Observable actions of algebraic groups

Let G be an affine algebraic group and let X be an affine algebraic variety. An action G × X → X is called observable if for any G-invariant, proper, closed subset Y of X there is a nonzero invariant f ∈ \Bbbk\Bbbk [X] ^G such that f| _Y = 0. We characterize this condition geometrically as follows. The action G × X → X is observable if and only if:

Hochschild cohomology and stratifying ideals

Suppose B is an algebra with a stratifying ideal BeB generated by an idempotent e. We will establish long exact sequences relating the Hochschild cohomology groups of the three algebras B, B/BeB and eBe. This provides a common generalization of various known results, all of which extend Happel’s long exact sequence for one-point extensions. Applying one of these sequences to Hochschild cohomology algebras modulo the ideal generated by homogeneous nilpotent elements shows, in some cases, that these algebras are finitely generated.     

Wild algebras have one-point extensions of representation dimension at least four

We show that any wild algebra has a one-point extension of representation dimension at least four, and more generally that it has an n-point extension of representation dimension at least n+3. We give two explicit constructions, and obtain new examples of small algebras of representation dimension four.     

Symplectic Dirac operators on Hermitian symmetric spaces

We describe the shape of the symplectic Dirac operators on Hermitian symmetric spaces. For this, we consider these operators as families of operators that can be handled more easily than the original ones.     

Existence, uniqueness and graph representation of weighted minimal hypersurfaces

By means of a weight matrix, we introduce the class of weighted minimal hypersurfaces which yield a natural generalisation of minimal surfaces. Generalising a classical result of Radó, we prove existence, uniqueness and graph representation for weighted minimal hypersurfaces in \mathbbRⁿ⁺¹{\mathbb{R}^{n+1}} with prescribed boundary manifold.     

Conversational Implicatures and Cancellability

In this paper I argue against a criticism by Matthew Weiner to Grice’s thesis that cancellability is a necessary condition for conversational implicature. I argue that the purported counterexamples fail because the supposed failed cancellation in the cases Weiner presents is not meant as a cancellation but as a reinforcement of the implicature. I moreover point out that there are special situations in which the supposed cancellation may really work as a cancellation.

Novel synthesis of CP-734432, an EP4 agonist, using Sharpless asymmetric dihydroxylation

A novel and efficient asymmetric route to CP-734432, a lactam analog of PGE2, that shows selective agonism against the EP4 receptor subtype, is reported herein. The key steps include a Heck coupling to introduce the aryl ring at C-16 and a highly diastereoselective Sharpless asymmetric dihydroxylation to set the C-15 center.     

Composite dipolar recoupling: anisotropy compensated coherence transfer in solid-state nuclear magnetic resonance

The efficiency of dipole-dipole coupling driven coherence transfer experiments in solid-state nuclear magnetic resonance (NMR) spectroscopy of powder samples is limited by dispersion of the orientation of the internuclear vectors relative to the external magnetic field. Here we introduce general design principles and resulting pulse sequences that approach full polarization transfer efficiency for all crystallite orientations in a powder in magic-angle-spinning experiments. The methods compensate for the defocusing of coherence due to orientation dependent dipolar coupling interactions and inhomogeneous radio-frequency fields. The compensation scheme is very simple to implement as a scaffold (comb) of compensating pulses in which the pulse sequence to be improved may be inserted. The degree of compensation can be adjusted and should be balanced as a compromise between efficiency and length of the overall pulse sequence. We show by numerical and experimental data that the presented compensation protocol significantly improves the efficiency of known dipolar recoupling solid-state NMR experiments.