Chaotic Homeomorphisms of Rn, Lifted from Torus Homeomorphisms

We establish the existence of self-homeomorphisms of Rⁿ, n 2, which are chaotic in the sense of Devaney, preserve volumeand are spatially periodic. Moreover, we show that in the spaceof volume-preserving homeomorphisms of the n-torus with meanrotation zero, those with chaotic lifts to Rⁿ are dense, withrespect to the uniform topology. An application is given forfixed points of 2-dimensional torus homeomorphisms (Conley–Zehnder–FranksTheorem). 1991 Mathematics Subject Classification 54H20.     

Application of Vegard's law to mixed cation sodalites: a simple method for determining the stoichiometry

Vegard’s law describes the empirical relationship between the crystal lattice parameter of a mixture and its components. This relationship holds for some sodalites, in particular those containing mixtures of Li, K and Na as the charge balancing cations. By utilizing previously published lattice parameters for Li/Na and K/Na mixed cation chloride sodalites, linear curves were drawn allowing the composition of the mixed cation sodalites to be determined from their lattice parameters. Further, by mathematical addition of the curves for Li/Na and K/Na mixed cation chloride sodalites, a linear curve was developed and tested for the mixed tri-cation Li/Na/K chloride sodalites. This provides a simple way to monitor the composition of mixed cation sodalites and has an application in monitoring the composition of multi-phase materials where the sodalite phase cannot be easily separated for elemental analysis.     

The nonexistence of colorings

The purpose of this note is to prove the following result about the nonexistence of colorings.     

A simple one-pot procedure for the iminium salt formation: an efficient route to β-arylethylamines

A practical and highly efficient process for the preparation of β-arylethylamines 7 was developed. Benzylic organozinc compounds 10 were reacted with the iminium salts 9 generated in situ from the amine salt 8 and paraformaldehyde in one pot and in a polar and aprotic solvent, such as NMP. A variety of the β-arylethylamines were prepared in 43-91% yields.     

A Recommender System based on Idiotypic Artificial Immune Networks

The immune system is a complex biological system with a highly distributed, adaptive and self-organising nature. This paper presents an Artificial Immune System (AIS) that exploits some of these characteristics and is applied to the task of film recommendation by Collaborative Filtering (CF). Natural evolution and in particular the immune system have not been designed for classical optimisation. However, for this problem, we are not interested in finding a single optimum. Rather we intend to identify a sub-set of good matches on which recommendations can be based. It is our hypothesis that an AIS built on two central aspects of the biological immune system will be an ideal candidate to achieve this: Antigen–antibody interaction for matching and idiotypic antibody–antibody interaction for diversity. Computational results are presented in support of this conjecture and compared to those found by other CF techniques.Mathematics Subject Classifications (2000) 68Rxx, 68Txx, 90Bxx.     

Novel crystalline carbon-cage structure synthesized from laser-driven shock wave loading of graphite

We report a novel crystalline carbon-cage structure synthesized from laser-driven shock wave loading of a graphite-copper mixture to about 14+/-2 GPa and 1000 +/- 200 K. Quite unexpectedly, it can be structurally related to an extremely compressed three-dimensional C60 polymer with random displacement of C atoms around average positions equivalent to those of distorted C60 cages. Thus, the present carbon-cage structure represents a structural crossing point between graphite interlayer bridging and C60 polymerization as the two ways of forming diamond from two-dimensional and molecular carbon.     

Positive eigenvalues of second order boundary value problems and a theorem of M. G. Krein

Conditions are given which guarantee that the least real eigenvalue is positive for certain boundary value problems for the vector-matrix equation . This leads to conditions which guarantee the stable boundedness, according to Krein, for solutions of with certain real values of . As a consequence, a result first stated by Krein is proven.

     

Bridging the Gap: Understanding the Chemistry of CMP

This laboratory exercise will expose upper-level undergraduate students to the aspect of chemistry known as Chemical Mechanical Planarization (CMP). CMP is used for the fabrication of computer chips and memory devices. Students investigate a representative slurry that is used for copper-based advanced integrated-circuit processes. More specifically, students monitor the generation of OH through the decomposition of hydrogen peroxide in the presence of a metal/amino acid complex, which is used as a catalyst. This introduces students to the fundamentals of OH trapping and provides practice in the techniques used for kinetic rate determination. The kinetics data obtained for these systems will be correlated with the static dissolution rate of Cu metal upon exposure to various control and hydroxyl radical generating solutions.     

A Uniqueness Theorem of Fourier Jacobi Models for Representations of Sp(4)

It is shown that every irreducible admissible representationof Sp₄(F), where F is a p-adic field, has at most one FourierJacobi model for given Fourier Jacobi data.