Effect of Substituents and of Wavelength of Irradiation on the Photo-Fries-Rearrangement of Enol-Esters Preliminary Communication

Enol-esters 1a-1e undergo clean Photo-Fries-rearrangements without side reactions. With anthroyl derivatives the reaction is observed only at 254 nm, not at 366 nm.     

Numerical calculations of Delbrück scattering amplitudes

The computation of the imaginary Delbrück amplitudes with the formulae of Constantini et al. gave results whose accuracy is greater by a factor of 10 than that available in the literature. The real amplitudes were computed using the code of Papatzacos and Mork. This computation was extended to all angular and energy regions of interest, and hence may be very useful in the interpretation of scattering experiments.     

Time-dependent-thermal-lensing (TDTL) studies on gas-phase azulene

Several aspects of the time-dependent-thermal-lensing (TDTL) technique were explored experimentally, including pressure effects, risetime behavior and falltime behavior. The experiments were performed using azulene vapor excited to high vibrational energies (≈ 17000 cm^?1). It was found that the energy appears in translational degrees of freedom at very early times, but the intrinsic limitations of the technique permitted only an estimate of the V-T rate constant for excited azulene deactivation by krypton. The result is discussed in terms of other recent experiments, and it is tentatively concluded that deactivation of excited azulene by unexcited azulene molecules may proceed primarily by a V-V process.     

The enumeration of extreme rigid honeycombs

Journal of Algebraic Combinatorics - Rigid honeycombs were introduced by Knutson et al. (J Am Math Soc 17:19–48, 2004), and they were shown in Bercovici et al. (J Funct Anal...     

On the Similarity of Analytic Matrix Functions

Consider a domain , and two analytic matrix-valued functions functions . Consider also points and positive integers n ₁, n ₂, . . . , n _N . We are interested in the existence of an analytic function such that X(ω) is invertible, and G(ω) coincides with X(ω)F(ω)X(ω)⁻¹ up to order n _j at the point ω _j . We will see that such a function exists provided that F(ω _j ),G(ω _j ) have cyclic vectors, and the characteristic polynomials of F,G coincide up to order n _j at ω _j . This allows one to give a short proof to a result of Huang, Marcantognini and Young concerning spectral interpolation in the unit disk. The author was partially supported by a grant from the National Science Foundation. Received: September 8, 2006. Accepted: January 11, 2007.     

Open source simulation tool for electrophoretic stacking,focusing, and separation

We present the development, formulation, and performance of a new simulation tool for electrophoretic preconcentration and separation processes such as capillary electrophoresis, isotachophoresis, and field amplified sample stacking. The code solves the one-dimensional transient advection-diffusion equations for multiple multivalent weak electrolytes (including ampholytes) and includes a model for pressure-driven flow and Taylor–Aris dispersion. The code uses a new approach for the discretization of the equations, consisting of a high resolution compact scheme which is combined with an adaptive grid algorithm. We show that this combination allows for accurate resolution of sharp concentration gradients at high electric fields, while at the same time significantly reducing the computational time. We demonstrate smooth, stable, and accurate solutions at current densities as high as 5000 A/m² using only 300 grid points, and a 75-fold reduction in computational time compared with equivalent uniform grid techniques. The code is available as an open source for free at http://microfluidics.stanford.edu.     

Reductive Bergman-type cyclizations of cross-conjugated enediynes to fulvene and fulvalene anions: the role of the substituent

Various cross-conjugated enediynes undergo "Bergman-type" cycloaromatizations upon reduction with potassium metal, generating anions of fulvenes and fulvalene derivatives. This new anionic cyclization is considerably more facile than the classic Bergman cyclization with linear enediynes, creating highly reactive diradicals at -78 degrees C. Not all cross-conjugated enediynes yield cyclized dianions upon reduction; some give uncyclized, Y-shaped, cross-conjugated dianions, while others apparently yield radical-anions that either dimerize or persist as monomers. One system yields both a cyclized and an uncyclized dianion. The substituents are thus shown to be a critical factor in determining the outcome of the reduction. Cyclization occurs within a specific "window of opportunity" that is governed by the substituents.     

A free analogue of Hincin's characterization of infinite divisibility

Hincin characterized the class of infinitely divisible distributions on the line as the class of all distributional limits of sums of infinitesimal independent random variables. We show that an analogue of this characterization is true in the addition theory of free random variables introduced by Voiculescu.