Algorithms and error bounds for multivariate piecewise constant approximation

We review the surprisingly rich theory of approximation of functions of many vari- ables by piecewise constants. This covers for example the Sobolev-Poincar´e inequalities, parts of the theory of nonlinear approximation, Haar wavelets and tree approximation, as well as recent results about approximation orders achievable on anisotropic partitions

Error bound for radial basis interpolation in terms of a growth function

We suggest an improvement of Wu-Schaback local error bound for radial basis interpolation by using a polynomial growth function. The new bound is valid without any assumptions about the density of the interpolation centers. It can be useful for the localized methods of scattered data fitting and for the meshless discretization of partial differential equation

Nuclei of categories with tensor products

Following the analogy between algebras (monoids) and monoidal categories the construction of nucleus for non-associative algebras is simulated on the categorical level. Nuclei of categories of modules are considered as an example

On the first Townsend coefficient at high electric field

Based on the simplified approach it is shown and experimentally confirmed that gas gain in wire chambers at very low pressure becomes higher on thicker wires at the same applied high voltage. This is a consequence of the fact that the first Townsend coefficient at high reduced electric field depends almost entirely on the mean free path of electrons.Comment: 10 pages, 3 figures; version 2: revised, a few references adde