On Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of an observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions. However, the mathematical theory of the proposed approach still requires futher research. In particular, the proof of global convergence of the method is an open problem.     

High temperature physical adsorption of gases on solids: a comparison of two-dimensional and three-dimensional treatments

Two theories of fluid adsorption are discussed and compared. One starts from the assumption of the existance of a strictly two-dimensional adsorbed phase on the adsorbent surface. The statistical mechanics of this model is solved in the Percus-Yevick approximation for both two dimensional and bulk phases. According to the second, three-dimensional treatment, the thermodynamic functions of adsorption are defined as surface excess functions, relative to the Gibbs dividing surface. Explicit results are given for hard spheres and a Lennard-Jones 6-12 gas in contact with a wall interacting via the Lennard-Jones 3-9 potential. The dependence of excess quantities upon the choice of the Gibbs dividing surface is also discussed.     

Multidimensional gravitational waves. I. Purely radiative spacetimes

The concept of gravitational radiation in multidimensional Einstein gravity is studied. Due to technical difficulties the Petrov classification of the conformal tensor and the peeling off theorem cannot be generalized to spaces of dimensiond > 4. A multidimensionalpp wave is defined by analogy with that ford = 4. If the definition is supplemented by the Lichnerowicz condition for purely radiative spacetimes, the admitted solutions of the dimensionally reduced gravity theory describe a scalar (dilaton) and a gravitationalpp wave moving in the external spacetime in the same direction. The existence of the extra dimensions can be traced back by measuring the frequence of thepp wave in the external space. The condition is equally restrictive in a more general case of the internal space being a flat anisotropic manifold (i.e. an abelian group space).     

铂合金氧还原催化剂:合成、结构和性能

质子交换膜燃料电池是一种将燃料中的化学能直接转化为电能的装置,它具有转化效率高、能量密度高、低温启动、易于操作等优点,因而被认为是最具发展前景的新能源利用方式,在电动汽车、便携电源及分散式电站有着广泛应用.但是,目前质子交换膜燃料电池技术的发展面临着巨大挑战,主要问题包括高成本、低功率密度和低寿命.众所周知,质子交换膜燃料电池中的阴极氧还原反应在酸性条件下是一个复杂的四电子过程,动力学速度缓慢,限制了电池的最终性能.目前大量使用的阴极氧还原催化剂是细小的铂或铂合金纳米颗粒负载在碳载体上,其成本占燃料电池总成本的比例最大.制约燃料电池商业化发展的另一个重要问题是电池寿命低,其中氧还原催化剂的稳定性是决定电池寿命的主要因素.在这样的研究背景下,如何降低催化剂中铂的用量、提高催化剂活性和稳定性显得尤为重要,这也是近年来国内外学者研究的热点.在铂基合金催化剂中,通常采用过渡金属元素作为掺杂元素,由于原子半径不匹配(几何效应)以及电子结构不同(电子效应),合金催化剂表现出优于纯铂催化剂的催化性能.近几年,对于铂基合金催化剂的研究已取得重大进展,以合金组成和结构研究为基础,通过精确控制原子结构、调控表面电子状态以及制备工艺,获得了各种特殊形貌的催化剂,大大提高了催化活性.本文深入综述了近年来铂基合金氧还原催化剂制备、形貌和性能,特别关注了催化剂形貌和催化活性之间的关系.值得注意的是,具有有序原子排列的铂合金催化剂不仅在半电池中表现出优异活性,在实际质子交换膜燃料电池中也显示了很好的活性和稳定性.另一方面,碳载体的形貌及微观结构也对提高催化活性和稳定性起到决定性作用,通过化学手段加强金属纳米颗粒与碳载体之间的相互作用也是提高催化剂稳定性的重要途径.尽管铂基氧还原催化剂在近几年取得了重要进展,但在实际商业化过程中还存在诸多挑战,本文在综述进展的基础上,对铂基催化剂的发展提出了展望.首先,对于氧还原反应机理仍需要深入研究,采用更加精确的理论模型模拟氧还原动力学过程,以获得影响催化活性的关键因素.其次,提高催化剂在膜电极中的催化活性和利用率.目前,氧还原催化剂在半电池测试中性能优异,但是实际燃料电池操作条件下其性能远不能达到要求,这与膜电极、催化剂层及扩散层结构相关.因此,基于不同铂基催化剂的特性,合理设计膜电极组件的结构是将催化剂进行实际应用的基础.最后,催化剂的稳定性仍需进一步提高,尽管目前大部分催化剂在实验室半电池研究中表现了很好的稳定性,但在实际燃料电池中的稳定性研究还不足,而且对催化剂在膜电极中性能衰退机理的研究也非常有限.因此,对于铂基氧还原催化剂的研发仍需要国内外科研工作者不懈的努力.     

The Synthesis And Chemical Properties Of N-D-Pentopyranosylamines,Derivatives Of Tryptamine And Tyramine.

Abstract

The synthesis and structure of N-D-pentopyranosylamines derived from the amines tiyptamine tyramine and the pentoses D-xylose, D-arabinose and D-lyxose are presented. NMR spectroscopy and mass spectrometry were used to verify the proposed α,β-D-pentopyranosylamine structures.     

Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain

We construct the asymptotics (as ε→0) of solutions to the Neumann problem for the Laplace equation and of the corresponding Dirichlet integral. The problem concerns a three-dimensional domain having two connected components of the boundary at the distance ε>0. To cite this article: G. Cardone et al., C. R. Mecanique 335 (2007).     

Reaction of selenite with biochemically active thiols: An X-ray photoelectron spectroscopic study

The usefulness of X-ray photoelectron spectroscopy for electron transport studies was shown by examining the reaction of selenite with mercapto-ethanol