20,783 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
Hamiltonian cycles in faulty random geometric networks
In this paper we analyze the Hamiltonian properties of
faulty random networks.
This consideration is of interest when considering wireless
broadcast networks.
A random geometric network is a graph whose vertices
correspond to points
uniformly and independently distributed in the unit square,
and whose edges
connect any pair of vertices if their distance is below some
specified bound.
A faulty random geometric network is a random geometric
network whose vertices
or edges fail at random. Algorithms to find Hamiltonian
cycles in faulty random
geometric networks are presented.Postprint (published version
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