Schwartz functions on Nash manifolds

In this paper we extend the notions of Schwartz functions, tempered functions and generalized Schwartz functions to Nash (i.e. smooth semi-algebraic) manifolds. We reprove for this case classically known properties of Schwartz functions on $R^n$ and build some additional tools which are important in representation theory.Comment: 35 pages, LaTex. v3:minor changes + reference to results of duClou

Non-orthogonal geometric realizations of Coxeter groups

We define in an axiomatic fashion a \emph{Coxeter datum} for an arbitrary Coxeter group $W$. This Coxeter datum will specify a pair of reflection representations of $W$ in two vector spaces linked only by a bilinear paring without any integrality and non-degeneracy requirements. These representations are not required to be embeddings of $W$ in the orthogonal group of any vector space, and they give rise to a pair of inter-related root systems generalizing the classical root systems of Coxeter groups. We obtain comparison results between these non-orthogonal root systems and the classical root systems. Further, we study the equivalent of the Tits cone in these non-orthogonal representations, and we show that strong results on the geometry in the equivalent of the Tits cone can be obtained

Morse matchings on polytopes

We show how to construct homology bases for certain CW complexes in terms of discrete Morse theory and cellular homology. We apply this technique to study certain subcomplexes of the half cube polytope studied in previous works. This involves constructing explicit complete acyclic Morse matchings on the face lattice of the half cube; this procedure may be of independent interest for other highly symmetric polytopes

Whittaker unitary dual of affine graded Hecke algebras of type E

This paper gives the classification of the Whittaker unitary dual for affine graded Hecke algebras of type E. By the Iwahori-Matsumoto involution, this is equivalent also to the classification of the spherical unitary dual for type E. This work completes the classification of the Whittaker Iwahori-spherical unitary dual, or equivalently, the spherical unitary dual, of split linear algebraic p-adic groups.Comment: 48 page

Branching integrals and Casselman phenomenon

Let $G$ be a real semisimple Lie group, $K$ its maximal complex subgroup, and $G_C$ its complexification. It is known that all the $K$-finite matrix elements on $G$ admit holomorphic continuation to branching functions on $G_C$ having singularities at the a prescribed divisor. We propose a geometric explanation of this phenomenon. The note also contsins a general survey of holomorphic continuations of infinite-dimensional representations.Comment: 13pp, an addendum is adde

The 2003 Quebec Declaration of Concern About Eel Declines-11 Years Later: Are Eels Climbing Back up the Slippery Slope?

In 2003, scientists gathered at the American Fisheries Society meeting in Québec and raised an urgent alarm in a Declaration of Concern about the state of eel stocks around the world, with less than 1% of juvenile resources remaining (as documented for northern temperate stocks). In the years since, precautionary protective measures have been implemented, monitoring and research have increased, and sustainable management methods have been developed. Recently, several juvenile resources have increased slightly. Reassembled in Québec in 2014, we reflect on what has been achieved since 2003 and what remains to be done

Ethnopharmacology – From Mexican Hallucinogens to a Global Transdisciplinary Science

Psychoactive natural substances have been reported from practically all regions of the world, but Mexican indigenous cultures have played a crucial role having influenced medical, toxicological, biological, chemical, pharmaceutical, and, of course, anthropological research. Especially in the 1950’s and 1960’s peyotl, teonanacatl and other psychoactives came to the attention of researchers and revelers alike. In this overview we highlight the developments of ethnopharmacology from the initial development of the term until today using one psychoactive species as an example - Salvia divinorum. In 1962 “ethnopharmacologists”, Albert Hofmann and R. Gordon Wasson, documented and collected a flowering specimen of Ska María Pastora allowing the species botanical description as Salvia divinorum Epling & Játiva. Five years later Efron et al. (1967) organised a symposium “Ethnopharmacologic search for psychoactive drugs” which over the next decades would give its name to a discipline which today is much more broadly defined, dealing with local and traditional medicines, their biological activities and chemistry. Globalisation has resulted in a world-wide commodification of many traditional medicines and psychoactives, as exemplified by S. divinorum. This fascinating Lamiaceae has become globally recognized for its best known active constituent salvinorin A, a kappa-opioid antagonist which has a unique effect on human physiology. While today ethnopharmacology is a thriving discipline, the interest in psychoactive substances is no longer central to the discipline. The search for anti-cancer agents (which also started in earnest in the 1960’s) had been of particular relevance and today includes among its many foci: • The scientific study of local and traditional knowledge not only in remote regions, but for example, also in urban immigrant communities • Research linking ethnopharmacology to biodiversity research both in terms of a sustainable use of natural resources (ecosystems) • Pharmacological studies with the aim of understanding the effects of complex mixtures on specific diseases or disease targets • The safety of herbal medicines • Anthropological and historical approaches on the use of medicinal and food plants and the link between food and medical uses of plants and fungi. / 50 years on ethnopharmacology is very different from what D. Efron and colleagues had envisioned

Omega time transmissions and receiving requirements

A short history is given of the development of dual VLF time transmission techniques. The theory of time recovery from the relative phase of the dual frequency transmission is presented. The transmission and receiving requirements for cycle identification and cycle ambiguity resolution are described. Finally, an experiment to test the capability of time transmission of the OMEGA system is propose