Solved and unsolved problems in surface structure determination

The range of surface structural problems of interest in understanding the physics and chemistry of solid surfaces is reviewed with reference to the available methods and their strengths and limitations. Key challenges being addressed currently concern the achievable precision of measurements and their physical and chemical significance, and the complexity of the problems which may be solved. Past progress and future problems are illustrated with a series of examples ranging from the relaxation of simple clean metal surfaces through complex semiconductor reconstructions to large molecular adsorption and coadsorption systems and complex adsorbate-induced reconstructions. The strengths and limitations of scanning tunnelling microscopy as a complement to true quantitative structural methods are discussed, as is the role of chemical state specificity and elemental specificity in solving complex molecular adsorbate systems.     

Complex point sources in probe-corrected cylindrical near-field scanning

A probe-corrected theory based on complex point sources is presented for computing the acoustic field of an arbitrary finite source from measurements of the near field on a cylindrical scanning surface. The complex point sources are used both as basis functions for the expansion of the field outside the scan cylinder and for the representation of the probe. The resulting probe-corrected formulas are considerably simpler than the standard probe-corrected formulas based on cylindrical waves. The new formulation makes simulations of near-field scanning systems much less computationally intensive than simulations based on standard theory. The complex point-source theory is validated through numerical examples involving a baffled circular piston transducer probe.     

Boundaries for algebras of holomorphic functions

Let A_u(B_G) be the Banach algebra of all complex valued functions defined on the closed unit ball B_G of a complex Banach space G which are uniformly continuous on B_G and holomorphic in the interior of B_G, endowed with the sup norm. A characterization of the boundaries for A_u(B_G) is given in case G belongs to a class of Banach spaces that includes the pre-dual of a Lorentz sequence space studied by Gowers in Israel J. Math. 69 (1990) 129-151. The non-existence of the Shilov boundary for A_u(B_G) is also proved.     

Hybrid systems: Modelling and analysis using emergent dynamics

In this paper, we discuss modelling and analysis of hybrid systems with physical interaction dynamics. Such systems are typically considered complex and they are modelled using abstractions. Abstractions may, however, unintentionally exclude critical details, leading to partial or false results. Therefore, we study here use of a particle system in modelling and analysis. The novelty of the particle system is that it is designed to reveal interaction dynamics as emergent dynamics; thus, supporting analysis of complex and intricate interaction dynamics with acceptable modelling effort. As the main contribution, we formalize the particle system, and use it to model and analyze hybrid systems, both mechanical and biological, with nontrivial interaction dynamics.     

复流形局部q-凸楔形上带权的同伦公式

本文得到复流形局部q-凸楔形上(r,s)型微分形式的带权的同伦公式和(r,s)型的方程的带权的连续解,并给出(r,s)型微分形式的不含边界积分的新的带权的同伦公式和(r,s)型的方程的新的带权的连续解.这些新的带权公式尤其适用于具有非光滑边界的局部q-凸楔形,这时不但可以避免边界积分的复杂估计,而且积分密度也不必在边界有定义,只要在区域上有定义就行.其次,引进权因子,带权的积分公式在应用上(比如在函数的插值方面)具有更大的灵活性.     

On the field of definition for modularity of CM elliptic curves

The purpose of this paper is to decide the conditions under which a CM elliptic curve is modular over its field of definition.     

抗坏血酸同顺磁离子Mn~(2+)、Gd~(3+)络会的~(13)C NMR研究

该文用顺磁离子对其近邻~(13)C核的NMR吸收增宽效应,系统地研究了抗坏血酸在不同溶剂中对金属离子Mn~(2+)、Gd~(3+)的配合行为.在水溶液中,抗坏血酸可通过两种配合方式与Mn~(2+)作用,但与Gd~(3+)的作用只有一种稳定的结构.在水中抗坏血酸对金属的配位活性部位分别是1位羟基氧,3位离解的羟基氧和6位羟基氧.在DMSO中,3位羟基由于H~+对该基团的静电遮蔽而变得对金属离子Mn~(2+)表现为配位惰性,同时6位羟基配位活性较大增强.对Gd~(3+)来说,此时没有优势配位活性部位存在.文章还讨论了抗坏血酸在H_2O-DMSO混合溶剂中的~(13)C NMR谱及在DMSO中NaOH对其~(13)C NMR谱及其与金属络合结构的影响.     

Macroscopic non-equilibrium thermodynamics in dynamic calorimetry

What is really measured in dynamic calorimetric experiments is still an open question. This paper is devoted to this question, which can be usefully envisaged by means of macroscopic non-equilibrium thermodynamics. From the pioneer work of De Donder on chemical reactions and with other authors along the 20th century, the question is tackled under an historical point of view. A special attention is paid about the notions of frequency dependent complex heat capacity and entropy production due to irreversible processes occurring during an experiment. This phenomenological approach based on thermodynamics, not widely spread in the literature of calorimetry, could open significant perspectives on the study of macro-systems undergoing physico-chemical transformations probed by dynamic calorimetry.     

Three-dimensional structure of the calcite-water interface by surface X-ray scattering

The three-dimensional structure of the calcite (104)-water interface has been determined with surface X-ray scattering. Nine crystal truncation rods (including specular and non-specular rods) were measured providing both vertical and lateral sensitivity to the interfacial structure. The results reveal that calcite is nearly ideally terminated with a single surface hydration layer that includes two inequivalent water molecules having distinct heights of 2.3 ± 0.1 and 3.5 ± 0.2 Å, each with a well-defined lateral registry with respect to the calcite surface. No additional layering of water is observed beyond this surface hydration layer. Small displacements in the outer two calcium carbonate layers were also observed. These results are compared with previous experimental and computational results.