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...

We find a complete set of supertraces on the algebras H W (R) (ν), the algebra of observables of the rational Calogero model with harmonic interaction based on the classical root systems R of B N , C N and D N types. These results extend the results known for the case A N −1. It is shown that H W (R) (ν) admits q(R) independent supertraces where q(B N) = q(C N) is a number of partitions of N in...

We study properties of coefficients of a linear form, originating from a multiple integral. As a corollary, we prove Vasilyev's conjecture, connected with the problem of irrationality of the Riemann zeta function at odd integers.

In 1957, H. Hadwiger conjectured that a convex body K in a Euclidean d-space, d 1, can always be covered by 2 smaller homothetic copies of K. We verify this conjecture when K is the polar of a cyclic d-polytope. Mathematics Subject Classifications (1991): 52A15, 52A20.

We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero–Sutherland models. A nontrivial modification of the exchange operator formalism is used to obtain several infinite families of eigenfunctions of these models in closed form.

We prove an equivariant version of the fact that word-hyperbolic groups have finite asymptotic dimension. This is important in connection with our forthcoming proof of the Farrell-Jones conjecture for K∗(RG) for every word-hyperbolic group G and every coefficient ring R.

A robust method for the reconstruction of 3D object shape is described based on the inverse perspective method [1,2], which uses a single camera mounted on a commercial manipulator arm for accurate 3D positioning and orientation of the sensor head in 3D space. Preliminary measurements are presented and the reconstruction theory used by the technique.

It is known that Szpiro’s conjecture, or equivalently the ABC-conjecture, implies Lang’s conjecture giving a uniform lower bound for the canonical height of nontorsion points on elliptic curves. In this note we show that a significantly weaker version of Szpiro’s conjecture, which we call “prime-depleted,” suffices to prove Lang’s conjecture.

In this paper we show that under some fairly general conditions the Overfull Conjecture about the chromatic index of a graph G implies the Conformability Conjecture about the total chromatic number of G. We also show that if G has even order and high maximum degree, then G is conformable unless the de0ciency is very small. c © 2001 Elsevier Science B.V. All rights reserved.

The conjecture is true in dimension 2 since the only surfaces which have positive Euler characteristic are S2 and RP2 and they are the only two which are not aspherical. In the special case where M2k is a nonpositively curved Riemannian manifold this conjecture is usually attributed to Hopf by topologists and either to Chern or to both Chern and Hopf by differential geometers. When I first hear...