Stiffness of ODEs

It is argued that even for a linear system of ODEs with constant coefficients, stiffness cannot properly be characterized in terms of the eigenvalues of the Jacobian, because stiffness is a transient phenomenon whereas the significance of eigenvalues is asymptotic. Recent theory from the numerical solution of PDEs is adapted to show that a more appropriate characterization can be based upon pseudospectra instead of spectra. Numerical experiments with an adaptive ODE solver illustrate these findings.Supported by a Dundee University Research Initiatives Grant.Supported by NSF Grant DMS-9116110.     

Applications of Mössbauer Spectroscopy in Industry

Hyperfine Interactions - The demand by industrial researchers to characterize commercial materials with high precision has seen the growth of many spectroscopic techniques in the broad area of...     

A new approach for the formation of fused cyclooctane or cyclohexane rings

The intramolecular regioselective addition of unsymmetrical allylsilanes to conjugated dienones is shown to permit facile entry into 5-6, 6-6, 5-8, and 6-8 bicyclic ring systems.     

The structured sensitivity of Vandermonde-like systems

Summary We consider a general class of structured matrices that includes (possibly confluent) Vandermonde and Vandermonde-like matrices. Here the entries in the matrix depend nonlinearly upon a vector of parameters. We define, condition numbers that measure the componentwise sensitivity of the associated primal and dual solutions to small componentwise perturbations in the parameters and in the right-hand side. Convenient expressions are derived for the infinity norm based condition numbers, and order-of-magnitude estimates are given for condition numbers defined in terms of a general vector norm. We then discuss the computation of the corresponding backward errors. After linearising the constraints, we derive an exact expression for the infinity norm dual backward error and show that the corresponding primal backward error is given by the minimum infinity-norm solution of an underdetermined linear system. Exact componentwise condition numbers are also derived for matrix inversion and the least squares problem, and the linearised least squares backward error is characterised.     

An efficient chemoenzymatic approach to (S)-gamma-fluoroleucine ethyl ester

[reaction: see text] An asymmetric synthesis of (S)-gamma-fluoroleucine ethyl ester 1 is described. The key transformation involves a lipase-catalyzed dynamic ring-opening of 2-(3-butenyl)azlactone 7b with EtOH to give amide ester (S)-6b in 84% enantiomeric excess. Removal of the N-pentenoyl group with N,N'-dibromodimethylhydantoin in the presence of trifluoroacetic acid afforded the titled compound, which was isolated as its hydrogen sulfate salt in 75% yield and >97% ee.     

Oligomeric proanthocyanidins: naturally occurring O-heterocycles

This review covers the flavan-3-ols (catechins), flavan-4-ols/flavan-3,4-diols (leucoanthocyanidins), A-type proanthocyanidins, B-type proanthocyanidins including the procyanidins, prodelphinidins, propelargonidins, proteracacinidins, promelacacinidins, procassinidins, probutinidins, and non-proanthocyanidins with flavan-3-ol constituent units. Newly isolated proanthocyanidins, structure elucidation, syntheses, HPLC/MS analysis, NMR/ conformational analysis, and the effects of proanthocyanidins on human nutrition and health are reported. The literature from January 1999 to December 2001 is reviewed, and 130 references are cited.     

Asymmetry through time dependency

Given a single network of interactions, asymmetry arises when the links aredirected. For example, if protein A upregulates protein B and protein Bupregulates protein C, then (in the absence of any further relationships between them) Amay affect C but not vice versa. This type of imbalance is reflected in the associatedadjacency matrix, which will lack symmetry. A different type of imbalance can arise wheninteractions appear and disappear over time. If A meets B today and B meets C tomorrow,then (in the absence of any further relationships between them) A may pass a message ordisease to C, but not vice versa. Hence, even when each interaction is a two-way exchange,the effect of time ordering can introduce asymmetry. This observation is very closelyrelated to the fact that matrix multiplication is not commutative. In this work, wedescribe a method that has been designed to reveal asymmetry in static networks and showhow it may be combined with a measure that summarizes the potential information flowbetween nodes in the temporal case. This results in a new method that quantifies theasymmetry arising through time ordering. We show by example that the new tool can be usedto visualize and quantify the amount of asymmetry caused by the arrow of time.     

Synthesis and photophysical properties of lead phthalocyanines

This work reports on the synthesis and photophysical parameters of tetra-and octa-substituted new lead phthalocyanines. The complexes synthesized are: 1,4-(tetraphenoxyphthalocyaninato)lead (7a), 1,4-(tetra-tert-butylphenoxyphthalocyaninato)lead (7b), 2,3-(tetraphenoxyphthalocyaninato)lead (8a), 2,3-(tetra-tert-butylphenoxyphthalocyaninato)lead (8b), 2,3-octaphenoxyphthalocyaninatolead (9a) 2,3-[octakis(4-t-butylphenoxyphthalocyaninato)]lead (9b). Photophysical properties were studied for these complexes in a dimethylsulfoxide, dimethylformamide, toluene, tetrahydrofuran and chloroform. The fluorescence spectra were different from excitation spectra due to demetallation upon excitation. High triplet quantum yields ranging from 0.70 to 0.88 (in DMSO, DMF and toluene) and low triplet lifetimes (20–50 μs in DMSO, and <10 μs in the rest of the solvents) were observed due to the presence of heavy atom.     

Synthesis of a tertiary carbinamide via a novel Rh-catalyzed asymmetric hydrogenation

Asymmetric hydrogenation of allylic dimethylcarbinamide 2 with 1 mol % of cationic Rh(I)-Josiphos complex in THF under 500 psi of H2 generated the corresponding tertiary carbinamide 1 in 98.5% assay yield and a 94:6 enantiomeric ratio. Upon crystallization, the product was isolated in 91% isolated yield and 95:5 enantiomeric ratio.     

Synthetic approaches for noncentrosymmetric molybdates

The use of second-order Jahn-Teller active Mo (VI) centers and chiral organic amines is discussed as an approach to crystallographic noncentrosymmetry. Several series of reactions, conducted under mild hydrothermal conditions, were designed to probe important reaction variables. Correlations between reagent and solvent concentrations and the molybdate structure were investigated using composition space analysis, which allows for the isolation of specific reaction variables. The effects of amine structure variation were probed using multiple series of related amines, which consisted of either linear diamines or ethylenediamine derivatives. The addition of fluoride results in the loss of amine-based structural variations. Chiral organic amines were used to demonstrate the viability of using such components to control the three-dimensional symmetry in new materials. The synthesis, structure, and characterization of eight new organically templated polyoxomolybdates and polyoxofluoromolybdates are reported.