一个造血模型的持久生存

考虑下述造血模型dN(t)/dt=-δN(t)-βθ^nN(t)/θ^n N^n(t) 2βθ^nN(t-τ）/θ^n N^n(t-τ)e^γτ,t≥0,其中δ、β、θ、γ、τ∈（0, ∞）,n∈（1, ∞）,得到持久生存的充分条件。     

一个捕食-被捕食-互惠模型反应扩散系统的稳定性条件

本文利用Lyapunov直接方法讨论了一类捕食-被捕食-互惠模型的正值常态平衡解的稳定性．稳定性条件中包含对捕食与互惠种群扩散强度比例的限制．     

Multiallelic selection polymorphism

The existence and stability of an internal (i.e., completely polymorphic) equilibrium for viability selection at a single multiallelic locus is investigated. Generations are discrete and nonoverlapping; the population is panmictic, monoecious, and diploid. Various necessary and sufficient conditions for the existence of an internal equilibrium are established and applied to the loss of alleles. Some necessary conditions for the existence of an asymptotically stable internal equilibrium are also established. All these conditions are simpler and yield general biological conclusions more easily than the classical necessary and sufficient conditions.     

Equilibrium distribution of species among vessels of a gradostat

The distribution of concentrations of two competing microbial species among the vessels of an n-vessel gradostat at equilibrium is studied for the standard mathematical model of the gradostat. As the equilibrium concentrations cannot be explicitly computed, a continuum limit, as the number of vessels becomes large, is considered which yields a singularly perturbed boundary value problem. Standard singular perturbation techniques yield information on equilibrium species concentration distributions which agree well with numerical calculations for even moderate values of n.Research supported by NSF Grant DMS 8922654     

Spatial patterns in a discrete-time SIS patch model

How do spatial heterogeneity, habitat connectivity, and different movement rates among subpopulations combine to influence the observed spatial patterns of an infectious disease? To find out, we formulated and analyzed a discrete-time SIS patch model. Patch differences in local disease transmission and recovery rates characterize whether patches are low-risk or high-risk, and these differences collectively determine whether the spatial domain, or habitat, is low-risk or high-risk. In low-risk habitats, the disease persists only when the mobility of infected individuals lies below some threshold value, but for high-risk habitats, the disease always persists. When the disease does persist, then there exists an endemic equilibrium (EE) which is unique and positive everywhere. This EE tends to a spatially inhomogeneous disease-free equilibrium (DFE) as the mobility of susceptible individuals tends to zero. The limiting DFE is nonempty on all low-risk patches and it is empty on at least one high-risk patch. Sufficient conditions for the limiting DFE to be empty on other high-risk patches are given in terms of disease transmission and recovery rates, habitat connectivity, and the infected movement rate. These conditions are also illustrated using numerical examples.     

一类相互干扰的捕食与被捕食种群模型的稳定性

本文运用常微分方程稳定性理论及方法讨论了一类具有相互干扰的捕食与被捕食模型的稳定性,得到了正平衡点的局部稳定性条件,正平衡点在第一象限的全局稳定性条件及解的有界性．     

Computation of pH evolution versus ionic products concentration in a fermentation broth

An algorithm developed for pH computation has been tested to calculate the theoretical pH changes in a culture medium during the course of a fermentation. A divergence between the computed pH value and the value measured with the electrode allows us to highlight the presence of undetected ionic products. The calculation with the algorithm by means of a computer requires only the knowledge of the ionic properties of the substrates and detected products and existing thermodynamic constants. (c) 1993 Wiley & Sons, Inc.     

一类具有稀疏效应的生态系统的极限环

研究如下一类具有稀疏效应的生态系统模型应用微分方程定性理论,得到了该系统极限环的存在性、唯一性及存在性的参数范围．     

一类生化反应系统的定性分析

研究如下一类具米氏（Michalis）反应速度的化学反应模型dX/dt=A-BX-XY~2,dY/dt BX XY~2-υY/k Y'其中A,B,v及k为正常数,应用微分方程定性理论,在一定条件下研究了上述系统极限环的存在性,不存在性及唯一性问题．     

Bioeconomic harvesting of a prey–predator fishery

This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-efforthypothesis. Here both the prey and the predator species obey the law of logistic growth. We have taken the predator functional response to prey density in such a form that each predator's functional response to the prey density approaches a constant as the prey population increases. Boundedness of the exploited system is examined. The existence of its steady states and their stability (local and global) are studied using Eigenvalue analysis. The existence of bionomic equilibria has been illustrated using a numerical example. The problem of determining the optimal harvesting policy is then solved by using Pontryagin's maximum principle.     

一类具常数接触率传染病模型的稳定性分析

本文研究了一类具常数接触率的传染病模型,用上下解方法和Liapnuov泛函讨论了地方病平衡点及无病平衡点的渐近行为,得到了各自全局稳定的充分条件.     

两捕食-食饵扩散系统正平衡点的存在性与稳定性

本文是《两捕食-食饵自治扩散系统的持续生存》一文的续篇.主要证明了系统正平衡点的存在性与全局稳定性．     

单资源中带有化感作用的两种浮游植物的动力学行为（英文）

讨论了带有化感作用机制的两种浮游植物的营养竞争模型,获得系统平衡点的存在性和稳定性条件.     

Harvesting induced fluctuations: insights from a threshold management policy

In this work, it is shown that in a deterministic context, a threshold policy can induce cyclic behavior in an otherwise exploited stable population. These dynamics ensue as a result of the combination of the degree of harvesting pressure and more protective threshold densities. Virtual equilibrium in variable structure systems plays a determinant role in this dynamical outcome.     

一类捕食者与被捕食者模型的持久性与稳定性

研究了一类捕食者与被捕食者模型,该生态系统是一个食饵种群被一个捕食种群捕食.当给定参数满足一定条件下,利用比较原理和构造Lyapunov函数的方法,证明了系统的持久性和全局渐近稳定性,并讨论了正平衡点的渐近稳定性.     

Protein folding: defining a "standard" set of experimental conditions and a preliminary kinetic data set of two-state proteins

Recent years have seen the publication of both empirical and theoretical relationships predicting the rates with which proteins fold. Our ability to test and refine these relationships has been limited, however, by a variety of difficulties associated with the comparison of folding and unfolding rates, thermodynamics, and structure across diverse sets of proteins. These difficulties include the wide, potentially confounding range of experimental conditions and methods employed to date and the difficulty of obtaining correct and complete sequence and structural details for the characterized constructs. The lack of a single approach to data analysis and error estimation, or even of a common set of units and reporting standards, further hinders comparative studies of folding. In an effort to overcome these problems, we define here a "consensus" set of experimental conditions (25 degrees C at pH 7.0, 50 mM buffer), data analysis methods, and data reporting standards that we hope will provide a benchmark for experimental studies. We take the first step in this initiative by describing the folding kinetics of 30 apparently two-state proteins or protein domains under the consensus conditions. The goal of our efforts is to set uniform standards for the experimental community and to initiate an accumulating, self-consistent data set that will aid ongoing efforts to understand the folding process.     

Trp203 mutation in GroEL promotes a self-association reaction: a hydrodynamic study

A combination of sedimentation equilibrium and sedimentation velocity in the analytical ultracentrifuge is used to investigate the hydrodynamic integrity and increased self-association interactions of the mutant GroEL Y203W when compared to the wild-type GroEL molecule, which may be derived from increased hydrophobic exposure caused by the mutation. Sedimentation velocity has revealed that three distinct species were present throughout the concentration ranges used, corresponding to 14-mer (GroEL “super monomer”) and 28-mer (“super dimer”) subunit compositions with a small amount of 42-mer (“super trimer”), which, from the relative concentration of each species, would give an estimated weight average molecular weight of (1.0 ± 0.1) × 10⁶ Da. Sedimentation equilibrium gave an apparent weight average molecular weight (M _w,app) of (910,000 ± 5000) Da, which is in agreement with these findings. These results are in contrast to wild-type GroEL which, in excellent agreement with the previous findings of Behlke and co-workers, revealed a single species with an M _w,_app of (805,000 ± 5200) Da and a sedimentation coefficient s ⁰ _20,w of (21.6 ± 0.3) S. We therefore conclude that the tryptophan mutation at the Y203 location causes a significant degree of self-association of the GroEL 14-mer assembly (with dimer and trimer present). These findings would appear to correlate well with the findings of Gibbons et al., who showed an increase in hydrophobic exposure due to this mutation. Received: 4 January 2000 / Revised version: 5 April 2000 / Accepted: 5 April 2000     

Role of pericellular matrix in development of a mechanically functional neocartilage

The role of the chondrocyte pericellular matrix (PCM) was examined in a three-dimensional chondrocyte culture system to determine whether retention of the native pericellular matrix could stimulate collagen and proteoglycan accumulation and also promote the formation of a mechanically functional hyaline-like neocartilage. Porcine chondrocytes and chondrons, consisting of the chondrocyte with its intact pericellular matrix, were maintained in pellet culture for up to 12 weeks. Sulfated glycosaminoclycans and type II collagen were measured biochemically. Immunocytochemistry was used to examine collagen localization as well as cell distribution within the pellets. In addition, the equilibrium compressive moduli of developing pellets were measured to determine whether matrix deposition contributed to the mechanical stiffness of the cartilage constructs. Pellets increased in size and weight over a 6-week period without apparent cell proliferation. Although chondrocytes quickly rebuilt a PCM rich in type VI collagen, chondron pellets accumulated significantly more proteoglycan and type II collagen than did chondrocyte pellets, indicating a greater positive effect of the native PCM. After 5 weeks in chondron pellets, matrix remodeling was evident by microscopy. Cells that had been uniformly distributed throughout the pellets began to cluster between large areas of interterritorial matrix rich in type II collagen. After 12 weeks, clusters were stacked in columns. A rapid increase in compressive strength was observed between 1 and 3 weeks in culture for both chondron and chondrocyte pellets and, by 6 weeks, both had achieved 25% of the equilibrium compressive stiffness of cartilage explants. Retention of the in vivo PCM during chondrocyte isolation promotes the formation of a mechanically functional neocartilage construct, suitable for modeling the responses of articular cartilage to chemical stimuli or mechanical compression.