一类时滞反应扩散方程的稳态解和行波解

本文讨论了一类造血生物模型在Dirichlet边值条件下稳态解的全局吸引性,并利用上、下解技术和单调迭代方法讨论了行波解的存在性.     

一类捕食-被捕食系统周期解的存在性

对于二维非自治捕食-被捕食系统,本文讨论了它的解的有界性,进而得到周期解和正周期解的存在性。     

一类具年龄结构和接种的非终生免疫型传染病模型

研究一类具年龄结构和接种的非终生免疫SIRS传染病模型平衡解的稳定性.首先利用特征线法讨论了模型平衡解的存在性,然后利用比较定理和逐次迭代法得到无病平衡解与地方病平衡解全局稳定性的充分条件.     

生态学中一类n维反应扩散方程组解的性质

本文讨论一类不满足所谓的拟单调条件的反应扩散方程组的初边值问题．应用谱论和单调性方法证明了问题解的存在唯一性和平衡解的渐近稳定性．并进一步讨论了生态学中n种群单食物链模型的第二初值问题,得到了问题的非负平衡解的存在性和渐近性以及相应的吸引区域．     

具年龄结构和时滞的自食种群系统的周期解

利用延拓定理讨论具年龄结构和时滞的自食种群系统正周期解的存在性,得到周期解存在的条件,推广了已有结论.     

传染病SIRk模型的解的收敛速度估计

本文基于考虑人口出生率的传染病SIRk模型,研究模型的解趋于平衡点的速度;通过对系数矩阵特征值的三种不同情形的分析讨论,得出模型的解指数收敛到系统的平衡解。     

非线性中立双曲型脉冲偏微分方程解的振动性质

讨论一类非线性中立双曲型脉冲偏微分方程解的振动性质,应用积分不等式,在第二类边界条件下获得了其一切解振动的充分条件.     

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.     

时变系数Lotka-volterra互惠共存系统正解的全局渐近性

本文就对变系统Lotka-volterra互惠共存系统的渐近系统进行讨论,得到渐近系统（2）的解关于（l）的解的全局渐近性．     

密度分布非均匀的害虫和天敌生态模型的平衡解的稳定性

讨论一类密度分布非均匀的害虫和天敌生态模型平衡解的稳定性，得到该问题非负平衡解的存在性、渐适性和相应吸引区域。     

THE PROBLEM OF THE MENTALLY DEFECTIVE CHILD

Continued effort is necessary not only to prevent mental deficiency but to find methods of treating it. Meanwhile, physicians must have a keener appreciation of the feelings of the parents about their retarded children and must interpret the implications of the problems in a way the parents can understand. Further community effort is necessary to provide institutional and foster home care for those who need it. Educational and training programs should be extended and developed for all those who can benefit from such programs.The problem of mental deficiency is not that of the parents alone, nor of physicians, nor of the psychologists, nor of the social workers, nor of the educators. It is a problem which requires the cooperation of all these groups for solution.     

密度制约竞争二种群Volterra方程解的有界性及参数估计

本文给出密度制约且相互竞争二种群Volterra方程解的一种有界性及存在唯一性的证明。基于此,参考单种群Logistic方程反问题的方法”,给出了该Volterra方程参数的一种估计。     

不同处理对海甘蓝种子发芽和幼苗生长的影响

由于受种子生理休眠作用的影响和硬而厚的种皮所产生的抑制作用,使海甘蓝（ＣｒａｍｂｅｍａｒｉｔｉｍａＬ．）种子发芽慢,发芽率低。为探索加快海甘蓝种子发芽和提高种子发芽率的有效方法,我们先后进行了８种不同的种子预处理试验和６种不同次氯酸钠溶液浸种的发芽试验。结果发现：（１）种子剥皮处理可以很大程度地促进发芽和提高发芽率;（２）用浓度为０．０５％的赤霉酸溶液浸种１８ｈ对海甘蓝种子发芽也有很好的促进作用;（３）用０．２０％的代森锰锌４５Ｍ（Ｄｉｉｔｈａｎｅ４５Ｍ）溶液浸种２０ｍｉｎ的消毒处理对海甘蓝种子发芽产生一定程度的抑制作用,但可减少海甘蓝幼苗死亡率;（４）适宜浓度的次氯酸钠漂白水（法文名１＇ＥａｕｄｅＪａｖｅｌ）的溶液（１０％）浸种５ｍｉｎ对促进海甘蓝种子发芽和减少幼苗死亡均有良好效果;浓度低于１０％时．不足以腐蚀种子硬而厚的种皮而促进种子发芽,也不足以杀死种子携带的病菌而减少幼苗死亡率;浓度大于１０％时,对种子的胚和种子内的酶活性产生不良影响,从而抑制种子发芽和影响幼苗的正常生长。     

THE ROLE OF AUXINS AND CYTOKININS IN THE RELEASE OF BUDS FROM DOMINANCE

The paper deals with the general problem of the physiological basis of branching, and the roles of known and unexplored factors in sensitivity to apical dominance. It is shown that when pea seedling shoots are completely or partially inhibited by other shoots on the same plant auxin can promote their elongation, even though it does not have this effect on inhibited buds. This influence of auxin is only exerted on internodal elongation and not on apical growth. When kinetin in a solution of alcohol and carbowax is applied directly to the lateral buds of pea seedlings, it releases them from inhibition by the growing apex. It is shown that the role of alcohol in this solution is to act as a surfactant, permitting good contact with the buds, while that of carbowax, being hygroscopic, is to maintain a thin film of solution over the buds. Buds thus released from apical dominance by kinetin do not elongate as much as do uninhibited control buds. Such kinetin-treated buds can, however, be made to elongate normally by the application of auxin locally to their apices. It is concluded that growing shoots are relatively insensitive to correlative inhibition because they synthesize two types of growth substances, namely, auxin, which antagonizes the inhibitory effect on internodal elongation, and cytokinins, which permit the apex itself to develop. In the discussion it is brought out that many cases of branching, which appear at first to bear little relation to one another, can be understood on the basis of two principles, namely: (1) Any reduction in the growth rate of a dominant apex reduces its inhibitory effect on other apices, and (2) once an apex starts growing it becomes less sensitive to inhibition by other apices These generalizations and the experimental results are tentatively interpreted in terms of an interaction between the syntheses of auxin and of cytoldnin.     

THE COMPOSITION OF THE CELL SAP OF THE PLANT IN RELATION TO THE ABSORPTION OF IONS

1. Chemical examination of the cell sap of Nitella showed that the concentrations of all the principal inorganic elements, K, SO₄, Ca, Mg, PO₄, Cl, and Na, were very much higher than in the water in which the plants were growing. 2. Conductivity measurements and other considerations lead to the conclusion that all or nearly all of the inorganic elements present in the cell sap exist in ionic state. 3. The insoluble or combined elements found in the cell wall or protoplasm included Ca, Mg, S, Si, Fe, and Al. No potassium was present in insoluble form. Calcium was predominant. 4. The hydrogen ion concentration of healthy cells was found to be approximately constant, at pH 5.2. This value was not changed even when the outside solution varied from pH 5.0 to 9.0. 5. The penetration of NO₃ ion into the cell sap from dilute solutions was definitely influenced by the hydrogen ion concentration of the solution. Penetration was much more rapid from a slightly acid solution than from an alkaline one. It is possible that the NO₃ forms a combination with some constituent of the cell wall or of the protoplasm. 6. The exosmosis of chlorine from Nitella cells was found to be a delicate test for injury or altered permeability. 7. Dilute solutions of ammonium salts caused the reaction of the cell sap to increase its pH value. This change was accompanied by injury and exosmosis of chlorine. 8. Apparently the penetration of ions into the cell may take place from a solution of low concentration into a solution of higher concentration. 9. Various comparisons with higher plants are drawn, with reference to buffer systems, solubility of potassium, removal of nitrate from solution, etc.     

钼铁蛋白铁钼辅因子的有机组分对其功能的影响

棕色固氮菌(Azotobacter vinelandii)固氮酶的钼铁蛋白经邻菲啰啉在厌氧或有氧环境中处理后,变为 P-cluster 单一缺失或 P-cluster 和 FeMoco 同时缺失的失活钼铁蛋白。含柠檬酸盐或高柠檬酸盐的重组液都使这两种失活蛋白能恢复固氮酶重组的 H~ 和 C_2H_2还原活性,活性恢复程度随反映钼铁蛋白中金属原子簇含量变化的圆二色和磁圆二色谱及金属含量的恢复程度的提高而提高,但它们固 N_2能力的恢复程度则不相同:P-cluster 单一缺失的蛋白用两种重组液重组后均可恢复其固 N_2能力,而 P-cluster 和 FeMoco 同时缺失的蛋白,只有用含高柠檬酸盐的重组液重组才恢复其固 N_2能力,表明含不同有机组分的重组液所组装的 P-cluster 均与天然状态相同,只有含高柠檬酸盐的重组液所组装的 FeMoco 才与天然状态相同,从而证明高柠檬酸盐是 FeMoco 的必需的有机组分。     

EFFECT OF THE FORMATION OF INERT PROTEIN ON THE KINETICS OF THE AUTOCATALYTIC FORMATION OF TRYPSIN FROM TRYPSINOGEN

A solution of crystalline trypsinogen in dilute buffer containing a trace of active trypsin when allowed to stand at pH 5.0–9.0 and 5°C. is gradually transformed partly into trypsin protein and partly into an inert protein which can no longer be changed into trypsin either by enterokinase or mold kinase. During the process of formation of trypsin and inert protein the ratio of the concentrations of the two products in any reaction mixture remains constant and is independent of the original concentration of trypsinogen protein. This ratio varies, however, with the pH of the solution, the proportion of trypsin formed being greater in the acid range of pH. The experimental curves for the rate of formation of trypsin, as well as for the rate of formation of inert protein are symmetrical S shaped curves closely resembling those of simple autocatalytic reactions. The kinetics of formation of trypsin and inert protein can be explained quantitatively on the theoretical assumptions that both reactions are of the simple unimolecular type, that in each case the reaction is catalyzed by trypsin, and that the rate of formation of each of the products is proportional to the concentration of trypsin as well as to the concentration of trypsinogen in solution.     

ON THE INFLUENCE OF AGGREGATES ON THE MEMBRANE POTENTIALS AND THE OSMOTIC PRESSURE OF PROTEIN SOLUTIONS

1. It is shown that when part of the gelatin in a solution of gelatin chloride is replaced by particles of powdered gelatin (without change of pH) the membrane potential of the solution is influenced comparatively little. 2. A measurement of the hydrogen ion concentration of the gelatin chloride solution and the outside aqueous solution with which the gelatin solution is in osmotic equilibrium, shows that the membrane potential can be calculated from this difference of hydrogen ion concentration with an accuracy of half a millivolt. This proves that the membrane potential is due to the establishment of a membrane equilibrium and that the powdered particles participate in this membrane equilibrium. 3. It is shown that a Donnan equilibrium is established between powdered particles of gelatin chloride and not too strong a solution of gelatin chloride. This is due to the fact that the powdered gelatin particles may be considered as a solid solution of gelatin with a higher concentration than that of the weak gelatin solution in which they are suspended. It follows from the theory of membrane equilibria that this difference in concentration of protein ions must give rise to potential differences between the solid particles and the weaker gelatin solution. 4. The writer had shown previously that when the gelatin in a solution of gelatin chloride is replaced by powdered gelatin (without a change in pH), the osmotic pressure of the solution is lowered the more the more dissolved gelatin is replaced by powdered gelatin. It is therefore obvious that the powdered particles of gelatin do not participate in the osmotic pressure of the solution in spite of the fact that they participate in the establishment of the Donnan equilibrium and in the membrane potentials. 5. This paradoxical phenomenon finds its explanation in the fact that as a consequence of the participation of each particle in the Donnan equilibrium, a special osmotic pressure is set up in each individual particle of powdered gelatin which leads to a swelling of that particle, and this osmotic pressure is measured by the increase in the cohesion pressure of the powdered particles required to balance the osmotic pressure inside each particle. 6. In a mixture of protein in solution and powdered protein (or protein micellæ) we have therefore two kinds of osmotic pressure, the hydrostatic pressure of the protein which is in true solution, and the cohesion pressure of the aggregates. Since only the former is noticeable in the hydrostatic pressure which serves as a measure of the osmotic pressure of a solution, it is clear why the osmotic pressure of a protein solution must be diminished when part of the protein in true solution is replaced by aggregates.     

ON THE CAUSE OF THE INFLUENCE OF IONS ON THE RATE OF DIFFUSION OF WATER THROUGH COLLODION MEMBRANES. I

1. In three previous publications it had been shown that electrolytes influence the rate of diffusion of pure water through a collodion membrane into a solution in three different ways, which can be understood on the assumption of an electrification of the water or the watery phase at the boundary of the membrane; namely, (a) While the watery phase in contact with collodion is generally positively electrified, it happens that, when the membrane has received a treatment with a protein, the presence of hydrogen ions and of simple cations with a valency of three or above (beyond a certain concentration) causes the watery phase of the double layer at the boundary of membrane and solution to be negatively charged. (b) When pure water is separated from a solution by a collodion membrane, the initial rate of diffusion of water into a solution is accelerated by the ion with the opposite sign of charge and retarded by the ion with the same sign of charge as that of the water, both effects increasing with the valency of the ion and a second constitutional quantity of the ion which is still to be defined. (c) The relative influence of the oppositely charged ions, mentioned in (b), is not the same for all concentrations of electrolytes. For lower concentrations the influence of that ion usually prevails which has the opposite sign of charge from that of the watery phase of the double layer; while in higher concentrations the influence of that ion begins to prevail which has the same sign of charge as that of the watery phase of the double layer. For a number of solutions the turning point lies at a molecular concentration of about M/256 or M/512. In concentrations of M/8 or above the influence of the electrical charges of ions mentioned in (b) or (c) seems to become less noticeable or to disappear entirely. 2. It is shown in this paper that in electrical endosmose through a collodion membrane the influence of electrolytes on the rate of transport of liquids is the same as in free osmosis. Since the influence of electrolytes on the rate of transport in electrical endosmose must be ascribed to their influence on the quantity of electrical charge on the unit area of the membrane, we must conclude that the same explanation holds for the influence of electrolytes on the rate of transport of water into a solution through a collodion membrane in the case of free osmosis. 3. We may, therefore, conclude, that when pure water is separated from a solution of an electrolyte by a collodion membrane, the rate of diffusion of water into the solution by free osmosis is accelerated by the ion with the opposite sign of charge as that of the watery phase of the double layer, because this ion increases the quantity of charge on the unit area on the solution side of the membrane; and that the rate of diffusion of water is retarded by the ion with the same sign of charge as that of the watery phase for the reason that this ion diminishes the charge on the solution side of the membrane. When, therefore, the ions of an electrolyte raise the charge on the unit area of the membrane on the solution side above that on the side of pure water, a flow of the oppositely charged liquid must occur through the interstices of the membrane from the side of the water to the side of the solution (positive osmosis). When, however, the ions of an electrolyte lower the charge on the unit area of the solution side of the membrane below that on the pure water side of the membrane, liquid will diffuse from the solution into the pure water (negative osmosis). 4. We must, furthermore, conclude that in lower concentrations of many electrolytes the density of electrification of the double layer increases with an increase in concentration, while in higher concentrations of the same electrolytes it decreases with an increase in concentration. The turning point lies for a number of electrolytes at a molecular concentration of about M/512 or M/256. This explains why in lower concentrations of electrolytes the rate of diffusion of water through a collodion membrane from pure water into solution rises at first rapidly with an increase in concentration while beyond a certain concentration (which in a number of electrolytes is M/512 or M/256) the rate of diffusion of water diminishes with a further increase in concentration.