6 research outputs found
Tensor rectifiable G-flat chains
A rigidity result for normal rectifiable -chains in with
coefficients in an Abelian normed group is established. Given some
decompositions , and some rectifiable -chain in
, we consider the properties:(1) The tangent planes to
split as for some -plane
and some -plane
.(2) for
some sets ,
such that is -rectifiable and is -rectifiable
(we say that is -rectifiable).The main result is that for normal
chains, (1) implies (2), the converse is immediate. In the proof we introduce
the new groups of tensor flat chains (or -chains) in
which generalize Fleming's -flat
chains. The other main tool is White's rectifiable slices theorem. We show that
on the one hand any normal rectifiable chain satisfying~(1) identifies with a
normal rectifiable -chain and that on the other hand any normal
rectifiable -chain is -rectifiable
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal