Generalized Flows and Singular ODEs on Differentiable Manifolds

Based on the concept of manifold-valued generalized functions, we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right-hand sides in a global setting. After establishing several existence and uniqueness results for solutions of such equations and flows of singular vector fields, we compare the solution concept employed here with the purely distributional setting. Finally, we derive criteria securing that a sequence of smooth flows corresponding to the regularization of a given singular vector field converges to a measurable limiting flow.     

Tetrakis(imidazolium) macrocyclic receptors for anion binding

New (tetrakis)imidazolium macrocyclic receptor systems of variable cavity size have been synthesised by stepwise alkylation reactions of bis(imidazolium) precursor compounds. Proton NMR titration studies reveal the macrocycles to strongly bind halide and benzoate anions, with two receptor systems displaying notable selectivity for fluoride in competitive acetonitrile-water (9:1) solvent media.     

Dynamic Models of Simple Judgments: II. Properties of a Self-Organizing PAGAN (Parallel, Adaptive, Generalized Accumulator Network) Model for Multi-Choice Tasks

This is the second of two papers comparing connectionist and traditional stochastic latency mechanisms with respect to their ability to account for simple judgments. In the first, we reviewed evidence for a self-regulating accumulator module for two- and three-category discrimination. In this paper, we examine established neural network models that have been applied to predicting response time measures, and discuss their representational and adaptational limitations. We go on to describe and evaluate the network implementation of a Parallel Adaptive Generalized Accumulator Network (PAGAN), based on the interconnection of a number of self-regulating, generalized accumulator modules. The enhancement of PAGAN through the incorporation of distributed connectionist representation is briefly discussed.     

Asymmetric synthesis of substituted 1-aminocyclopropane-1-carboxylic acids via diketopiperazine methodology

Diketopiperazinespirocyclopropane 12 is prepared in > 98% d.e. via the conjugate addition of a phosphorus ylide to (6S)-N,N'-bis(p-methoxybenzyl)-3-methylenepiperazine-2,5-dione 2. Deprotection and hydrolysis of adduct 12 and subsequent peptide coupling demonstrate the applicability of this methodology to the asymmetric synthesis of 1-aminocyclopropane-1-carboxylic acids for incorporation into novel peptides. A model for the high level of diastereofacial selectivity observed in the cyclopropanation reaction is presented. A highly selective asymmetric approach (> 98% d.e.) to (S)-[2,2-(2)H2]-1-aminocyclopropane-1-carboxylic acid 29 is also reported via a deuterated sulfur ylide addition to acceptor 2.     

On successors of Jónsson cardinals

We show that, like singular cardinals, and weakly compact cardinals, Jensen's core model K for measures of order zero [4] calculates correctly the successors of Jónsson cardinals, assuming does not exist. Namely, if is a Jónsson cardinal then , provided that there is no non-trivial elementary embedding . There are a number of related results in ZFC concerning in V and inner models, for a Jónsson or singular cardinal. Received: 8 December 1998