On (q 2 + q + 2, q + 2)-arcs in the Projective Plane PG(2, q)

A (k,n)-arc in PG(2,q) is usually defined to be a set of k points in the plane such that some line meets in n points but such that no line meets in more than n points. There is an extensive literature on the topic of (k,n)-arcs. Here we keep the same definition but allow to be a multiset, that is, permit to contain multiple points. The case k=q ²+q+2 is of interest because it is the first value of k for which a (k,n)-arc must be a multiset. The problem of classifying (q ²+q+2,q+2)-arcs is of importance in coding theory, since it is equivalent to classifying 3-dimensional q-ary error-correcting codes of length q ²+q+2 and minimum distance q ². Indeed, it was the coding theory problem which provided the initial motivation for our study. It turns out that such arcs are surprisingly rich in geometric structure. Here we construct several families of (q ²+q+2,q+2)-arcs as well as obtain some bounds and non-existence results. A complete classification of such arcs seems to be a difficult problem.     

Generic existence and uniqueness of positive eigenvalues and eigenvectors

We consider a closed cone of positive operators on an ordered Banach space and prove that a generic element of this cone has a unique positive eigenvalue and a unique (up to a positive multiple) positive eigenvector. Moreover, the normalized iterations of such a generic element converge to its unique eigenvector.     

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.     

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.     

Charting the landscape of supercritical string theory

Special solutions of string theory in supercritical dimensions can interpolate in time between theories with different numbers of spacetime dimensions and different amounts of world sheet supersymmetry. These solutions connect supercritical string theories to the more familiar string duality web in ten dimensions and provide a precise link between supersymmetric and purely bosonic string theories. Dimension quenching and c duality appear to be natural concepts in string theory, giving rise to large networks of interconnected theories.     

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...