人口问题中具广义Ginzbur-Landau型方程解的渐近性和Blow-up

在文献[1][2][3]和[4]的基础上,研究人口问题中具广义Ginzbur-Landau型弥散方程（0.21）,（0.22）及更一般的非线性高阶抛物型方程（0.23）初边值问题,在古典解存在且唯一的条件下,利用文[7,8]的相应方法,深入探讨问题的广义解和古典解的渐近性及Blow-up现象,得到许多新结果。     

中立型时滞逻辑斯谛方程的全局渐近稳定性和振动性

本文研究中立型时滞Logistic方程N（t）=N（t）)〔a－bN(t－τ)－cN(t－τ)－dN(t)〕,t≥t_0(E),其中τ,φ∈［0,∞],a,b,c,d∈R,得到方程（E）的正解关于正常数平衡点全局渐近稳定和振动的充分条件．本文所用方法与其他文献不同,所得结果发展了文献[1—4]的结果,其中定理4回答了文献[10]所提出的一个公开问题．     

Willis环状脑动脉瘤生物数学模型的渐近解

一、引言 G. Austin在1971年制作了模拟脑动脉瘤的物理装置实验,用一个模拟电路来描述动脉瘤内血液的流动状态,得出了一个数学模型。文[2]对文[1]的模拟电路再进行分析,归结出较文[1]完善的数学模型,是下列具阻尼项及外激励的三次非线性的Duffing方程     

具有负扰动项二阶中立型非线性动力方程的振动性与渐近性质

本文讨论时标上具有负扰动项的二阶中立型非线性动力方程的振动性与渐近性质,获得了适用于所有时标的动力方程解的振动性和渐近性的充分条件,阐述了方程中各项的系数在方程解的定性性质中的作用,推广和改进了已有文献的有关结果,并给出了应用实例.     

一类害虫与天敌模型的稳定性

本文研究一类害虫——天敌模型的稳定性,得到系统（E）的正常数平衡点为渐近稳定的充分条件,发展了文献[1],[2]的结果．     

时滞逻辑斯谛方程的稳定性和振动性

本文研究时滞逻辑斯谛方程其中得到方程（E）关于正常数平衡点为渐近稳定和振动的条件,也得到方程（E）存在正周期解的条件,所得结果发展和推广了文献［1］,［2］的结果。     

时滞Logistic型差分方程的振动及稳定性

本文获得了如下Xn 1=xnexp(a bxn-k^p-cxn-1^q）时滞Logistic型差分方程所有正解关于其平衡点振动的充要条件，同时还获得了一个正平衡点渐近稳定的充分条件，其中A∈（0，∞），B∈（-∞，O]，C∈（0，∞），K,l∈N。     

一类Kolmogorov系统的动力性质

用定性分析的方法对一类Kolmogorov系统(dx)/(dt)=x(a_0-a_11x a_2x~(n-1)-a3x~n a_4xy~m),(dy)/(dt)=y(b_1x~n-b_2),进行了研究．讨论了系统平衡点的性态,给出了系统无闭轨的充分条件以及存在唯一稳定极限环的条件．包含并推广了文献[3]的相关结果．     

带跳与年龄相关随机种群模型方程收敛性分析

本文研究了与年龄相关的带跳随机种群方程半隐式Euler方法的收敛性.运用Burkholder-Davis-Gundy不等式以及矫正条件,证明了半隐式Euler方法以1/2阶收敛.推广了文献[6,7]主要结果.     

遗传工程外文文献选录

[1]本选录选择报道有关遗传工程的英、法、德、日文文献(其中,以综述性内容的为主) [2]文献在刊物中页序后面括弧内是该项刊物发行日期 [3]在中国科学院图书馆自然科学服务部以外单位查到的文献,在发行日期后面,注明了单位名称     

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。     

Mathematical analysis of a model for the renal concentrating mechanism

A system of ordinary differential equations, designed to model the counterflow system in the renal medulla, is studied. An existence theorem for solutions of the model equations is obtained. An exact solution of the system is obtained in the limiting case of infinite water permeability. If there is diffusion in the core, evaluation of the exact solution leads to multiple stable solutions of the model equations. One solution has a large concentration ratio, which tends to a finite asymptotic limit as the pump strength tends to infinity.     

Analysis of the equations of renal network flows

Solution of the nonlinear differential equations for renal network flows are investigated, and conditions are given under which a unique solution to these equations exists.     

The solution of hollow fiber bioreactor design equations.

A methodology for simplifying the solution procedure for hollow fiber bioreactor design equations has been described. Such a procedure facilitates decoupling of membrane and spongy matrix equations from the tube side equations. The equivalence between the reduced equations and the hemodialyzer problem has been explicitly obtained.     

Osmotic Transport across Cell Membranes in Nondilute Solutions: A New Nondilute Solute Transport Equation

The fundamental physical mechanisms of water and solute transport across cell membranes have long been studied in the field of cell membrane biophysics. Cryobiology is a discipline that requires an understanding of osmotic transport across cell membranes under nondilute solution conditions, yet many of the currently-used transport formalisms make limiting dilute solution assumptions. While dilute solution assumptions are often appropriate under physiological conditions, they are rarely appropriate in cryobiology. The first objective of this article is to review commonly-used transport equations, and the explicit and implicit assumptions made when using the two-parameter and the Kedem-Katchalsky formalisms. The second objective of this article is to describe a set of transport equations that do not make the previous dilute solution or near-equilibrium assumptions. Specifically, a new nondilute solute transport equation is presented. Such nondilute equations are applicable to many fields including cryobiology where dilute solution conditions are not often met. An illustrative example is provided. Utilizing suitable transport equations that fit for two permeability coefficients, fits were as good as with the previous three-parameter model (which includes the reflection coefficient, σ). There is less unexpected concentration dependence with the nondilute transport equations, suggesting that some of the unexpected concentration dependence of permeability is due to the use of inappropriate transport equations.     

One-dimensional food chain equations and their generalization

Two equations describing one-dimensional food chains are known to possess soliton solutions. It is demonstrated that both equations are embraced within another equation, which arises in the theory of chains of enzymic reactions. We find an elliptic function solution to this equation. We obtain a one-soliton solution from it and re-derive the elliptic function solutions of the two ecological equations.     

Stochastic models for an open biochemical system

This paper uses the theory of Markov processes to derive stochastic models for a single open biochemical system at st?ady state under 3 sets of assumptions. The system is a one substrate, one product reaction. Each set of assumptions results in a separate solution for the probability functions. A system of linear equations in the probability function as well as an equivalent differential equation in its generating function are derived. The assumption of no flux leads to the first (exact) solution of the linear equations. The form agrees with that of the closed systems. Making assumptions that simplify the system to model active transport results in the second (exact) solution to the linear equations. Assuming the presence of a large number of molecules in the system facilitates obtaining the third (approximate) solution to the differential equations.     

A Theory of Fluid Flow in Compliant Tubes

Starting with the Navier-Stokes equations, a system of equations is obtained to describe quasi-one-dimensional behavior of fluid in a compliant tube. The nonlinear terms which cannot be shown to be small in the original equations are retained, and the resulting equations are nonlinear. A functional pressure-area relationship is postulated and the final set of equations are quasi-linear and hyperbolic, with two independent and two dependent variables. A method of numerical solution of the set of equations is indicated, and the application to cases of interest is discussed.     

Comparison of experimentally determined protein structures by solution of Bloch equations

Nuclear Overhauser enhancement (NOESY) spectra were theoretically generated by solving the generalized Bloch equations with the appropriate initial conditions. The input to the equations were the coordinates of the protons of two similar crystal structures of basic pancreatic trypsin inhibitor. The two NOESY spectra obtained were compared to published experimental spectra of the protein in solution. It was found that the two crystal structures of basic pancreatic trypsin inhibitor give different theoretical spectra. The solution of the Bloch equations is very sensitive to small variations in the distance between protons (approx. 0.2 A), and to differences in the surrounding configurations. The method allows a detailed comparison of the crystal and solution structures of proteins. The structure of the trypsin inhibitor in solution was found to be similar to either one or the other crystal forms in different regions of the molecule.     

The central core model of the renal medulla: A particular solution

A simple particular solution of a set of differential equations that model the behavior of the human kidney is obtained. This solution is extended by means of an expansion procedure, and numerical results are presented in graphical form. These results may have application to kidney malfunction and also provide values with which to compare numerical results of the basic equations.