Stereochemical control of the Passerini reaction

A catalytic asymmetric Passerini reaction using tridentate indan (pybox) Cu(II) Lewis acid complex 4 with substrates capable of bidentate coordination has been achieved. The reaction occurs via ligand-accelerated catalysis.     

Syntheses of stereochemically diverse nine-membered ring-containing biaryls

[reaction: see text] A library of nine-membered, biaryl-containing rings has been synthesized in parallel on polystyrene macrobeads. Dimeric medium rings were shown to be accessible via a regio- and stereoselective double cyclization.     

Unstable extremal surfaces of the “Shiffman-functional”

We establish a new way to Shiffmans result [16], which yields a sufficient condition for the existence of unstable extremal surfaces of a parametric functional with a dominant area term via the mountain-pass-principle. In this paper we consider H ^1,2-surfaces spanned by a piecewise linear closed Jordan-curve in ( ). This enables us to generalize Courants ideas for the area functional to the more complex functional Shiffman was considering.Received: 3 October 2003, Accepted: 18 November 2003, Published online: 2 April 2004Mathematics Subject Classification (2000): 01X23R. Jakob: It is a pleasure for the author to thank Prof. Dr. S. Hildebrandt and Priv.-Doz. Dr. H. von der Mosel for their support during the preparation of this paper.     

On Allee effects in structured populations

Maps of the nonnegative cone of into itself are considered where are nonnegative, primitive matrices with nondecreasing entries and at least one increasing entry. Let denote the dominant eigenvalue of and . These maps are shown to exhibit a dynamical trichotomy. First, if , then for all nonzero . Second, if , then for all . Finally, if and 1$">, then there exists a compact invariant hypersurface separating . For below , , while for above, . An application to nonlinear Leslie matrices is given.

     

LP formulations of the shortest path tree problem

Based on a pair of primal-dual LP formulations of the shortest path tree problem, the first algorithmic approach to reoptimizing the shortest paths subject to changes in the edge weights was proposed by S. Pallottino and M.G. Scutellá in 2003. We shall here focus solely on their introductory sections, propose some simplifications of the models considered, and finally relate the resulting models to the presentation of single-source shortest path problems in textbooks treating this subject with but limited or no reference to LP.Received: April 2004, Revised: August 2004, MSC classification: 90C05, 90C35, 90B10 Dedicated to the memory of Stefano Pallottino     

Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source

A coherent anti-Stokes Raman scattering microscope based on a Ti:sapphire femtosecond oscillator and a photonic crystal fiber is demonstrated. The nonlinear response of the fiber is used to generate the additional wavelength needed in the Raman process. The applicability of the setup is demonstrated by imaging of micrometer-sized polystyrene beads.     

NMR-microscopy with TrueFISP at 11.75T

The purpose of this paper is to demonstrate that a fully balanced gradient echo technique (TrueFISP) can be used for microscopic experiments at high static magnetic field strengths. TrueFISP experiments were successfully performed on homogeneous and inhomogeneous objects at 11.75T. High-resolution TrueFISP images were obtained from phantoms, plants, formalin-fixed samples, and from an isolated beating rat heart with an in-plane resolution of 78 micro m and a slice thickness of 500 micro m. The signal-to-noise ratio (SNR) gain of TrueFISP compared to conventional gradient echo or spin echo sequences will allow faster acquisition times or an improvement in spatial resolution for microscopic experiments.     

New air-stable planar chiral ferrocenyl monophosphine ligands: Suzuki cross-coupling of aryl chlorides and bromides

[reaction: see text] A novel class of planar chiral electron-rich monophosphine ligands has been developed. The modular design allows a short and efficient synthesis of an array of aryl-ferrocenyl derivatives carrying the donating bis(dicyclohexyl)phosphino moiety. These new ligands have successfully been applied in the palladium-catalyzed Suzuki cross-coupling of activated as well as nonactivated aryl chlorides at room temperature. The asymmetric coupling of an aryl bromide and an aryl boronic acid was also tested, giving ees up to 54%.     

The Ground State Energy of a Dilute Two-Dimensional Bose Gas

The ground state energy per particle of a dilute, homogeneous, two-dimensional Bose gas, in the thermodynamic limit is shown rigorously to be E₀/N=(2²/m)|ln(a²)|^–1, to leading order, with a relative error at most O(|ln(a²)|^–1/5). Here N is the number of particles, =N/V is the particle density and a is the scattering length of the two-body potential. We assume that the two-body potential is short range and nonnegative. The amusing feature of this result is that, in contrast to the three-dimensional case, the energy, E₀ is not simply N(N–1)/2 times the energy of two particles in a large box of volume (area, really) V. It is much larger.     

Pairwise use of complexity-generating reactions in diversity-oriented organic synthesis

[reaction: see text] Two pairs of complexity-generating reactions with an essential product-substrate relationship along a synthetic pathway are demonstrated. This pathway illustrates a key element in a planning algorithm for diversity-oriented synthesis. This element facilitates the efficient synthesis of structurally complex compounds, and it can be integrated with ones that provide structurally diverse compounds.