Willis环状脑动脉瘤的生物数学模型的周期解

本文运用扭转映射的不动点定理,通过Poincare'映射,在(μ/2)+((β~2)/(4a))<1的条件下,证明了Willis环状脑动脉瘤生物数学模型 +μ+αx-βx~2+γx~3=Fcosωt(其中μ,α,β,γ,F,ω都是正常数)至少存在一个(2π)/ω周期解。     

一类中心型半连续动力系统的周期解

讨论了一类中心型半连续动力系统的阶1周期解和阶2周期解的存在性、个数及其稳定性,给出该中心型系统存在唯一、两个、无穷多个阶1周期解和阶2周期解的条件,并给出了相应理论结果的数值模拟.     

具有周期传染率的SIR传染病模型的周期解

考虑了具有周期传染率的SIR流行病模型,定义了基本再生数^-R0=β／（μ＋γ）,分析了该模型的动力学性态,证明了当^-R0〈1时无病平衡点是全局稳定的;^-R0〉1时,无病平衡点是不稳定的,模型至少存在一个周期解。对小振幅的周期传染率模型,给出了模型周期解的近似表达式,证明了该周期解的稳定性,最后做了数值模拟,结果显示周期解可能是全局稳定的。     

高维非自治系统的周期解

本文通过建立并利用齐次线性方程解的估计公式,获得了周期系统（1）的周期解的存在性、唯一性定理,对周期系统（2）给出了一个平稳振荡定理,最后给出了实例。     

一个造血模型的全局吸收性和周期解相交

本文将Ｍａｃｋｅｙ和Ｇｌａｓｓ提出的一个造血模型推广到具有周期系数和无穷时滞的情形,研究该模型的全局吸收性和周期解相交,并相应地得到两个充分条件。     

二阶混合型周期系统的周期解

本文应用Fourier分析的方法,改进了文〔1〕的主要结果。即把文〔l〕中定理1到定理4的条件|b_2|＋|c_2|＜2~(1/2)改讲为|b_2|＋|c_2|≠1．并指出用本文的方法可以类似研究高阶混合型周期系统的周期解。     

一个造血模型的全局吸引性和周期解相交

本文将Mackey和Glass提出的一个造血模型推广到具有周期系数和无穷时滞的情形．研究该模型的全局吸引性和周期解相交,并相应地得到两个充分条件.     

高阶中立型周期系统的周期解

本文应用傅氏分析的方法．结合一些不等式技巧得到了n阶常系数线性中立型周期系统存在周期解的充要条件,从而推广并改进了前人的工作,使定理的适用范围由原来的│b_n│＜2_(1／2)改进为│b_n│≠1．     

非线性非自治中立型时滞微分方程的周期解

本文研究非线性非自治中立型时滞微分方程N（t）=r（t）N（t）[a（t）-N（t-1）-c（t）N（t-1）],（E）得到方程（E）存在正周期解的充分条件．所得结果解决了Y·Kuang和A·Feldstein所提出的一个公开问题．     

几类具有无穷时滞泛函微分方程正周期解的存在性

运用Leray-Schauder不动点定理研究具有无穷时滞的泛函微分方程的正周期解的存在性问题,获得了存在正周期解的充分条件,改进了文献[3]中的结果.     

THE PREPARATION AND STERILIZATION OF OPHTHALMIC SOLUTIONS

Ophthalmic solutions should be prepared and preserved according to whether they are to be used in surgical procedures, in the clinic or office, or by the patient at home.There is an optimum pH level at which the solutions of individual drugs should be buffered in order to obtain the maximum efficiency and stability.Deterioration of the drugs used is greatly diminished when they are dispensed at the proper pH.Quaternary ammonium chloride solutions in proper strength have been shown to be adequate for the preservation of ophthalmic solutions.     

The dynamics of production and destruction: Analytic insight into complex behavior

This paper analytically explores the properties of simple differential-difference equations that represent dynamic processes with feedback dependent on prior states of the system. Systems with pure negative and positive feedback are examined, as well as those with mixed (positive/negative) feedback characteristics. Very complex time dependent behaviors may arise from these processes. Indeed, the same mechanism may, depending on system parameters and initial conditions, produce simple, regular, repetitive patterns and completely irregular random-like fluctuations.For the differential-delay equations considered here we prove the existence of: (i) stable and unstable limit cycles, where the stable cycles may have an arbitrary number of extrema per period; and (ii) chaos, meaning the presence of infinitely many periodic solutions of different period and of infinitely many irregular and mixing solutions.     

FREEZING POINTS OF ANTI-COAGULANT SALT SOLUTIONS

By a method involving equilibration of ice and solution, and analysis of the solution, freezing point depressions of solutions of sodium citrate, oxalate, and fluoride have been determined over the range Δ = 0.45 to 0.65°C. Determinations with sodium chloride solutions have confirmed the accuracy of the method. In each case the freezing point depression is given, within 0.002°C., as a linear function of the concentration. By the use of these linear equations it is possible to prepare a solution of any of these four salts isotonic with a given biological fluid of known freezing point, provided the latter falls within the range studied.     

SWELLING OF ERYTHROCYTES IN SOLUTIONS OF AMMONIUM SALTS

Two rather simple equations have been derived, which make it possible to express in a single number the result of a series of determinations of the volume of erythrocytes swelling in solutions of ammonium salts. In all experiments made with several combinations of different concentrations of permeating and non-permeating salts, the curves calculated from the equations have covered the points found by experiment.     

Lotka-Volterra方程的概周期解的存在性

本文讨论具有概周期系数的Lotka-Volterra微分方程.给出该微分方程存在大于零的概周期解的一个实用、简沽的充分条件.     

THE ELIMINATION OF DISCREPANCIES BETWEEN OBSERVED AND CALCULATED P.D. OF PROTEIN SOLUTIONS NEAR THE ISOELECTRIC POINT WITH THE AID OF BUFFER SOLUTIONS

1. It had been noticed in the previous experiments on the influence of the hydrogen ion concentration on the P.D. between protein solutions inside a collodion bag and aqueous solutions free from protein that the agreement between the observed values and the values calculated on the basis of Donnan''s theory was not satisfactory near the isoelectric point of the protein solution. It was suspected that this was due to the uncertainty in the measurements of the pH of the outside aqueous solution near the isoelectric point. This turned out to be correct, since it is shown in this paper that the discrepancy disappears when both the inside and outside solutions contain a buffer salt. 2. This removes the last discrepancy between the observed P.D. and the P. D. calculated on the basis of Donnan''s theory of P.D. between membrane equilibria, so that we can state that the P.D. between protein solutions inside collodion bags and outside aqueous solutions free from protein can be calculated from differences in the hydrogen ion concentration on the opposite sides of the membrane, in agreement with Donnan''s formula.     

ISOPYCNIC CENTRIFUGATION OF CHROMATIN IN RENOGRAFIN SOLUTIONS

Solutions of Renografin (30–60%) can be centrifuged to form density gradients in the range from 1.0 g/cm³ to 1.4 g/cm³ or, alternatively, preformed gradients can be made which under appropriate conditions of centrifugation have an indefinite stability. Such solutions have a low viscosity and a relatively low ionic strength. The density of DNA in such solutions is surprisingly low (~1.14 g/cm³). Crude chromatin can be sedimented to an equilibrium position in such gradients, corresponding to a density of 1.2₄ g/cm³, or slightly lower, depending on the method of preparation. The complex is shown to contain DNA, RNA, protein, and possibly some lipoprotein. Most of the RNA can be removed with RNase without any significant effect on the density of the chromatin.     

CHEMICAL AND PHYSICAL BEHAVIOR OF CASEIN SOLUTIONS

The experiments on casein solutions therefore confirm the conclusion at which we arrived from the behavior of gelatin and crystalline egg albumin that the forces determining the combination between proteins and acids or alkalies are the same forces of primary valency which also determine the reaction between acids and alkalies with crystalloids, and that the valency and not the nature of the ion in combination with a protein determines the effect on the physical properties of the protein.     

非自治LOTKA-VOLTERRA生态系统的有界性及周期解的存在性

本文利用图论和Liapunov方法研究了非自治LOTKA-VOLTERRA生态系统的有界性和周期解的存在性,得到了一些新的结果．     

Some analytical results about a simple reaction-diffusion system for morphogenesis

Summary The reaction-diffusion system considered involves only one nonlinear term and is a gradient system. In a bifurcation analysis for the equilibrium states, the global existence of infinitely many solution branches can be shown by the method of Ljusternik-Schnirelmann. Their stability is studied. Using a Ljapunov functional it can be shown that the solutions of the time-dependent system converge to the equilibrium states.