Intramolecular 2+2 addition of a difluorovinyl ether aldehyde yields [3.2.0] And no [3.1.1] products

Irradiation of the difluorovinyl ether aldehyde 6 yields the tricyclic products 7 and 8 and the bicyclic dioxepene 9. There was no evidence for the formation of the isomeric [3.1.1] structure 1 containing the ring system of thromboxane A₂.     

The interior BMO – regularity for a weak solution of nonlinear second order elliptic systems

The interior BMO - regularity for a weak solution of nonlinear second order elliptic systems is investigated.     

On a variational problem for an elastic membrane supporting a heavy ball

An elastic membrane or a soap film is investigated that is bounded by a planar curve and supports a heavy ball. The ball is allowed to move on the surface, and its position, together with the shape of the membrane will furnish a minimum to the potenial energy. This leads to an obstacle problem for Dirichlet's integral or the area functional where only the shape of the obstacle but not its position in space is given.     

Higher order valued reduction theorems for classical connections

We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection. This paper has been supported by the Grant Agency of the Czech Republic under the Project number GA 201/02/0225.     

Short universal generators via generalized ratio-of-uniforms method

We use inequalities to design short universal algorithms that can be used to generate random variates from large classes of univariate continuous or discrete distributions (including all log-concave distributions). The expected time is uniformly bounded over all these distributions for a particular generator. The algorithms can be implemented in a few lines of high level language code.