Gaussian processes with biconvex covariances

Let R(s, t) be a continuous, nonnegative, real valued function on a ≤ s ≤ t ≤ b. Suppose $\text{?R}\text{?s}\text{≥ 0}$, $\text{?R}\text{?t}\text{≤ 0}$, and $\text{?}{}^2\text{R}\text{?t}\text{?t ≤ 0}$ in the interior of the domain. Then the extension of R to a symmetric function on [a, b] × [a, b] is a covariance function. Such a covariance is called biconvex. Let X(t) be a Gaussian process with mean 0 and biconvex covariance. X has a representation as a sum of simple moving averages of white noises on the line and plane. The germ field of X at every point t is generated by X(t) alone. X is locally nondeterministic. Under an additional assumption involving the partial derivatives of R near the diagonal, the local time of the sample function exists and is jointly continuous almost surely, so that the sample function is nowhere differentiable.     

Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces

LetA be anm-accretive operator in a Banach spaceE. Suppose thatA ⁻¹0 is not empty and that bothE andE ^* are uniformly convex. We study a general condition onA that guarantees the strong convergence of the semigroup generated by—A and of related implicit and explicit iterative schemes to a zero ofA. Rates of convergence are also obtained. In Hilbert space this condition has been recently introduced by A. Pazy. We also establish strong convergence under the assumption that the interior ofA ⁻¹0 is not empty. In Hilbert space this result is due to H. Brezis. Sponsored by the United States Army under Contract No. DAAG29-75-C-0024.     

Tethering for Selective Synthesis of 2,2′‐Biphenols: The Acetal Method

2,2'‐Biphenols are a large and diverse group of compounds with exceptional properties both as ligands and bioactive agents. Traditional methods for their synthesis by oxidative dimerisation are often problematic and lead to mixtures of ortho‐ and para‐connected regioisomers. To compound these issues, an intermolecular dimerisation strategy is often inappropriate for the synthesis of heterodimers. The ‘acetal method’ provides a solution for these problems: stepwise tethering of two monomeric phenols enables heterodimer synthesis, enforces ortho regioselectivity and allows relatively facile and selective intramolecular reactions to take place. The resulting dibenzo[1,3]dioxepines have been analysed by quantum chemical calculations to obtain information about the activation barrier for ring flip between the enantiomers. Hydrolytic removal of the dioxepine acetal unit revealed the 2,2′‐biphenol target.     

PMMA films refractive index modulation via TiO2 nanoparticle inclusions and corona poling

The present study is focused on the characterization of optical properties of poly (methyl methacrylate) (PMMA) films and the possibilities of modulation and fine tuning of their refractive index by the inclusion of different concentrations of nano-sized titanium dioxide (TiO₂) particles (less than 33 nm) and corona poling. The samples are prepared by the “spin coating” method and they are charged in a conventional point-to-plain corona system. The transparent PMMA/TiO₂ films exhibit good optical properties in the visible range. An investigation of the film’s surface refractive index by two wavelengths laser refractometry utilizing the disappearing diffraction pattern method is carried out. The refractive index increases with increasing the TiO₂ content in the nanocomposite films. The corona poling increases the refractive index values for all samples regardless of the polarity and concentration of TiO₂ nanoparticles. The results show that the prepared nanocomposite films have a potential application for optical devices.     

Removal of Model Pollutants in Aqueous Solution by Gliding Arc Discharge. Part II: Modeling and Simulation Study

Plasma Chemistry and Plasma Processing - The aim of this work is the modeling of plasma-chemical reactions taking place between highly oxidizing gaseous species (·OH, ·NO and...     

Prenylated anthraquinones and other constituents from the seeds of Vismia laurentii

Two new prenylated anthraquinones, laurenquinone A (1) and B (2) were isolated from the seeds of Vismia laurentii together with four known compounds; xanthone V(1) (3), physcion (4), 3-geranyloxyemodin anthrone (5) and friedelin (6). The structures of the new metabolites were determined with the help of spectroscopic data including extensive 2D-NMR spectroscopy. The known compounds were identified by comparison of their physical and spectroscopic data with those reported in the literature. Compounds 1, 4 and 5 exhibited moderate algicidal activity against Chlorella fusca and 3 showed moderate activity against the gram-positive bacterium Bacillus megaterium.     

Outer approximation methods for solving variational inequalities in Hilbert space

In this paper, we study variational inequalities in a real Hilbert space, which are governed by a strongly monotone and Lipschitz continuous operator F over a closed and convex set C. We assume that the set C can be outerly approximated by the fixed point sets of a sequence of certain quasi-nonexpansive operators called cutters. We propose an iterative method, the main idea of which is to project at each step onto a particular half-space constructed using the input data. Our approach is based on a method presented by Fukushima in 1986, which has recently been extended by several authors. In the present paper, we establish strong convergence in Hilbert space. We emphasize that to the best of our knowledge, Fukushima’s method has so far been considered only in the Euclidean setting with different conditions on F. We provide several examples for the case where C is the common fixed point set of a finite number of cutters with numerical illustrations of our theoretical results.