Balancing domain decomposition for problems with large jumps in coefficients

The Balancing Domain Decomposition algorithm uses in each iteration solution of local problems on the subdomains coupled with a coarse problem that is used to propagate the error globally and to guarantee that the possibly singular local problems are consistent. The abstract theory introduced recently by the first-named author is used to develop condition number bounds for conforming linear elements in two and three dimensions. The bounds are independent of arbitrary coefficient jumps between subdomains and of the number of subdomains, and grow only as the squared logarithm of the mesh size . Computational experiments for two- and three-dimensional problems confirm the theory.

     

Influence of a background gas on expanding plasma clots

An expansion of finite plasma clots into the background neutral gas is studied numerically. The presented model includes the quasineutrality violation as well as the interpenetration of plasma and neutral gas at the boundary of the plasma. We estimate the region of plasma parameters where the model is correct. Space distributions of main plasma parameters, cooling of electrons and the process of inter-penetration of the plasma and the neutral gas are analysed as well as an empiric formula for electron temperature is found. Finally, it is shown that the most intensive plasma-gas inter-penetration occurs in the case where the initial plasma and gas densities are the same.     

Whitehead test modules

A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.

A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.

     

Infinite products of finite simple groups

We classify the sequences of finite simple nonabelian groups such that has uncountable cofinality.

     

The acid-catalyzed and neutral solvolysis of benzoylphenyldiazomethane in water,aqueous t-butanol,and aqueous salt solutions

The acid-catalyzed and water-catalyzed solvolysis ofbenzoylphenyldiazomethane (1) have been studied in water and in t-butanol-water mixtures, the mole fraction of water (n_H2O) being varied from 0·75-1·00. Increasing t-butanol concentrations produce a pronounced decrease in both k_H⊕ and k_H2O. In the “water reaction” mutually compensatory changes of AH

and AS

are associated with the rate variations, with minima in AH

and AS

at about n_H2O = 0·95. In addition it was found that the magnitude of the salt effect of (n-Bu)₄NCl on the rate of hydrolysis of 1 in water at 25° is much larger than that of LiCl, NaCl and NaBr. Assuming that the rate of the “water reaction” is largely determined by water acidity, the data are suggestive for the existence of a relation between water acidity and solvent structural integrity in highly aqueous t-butanol-water solutions.     

Synthesis of 2,3′-biindolyls and indolo[3,2-a]carbazoles

Several highly activated 2,3′-biindolyls were prepared from methyl 5,6-dimethoxyindole-2-carboxylate and oxindoles. The 2,3′-biindolyls were further transformed into a hydroxy indolo[3,2-a]carbazole and a bisindole amide.     

Functionalization of Electrode Surfaces with Monolayers of Azocompounds and Gold Clusters

Properties of monolayers of azocrown compound self-assembled on gold substrates were studied using voltammetry and scanning tunneling microscopy. The surface concentrations of this compound in monolayers were determined from the area of the voltammetric reduction peaks. The area per one molecule estimated from voltammetry experiments is 0.65 nm². This value was comparable with the limiting molecular area of the compound in the Langmuir–Blodgett film at the air–water interface. We also observed the presence of gold clusters and other gold structures by STM when a gold electrode modified with azocrown compound was dipped into the tetrachloroaurate solution. Even better spectra of clusters were obtained following one voltammetric scan in the range 0.5 to ?0.6 V. After more cycles or if we condition the electrode at 0.4 V the clusters aggregate into wires.     

The heliobacteria, a new group of photosynthetic bacteria

A review is given of the photosynthetic properties of the heliobacteria, a new group of photosynthetic bacteria, discovered only 14 years ago. These bacteria contain a “new” pigment, bacteriochlorophyll g, and they have a relatively simple pigment system, consisting of a core-reaction center complex only. Like the green sulfur bacteria, they have a Photosystem I-type reaction center, with a chlorophyll a derivative as primary electron acceptor. Because of the absence of an extensive peripheral antenna system, the reaction center processes in these bacteria are much easier to study than those in the green sulfur bacteria.     

ESR study of monoalkylzinc-2,2′-bipyridine complexes RZn · Bipy

Paramagnetic species are formed when LiBipy is treated with various alkylzinc halides at ?100°C and the ESR spectra are discussed. The observation that the half-life times of the radical species appear to depend only on the nature of the alkyl group bound to zinc proves that monoalkylzinc-2,2′-bipyridine complexes are formed. The nature of the bonding between zinc and 2,2′-bipyridine is discussed.     

Cosmic numbers and quantum theory

The cosmic numbers are considered, with emphasis on the relationN ². (HereN is the number of nucleons in the universe, and, its radius in atomic units.) This relation is interpreted in terms of a quantum mechanical model.