Boron carboxylate catalysis of homoallylboration.

Boron tris(trifluoroacetate) is identified as the first effective catalyst for the homoallyl- and homocrotylboration of aldehydes by cyclopropylcarbinylboronates. NMR spectroscopic studies and theoretical calculations of key intermediates and transition states both suggest that a ligand-exchange mechanism, akin to our previously reported PhBCl2-promoted homoallylations, is operative. Our experimental and theoretical results also suggest that the catalytic activity of boron tris(trifluoroacetate) might originate from more facile catalytic turnover of the trifluoroacetate ligands (in agreement with DFT calculations) or from a lower propensity for formation of off-pathway reservoir intermediates (as observed by (1)H NMR). This work shows that carboxylates are viable catalytic ligands for homoallyl- and homocrotylations of carbonyl compounds and opens the door to the development of catalytic asymmetric versions of this transformation

An "almost" full embedding of the category of graphs into the category of groups

We construct a functor from the category of graphs to the category of groups which is faithful and "almost" full, in the sense that it induces bijections of the Hom sets up to trivial homomorphisms and conjugation in the category of groups. We provide several applications of this construction to localizations (i.e. idempotent functors) in the category of groups and the homotopy category.Comment: 24 pages; to appear in Adv. Math

Asynchronous Course Delivery: Instructor and Student Views

Accompanying the projected growth in computers, bandwidth improvements will make Internet use a more satisfying experience, leading to increased usage. It follows that faculty in higher education will explore strategies that increase student achievement and satisfaction in asynchronous teaching and learning. Use of the Internet for course and program delivery will increase. The potential of the Web as both a set of tools and a medium for course delivery offers limitless possibilities for creating innovative course design that can be more effective than some classroom experiences (Hafner & Oblinger, 1998). There is evidence that building an online community begins with establishing good online program administration. Central to this is the infrastructure to support online delivery coupled with the faculty who create, deliver, and manage the courses. The debate continues among educators as to the effectiveness of asynchronous teaching and learning in higher education. Some argue it provides a new context for teaching and learning, chiefly because it removes the constraints of time and physical presence

Nontrivial temporal scaling in a Galilean stick-slip dynamics

We examine the stick-slip fluctuating response of a rough massive non-rotating cylinder moving on a rough inclined groove which is submitted to weak external perturbations and which is maintained well below the angle of repose. The experiments presented here, which are reminiscent of the Galileo's works with rolling objects on inclines, have brought in the last years important new insights into the friction between surfaces in relative motion and are of relevance for earthquakes, differing from classical block-spring models by the mechanism of energy input in the system. Robust nontrivial temporal scaling laws appearing in the dynamics of this system are reported, and it is shown that the time-support where dissipation occurs approaches a statistical fractal set with a fixed value of dimension. The distribution of periods of inactivity in the intermittent motion of the cylinder is also studied and found to be closely related to the lacunarity of a random version of the classic triadic Cantor set on the line.Comment: 7 pages including 6 figure

Tilting mutation of weakly symmetric algebras and stable equivalence

We consider tilting mutations of a weakly symmetric algebra at a subset of simple modules, as recently introduced by T. Aihara. These mutations are defined as the endomorphism rings of certain tilting complexes of length 1. Starting from a weakly symmetric algebra A, presented by a quiver with relations, we give a detailed description of the quiver and relations of the algebra obtained by mutating at a single loopless vertex of the quiver of A. In this form the mutation procedure appears similar to, although significantly more complicated than, the mutation procedure of Derksen, Weyman and Zelevinsky for quivers with potentials. By definition, weakly symmetric algebras connected by a sequence of tilting mutations are derived equivalent, and hence stably equivalent. The second aim of this article is to study these stable equivalences via a result of Okuyama describing the images of the simple modules. As an application we answer a question of Asashiba on the derived Picard groups of a class of self-injective algebras of finite representation type. We conclude by introducing a mutation procedure for maximal systems of orthogonal bricks in a triangulated category, which is motivated by the effect that a tilting mutation has on the set of simple modules in the stable category.Comment: Description and proof of mutated algebra made more rigorous (Prop. 3.1 and 4.2). Okuyama's Lemma incorporated: Theorem 4.1 is now Corollary 5.1, and proof is omitted. To appear in Algebras and Representation Theor