25 research outputs found
Two ideals connected with strong right upper porosity at a point
Let be the set of upper strongly porous at subsets of and let be the intersection of maximal ideals . Some characteristic properties of sets are obtained. It
is shown that the ideal generated by the so-called completely strongly porous
at subsets of is a proper subideal of Comment: 18 page
A compact null set containing a differentiability point of every Lipschitz function
We prove that in a Euclidean space of dimension at least two, there exists a
compact set of Lebesgue measure zero such that any real-valued Lipschitz
function defined on the space is differentiable at some point in the set. Such
a set is constructed explicitly.Comment: 28 pages; minor modifications throughout; Lemma 4.2 is proved for
general Banach space rather than for Hilbert spac
Surfaces Meeting Porous Sets in Positive Measure
Let n>2 and X be a Banach space of dimension strictly greater than n. We show
there exists a directionally porous set P in X for which the set of C^1
surfaces of dimension n meeting P in positive measure is not meager. If X is
separable this leads to a decomposition of X into a countable union of
directionally porous sets and a set which is null on residually many C^1
surfaces of dimension n. This is of interest in the study of certain classes of
null sets used to investigate differentiability of Lipschitz functions on
Banach spaces
Online Scheduling of Parallel Jobs on Hypercubes: Maximizing the Throughput
We study the online problem of scheduling unit-time parallel jobs on hypercubes. A parallel job has to be scheduled between its release time and deadline on a subcube of processors. The objective is to maximize the number of early jobs. We provide a 1.6-competitive algorithm for the problem and prove that no deterministic algorithm is better than 1.4-competitive.