Spherical r-designs are Chebyshev-type averaging sets on the d-dimensional unit sphere Sd-l that are exact for all polynomials of degree at most t. The concept of such designs was introduced by Delsarte , Goethals and Seidel in 1977. The existence of spherical designs for every t and d was proved by Seymour and Zaslavsky in 1984. Although some sporadic examples are known, no general constructio...

Classical W -algebras in higher dimensions are constructed. This is achieved by generalizing the classical Gel’fand-Dickey brackets to the commutative limit of the ring of classical pseudodifferential operators in arbitrary dimension. These W -algebras are the Poisson structures associated with a higher dimensional version of the Khokhlov-Zabolotskaya hierarchy (dispersionless KP-hierarchy). Th...

Until 1991, the simulation of coupled systems, in which electrochemical reactions are coupled with homogeneous chemical reactions in such a way that at least some of the relevant partial differential transport equations (pdes) contain terms for more than one species, was considered hard. The reason is that many such reaction mechanisms lead to thin reaction layers [1], necessitating the use of ...