25,260 research outputs found
Lower Bounds for On-line Interval Coloring with Vector and Cardinality Constraints
We propose two strategies for Presenter in the on-line interval graph
coloring games. Specifically, we consider a setting in which each interval is
associated with a -dimensional vector of weights and the coloring needs to
satisfy the -dimensional bandwidth constraint, and the -cardinality
constraint. Such a variant was first introduced by Epstein and Levy and it is a
natural model for resource-aware task scheduling with different shared
resources where at most tasks can be scheduled simultaneously on a single
machine.
The first strategy forces any on-line interval coloring algorithm to use at
least different colors on an -colorable set of intervals. The second strategy forces any
on-line interval coloring algorithm to use at least
different colors on an
-colorable set of unit intervals
Subelliptic SpinC Dirac Operators, IV Proof of the Relative Index Conjecture
We prove the relative index conjecture, which in turn implies that the set of
embeddable deformations of a strictly pseudoconvex CR-structure on a compact
3-manifold is closed in the C\infty-topology.Comment: 5 page
Harnack Inequalities and Heat-kernel Estimates for Degenerate Diffusion Operators Arising in Population Biology
This paper continues the analysis, started in [2, 3], of a class of
degenerate elliptic operators defined on manifolds with corners, which arise in
Population Biology. Using techniques pioneered by J. Moser, and extended and
refined by L. Saloff-Coste, Grigoryan, and Sturm, we show that weak solutions
to the parabolic problem defined by a sub-class of these operators, which
consists of those that can be defined by Dirichlet forms and have non-vanishing
transverse vector field, satisfy a Harnack inequality. This allows us to
conclude that the solutions to these equations belong, for positive times, to
the natural anisotropic Holder spaces, and also leads to upper and, in some
cases, lower bounds for the heat kernels of these operators. These results
imply that these operators have a compact resolvent when acting on or
The proof relies upon a scale invariant Poincare inequality that we
establish for a large class of weighted Dirichlet forms, as well as estimates
to handle certain mildly singular perturbation terms. The weights that we
consider are neither Ahlfors regular, nor do they generally belong to the
Muckenhaupt class Comment: This version corrects a small gap in the argument used to estimate
the contribution of vector fields and potentials with log-divergent
coefficients (the old Lemma B.2
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