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.     

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.     

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.     

Zur Theorie der Bildung von Gelen

Colloid and Polymer Science -     

Stereospecific total synthesis of (±)-strempeliopine

The 18-methylene-1,2-dehydroaspidospermidine (III) was stereospecifically transformed into the schizozygane alkaloid strempeliopine (II) in 16,6 % overall yield.     

The role of natural and man-made ice-forming nuclei in the atmosphere

Water-soluble and insoluble, organic and inorganic, natural and man-made aerosol particles participate in vapor-liquid, vapor-solid (ice), and liquid-solid phase transitions in the atmosphere. Hydrosol particles (aerosol particles that have been transferred into water droplets) nucleate ice through freezing. A small without scavenging or being scavenged by another aerosol particle. It is also difficult to imagine that pure mineral particles can be lifted from soil surfaces. In view of this, an ice-nucleating site may be a much smaller particle attached to a larger clay particle. To this category belong, e.g., silver iodide-clay mixed particles. Limited studies indicate that decaying leaves and forest litter under the surface of soils are a potential source of biogenic ice-forming nuclei but that their contribution to the atmosphere is very limited. Research should be directed to study possible relations between cloud condensation nuclei and ice-forming nuclei derived from natural organic compounds (terpenes, leaf-derived nuclei, bacteria, etc.).

A balance must be maintained between large cloud chambers, in which duplication of in-cloud processes is possible, and the special instrumentation which provides information about the modes of ice nucleation on aerosol particles. The two modes of instrumentation should supplement each other.

The greatest difficulty in attempting to make a comparison between the number of ice-forming nuclei estimated in the laboratory and the number in a cloud is the lack of knowledge of the time-temperature-humidity history of the aerosol particles. In nature, the ability of an aerosol particle to nucleate ice may be destroyed or“poisoned“ in the presence of pollutants. An aerosol particle may, on the other hand, become an activated or warmer ice-forming nucleus, e.g.,after the sublimation of ice once formed on it. The temperature of ice nucleation is not a singular property of a particle; the warmest temperatures of ice nucleation of, e.g., particles of a certain soil 10cm in diameter are-15°C,-10°C, and-8°C for nucleation through freezing, condensation followed by freezing and contact, respectively (ref.26). The progress made in instrumentation permits studies of the modes of ice nucleation. Understanding the physical and chemical processes taking place in clouds makes estimates of the rates of ice particle formation more realistic (Young [ref.157]).

The reader should examine two previous reviews written by Mossop (1963) and Montefinale . (1971) for a more complete list of references.