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).     

Discovery of enzyme inhibitors through combinatorial chemistry

Summary This review serves to highlight the recent examples of combinatoric methodology as applied to the discovery and optimization of enzyme inhibitors. Early research efforts focused on the identification of polypeptides from libraries as inhibitors of proteases. As solution- and solid-phase chemistries gain in sophistication, libraries containing less peptidic structural motifs have been created. A recurring design stratagem relies on the synthesis of libraries incorporating pharmacophores with known affinity for the target enzyme. Screening of these structure-based libraries has led to the discovery of small-molecule inhibitors of both proteolytic and non-proteolytic enzymes alike. Two tables are provided listing the enzyme targeted libraries through 1996. A name, generic structure and size is given for each library citation, accompanied by the enzyme screen and the structure and potency of the most active library member.     

Trees, set compositions and the twisted descent algebra

We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the linear span of set compositions (the twisted descent algebra). Among others, a number of enveloping algebra structures are introduced and studied in detail. For example, it is shown that the linear span of trees carries an enveloping algebra structure and embeds as such in an enveloping algebra of increasing trees. All our constructions arise naturally from the general theory of twisted Hopf algebras.