Common homoclinic points of commuting toral automorphisms

The points homoclinic to 0 under a hyperbolic toral automorphism form the intersection of the stable and unstable manifolds of 0. This is a subgroup isomorphic to the fundamental group of the torus. Suppose that two hyperbolic toral automorphisms commute so that they determine a ℤ²-action, which we assume is irreducible. We show, by an algebraic investigation of their eigenspaces, that they either have exactly the same homoclinic points or have no homoclinic point in common except 0 itself. We prove the corresponding result for a compact connected abelian group, and compare the two proofs. The second author would like to thank the Austrian Academy of Sciences and the Royal Society for partial support while this work was done.     

Preparation,characterization and copolymerization of the 12‐membered cyclic diamide 1,6‐diazacyclododecane‐2,5‐dione

A 12‐membered cyclic diamide monomer for nylon 64 was successfully synthesized in fairly high yield (～45%). The synthesis conditions were varied to see the effect of the diamine and succinyl chloride reactants on yield. Threefold excess of 1,6‐hexamethylenediamine (HDA) gave the highest yield, while further increasing the amount of HDA decreased the yield. Using N,N‐diisopropylethylamine as acid scavenger resulted in the formation of two different cyclic amides, which were fully analyzed by ¹H and ¹³C solution nuclear magnetic resonance spectrometry and mass spectrometry. Copolymerization of cyclic amides with ε‐caprolactam via an anionic route gave a block copolyamide with a two distinct endotherms in the differential scanning calorimetry analysis. However, copolymerization by the hydrolytic route gave only nylon 6 with terminal 64 units. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 96–103     

Applications of stable isotope ratio mass spectrometry in cattle dung carbon cycling studies

Understanding the fate of dung carbon (C) in soils is challenging due to the ubiquitous presence of the plant‐derived organic matter (OM), the source material from which both dung‐derived OM and soil organic matter (SOM) predominantly originate. A better understanding of the fate of specific components of this substantial source of OM, and thereby its contribution to C cycling in terrestrial ecosystems, can only be achieved through the use of labelled dung treatments. In this short review, we consider analytical approaches using bulk and compound‐specific stable carbon isotope analysis that have been utilised to explore the fate of dung‐derived C in soils. Bulk stable carbon isotope analyses are now used routinely to explore OM matter cycling in soils, and have shown that up to 20% of applied dung C may be incorporated into the surface soil horizons several weeks after application, with up to 8% remaining in the soil profile after one year. However, whole soil δ¹³C values represent the average of a wide range of organic components with varying δ¹³C values and mean residence times in soils. Several stable ¹³C isotope ratio mass spectrometric methods have been developed to qualify and quantify different fractions of OM in soils and other complex matrices. In particular, thermogravimetry‐differential scanning calorimetry‐isotope ratio mass spectrometry (TG‐DSC‐IRMS) and gas chromatography‐combustion‐IRMS (GC‐C‐IRMS) analyses have been applied to determine the incorporation and turnover of polymeric plant cell wall materials from C₄ dung into C₃ grassland soils using natural abundance ¹³C isotope labelling. Both approaches showed that fluxes of C derived from polysaccharides, i.e. as cellulose or monosaccharide components, were more similar to the behaviour of bulk dung C in soil than lignin. However, lignin and its 4‐hydroxypropanoid monomers were unexpectedly dynamic in soil. These findings provide further evidence for emerging themes in biogeochemical investigations of soil OM dynamics that challenge perceived concepts of recalcitrance of C pools in soils, which may have profound implications for the assessment of the potential of agricultural soils to influence terrestrial C sinks. Copyright © 2010 John Wiley & Sons, Ltd.     

Use of computer simulations to determine steady-state distributions in ion bombardment

Abstract

Computer simulations typically determine the particle-distribution function corresponding to a single-event point source. This distribution function contains all the information needed to determine the corresonding steady-state distribution. From the single-event point-source distribution one can also deduce the distributions resulting from plane and volume-homogeneous sources, both for single event and steady state. A formalism for making these deductions is developed, based on the observation that the distribution determined by computer simulation obeys the Boltzmann transport equation, and on the properties of the Green's functions solutions of that equation, particularly the consequences of space- and time-translation invariance. The treatment deals explicitly with a homogeneous target infinite in every direction, but is easily generalized to cases with boundary conditions, such as a beam bombarding a layered target in slab geometry.     

Naturally occurring organic matter as a chemical trap to scan an ecosystem for natural products

A model is proposed that tests an ecosystem for natural products (NPs) using a nonpolar extract of naturally occurring organic matter (NOM), which we demonstrate to be an efficient chemical trap for relatively nonpolar organic molecules. To test the model we collected twenty-six samples of NOM from various locations on the Suwannee River, from its headwaters in the Okeefenokee Swamp to the Gulf of Mexico. We have tentatively identified stearic acid, DDT, chincodine, and a potential precursor to bryostatin. Our data provide evidence that NOM can trap, hold for several decades, concentrate, and transport NP in the environment.     

Cellulase production and regulation byAgaricus bisporus

Cellulose is degraded during the growth of the cultivated mushroomA. bisporus on composted straw. At the time of sporophore enlargement, a marked increase in extracellular endocellulase activity occurs. A high level of enzyme activity is maintained during subsequent cropping cycles. Some of the factors affecting growth and production of extracellular endocellulase activity byA. bisporus cultured in simple defined liquid media have been examined. Endocellulase production by the fungus closely paralleled mycelial growth in cultures containing microcrystalline cellulose. The enzyme was induced by various celluloses and cellobiose. In the presence of a cellulose inducer, glucose and cellobiose repressed enzyme production. Endocellulase activity in culture filtrates was inversely related to cellulose concentration in the culture. Although the activity of free enzyme was low, in high concentrations of cellulose more cellulose was degraded. Evidence was obtained for the existence of two forms of endocellulase activity. One form adsorbed strongly to cellulose and was predominant in cultures low in cellulose. In cultures with a high cellulose content, a nonadsorbable form of the enzyme was more abundant. It is suggested that the pattern of cellulase activities produced whenA. bisporus is grown on different concentrations of cellulose is partly accounted for by its adsorption to the cellulose.     

Logarithmic Capacity and Renormalizability for Landing on the Mandelbrot Set

We study renormalizability of external angles of the Mandelbrotset M. Estimates are made of the logarithmic capacity of setsof angles that are infinitely renormalizable with a specificsequence of periods, using a substitution due to Douady. Theseshow that many of the infinitely renormalizable rays do landon M, which provides further evidence in support of the conjecturethat M is locally connected.     

Reversed-phase liquid chromatography of elastin peptides

Soluble fragments of elastin are frequently present in biological tissue in small amounts. Because of their hydrophobic character, these peptides are not well resolved by a number of conventional techniques. However, their separation should be possible by reversed-phase chromatography. A wide range of columns, gradients and solvents were evaluated. Two systems are described. One was a C18 liganded silica column eluted isocratically by gravity flow. Some degree of size fractionation was achieved with larger peptides being eluted with methanol and smaller ones with isopropanol. The second system uses a pressurized elution from another C18 ligand column. A concave gradient of trifluoroacetic acid-acetonitrile with a decreasing acetonitrile concentration was optimal. Similar resolution of peptides produced by a variety of digestion methods was obtained with the lower-molecular-mass peptides eluting in the middle of the gradient.