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.     

Critical percolation exploration path and SLE 6: a proof of convergence

It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE ₆. We provide here a detailed proof, which relies on Smirnov’s theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy’s formula). The version of convergence to SLE ₆ that we prove suffices for the Smirnov–Werner derivation of certain critical percolation crossing exponents and for our analysis of the critical percolation full scaling limit as a process of continuum nonsimple loops. Research of Charles M.Newman was partially supported by the US NSF under grants DMS-01-04278 and DMS-06-06696.     

General Aspects and Optimization of Enantioselective Biocatalysis in Organic Solvents: The Use of Lipases [New Synthetic Methods (76)]

Enantioselective biocatalysis in nonaqueous media is becoming increasingly important in preparative synthetic chemistry. This article discusses (1) the general catalytic properties of enzymes in nonaqueous environments, (2) the basic principles that govern lipase-catalyzed enantioselective esterification and transesterification reactions in organic media for the preparation of optically active acids and alcohols, (3) the determination of kinetic and thermodynamic parameters, and (4) the quantitative analysis of published data.     

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.     

Autour du théorème de Ferrand–Obata (Concerning the Theorem of Ferrand–Obata)

The aim of this article is to give a new dynamical proof of the Ferrand–Obata theorem when the manifold is compact. This will give us a generalisation of this theorem to transversally conformal foliations ofcodimension greater than three and constant basic functions.     

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.     

Continuous-Wave Operation of a 460-GHz Second Harmonic Gyrotron Oscillator

We report the regulated continuous-wave (CW) operation of a second harmonic gyrotron oscillator at output power levels of over 8 W (12.4 kV and 135 mA beam voltage and current) in the TE(0,6,1) mode near 460 GHz. The gyrotron also operates in the second harmonic TE(2,6,1) mode at 456 GHz and in the TE(2,3,1) fundamental mode at 233 GHz. CW operation was demonstrated for a one-hour period in the TE(0,6,1) mode with better than 1% power stability, where the power was regulated using feedback control. Nonlinear simulations of the gyrotron operation agree with the experimentally measured output power and radio-frequency (RF) efficiency when cavity ohmic losses are included in the analysis. The output radiation pattern was measured using a pyroelectric camera and is highly Gaussian, with an ellipticity of 4%. The 460-GHz gyrotron will serve as a millimeter-wave source for sensitivity-enhanced nuclear magnetic resonance (dynamic nuclear polarization) experiments at a magnetic field of 16.4 T.