Some remarks on Newton–Sabatier methods

It is shown how Newton–Sabatier methods (arising in inverse scattering at fixed energy) can be related to spectral measures and typically when they correspond to regular potentials. A number of spectral formulae for various transmutation kernels are also given in terms of general Kontorovi?–Lebedev theory and connections to generating functions, generalized orthogonal polynomials, etc. are indicated.     

Microstructure array on Si and SiOx generated by micro-contact printing, wet chemical etching and reactive ion etching

A method, combining micro-contact printing (μCP), wet chemical etching and reactive ion etching (RIE), is reported to fabricate microstructures on Si and SiOx. Positive and negative structures were generated based on different stamps used for μCP. The reproducibility of the obtained microstructures shows the methodology reported herein could be useful in Micro-Electro-Mechanical Systems (MEMS), optical and biological sensing applications.     

Colliding stacks: A large deviations analysis

We analyze the performance of a prototypical scheme for shared storage allocation: two initially empty stacks evolving in a contiguous block of memory of size m. We treat the case in which the stacks are more likely to shrink than grow, but with the probabilities of insertion and deletion allowed to depend arbitrarily on stack height as a fraction of m. New results are obtained on the m → ∞ asymptotics of the stack collision time, and of the final stack heights. The results of Wentzell and Freidlin on the large deviations of Markov chains are used, and the relation of their formalism to the Hamiltonian formulation of classical mechanics is emphasized. Certain results on higher-order asymptotics follow from WKB expansions.     

Loss without recovery of Gibbsianness during diffusion of continuous spins

We consider a specific continuous-spin Gibbs distribution μ_t=0 for a double-well potential that allows for ferromagnetic ordering. We study the time-evolution of this initial measure under independent diffusions. For `high temperature' initial measures we prove that the time-evoved measure μ<sub>t</sub> is Gibbsian for all t. For `low temperature' initial measures we prove that μ_t stays Gibbsian for small enough times t, but loses its Gibbsian character for large enough t. In contrast to the analogous situation for discrete-spin Gibbs measures, there is no recovery of the Gibbs property for large t in the presence of a non-vanishing external magnetic field. All of our results hold for any dimension d≥2. This example suggests more generally that time-evolved continuous-spin models tend to be non-Gibbsian more easily than their discrete-spin counterparts. Research carried out at EURANDOM and supported by Deutsche Forschungsgemeinschaft     

Optimality relationships forp-cyclic SOR

Summary The optimality question for blockp-cyclic SOR iterations discussed in Young and Varga is answered under natural conditions on the spectrum of the block Jacobi matrix. In particular, it is shown that repartitioning a blockp-cyclic matrix into a blockq-cyclic form,q, results in asymptotically faster SOR convergence for the same amount of work per iteration. As a consequence block 2-cyclic SOR is optimal under these conditions.Research supported in part by the US Air Force under Grant no. AFOSR-88-0285 and the National Science Foundation under grant no. DMS-85-21154 Present address: Boeing Computer Services, P.O. Box 24346, MS 7L-21, Seattle, WA 98124-0346, USA     

A short synthesis of 3,3-di(hetero)arylpropylamines obtained from bis-(hetero)aryl ketones via palladium catalysis

A palladium-catalyzed parallel synthesis of bis-hetero(aryl) ketones is described with two further synthetic steps allowing easy entry to 3,3-di(hetero)arylpropylamines.