Directed Sets and Malitz-Cauchy-Completions

This is a study of the set of the Malitz-completions (which are a special case of Cauchy-completions) of a given infinite first-order structure, put in relation with properties of directed sets.     

Solid-Phase Total Synthesis of Cyclosporine Analogues

Syntheses of cyclosporine analogues are reported wherein the peptide couplings were achieved in solid phase. The Wang resin was used as the solid support, and the peptide couplings commenced with the residue 11 of the cyclosporine skeleton. The couplings proceeded in a stepwide manner up to the residue MeBmt¹, using symmetric anhydrides. The peptides were then cleaved off the resin, and the cyclization was achieved in solution using Castro's reagent. The solid-phase synthesis described herein offers a very efficient method for the rapid synthesis of structurally diverse cyclosporine analogues in small quantities. The biological activities of the synthetic cyclosporine analogues were evaluated in two in vitro assays, including the IL-2 reporter gene assay and the cyclophilin binding assay. The structure-activity relationship is discussed.     

Infinite measure preserving transformations with compact first regeneration

We study ergodic infinite measure preserving transformations T possessing reference sets of finite measure for which the set of densities of the conditional distributions given a first return (or entrance) at time n is precompact in a suitable function space. Assuming regular variation of wandering rates, we establish versions of the Darling-Kac theorem and the arcsine laws for waiting times and for occupation times which apply to transformations with indifferent orbits and to random walks driven by Gibbs-Markov maps. This research was supported by an APART [Austrian programme for advanced research and technology] fellowship of the Austrian Academy of Sciences. Much of this work was done at the Mathematics Department of Imperial College London. I also benefitted from a JRF at the ESI in Vienna.     

Lie Representations and an Algebra Containing Solomon's

We introduce and study a Hopf algebra containing the descent algebra as a sub-Hopf-algebra. It has the main algebraic properties of the descent algebra, and more: it is a sub-Hopf-algebra of the direct sum of the symmetric group algebras; it is closed under the corresponding inner product; it is cocommutative, so it is an enveloping algebra; it contains all Lie idempotents of the symmetric group algebras. Moreover, its primitive elements are exactly the Lie elements which lie in the symmetric group algebras.     

An efficient synthesis of 1,6- and 1,7-dibromo-3-aminoisoquinolines: versatile templates for the preparation of functionalized isoquinolines

An efficient synthetic route to 1,6- and 1,7-dibromo-3-aminoisoquinoline was devised. These intermediates served as ideal templates for the preparation of 3-aminoisoquinoline analogues functionalized at C(6) or C(7).