L-Splines

In this paper, we study the problem of unique interpolation and approximation by a class of spline functions,L-splines, containing as special cases the deficient and generalized spline functions ofAhlberg, Nilson, andWalsh [3, 5, 6], the Chebyshevian spline functions ofKarlin andZiegler [27], and the piecewise Hermite polynomial functions, as considered in [17]. We first give sufficient conditions for unique interpolation byL-spline functions in Section 2. Then, we obtain newL andL ² error estimates for interpolation byL-splines in Section 4, and show that these error estimates are, in a certain sense, sharp. In addition, we make a similar study for theg-splines ofSchoenberg, cf. [44, 3], in Section 5. In Section 6, an application of these new error estimates is made to the analysis of the error made in the use of finite dimensional subspaces ofL-splines andg-splines. in the Rayleigh-Ritz procedure for the class of nonlinear two-point boundary value problems studied in [17].Because of the rapid growth of the number of papers devoted to or connected with the topic of splines, we believe that a compilation of papers on splines for the reader's use is desirable, and such a list is found in the References at the end of this paper.This research was supported in part by NSF Grant GP-5553Papers not specifically concerned with splines are referred to in the text by [1, 2], etc.     

Surface composition of Pt25Ni75(111) investigated by ISS and STM

Summary Ion scattering spectroscopy results show Pt enrichment in the topmost atomic layers of a Pt₂₅Ni₇₅(111) single crystal due to preferential sputtering. The increased lattice constant caused thereby leads to subsurface lattice mismatch dislocations, which have been studied by scanning tunneling microscopy. Agreement is found for the Pt concentration estimated from the density of dislocations and the results obtained by ISS. Thermal annealing induces further segregation of Pt in the topmost atomic layer. The composition of the subsurface layers has been studied and a strong dependence on the annealing temperature has been found. The observed Pt enrichment in the first monolayer for the thermodynamic equilibrium state agrees well with a thermodynamic theory.     

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.     

Solution-phase parallel synthesis of a pyridinium pyrazol-3-olate inner salt library using a three-component reaction

We present here the discovery of a novel, versatile, multicomponent reaction leading to various 4-[4-(pyridinium-1-yl)-2,5-dioxo-2,5-dihydro-1H-pyrrol-3-yl]-2H-pyrazol-3-olate inner salts. The structure of the unusual zwitterionic inner salts was elucidated, and the scope of the novel reaction was investigated. After rapid optimization, the reaction was adapted to parallel synthesis, and an 800-membered compound library was produced.     

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.