21,383 research outputs found
Holder estimates for advection fractional-diffusion equations
We analyse conditions for an evolution equation with a drift and fractional
diffusion to have a Holder continuous solution. In case the diffusion is of
order one or more, we obtain Holder estimates for the solution for any bounded
drift. In the case when the diffusion is of order less than one, we require the
drift to be a Holder continuous vector field in order to obtain the same type
of regularity result.Comment: some typos fixe
On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion
We prove that the Hamilton Jacobi equation for an arbitrary Hamiltonian
(locally Lipschitz but not necessarily convex) and fractional diffusion of
order one (critical) has classical solutions. The proof is
achieved using a new H\"older estimate for solutions of advection diffusion
equations of order one with bounded vector fields that are not necessarily
divergence free
Upper bounds for multiphase composites in any dimension
We prove a rigorous upper bound for the effective conductivity of an
isotropic composite made of several isotropic components in any dimension. This
upper bound coincides with the Hashin Shtrikman bound when the volume ratio of
all phases but any two vanish
A Brief Critical Introduction to the Ontological Argument and its Formalization: Anselm, Gaunilo, Descartes, Leibniz and Kant
The purpose of this paper is twofold. First, it aims at introducing the ontological argument through the analysis of five historical developments: Anselm’s argument found in the second chapter of his Proslogion, Gaunilo’s criticism of it, Descartes’ version of the ontological argument found in his Meditations on First
Philosophy, Leibniz’s contribution to the debate on the ontological argument and his demonstration of the possibility of God, and Kant’s famous criticisms against the (cartesian) ontological argument. Second, it intends to critically examine the enterprise of formally analyzing philosophical arguments and, as
such, contribute in a small degree to the debate on the role of formalization in philosophy. My focus will be mainly on the drawbacks and limitations of such enterprise; as a guideline, I shall refer to a Carnapian, or Carnapian-like theory of argument analysis
Combining spectral sequencing and parallel simulated annealing for the MinLA problem
In this paper we present and analyze new sequential and parallel
heuristics to approximate the Minimum Linear Arrangement problem
(MinLA). The heuristics consist in obtaining a first global solution
using Spectral Sequencing and improving it locally through Simulated
Annealing. In order to accelerate the annealing process, we present a
special neighborhood distribution that tends to favor moves with high
probability to be accepted. We show how to make use of this
neighborhood to parallelize the Metropolis stage on distributed memory
machines by mapping partitions of the input graph to processors and
performing moves concurrently. The paper reports the results obtained
with this new heuristic when applied to a set of large graphs,
including graphs arising from finite elements methods and graphs
arising from VLSI applications. Compared to other heuristics, the
measurements obtained show that the new heuristic improves the
solution quality, decreases the running time and offers an excellent
speedup when ran on a commodity network made of nine personal
computers.Postprint (published version
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