A class of gap functions for variational inequalities

Recently Auchmuty (1989) has introduced a new class of merit functions, or optimization formulations, for variational inequalities in finite-dimensional space. We develop and generalize Auchmuty's results, and relate his class of merit functions to other works done in this field. Especially, we investigate differentiability and convexity properties, and present characterizations of the set of solutions to variational inequalities. We then present new descent algorithms for variational inequalities within this framework, including approximate solutions of the direction finding and line search problems. The new class of merit functions include the primal and dual gap functions, introduced by Zuhovickii et al. (1969a, 1969b), and the differentiable merit function recently presented by Fukushima (1992); also, the descent algorithm proposed by Fukushima is a special case from the class of descent methods developed in this paper. Through a generalization of Auchmuty's class of merit functions we extend those inherent in the works of Dafermos (1983), Cohen (1988) and Wu et al. (1991); new algorithmic equivalence results, relating these algorithm classes to each other and to Auchmuty's framework, are also given.Corresponding author.     

INTERACTIONS IN PHOSPHOLIPID STABILIZED EMULSION SYSTEM

The interaction between a phospholipid stabilized triglyceride emulsion and a hydrophilic silica surface has been studied at varying pH and electrolyte content using ellipsometry. The adsorbed amount decreases with pH and increases with increasing electrolyte content in the emulsion, and this can be rationalized on the basis of the electrostatic interaction between the emulsion droplet and the surface. The layer thickness, however, is essentially independent of these parameters.

In addition, the emulsion has been studied during turbulent shear conditions (applied mechanical stress), with the same variation of pH and electrolyte as in the adsorption experiments. A decrease in pH and an increase in electrolyte content, decreasing the repulsive interaction between the droplets, leads to a deterioration in emulsion stability with time.     

Spectroscopic characterization of cobalt-containing mesoporous materials

Cobalt-containing mesoporous materials that have been prepared using different procedures have been comparatively characterized by transmission electron microscopy/energy-dispersive X-ray spectroscopy (TEM/EDS), extended X-ray absorption fine structure spectroscopy (EXAFS), X-ray absorption near edge spectroscopy (XANES), and ultraviolet-visible (UV-vis), near-infrared (NIR), and mid-infrared (mid-IR) spectroscopies, and the results provide new insights into the local environment and properties of cobalt in this type of material. TEM/EDS analyses have shown that tetraethyl orthosilicate (TEOS) may be less appropriate as a silicon source during the syntheses of cobalt-containing mesoporous materials, because the distribution of cobalt throughout the framework may become uneven. EXAFS has been determined to be the most suitable method for direct verification of framework incorporation, by identifying silicon as the backscatterer in the second shell. Such a direct verification may not be obtained using UV-vis spectroscopy. From EXAFS analyses, it is also possible to distinguish between surface-bound and framework-incorporated cobalt. There is a good agreement between the results obtained from XANES and UV-vis regarding the coordination symmetry of cobalt in the samples. The presence of cobalt in the silica framework has been determined to create Lewis acid sites, and these acid sites are suggested to be located at tetrahedral cobalt sites at the surface.     

Protochlorophyllide a: A Comprehensive Photophysical Picture

The photochemistry of protochlorophyllide a, a precursor in the biosynthesis of chlorophyll and substrate of the light regulated enzyme protochlorophyllide oxidoreductase, is investigated by pump‐probe spectroscopy. Upon excitation into the lowest lying Q‐band the light induced changes are recorded over a wide range of probe wavelengths in the visible and near‐IR region between 500 and 1000 nm. Following excitation, an initial ultrafast 450 fs process is observed related to the motion out of the Franck‐Condon region on the excited state surface; thus directly unraveling previous suggestions based on time‐resolved fluorescence measurements (ChemPhysChem 2006 , 7, 1727–1733). Furthermore, the data reveals a previously concealed photointermediate, whose formation on a nanosecond timescale matches the overall fluorescence decay and is assigned to a triplet state. The implications of this finding with respect to the photochemistry of NADPH:protochlorophyllide oxidoreductase (POR) are discussed.     

On stochastic stationarity of renewal processes

We shall consider point systems inR ₁ which are stationary renewal distributed. We let the points undergo random translations which are assumed to be independent identically distributed random variables with a non-degenerate distribution function. The translations are also independent of the starting positions. It is shown in theorem 3.1 that the only distribution of the points which is conserved after the random translations is the Poisson one. Finally in section 4 we give a characterization of renewal processes on the positive semiaxis in terms of conditional mean values.     

Application of a rapid scanning photodiode-array spectrophotometer to the continuous determination of nickel and cobalt

A computer-processed linear photodiode-array spectrophotometer is used for the continuous and simultaneous determination of nickel and cobalt in the process water of a storage battery. Disodium ethyl-bis(5-tetrazolylazo) acetate is used as the pnotometric reagent. The interference of copper(II) is eliminated by reduction and complexation of copper(I).