Semiclassical limits of generic multiparameter quantized coordinate rings A = Oq(k) of affine spaces are constructed and related to A, for k an algebraically closed field of characteristic zero and q a multiplicatively antisymmetric matrix whose entries generate a torsionfree subgroup of k×. A semiclassical limit of A is a Poisson algebra structure on the corresponding classical coordinate ring...

In the remainder, we call such a variety a convex symplectic variety. A convex symplectic variety has been studied in [K-V], [Ka 1] and [G-K]. One of main difficulties we meet is the fact that tangent objects TX and T 1 Y are not finite dimensional, since Y may possibly have non-isolated singularities; hence the usual deformation theory does not work well. Instead, in [K-V], [G-K], they introdu...

In the remainder, we call such a variety a convex symplectic variety. A convex symplectic variety has been studied in [K-V], [Ka 1] and [G-K]. One of main difficulties we meet is the fact that tangent objects TX and T 1 Y are not finite dimensional, since Y may possibly have non-isolated singularities; hence the usual deformation theory does not work well. Instead, in [K-V], [G-K], they introdu...

We extend to the sl(N) case the results that we previously obtained on the construction of Wq,p algebras from the elliptic algebra Aq,p(ŝl(2)c). The elliptic algebra Aq,p(ŝl(N)c) at the critical level c = −N has an extended center containing trace-like operators t(z). Families of Poisson structures indexed by N(N −1)/2 integers, defining q-deformations of the WN algebra, are constructed. The op...

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...

let denote the unit circle in the complex plane. given a function , one uses t usual (harmonic) poisson kernel for the unit disk to define the poisson integral of , namely . here we consider the biharmonic poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . we then consider the dilations for and . the ...

Consider the region L := {(x, y) : 0 ≤ y ≤ C log(1 + x), x > 0} for a constant C > 0. We study the percolation and coverage properties of this region. For the percolation properties we place a Poisson point process of intensity λ on the region L. At each point of the process we centre a box of a random side length ρ. In case ρ ≤ R for some fixed R > 0 we study the critical intensity λc of perco...

In this article we study the properties of the hyperinterpolation operator on the unit disk D in R, approximating the orthogonal projection of a function onto the family of polynomials of degree n. A bound for the norm of the hyperinterpolation operator in the space C(D) is derived. Our results then prove the uniform convergence of the hyperinterpolation approximation of functions in the class ...