The microdetermination of chloride,sulphate, phosphate and nitrite by reflectance spectrometry

Quantitative spot tests with a reflectance spectrometer have been developed for chloride (10–320 p.p.m.), sulphate (10–120 p.p.m.), phosphate (2–30 and 10–180 p.p.m.) and nitrite (1–35 and 10–100 p.p.m.). There are few interferences with these tests, and their effects can be overcome by standard techniques except for the interference from phosphate when it is present in the sulphate test, in large concentrations.     

Symmetries of the Discrete Nonlinear Schrödinger Equation

The Lie algebra L(h) of point symmetries of a discrete analogue of the nonlinear Schrödinger equation (NLS) is described. In the continuous limit, the discrete equation is transformed into the NLS, while the structure of the Lie algebra changes: a contraction occurs with the lattice spacing h as the contraction parameter. A five-dimensional subspace of L(h), generated by both point and generalized symmetries, transforms into the five-dimensional point symmetry algebra of the NLS.     

Functional characterizations of certain p-spaces

In this paper we prove that p-spaces and ?ech-complete spaces with G_δ-diagonals can be characterized by a familiar function extension property.     

A new method for the determination of the compound nucleus coherence width at high excitation energy

The coherence width of the compound nucleus can be obtained from cross correlations of the energy spectra taken at different energies instead of the correlation function of the excitation function. In this way it is sufficient to cover an incident energy interval of the order of the compound nucleus width. We have applied this method to the reaction ¹²C + ²⁸Si. The coherence width of ⁴⁰Ca is found in reasonable agreement with previous determinations. Indication is obtained for the presence of a second (smaller) coherence width which could correspond to anomalous long-living compound nucleus states.     

Topics in surface structure and crystal growth

Crystal growth occurs following widely different modes; in particular the transition from layer-by-layer to continuous growth, and the transition from stable to dendritic growth have attracted much theoretical attention. The former transition (corresponding, for equilibrium surfaces, to the roughening transition) is considered from the point of view of atom-surface scattering used as a tool to probe the state of the surface, and the effects of roughness on the height, width and shape of the incoherent peaks are studied. As an approach to the latter transition, simulations of cluster growth are considered where dendritic shapes are obtained by letting “atoms” fall along random straight trajectories from a “vapour” onto the growing cluster. Two geometries are considered: either the “atoms” fall along the cords from an outer large circle, or they fall obliquely on to a line from points of a parallel line. In both cases ramified structures are obtained, although less open that from diffusion-limited aggregation (DLA), and their fractal nature is studied.     

Quantum theory of atom-surface scattering: Incommensurate and fluid adsorbates

The problem of atomic scattering from adsorbate-covered surfaces, treated earlier for the case of commensurate overlayers, is considered again in the eikonal approximation for incommensurate lattice phases and for fluid phases. Stochastic methods are employed and for a specific model (hard bosses on a plane) it is shown how the statistical and geometric problems can be separately solved. In order to explain the meaning of the coherent and incoherent scattering contributions a time-dependent theory is introduced and it is shown that the incoherent “elastic” scattering is in fact weakly inelastic and (for classical diffusion with diffusion coefficient D) has an energy width of the order ?DQ², where Q is the parallel momentum transfer. The problem of the decay of substrate diffraction intensities when the coverage of random impurities is increased is also discussed.     

Ein geometrisches Überdeckungsproblem

Ohne Zusammenfassung Alexander Ostrowski zum 60. Geburtstag gewidmet