Dinuclear ruthenium complex, with a bridging carbide and a hydride ligand, and methyltricyclohexylphosphonium chloride result from thermal decomposition of olefin metathesis catalyst, (IMesH2)(PCy3)(Cl)2Ru=CH2. Involvement of dissociated phosphine in the decomposition is proposed. The dinuclear complex has catalytic olefin isomerization activity, which can be responsible for competing isomeriza...

More than two decades elapsed since Levin set forth a theory of average-case complexity. In this survey we present the basic aspects of this theory as well as some of the main results regarding it. The current presentation deviates from our old “Notes on Levin’s Theory of Average-Case Complexity” (ECCC, TR97-058, 1997) in several aspects.

We show how the Riemann surface Σ of N = 2 Yang-Mills field theory arises in type II string compactifications on Calabi-Yau threefolds. The relevant local geometry is given by fibrations of ALE spaces. The 3-branes that give rise to BPS multiplets in the string descend to self-dual strings on the Riemann surface, with tension determined by a canonically fixed Seiberg-Witten differential λ. The ...

Flourescent iron line profiles currently provide the best diagnostic for active galactic nuclei (AGN) engine geometries. Here we construct a method for calculating the relativistic iron line profile from an arbitrarily warped accretion disc, illuminated from above and below by hard X-ray sources. This substantially generalises previous calculations of reprocessing by accretion discs by includin...

LetM = (M,OM) be a smooth supermanifold with connection ∇ and Batchelor model OM ∼= ΓΛE∗ . From (M,∇) we construct a connection on the total space of the vector bundle E →M . This reduction of∇ is well-defined independently of the isomorphism OM ∼= ΓΛE∗ . It erases information, but however it turns out that the natural identification of supercurves inM (as maps from R1|1 toM) with curves in E r...

It is well known that the geodesic, i.e., the shortest curve, connecting two prescribed points in the Euclidean plane is the line segment connecting them. But the geodesic, especially the closed geodesic, problem on the earth is very difficult. In fact, the closed geodesic problem is a very important subject in both dynamical systems and differential geometry, and has stimulated many creative i...

We present an algorithm for determining the shortest path between a source and a destination on an arbitrary (possibly nonconvex) polyhedral surface. The path is constrained to lie on the surface, and distances are measured according to the Euclidean metric. Our algorithm runs in time O(n log n) and requires O(n2) space, where n is the number of edges of the surface. After we run our algorithm,...