Mathematical characterization and shape analysis of localized,fractal, and complex distributions in extended systems

The availability of recent supercomputers and massively parallel computing facilities makes possible the calculation of the electronic structure of highly extended (mesoscopic) molecular networks. Disorder, which is practically always present in these systems, causes an extreme complexity of the wave function that typically shows multifractal behavior in the intermediate length scale. Multifractal analysis, however, is possible only on systems that cover several orders of length scales. Though such calculation can be carried out on model systems, it is beyond the bounds of present ab initio or semiempirical treatments. In this contribution, a shape-analysis method of the wave function is given that is applicable both for localized and multifractal one-particle states even in moderately large networks without a regular geometrical structure. No boxing of the distributions is necessary through several orders of magnitude of scaling distances. Multifractal behavior and different regularly decaying localization shape functions can be distinguished. Finite-size multifractal distributions are also discussed. The described method is intended to serve as an easily applicable and efficient tool for bridging over the gap between the wave-function analysis of systems containing macroscopic and moderately large number of particles. © 1994 John Wiley & Sons, Inc.     

Inclusive production of charged kaons in p+p collisions at 158 GeV/c beam momentum and a new evaluation of the energy dependence of kaon production up to collider energies

New data on the production of charged kaons in p+p interactions are presented. The data come from a sample of 4.8 million inelastic events obtained with the NA49 detector at the CERN SPS at 158 GeV/c beam momentum. The kaons are identified by energy loss in a large TPC tracking system. Inclusive invariant cross sections are obtained in intervals from 0 to 1.7 GeV/c in transverse momentum and from 0 to 0.5 in Feynman x. Using these data as a reference, a new evaluation of the energy dependence of kaon production, including neutral kaons, is conducted over a range from 3 GeV to $\mathrm{p}+\overline{\mathrm{p}}$ collider energies.     

Characterization of disorder in semiconductors via single-photon interferometry

The method of angular photonic correlations of spontaneous emission is introduced as an experimental, purely optical scheme to characterize disorder in semiconductor nanostructures. The theoretical expression for the angular correlations is derived and numerically evaluated for a model system. The results demonstrate how the proposed experimental method yields direct information about the spatial distribution of the relevant states and thus on the disorder present in the system.     

Observation and destruction of an elusive adsorbate with STM: O₂/TiO₂(110)

When a slightly defective rutile TiO?(110) surface is exposed to O?at elevated temperatures, the molecule dissociates at defects, filling O vacancies (V(O)) and creating O adatoms (O(ad)) on Ti(5c) rows. The adsorption of molecular O? at low temperatures has remained controversial. Low-temperature scanning tunneling microscopy of O?, dosed on TiO?(110) at a sample temperature of ≈100 K and imaged at 17 K, shows a molecular precursor at V(O) as a faint change in contrast. The adsorbed O? easily dissociates during the STM measurements, and the formation of O(ad)'s at both sides of the original V(O) is observed.     

Unexpected formation of higher polythionates in the oxidation of thiosulfate by hypochlorous acid in a slightly acidic medium

It has been clearly shown that not only tetrathionate but also pentathionate or even higher polythionates is formed in the oxidation of thiosulfate by hypochlorous acid in a slightly acidic medium. In thiosulfate excess, the absorbance-time curves registered at 250 nm may go through a maximum followed by a minimum, suggesting the presence of a short-lived absorbing intermediate proposed to be S(2)O(3)OCl(3-). Matrix rank analysis (MRA) studies have revealed that altogether five independent absorbing species are present in the wavelength range 240-400 nm. A kinetic model is suggested to take all of the experimental observations into account.     

Oxygen-deficient line defects in an ultrathin aluminum oxide film

A model for the straight antiphase domain boundary of the ultrathin aluminum oxide film on the NiAl(110) substrate is derived from scanning tunneling microscopy measurements and density-functional theory calculations. Although the local bonding environment of the perfect film is maintained, the structure is oxygen deficient and possesses a favorable adsorption site. The domain boundary exhibits a downwards band bending and three characteristic unoccupied electronic states, in excellent agreement with scanning tunneling spectroscopy measurements.     

On additive solutions of a linear equation

We investigate the functional equation $$ \sum\limits_{i = 1}^n {\alpha _i A(\beta _i x)} = 0 $$ which holds for all x ∈ ? with an unknown additive function A: ? → ? and fixed real parameters α _i , β _i , where i = 1; …; n. Here we give sufficient and necessary conditions for the existence of non-trivial additive solutions of the equation above in some cases depending on the algebraic properties of the parameters.     

Multiple critical points for non-differentiable parametrized functionals and applications to differential inclusions

In this paper we deal with a class of non-differentiable functionals defined on a real reflexive Banach space X and depending on a real parameter of the form ${\mathcal{E}_\lambda(u)=L(u)-(J_1\circ T)(u)-\lambda (J_2\circ S)(u)}$ , where ${L:X \rightarrow \mathbb R}$ is a sequentially weakly lower semicontinuous C ¹ functional, ${J_1:Y\rightarrow\mathbb R, J_2:Z\rightarrow \mathbb R}$ (Y, Z Banach spaces) are two locally Lipschitz functionals, T : X → Y, S : X → Z are linear and compact operators and λ > 0 is a real parameter. We prove that this kind of functionals posses at least three nonsmooth critical points for each λ > 0 and there exists λ* > 0 such that the functional ${\mathcal{E}_{\lambda^\ast}}$ possesses at least four nonsmooth critical points. As an application, we study a nonhomogeneous differential inclusion involving the p(x)-Laplace operator whose weak solutions are exactly the nonsmooth critical points of some “energy functional” which satisfies the conditions required in our main result.     

Comparative analysis of the full set of methylated β‐cyclodextrins as chiral selectors in capillary electrophoresis

The chiral separation ability of the full library of methylated‐β‐cyclodextrins towards pharmacologically significant racemic drugs including basic compounds was studied by chiral CE. The syntheses of all the methylated, single isomer β‐cyclodextrins were revised and optimized and the aqueous solubility of the derivatives was unambiguously established. The three most relevant commercially available methylated isomeric mixtures were also included in the screening, so a total of ten various methylated CDs were investigated. The effects of the selector concentration on the enantiorecognition properties at acidic pH were investigated. Among the dimethylated β‐cyclodextrins, the heptakis (2,6‐di‐O‐methyl)‐β‐cyclodextrin isomer (2,6‐DIMEB) resulted to be the most versatile chiral selector. Terbutaline was selected as a model compound for the in‐depth investigation of host‐guest enantiodiscrimination ability. The association constants between the two terbutaline enantiomers and 2,6‐DIMEB were determined in order to support that the enantioseparation is driven by differences is host‐guest binding. The migration order of the enantiomers was confirmed by performing spiking experiments with the pure enantiomers. 1D and 2D NMR spectroscopy was applied to the 2,3‐, and 2,6‐DIMEB/terbutaline systems to rationalize at molecular level the different enantioseparation ability of the dimethylated β‐cyclodextrin selectors.