A Miura of the Painlevé I Equation and Its Discrete Analogs

We present Miura transformations for the continuous and several discrete Painlev\'e I equations. In the case of the continuous P_I, we use the Hamiltonian formulation of the Painlev\'e equations and show that there exists a Miura transformation between P_I and the binomial, second degree, equation of Cosgrove SD_V. In the case of the discrete P_I's we obtain two different kinds of Miuras. One kind relates a d-P_I to some other d-P_I while the other leads to discrete four-point equations which are the discrete analogs of the derivative of Cosgrove's equation SD_V.     

USING A SYSTEM DYNAMICS APPROACH TO MODEL SUSTAINABILITY INDICATORS FOR IRRIGATION SYSTEMS IN AUSTRALIA

ABSTRACT. An indicator defined as a function of the total water diversion through the Coleambally canal and the potential irrigation demand is selected to represent the sustainability of the irrigation water system in the Coleambally irrigation area, Australia. A simulation procedure using a system dynamics approach was developed to evaluate the indicator. The procedure includes water diversion assessment, potential crop water demand and total gross margin. Three cases of water supply options (surface water, ground water pumping and water trading), two cases of changes in the total agricultural area and three cropping pattern scenarios were simulated to better understand their impact on sustainability. The simulated results indicate that increasing the agricultural area reduces the sustainability of the irrigation system because the demand of water increased despite increase in the gross margin. The scenarios show that imposed water trading and ground water pumping would considerably increase the supply system having a positive impact on the sustainability. The paper concludes that a multi‐objective sustainability indicator taking account of economic and environmental issues could be more useful.     

Boundary control of a hyperbolic system with time lags

This paper considers an optimal boundary control problem fora hyperbolic system in which constant time lags appear in thestate equation and in the boundary condition simultaneously.Making use of Lion's scheme, necessary and sufficient conditionsof optimality for the Neumann problem are derived.     

A remark on the KAM theorem applied to a four-vortex system

We consider a planar four-vortex system with unit intensities and apply the KAM theorem for two-dimensional tori with fixed frequency. We obtain a rigorous lower bound for the stochasticity threshold of the torus with rotation number=(5—1)/2 and compare our result with numerical experiments.     

合成丙交酯中微量水分分析

合成丙交酯中微量水分分析徐溢，柳胜春（重庆大学化工学院分析教研室６３００４４）关键词丙交酯，微量水，定量分析丙交酯是人工合成骨材料聚乳酸的合成中间体，其性能决定着合成产品的品质，要获得高质量的合成材料，对中间体的分析和监测十分重要。一般要求丙交酯中间...     

PHASE INVERSION AND ITS MECHANICAL MODEL STUDIES FOR THE TWO-PHASE POLYMER BLEND SYSTEMS (Ⅱ)——DYNAMIC VISCOELASTIC RESPONSE

The dynamic viscoelastic response of the two-phase polymer blend systems shows the characteristics of the thermorheologically complex materials. In this paper theoretical equations for describing the dynamic viscoelastic response of such polymer blend systems have been established by means of the mechanical modeling technique. The dynamic viscoelastic response of the blend systems at any blend composition can be predicted theoretically by using the equations established, provided that the dynamic viscoelastic response of the two pure components and the mechanical model parameters are known in advance. Thus, we provide an effective method for studying the dynamic mechanical properties and the molecular relaxation characteristics of the two-phase polymer blend systems.     

Spin interaction with an ideal Fermi gas

We consider the equilibrium dynamics of a system consisting of a spin interacting with an ideal Fermi gas on the lattice , 3. We present two examples: when this system is unitarily equivalent to an ideal Fermi gas or to a spin in an ideal Fermi gas without interaction between them.     

Existence of finitely optimal solutions for infinite-horizon optimal control problems

In this paper, we investigate the existence of finitely optimal solutions for the Lagrange problem of optimal control defined on [0, ) under weaker convexity and seminormality hypotheses than those of previous authors. The notion of finite optimality has been introduced into the literature as the weakest of a hierarchy of types of optimality that have been defined to permit the study of Lagrange problems, arising in mathematical economics, whose cost functions either diverge or are not bounded below. Our method of proof requires us to analyze the continuous dependence of finite-interval Lagrange problems with respect to a prescribed terminal condition. Once this is done, we show that a finitely optimal solution can be obtained as the limit of a sequence of solutions to a sequence of corresponding finite-horizon optimal control problems. Our results utilize the convexity and seminormality hypotheses which are now classical in the existence theory of optimal control.This research forms part of the author's doctoral dissertation written at the University of Delaware, Newark, Delaware under the supervision of Professor Thomas S. Angell.     

四元缔合物体系薄层树脂相分离与光度法联用测定痕量钴

提出了在酸性条件下 (pH=5.0),利用阳离子交换树脂-丁二酮肟-碘-钴四元体系,通过薄层树脂相光度法测定钴的新方法。本法灵敏度高 (e454=1.7105L/molcm),比水相光度法提高14倍,精密度理想 (测定2.0礸/ml Co(II) 6次,RSD=1.3%),选择性好。实测药品VB12及天然水中钴,线性范围0.024~2.0礸/ml (定容50ml),检出限10.4ng/ml。     

Reagentless system for sulphite determination based on polyaniline

A new reagentless system for sulphite (or sulphur dioxide) determination is reported based on the use of an organic conducting polymer, polyaniline, and its absorbance variation at 550 nm, depending on the sulphite concentration. After chemical polymerisation of aniline a very thin film of polyaniline is obtained. Although the response is not fully reversible, each film can be used for at least 10 measurements for low analyte concentrations (up to 0.5 mg l⁻¹) and five measurements for higher sulphite concentrations. Moreover, the reproducibility, ease of preparation and low cost of the films, permit the use of a new disposable system for each measurement. When the change in absorbance at 550 nm was measured for 210 s (stabilisation time), the system showed a linear response, which ranged from 0.025 to 1.50 mg l⁻¹ of sulphite. A theory with regard to the reaction mechanism between the polyaniline films and sulphite is also proposed. The system was applied to sulphite determination in wine samples and the results were in agreement with those obtained by the Official Method of Analysis (iodometric titration).