The geometry of spheres in free abelian groups

We study word metrics on ${\mathbb{Z}^d}$ by developing tools that are fine enough to measure dependence on the generating set. We obtain counting and distribution results for the words of length n. With this, we show that counting measure on spheres always converges to cone measure on a polyhedron (strongly, in an appropriate sense). Using the limit measure, we can reduce probabilistic questions about word metrics to problems in convex geometry of Euclidean space. We give several applications to the statistics of ??size-like?? functions.     

Generalizing the Croke-Kleiner construction

It is well known that every word hyperbolic group has a well-defined visual boundary. An example of C. Croke and B. Kleiner shows that the same cannot be said for CAT(0) groups. All boundaries of a CAT(0) group are, however, shape equivalent, as observed by M. Bestvina and R. Geoghegan. Bestvina has asked if they also satisfy the stronger condition of being cell-like equivalent. This article describes a construction which will produce CAT(0) groups with multiple boundaries. These groups have very complicated boundaries in high dimensions. It is our hope that their study may provide insight into Bestvina's question.     

Ligand replacement reactions of ferrous phthalocyanine in dimethylsulphoxide: confirmation that both steps can be observed

Reactions of ferrous phthalocyanine with 4–aminopyridine, imidazole or pyridine in dimethylsulphoxide have been re-investigated using exacting stopped-flow techniques focusing attention on the rapid first stage forming the intermediate FePc(dmso)(base). Effects of impurities in ferrous phthalocyanine samples formed during storage, and the presence of -oxo dimer, on the observed kinetic behaviour with base were examined. The correctness of the findings of an Italian group that kinetic data can be obtained for the first step was affirmed. New results and reassigned published data enabled rate and equilibrium constants to be assigned to the first and second steps for reactions of ferrous phthalocyanine with each of the three nitrogenous bases employed.     

A comparative study of chaotic and white noise signals in digital watermarking

Digital watermarking is an ever increasing and important discipline, especially in the modern electronically-driven world. Watermarking aims to embed a piece of information into digital documents which their owner can use to prove that the document is theirs, at a later stage. In this paper, performance analysis of watermarking schemes is performed on white noise sequences and chaotic sequences for the purpose of watermark generation. Pseudorandom sequences are compared with chaotic sequences generated from the chaotic skew tent map. In particular, analysis is performed on highpass signals generated from both these watermark generation schemes, along with analysis on lowpass watermarks and white noise watermarks. This analysis focuses on the watermarked images after they have been subjected to common image distortion attacks. It is shown that signals generated from highpass chaotic signals have superior performance than highpass noise signals, in the presence of such attacks. It is also shown that watermarks generated from lowpass chaotic signals have superior performance over the other signal types analysed.     

Auto-inhibition of hydrogen gas evolution on gold in aqueous acid solution

It was demonstrated recently that dramatic changes in the redox behaviour of gold/aqueous solution interfaces may be observed following either cathodic or thermal electrode pretreatment. Further work on the cathodic pretreatment of gold in acid solution revealed that as the activity of the gold surface was increased, its performance as a substrate for hydrogen gas evolution under constant potential conditions deteriorated. The change in activity of the gold atoms at the interface, which was attributed to a hydrogen embrittlement process (the occurrence of the latter was subsequently checked by surface microscopy), was confirmed, as in earlier work, by the appearance of a substantial anodic peak at ca. 0.5 V (RHE) in a post-activation positive sweep. Changes in the catalytic activity of a metal surface reflect the fact that the structure (or topography), thermodynamic activity and electronic properties of a surface are dependent not only on pretreatment but also, in the case of the hydrogen evolution reaction, vary with time during the course of reaction. As will be reported shortly, similar (and often more dramatic) time-dependent behaviour was observed for hydrogen gas evolution on other metal electrodes. Electronic Publication     

The effect of severe thermal pretreatment on the redox behaviour of gold in aqueous acid solution

Severe thermal pretreatment of gold wire electrodes in an inert gas atmosphere resulted in the appearance of dramatic premonolayer oxidation responses, which in some instances commenced at 0.25 V (RHE), for the resulting active gold electrodes in aqueous acid media. Similar behaviour was reported earlier for platinum and gold activated by cathodic pretreatment in acid solution; these active noble metal surfaces are evidently more susceptible to oxidation than bulk copper. Such behaviour was attributed to the effect of surface disorder; many of the metal atoms at the interface are assumed to be in a very active, metastable state possessing quite low lattice stabilization energy. Premonolayer oxidation responses are again correlated with electrocatalytic behaviour and the existence of unusual chemisorption behaviour for molecules reacting at highly active states of metals is outlined. Electronic Publication     

Thin tantalum pentoxide films deposited by photo-induced chemical vapor deposition using an injection liquid source

We report the growth of thin tantalum pentoxide films on Si (100) by ultraviolet-assisted injection liquid source (UVILS) chemical vapor deposition (CVD) at low temperatures (200-350 °C). This new technique combines the intense radiation from an excimer lamp (5=222 nm) with a novel injection liquid source capable of delivering precisely controllable quantities of a liquid metalorganic precursor into the CVD chamber. The composition and optical properties of the oxides were determined using a variety of standard characterization methods. After optimization of the deposition parameters, the best layers were incorporated into simple MOS test structures to enable electrical characterization. Refractive index values of 2.09ǂ.07, fixed oxide charge content of <5᎒¹⁰ cm^-2, breakdown fields higher than 2 MV/cm and dielectric constant values of 18-24 were readily achievable in the as-deposited films. These properties compare favorably with those for layers prepared by conventional thermal-CVD at significantly higher temperatures of 500 °C.