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.     

Bounds for codes and designs in complex subspaces

We introduce the concepts of complex Grassmannian codes and designs. Let $\mathcal{G}_{m,n}$ denote the set of m-dimensional subspaces of ? ⁿ : then a code is a finite subset of $\mathcal{G}_{m,n}$ in which few distances occur, while a design is a finite subset of $\mathcal{G}_{m,n}$ that polynomially approximates the entire set. Using Delsarte’s linear programming techniques, we find upper bounds for the size of a code and lower bounds for the size of a design, and we show that association schemes can occur when the bounds are tight. These results are motivated by the bounds for real subspaces recently found by Bachoc, Bannai, Coulangeon and Nebe, and the bounds generalize those of Delsarte, Goethals and Seidel for codes and designs on the complex unit sphere.     

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.     

Kunststoffe

Ohne Zusammenfassung     

Anti-flooding cathode catalyst layer for high performance PEM fuel cell

Water management in cathode catalyst layer (CCL) plays an important role in the PEM fuel cell operation. A novel anti-flooding CCL is developed with the addition of oxygen permeable and hydrophobic dimethyl silicone oil (DSO) into the catalyst layer (CL) to improve the water balance and oxygen transport within the cathode. With the addition of 0.5 mg cm^?2 DSO in the CCL, the ability of water management has been enhanced greatly compared to that with a normal cathode. Electrochemical impedance spectroscopy has been employed to characterize the electrochemical behavior of the single fuel cell. The results show that the increased hydrophobicity of the CCL by DSO modification effectively expels water out of the voids of CCL. In addition, DSO in the CCL enhances oxygen accessibility to the CCL, thus improving the performance of the PEM fuel cell significantly.     

Noncommutative Manifolds from Graph and <Emphasis Type="Italic">k</Emphasis>-Graph <Emphasis Type="Italic">C</Emphasis>*-Algebras

In [PRen] we constructed smooth (1, ∞)-summable semifinite spectral triples for graph algebras with a faithful trace, and in [PRS] we constructed (k, ∞)-summable semifinite spectral triples for k-graph algebras. In this paper we identify classes of graphs and k-graphs which satisfy a version of Connes’ conditions for noncommutative manifolds.