On the evolution of sharp fronts for the quasi‐geostrophic equation

We consider the problem of the evolution of sharp fronts for the surface quasi‐geostrophic (QG) equation. This problem is the analogue to the vortex patch problem for the two‐dimensional Euler equation. The special interest of the quasi‐geostrophic equation lies in its strong similarities with the three‐dimensional Euler equation, while being a two‐dimen‐sional model. In particular, an analogue of the problem considered here, the evolution of sharp fronts for QG, is the evolution of a vortex line for the three‐dimensional Euler equation. The rigorous derivation of an equation for the evolution of a vortex line is still an open problem. The influence of the singularity appearing in the velocity when using the Biot‐Savart law still needs to be understood. We present two derivations for the evolution of a periodic sharp front. The first one, heuristic, shows the presence of a logarithmic singularity in the velocity, while the second, making use of weak solutions, obtains a rigorous equation for the evolution explaining the influence of that term in the evolution of the curve. Finally, using a Nash‐Moser argument as the main tool, we obtain local existence and uniqueness of a solution for the derived equation in the C^∞ case. © 2004 Wiley Periodicals, Inc.     

KxCoO2·yH2O(x《0.2,y≤0.8)的晶体结构、输运及磁学性质

利用熔融KOH和Co3O4在较低温度(480℃)下反应制备出K0.36CoO2,然后用高锰酸钾溶液和饱和的过硫酸钾溶液进行氧化处理.氧化的同时伴随有水分子嵌入.K0.36CoO2用高锰酸钾和过硫酸钾溶液处理后分别得到K0.12CoO2·0.8H2O和K0.16CO2·0.6H2O.这两种化合物都属于六角晶系,表现出金属行为,脱水后主相变为正交结构并且呈现出半导体特性.K0.16CoO2·0.6H2O在56K附近可能存在自旋玻璃转变行为或其他涨落.随着钾含量的减少和水含量的增多,样品的自旋玻璃行为受到抑制或发生磁性相分离.样品K0.12CoO2·0.8H2O在零场冷却和有场冷却曲线上的分叉现象基本上消失.还讨论了产生KxCoO2与NaxCoO2体系结构和物性差别的原因.     

Simultaneous determination of cloramphenicol, salicylic acid and resorcinol by capillary zone electrophoresis and its application to pharmaceutical dosage forms

This study demonstrates the separation of active ingredients in acne formulations (salicylic acid, cloramphenicol and resorcinol in presence of azulene) by capillary zone electrophoresis. Factors affecting their separations were the buffer pH and concentration, applied voltage, sample preparation, and presence of additives. Optimun results were obtained with a 50 mM sodium tetraborate-50 mM sodium phosphate, pH 9.0. The carrier electrolyte gave baseline separation with good resolution, short migration times (<6 min), great reproducibility and accuracy. Calibration plots were linear over at least three orders of magnitude of analyte concentrations, the lower limits of detection being within the range 0.39-1.25 μg ml⁻¹. The procedure was fast and reliable and commercial pharmaceuticals could be analysed without prior sample clean-up procedure.     

土壤盐渍化的研究进展

根据近年来国内外土壤学者在土壤盐渍化的研究成果，从土壤盐渍化的基本理论，改良方法以及预测预报方面的研究，综述了土壤盐渍化的研究现状，通过分析土壤盐渍化研究多方面存在的问题，对其发展趋势和今后研究重点进行了展望，望能为进一步的深入研究工作提供帮助．     

A simple Markov chain structure for the evolution of credit ratings

We focus on continuous Markov chains as a model to describe the evolution of credit ratings. In this work it is checked whether a simple, tridiagonal type of generator provides a good approximation to a general one. Three different tridiagonal approximations are proposed and their performance is checked against two generators, corresponding to a volatile and a stable period, respectively. Copyright © 2007 John Wiley & Sons, Ltd.     

A transport model for the evolution of urban systems

When comparing an urban system to an elasto-plastic lattice, an analogy to the solid state of matter can be exploited using the concepts of the band theory similarly. Thereafter, the population dynamics – in a region of certain stability in the state space and within appropriate energy bands – can be described in terms of Cellular Automata, with two mobile agents or pseudo particles: the inhabitant (representative of an average individual) and the recurson (representative of its multidimensional resources). As in the solid state, transition rules take the form of two coupled transport equations, comprising the terms equivalent to the generation-recombination and circulation processes. The first process can be compared to a predator–prey growth model, typical of Ecology; whereas the circulation process – composed of a drift component and a diffusion component – should be compared to the concentration-sprawl demographic balance seen in urban occupation and dynamics. Thus, it needs to be defined and determined an urban potential function, an equivalent population charge, mobility and diffusion parameters, as well as net growth factors. This analogy, discussed within the context of a case study for Great Mendoza, plausibly explains the varied growth rates of the political departments, as well as the principal urban trends for spatial occupation.     

Necessary conditions and duality for inexact nonlinear semi-infinite programming problems

First order necessary conditions and duality results for general inexact nonlinear programming problems formulated in nonreflexive spaces are obtained. The Dubovitskii–Milyutin approach is the main tool used. Particular cases of linear and convex programs are also analyzed and some comments about a comparison of the obtained results with those existing in the literature are given.     

Estimation of the aggregation number and core radius of microemulsions

Summary A simple working method for the estimation of the aggregation numbers and core radii from weight measurements of sodium bis-2-ethylhexylsulphosuccinate (aerosol-OT orAOT)/decane/water microemulsions of several compositions is proposed.Starting out from the hypotheses that (i) the density of the water inside the droplets is the same as that of free water, (ii) all the surfactant is localized as interface, and (iii) the penetration of the organic phase into the interface is negligible, values for the aggregation number and core radii comparable to those determined using more sophisticated methods were obtained.The results/methodological simplicity ratio may be of great advantage in kinetic work on reaction mechanisms in microemulsions.

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Abschätzung von Aggregationszahl und Radius von Mikroemulsionen

Zusammenfassung Es wird eine einfache Methode zur Abschätzung von Aggregationszahl und Core-Radius von Mikroemulsionen aus Gewichtsmessungen von Natriumbis-2-ethylhexylsulphosuccinat (aerosol-OT oderAOT)/Decan/Wasser-Mikroemulsionen verschiedener Zusammensetzung vorgeschlagen. Unter den Annahmen, daß (i) die Dichte von Wasser innerhalb der Aggregationen die gleiche als bei freiem Wasser ist, (ii) das ganze Emulsionsmittel in der Grenzfläche vorliegt und (iii) das Eindringen der organischen Phase in die Grenzfläche vernachlässigbar ist, können Werte für Aggregationszahlen und Core-Radien erhalten werden, die durchaus mit entsprechenden Werten aus aufwendigeren Methoden vergleichbar sind. Das Leistungsverhältnis (Ergebnisse/geringer Aufwand) ist sehr vorteilhaft und macht die Methode für kinetische Arbeiten zur Bestimmung von Reaktionsmechanismen in Mikroemulsionen interessant.

     

Aggregation Properties of an Amphiphilic Methanofullerene Derivative in THFH_2O Solvent Mixtures

Water-soluble fullerenes not only have a number of important applications in biological chemistry1, but also form ordered aggregate structures that can be utilized in materials science2. There are reports that some water-soluble fullerene derivatives can form ordered structures in water, such as vesicle, nanorod and nanoparticle2-5. However, relatively few reports on the aggregation process have been reported. Knowledge of factors that affect the cluster formation in solution is of consider…