A Set Theory with Support for Partial Fun tions

Interpolation and approximation in Taylor spaces

Barbara Zwi knagl1 and Robert S haba k2 Abstra t: The univariate Taylor formula without remainder allows to reprodu e a fun tion ompletely from ertain derivative values. Thus one an look for Hilbert spa es in whi h the Taylor formula a ts as a reprodu tion formula. It turns out that there are many Hilbert spa es whi h allow this, and they should be alled Taylor spa es. They have ertain reprodu ...

The meshless Kernel-based method of lines for parabolic equations

1. Introdu tion. There are plenty of appli ation papers in whi h kernels or radial basis fun tions are su essfully used for solving partial di erential equations by meshless methods. The usage of kernels is typi ally based on spatial interpolation at s attered lo ations, writing the trial fun tions entirely in terms of nodes [2℄. For stationary partial di erential equations, the dis retization ...

Äääöòòòò Ùò Blockinøøóò× Óó Ööððúòø Úööööðð×

We onsider a fundamental problem in omputational learning theory: learning an arbitrary Boolean fun tion that depends on an unknown set of k out of n Boolean variables. We give an algorithm for learning su h fun tions from uniform random examples that runs in time roughly (n k ) ! !+1 ; where ! < 2:376 is the matrix multipli ation exponent. We thus obtain the rst polynomial fa tor improvement o...

Rationality of Partial Zeta Fun tions

Partial Fun tions in ACL 2