An analysis of facilitated-diffusion problems

This paper develops the mathematical analysis of nonlinear boundary-value problems that model the facilitated diffusion of a substrate across a membrane. The analysis includes bounds for solutions, global existence results, local uniqueness and continuity results, and estimates for parameter ranges for uniqueness of solutions.     

Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrients

In this paper, the existence, uniqueness and exponential stability of almost periodic solutions for a mathematical model of tumour growth are studied. The establishment of the model is based on the reaction–diffusion dynamics and mass conservation law and is considered with a delay in the cell proliferation process. Using a fixed-point theorem in cones, the existence and uniqueness of almost periodic solutions for different parameter values of the model is proved. Moreover, by the Gronwall inequality, sufficient conditions are established for the exponential stability of the unique almost periodic solution. Results are illustrated by computer simulations.     

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.     

Disk-elektrophoretischer Nachweis des Lp(a)-Proteins in Lipoproteinfraktionen

Zusammenfassung Die Untersuchung der Serumlipoproteinfraktion HDL₂ (1,063< <1,125 g/ml) von 35 Personen mit Hilfe der Polyacrylamid-Gelelektrophorese zeigte, daß auch bei Anwendung dieser empfindlichen Technik eine eindeutige Einteilung in Lp(a+)- und Lp(a-)-Typen nicht möglich ist. Von den 20 Seren, die durch Agar-Gel-Doppeldiffusion als Lp(a-) bestimmt wurden, zeigten 19 in ihrer HDL₂-Fraktion in der für das Lp(a)-Lipoprotein typischen Position eine Bande. Dieser Befund bestätigt die Annahme, daß der Faktor Lp(a) als ein quantitatives genetisches Merkmal angesehen werden muß.Die -Lipoproteine des HDL₂-Bereiches erwiesen sich als disk-elektrophoretisch heterogen.

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Determination of the Lp(a)-protein by disc-electrophoresis of lipoprotein-fractions

Summary Gelelectrophoretic studies of the serum lipoprotein fraction HDL₂ (1.063< <1.125 g/ml)_of 35 individuals showed, that using this technique no clear classification into Lp(a+) and Lp(a-)-types could be made. 19 out of 20 sera typed Lp(a-) by double diffusion contained in their HDL₂-fraction a lipoprotein with the electrophoretic mobility characteristic of the Lp(a)-lipoprotein. This observation confirmes previous suggestions, that Lp(a) indeed is a quantitative genetic trait.The -lipoproteins of the HDL₂-fraction are heterogeneous in gelelectrophoresis.

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Untersuchung mit Unterstützung durch die Deutsche Forschungsgemeinschaft.     

一类复杂生态系统的周期解及其稳定性

本文研究了一类复杂生态系统,得到了保证其存在唯一周期解及渐近稳定的充分条件。     

A reaction-diffusion system of a predator-prey-mutualist model

Mutualism is part of many significant processes in nature. Mutualistic benefits arising from modification of predator-prey interactions involve interactions of at least three species. In this paper we investigate the Homogeneous Neumann problem and Dirichlet problem for a reaction-diffusion system of three species—a predator, a mutualist-prey, and a mutualist. The existence, uniqueness, and boundedness of the solution are established by means of the comparison principle and the monotonicity method. For the Neumann problem, we analyze the constant equilibrium solutions and their stability. For the Dirichlet problem, we prove the global asymptotic stability of the trivial equilibrium solution. Specifically, we study the existence and the asymptotic behavior of two nonconstant equilibrium solutions. The main method used in studying of the stability is the spectral analysis to the linearized operators. The O.D.E. problem for the same model was proposed and studied in [13]. Through our results, we can see the influences of the diffusion mechanism and the different boundary value conditions upon the asymptotic behavior of the populations.     

具有放牧率的某些概周期生态模型

文［１］研究了具有放牧率的周期生态模型的周期解的存在性、唯一性与稳定性等问题．本文考虑更加广泛的生态模型,即具有放牧率的概周期生态系统的概周期解的存在性、稳定性,通过利用指数型二分性和不动点方法,得到一些新结果．     

Threshold and stability results for an age-structured epidemic model

We study a mathematical model for an epidemic spreading in an age-structured population with age-dependent transmission coefficient. We formulate the model as an abstract Cauchy problem on a Banach space and show the existence and uniqueness of solutions. Next we derive some conditions which guarantee the existence and uniqueness for non-trivial steady states of the model. Finally the local and global stability for the steady states are examined.     

一类具延时的Hopfield型神经网络模型的周期解

本文利用不动点方法,讨论了一类具延时的Hopfield型神经网络模型周期解的存在性与唯一性,获得了若干充分条件．     

一类与传染病模型有关的积分方程的定性性质

证明了一类与传染病模型有关的积分方程解的唯一性,整体存在性和当t→∞时收敛到零的若干充分条件.利用Banach不动点定理证明了存在性结果,利用一个新的积分不等式证明了收敛性结果.     

微生物连续发酵模型及正解的存在性与稳定性分析

本文引入一个新的非线性动力系统,描述Klebsiella pneumoniae以甘油为底物发酵生成1,3-丙二醇的过程.此模型考虑了细胞内物质的浓度,研究甘油主动运输及1,3-丙二醇被动扩散的跨膜方式.证明模型解的存在唯一性,通过引入微分包含和上哈密尔顿函数证明正解的存在性.此外,以稀释速率0.1为例计算平衡点,并对系统的稳定性做出分析.     

水曲柳幼苗根系在不同浓度NH4NO3溶液中水流导度的变化

水分吸收过程是根系重要的生理过程。水孔蛋白在根系水分径向运输中起着重要的作用,根系水流导度(L_p)的测定是研究水孔蛋白的重要途径。该研究采用压力流的方法,对相同生长条件下的水曲柳(Fraxinus mandshurica)幼苗根系进行研究,测定了根系在去离子水和不同浓度NH₄NO₃溶液中的L_p。结果表明:未经处理的水曲柳幼苗根系,L_p随NH₄NO₃浓度的增加而上升,而且NH₄NO₃溶液中的L_p比去离子水中的L_p平均高77%;经HgCl₂处理后,水曲柳幼苗根系的L_p仍然随NH₄NO₃浓度的增加而增大,但是根系L_p在去离子水下降了22%,而在NH₄NO₃溶液中下降了68%,与以前的研究相比发现,经HgCl₂处理后,以营养液为吸水基质的根系L_p的降低值普遍高于以去离子水为基质的试验。因此,基质中养分离子的存在对根系中水孔蛋白活性产生了重要的影响,进而影响根系水分的吸收过程。     

具有庇护所的三种群捕食者-食饵模型

讨论了一类具有庇护所的自治三种群捕食者一食饵模型,运用Liapunov函数方法,得到了该模型持久性的充分条件．对于该模型的周期系统,在一定的条件下,将产生唯一一个全局渐近稳定的周期正解．对更具普遍意义的概周期现象,也得出了概周期正解唯一存在且全局渐近稳定性的充分条件．     

Dimensions and distribution of intercellular spaces in cryo-planed soybean nodules

The ability of legume nodules to regulate their permeability to gas diffusion has been attributed to physiological control over the size and distribution of gas-filed intercellular spaces within the nodule cortex. To examine the size and distribution of intercellular spaces and to determine whether they were filled with gas (high diffusion permeability) or liquid (low diffusion permeability), whole nodules were frozen in liquid nitrogen slush (-210°C), and then either cryo-fractured or cryo-planed before being examined by cold-stage scanning electron microscopy (SEM). The cryo-planed tissue was found to have many advantages over cryo-fractured nodules in providing images which were easier to interpret and quantify. Intercellular spaces throughout the nodule were examined in both tangential and medial planed faces. Since no differences were observed between views in either the size or shape of the open intercellular spaces, it was concluded that the intercellular spaces of nodules were not radially oriented as assumed in many mathematical models of gas diffusion. The inner cortex region in the nodules had the smallest intercellular spaces compared to other zones, and less than 10% of the intercellular spaces were occluded with any type of material in the central zone regions. Vacuum infiltration of nodules with salt solutions and subsequent cryo-planing for SEM examination showed that open and water-filled intercellular spaces could be differentiated. The potential is discussed for using this method to study the mechanism of diffusion barrier regulation in legume nodules.     

具有扩散和放养的时滞竞争系统的正周期解

主要研究缀块环境下具有扩散和放养的时滞Lotka-Volterra竞争系统,得到了系统的周期解存在性,唯一性和全局渐近稳定性的充分条件．     

Maintenance of air in intercellular spaces of plants

Although air-filled intercellular spaces are necessary and ubiquitous in higher plants, little attention has been paid to the possible mechanisms by which these spaces are kept from being flooded. The most likely mechanism is that the living plant cell may maintain a hydrophobic monolayer on the surfaces of adjacent intercellular spaces. The existence of `apparent free space' in cell walls and the fact that detergent solutions do not enter the intercellular spaces argue against this hypothesis. It is concluded that the mechanism by which these important air spaces are maintained is still unknown.     

具性别和阶段结构的非自治二种群捕食者-食饵系统研究

讨论了一类食饵具有性别结构,捕食者具有阶段结构的非自治捕食者．食饵系统,运用Liapunov函数方法,得到了该系统一致持续生存的充分条件．对于该模型的周期系统,在适当条件下,存在唯一、全局渐近稳定的周期解．对更具普遍意义的概周期现象,也得出了概周期正解唯一存在且全局渐近稳定的充分条件．     

Physical and transcriptional map of a 3-Mb region of mouse chromosome 1 containing the gene for the neural tube defect mutant loop-tail (Lp)

The Lp mouse mutant provides a model for the severe human neural tube defect (NTD), cranio-rachischisis. To identify the Lp gene, a positional cloning approach has been adopted. Previously, linkage analysis in a large intraspecific backcross was used to map the Lp locus to distal mouse chromosome 1. Here we report a detailed physical map of this region. The interval surrounding Lp has been cloned in a yeast artificial chromosome (YAC) contig consisting of 63 clones spanning approximately 3.2 Mb. Fifty sequence tagged sites (STSs) have been used to construct the contig and establish marker order across the interval. Based on the high level of conserved synteny between distal mouse chromosome 1 and human 1q21-q24, many of these STSs were designed from expressed sequences identified by cross-screening human and mouse databases of expressed sequence tags. Added to other known genes in the region, a total of 29 genes were located and ordered within the contig. Seven novel polymorphisms were identified within the region, allowing refinement of the genetic map and a reduction in the size of the physical interval containing the Lp gene. The Lp interval, between D1Mit113 and Tagln2, can be spanned by two nonchimeric overlapping YACs that define a physical distance of approximately 1 Mb. Within this region, 10 potential candidate genes have been mapped. The materials and genes described here will provide a resource for the identification and further study of the mutated Lp gene that causes this severe neural tube defect and will provide candidates for other defects known to map to the homologous region on human chromosome 1q.     

一个造血模型的概周期正解

应用Ｓｃｈａｕｄｅｒ不动点定理,研究了一个造血模型概周期正解的存在性及唯一性。     

具常数时滞细胞神经网络概周期解

利用矩阵不等式的分析技巧和Banach空间中不动点定理,得到了具常数时滞细胞神经网络概周期解的存在性、唯一性和全局指数稳定性,推广和改进了已有文献的结论。