Novel oxy-perfluoroalkylation

(Perfluoroalkyl)phenyliodonium sulfonates underwent novel oxy-perfluoroalkylation with alkenes under oxygen atmosphere in the presence of a base.     

Palladium-catalyzed allylic oxidation of olefins by t-butyl hydroperoxide and tellurium(IV) oxide

Treatment of several cyclic olefins, β-pinene, allylbenzene, and estragole with palladium(II) salt in acetic acid in the presence of t-butyl hydroperoxide and tellurium(IV) oxide afforded mainly the corresponding allylic acetates. The reaction proceeded catalytically with palladium(II) salt, t-BuOOH working as a reoxidizing agent.     

A general extension theorem for cohomology classes on non reduced analytic subspaces

The main purpose of this paper is to generalize the celebrated L~2 extension theorem of Ohsawa and Takegoshi in several directions: The holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety from which the extension is performed may be non reduced, the ambient manifold is K¨ahler and holomorphically convex, but not necessarily compact.     

A Nadel vanishing theorem via injectivity theorems

The purpose of this paper is to establish Nadel type vanishing theorems with multiplier ideal sheaves of singular metrics admitting an analytic Zariski decomposition (such as, metrics with minimal singularities and Siu’s metrics). For this purpose, we generalize Kollár’s injectivity theorem to an injectivity theorem for line bundles equipped with singular metrics, by making use of the theory of harmonic integrals. Moreover we give asymptotic cohomology vanishing theorems for high tensor powers of line bundles.     

Adjoint-based exact Hessian computation

BIT Numerical Mathematics - We consider a scalar function depending on a numerical solution of an initial value problem, and its second-derivative (Hessian) matrix for the initial value. The need...     

Harmonicity of totally geodesic maps into nonpositively curved metric spaces

We prove the harmonicity of totally geodesic maps from a Riemannian manifold to a nonpositively curved metric space in the sense of Alexandrov for both Korevaar-Schoen-type and Cheeger-type energies. This enables us to make many examples of harmonic maps of an unknown type. We also construct an example of totally geodesic map between CAT(0)-spaces which is not harmonic.Mathematics Subject Classification (2000): 53C22, 53C43, 58E20     

Eigenvalue asymptotics for the Schrödinger operators on the hyperbolic plane

In this paper we consider the Schrödinger operator on the hyperbolic plane , where is the hyperbolic Laplacian and V is a scalar potential on . It is proven that, under an appropriate condition on V at ‘infinity’, the number of eigenvalues of H_V less than λ is asymptotically equal to the canonical volume of the quasi-classically allowed region as λ→∞. Our proof is based on the probabilistic methods and the standard Tauberian argument as in the proof of Theorem 10.5 in Simon (Functional Integration and Quantum Physics, Academic Press, New York, 1979).