A series of previously unavailable derivatives of 2-alkyl- and 2-benzylderivatives of oxazolo[3,2-a]pyridines III were obtained via tandem ring opening and ring closure from stable mesoionic 3-acyloxazolo[3,2-a]pyridinium-2-olates I. The key intermediates of this tandem transformation are N-(b-oxoethyl)pyridones-2 II obtained by Dakin-West acylation of (pyridone-2-yl-1)acetic acid. An example o...

The title compound, C(12)H(9)ClN(4), was prepared from dichloro-pyridazine and tolyl-tetra-zole in a nucleophilic biaryl coupling followed by thermal ring transformation. The mol-ecule is essentially planar (r.m.s. deviation for all non-H atoms = 0.036 Å) and an intra-molecular C-H⋯N hydrogen bond occurs. In the crystal, the mol-ecules form dimers connected via π-π inter-actions [centroid-centr...

In this paper we consider the K-theory of smooth algebraic stacks, establish λ and Adams operations and show that the higher K-theory of such stacks is always a pre-λ-ring and is a λ-ring if every coherent sheaf is the quotient of a vector bundle. As a consequence we are able to define Adams operations and absolute cohomology for smooth algebraic stacks satisfying this hypothesis. We also defin...

A [4 + 4] annulation strategy for the synthesis of eight-membered carbocycles is reported that proceeds via a cascade involving two pericyclic processes. In the first step, the [4 + 2] cycloaddition of a conjugated enyne with an electron-deficient cyclobutene generates a strained six-membered cyclic allene that isomerizes to the corresponding 1,3-cyclohexadiene. In the second step, this bicyclo...

of A' over k. Since P and A' are centers of v, A' belongs to the set TIPI . Since P' is an isolated point of TIP), we must have dim A'7k = dim P'/k. From this it follows that A' and P' are isomorphic points over k (since P' is a specialization of A' over k) and that consequently the local rings of A' and P' coincide. Since o c o', the local field k(A') contains the local field k(P) of P, and he...

A kinetic equation for the joint probability distribution for fixed values of the classical action, momentum and density has been derived. Further the hydrodynamic equations of continuity and balance of momentum density have been transformed into a Schroedinger-like equation, describing particle motion in an effective electro-magnetic field and an expression for the gauge potentials has been ob...

Propargylic sulfides and dithioacetals are found to undergo similar transformations as propargylic carboxylates when catalyzed by AuCl or AuCl3, affording indene derivatives through pentannulation of aromatic rings. The reaction presumably involves Au carbene as the reactive intermediate.

The design of highly flexible framework materials requires organic linkers, whereas inorganic materials are more robust but inflexible. Here, by using linkable inorganic rings made up of tungsten oxide (P8W48O184) building blocks, we synthesized an inorganic single crystal material that can undergo at least eight different crystal-to-crystal transformations, with gigantic crystal volume contrac...

Using Fourier–Mukai transformations, we prove some results about the ring of unipotent vector bundles on elliptic curves in positive characteristics. This ring was determined by Atiyah in characteristic zero, who showed that it is a polynomial ring in one variable. It turns out that the situation in characteristic p > 0 is completely different and rather bizarre: the ring is nonnoetherian and c...

We define Hilbert-Siegel modular forms and Hecke “operators” acting on them. As with Hilbert modular forms (i.e. with Siegel degree 1), these linear transformations are not linear operators until we consider a direct product of spaces of modular forms (with varying groups), modulo natural identifications we can make between certain spaces. With Hilbert-Siegel forms (i.e. with arbitrary Siegel d...