In this note, a new proof for the positivity of Dunkl’s intertwining operator in the crystallographic case is given. It is based on an asymptotic relationship between the Opdam-Cherednik kernel and the Dunkl kernel as recently observed by M. de Jeu, and on positivity results of S. Sahi for the Heckman-Opdam polynomials and their nonsymmetric counterparts. 2000 AMS Subject Classification: 33C52,...

Heckman-Opdam system of differential equations is holonomic , with regular singularities and has locally |W |-dimensional space of solutions ( cf. corollary 3.9 of [12]), where |W | is the cardinality of the Weyl group W . The system is a generalization of radial parts of Laplace-Casimir operators on symmetric Riemannian spaces of nonpositive curvature and is isomorphic to Calogero-Sutherland m...

Although there are a variety of studies on the gender pay gap, only a few relate to managerial positions. The present study attempts to fill this gap. Managers in private companies in Germany are a highly selective group of women and men, who differ only marginally in their human capital endowments. The Oaxaca/Blinder decomposition shows that the gender pay gap in the gross monthly salary can h...

BACKGROUND Hypertension, diabetes and hypercholesterolemia are the most frequent and diagnosed chronic diseases in Argentina. They contribute largely to the burden of chronic disease and they are strongly influenced by a small number of risk factors. These risk factors are all modifiable at the population and individual level and offer major prospects for their prevention. We are interested in ...

Although there are a variety of studies on the gender pay gap, only a few relate to managerial positions. The present study attempts to fill this gap. Managers in private companies in Germany are a highly selective group of women and men, who differ only marginally in their human capital endowments. The Oaxaca/Blinder decomposition shows that the gender pay gap in the gross monthly salary can h...

After EU enlargement in 2004, thousands of Polish workers moved to the UK. This study evaluates market efficiency in sorting Polish-born workers to locations where they enjoyed the highest returns to their individual skills, exploring Polish and UK labour force survey data to establish whether the Poles that emigrated to the UK did so on rational premises. The expected gains from migration refl...

Heckman and Thomas conjectured that the fractional chromatic number of any triangle-free subcubic graph is at most 14/5. Improving on estimates of Hatami and Zhu and of Lu and Peng, we prove that the fractional chromatic number of any triangle-free subcubic graph is at most 32/11 ≈ 2.909.

We prove a Duistermaat-Heckman type formula in a suitable non-compact setting. We use this formula to evaluate explicitly the pushforward of the Liouville measure via the moment map of both an abelian and a non-abelian group action. As an application we obtain the classical analogues of well-known multiplicity formulas for the holomorphic discrete series representations.

We prove that every subcubic triangle-free graph has fractional chromatic number at most 14/5, thus confirming a conjecture of Heckman and Thomas [A new proof of the independence ratio of triangle-free cubic graphs. Discrete Math. 233 (2001), 233–237].