The Problem of Periodic Solution for Dynamical Systems（Ⅱ）

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔ：Ｈ：Ｒｎ×Ｒｎ→ＲｂｅａｓｍｏｏｔｈＨａｍｉｌｔｏｎｆｕｎｃｔｉｏｎ（ｑ，ｐ）→Ｈ（ｑ，ｐ）Ｇ：Ｒｎ×Ｒｎ→Ｒ２ｎｂｅｓｍｏｏｔｈｏｐｅｒａｔｏｒ（ｑ，ｐ）→Ｇ（ｑ，ｐ）＝（ｇ１（ｑ，ｐ），…，ｇ２ｎ（ｑ，ｐ））．　　Ｗｅｄｅｆｉｎｅｔｗｏｓｐａｃｅｓ：Ｌ＝ｓｐａｎ｛ｇｉ，｛Ｈ，ｇｉ｝，｛Ｈ，｛Ｈ，ｇｉ｝｝，…，ｉ＝１，２，…，２ｎ｝ｄＬ（ｚ）＝｛ｄｆ（ｚ）｜ｆ∈Ｌ｝　ｚ∈Ｒｎ×Ｒｎ．Ｈｅｒｅ｛，｝ｉｓｐｏｉｓｓｏｎｂｒａｃｋｅｔ．Ｔｈｒｏｕｇｈｏｕｔｔｈ…     

Polynomial Shift States of a Chaotic Map

We present a piecewise- linear map of the unit interval in which the resolvent of the Frobenius- Perron operator, considered in a polynomial basis, has an essen-tial singularity at the origin. Associated with the essential singularity are polynomial shift states, which are obtained from creation and annihilation operators in non- self- dual function spaces. Correlation functions of general polynomial observables have decay components that vanish in a finite time.     

Photo‐Induced Electron Transfer Between Photosystem 2 via Cross‐linked Redox Hydrogels

Photosystem 2 (PS2) that catalyses light driven water splitting in photosynthesis was ‘wired’ to electrode surfaces via osmium‐containing redox polymers based on poly(vinyl)imidazol. The redox polymer hydrogel worked as both immobilization matrix and electron acceptor for the enzyme. Upon illumination, the enzymatic reaction could be switched on and a catalytic current was observed at the electrode. The catalytic current is directly dependent on the intensity of light used for the excitation of PS2. A typical current density of 45 μA cm^?2 at a light intensity of 2.65 mW cm^?2 could be demonstrated with a significantly improved operational stability.     

High-pressure phase equilibria for chlorosilane + carbon dioxide mixtures

Fluid-phase equilibria, including dew points, bubble points, and critical points were measured for four binary systems composed of a chlorosilane and carbon dioxide. The measurements were carried out in a constant-composition, variable-volume cell equipped with a sapphire window, which allowed visual observation of the phases in the cell. A syringe pump was used to inject the CO₂ into the cell and to control its pressure. Methyltrichlorosilane, dimethyldichlorosilane, trimethylchlorosilane, and diethyldichlorosilane up to about 0.14 mol fraction were studied in this apparatus and a total of 243 phase-boundary points were obtained. Displacements in the critical point with respect to pure CO₂ of up to 11.81 MPa and 348.05 K were observed. Modeling of the fluid-phase equilibria for three of the four binary systems was done using the Peng–Robinson equation of state, standard van der Waals mixing rules with two binary interaction parameters, and a φ–φ formulation of the equilibrium. The binary interaction parameters were obtained by fitting the model to the experimental data. The model produced excellent agreement between computed and experimental data. Graphical representations of the modeling results are presented and compared to experimental results. The results indicate that the largest chlorosilane (diethyldichlorosilane) produced the largest shift in critical pressure and critical temperature with respect to pure CO₂.     

允许卖空的资本市场中存在非负均衡价格向量的充要条件

For the capital market satisfying standard assumptions that are widely adopted in the equilibrium analysis,a necessary and sufficient condition for the existence and uniqueness of a nonnegative equilibrium price vector that clears the mean-variance capital market with short sale allowed is derived. Moreover, the given explicit formula for the equilibrium price shows clearly the relationship between prices of assets and statistical properties of the rate of return on assets, the desired rates of return of individual investors as well as other economic quantities.The economic implication of the derived condition is briefly discussed. These results improve the available results about the equilibrium analysis of the mean-variance market.     

Transcendental geometric programs

This paper treats a class of posynomial-like functions whose variables may appear also as exponents or in logarithms. It is shown that the resulting programs, called transcendental geometric programs, retain many useful properties of ordinary geometric programs, although the new class of problems need not have unique minima and cannot, in general, be transformed into convex programs. A duality theory, analogous to geometric programming duality, is formulated under somewhat more restrictive conditions. The dual constraints are not all linear, but the notion ofdegrees of difficulty is maintained in its geometric programming sense. One formulation of the dual program is shown to be a generalization of the chemical equilibrium problem where correction factors are added to account for nonideality. Some of the computational difficulties in solving transcendental programs are discussed briefly.This research was partially supported by the National Institute of Health Grant No. GM-14789; Office of Naval Research under Contract No. N00014-75-C-0276; National Science Foundation Grant No. MPS-71-03341 A03; and the US Atomic Energy Commission Contract No. AT(04-3)-326 PA #18.     

Information patterns and Nash equilibria in extensive games — II

In Part I of this paper we introduced extensive games with a non-atomic continuum of players. It was shown that the Nash plays (outcomes) are invariant of the information patterns on the game, provided that no player's unilateral change in moves can be observed by others. This led to an enormous reduction in the Nash plays of the these games, as exemplified in the anti-folk theorem. Our concern in this sequel is to develop a finite version of these results.     

Chains of reinsurance: Non-cooperative equilibria and pareto optimality

The purpose of this paper is to extend Gerber's seminal paper on chains of reinsurance in three directions: (i) to throw some light on the rationale of finite chains under the Stackelberg equilibria introduced by Gerber, (ii) to propose new non-cooperative equilibrium concepts, of the Cournot type, which allow the first reinsured to transfer more than 50 percent of its risk if the risk aversion is the same for all companies, and (iii) to compare the Pareto optimal and the different equilibrium transfers of risk between reinsurers.     

国产航空有机玻璃(PMMA)的非线性应力松弛行为研究

实验测定了国产航空有机玻璃PMMA在室温(20℃)、3—20.45％应变量范围内的应力松驰曲线。将用于表述中低应变率下加卸载循环的应力—应变行为的非线性本构理论,也即以考虑弹性和粘弹性变形的标准线性体和考虑塑性变形的活化粘壶作串联耦合的本构模型扩展应用到应力松弛状态,给出了相应的本构理论方程。对实验测得的应力松弛曲线进行数值拟合计算,吻合结果良好。表明所提出的本构模型也适用于描述PMMA的非线性应力松弛行为。得到了平衡态的应力一应变曲线,曲线的单调变化,表明不存在屈服极大值及以后的应变软化效应。     

生命起源的新探索与生命现象的新解释

本文对从分子的化学演化到形成生命这个从量变到质变的过程进行了新的探讨,同时对一些生命现象的本质作了全新的解释。