechanisms that give relatively complicated rate equations.In the case of a 2:2 equation, the sign of curvature in a double reciprocal plot depends on the sign of the expression in the common-factor condition.     

Theoretical analysis of compartmented coupling in linear enzyme systems

Exact equations which describe the kinetic patterns of enzyme/enzyme complexes, when compartmented coupling occurs between them, are presented. Compartmented coupling refers to the creation of a local environment in which the concentration of an intermediate, shared by two enzymes, is higher than its solution concentration. This results in a higher coupling enzyme activity, a condition reflected in a shorter transition time for the system. In this paper, equations are presented which allow experimenters to quantitate the effect of compartmented coupling in terms of changes in the apparent Km and Vmax values. The equations presented in this paper are more exact than those previously derived since they do not incorporate first order assumptions before derivation.     

Asymptotic method for peristaltic transport

The purpose of this paper is to justify an asymptotic method developed for the study of peristaltic transport in a tube of arbitrary cross section. Within the framework of long wave approximation, the three-dimensional nonlinear Navier-Stokes equations are reduced to a sequence of two-dimensional linear boundary value problems of Laplace and biharmonic operators. It is shown that, if a Reynolds number is less than some constant, the solution of the approximate equations is indeed an asymptotic approximation to the exact solution of the problem as the ratio of the maximum radius of the tube to the wave length of the peristaltic motion of the wall tends to zero, and the error estimates are expressed inL ₂ norms. Furthermore, under the same condition the exact solution is shown to be unique and stable under arbitrary perturbation of spatially periodic disturbance. Application of the stability condition to peristaltic transport in a tube of circular cross section is given.     

具有阶段结构和脉冲控制的时滞生物防治害虫模型

基于昆虫病毒防治害虫的策略,建立具有脉冲效应的时滞微分方程模型,利用脉冲微分方程的Floquet乘子理论及比较定理,证明该模型害虫灭绝T周期解的全局吸引性.     

含扩散和时滞的偏微分方程解的振动性

研究一类含扩散和时滞的偏微分方程解的振动性,利用平均法,通过使用偏泛函微分方程上、下解思想和泛函微分方程振动性理论,获得了其解的非负性和关于正平衡态振动的充分条件．     

Weak convergence of a sequence of stochastic difference equations to a stochastic ordinary differential equation

We consider a sequence of discrete parameter stochastic processes defined by solutions to stochastic difference equations. A condition is given that this sequence converges weakly to a continuous parameter process defined by solutions to a stochastic ordinary differential equation. Applying this result, two limit theorems related to population biology are proved. Random parameters in stochastic difference equations are autocorrelated stationary Gaussian processes in the first case. They are jump-type Markov processes in the second case. We discuss a problem of continuous time approximations for discrete time models in random environments.     

Multiscale modelling as a tool to prescribe realistic boundary conditions for the study of surgical procedures

This work was motivated by the problems of analysing detailed 3D models of vascular districts with complex anatomy. It suggests an approach to prescribing realistic boundary conditions to use in order to obtain information on local as well as global haemodynamics. A method was developed which simultaneously solves Navier-Stokes equations for local information and a non-linear system of ordinary differential equations for global information. This is based on the principle that an anatomically detailed 3D model of a cardiovascular district can be achieved by using the finite element method. In turn the finite element method requires a specific boundary condition set. The approach outlined in this work is to include the system of ordinary differential equations in the boundary condition set. Such a multiscale approach was first applied to two controls: (i) a 3D model of a straight tube in a simple hydraulic network and (ii) a 3D model of a straight coronary vessel in a lumped-parameter model of the cardiovascular system. The results obtained are very close to the solutions available for the pipe geometry. This paper also presents preliminary results from the application of the methodology to a particular haemodynamic problem: namely the fluid dynamics of a systemic-to-pulmonary shunt in paediatric cardiac surgery.     

MHD Free Convective Boundary Layer Flow of a Nanofluid past a Flat Vertical Plate with Newtonian Heating Boundary Condition

Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.     

On global stability of discrete population models

A necessary and sufficient condition for the global stability of a large class of discrete population models is provided which does not require the construction of a Liapunov function. The general result is applied to difference equations defined in terms of “two hump” functions and to an example of frequency dependent selection.     

MHD stability condition of an anisotropic-pressure plasma in axially symmetric confinement systems formed by a poloidal field

A set of integrodifferential (over the longitudinal coordinate) equations for the transverse components of the plasma displacement minimizing the Kruskal-Oberman functional of the potential energy of MHD perturbations is derived. The stability condition corresponds to the absence of negative eigenvalues of this set for any magnetic surface in plasma.     

Models of Assembly and Disassembly of Individual Microtubules: Stochastic and Averaged Equations

In this paper we present solutions of the master equations for the microtubule length and show that the local probability for rescues or catastrophes can lead to bell-shaped length histograms. Conversely, as already known, non-local probabilities for these events result in exponential length histograms. We also derive master equations for a stabilizing cap and obtain a new boundary condition which provides an explanation of the results obtained in dilution and cutting experiments.     

Double Diffusive Magnetohydrodynamic (MHD) Mixed Convective Slip Flow along a Radiating Moving Vertical Flat Plate with Convective Boundary Condition

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables.