120,241 research outputs found
Sensitivity Analysis Using a Fixed Point Interval Iteration
Proving the existence of a solution to a system of real equations is a
central issue in numerical analysis. In many situations, the system of
equations depend on parameters which are not exactly known. It is then natural
to aim proving the existence of a solution for all values of these parameters
in some given domains. This is the aim of the parametrization of existence
tests. A new parametric existence test based on the Hansen-Sengupta operator is
presented and compared to a similar one based on the Krawczyk operator. It is
used as a basis of a fixed point iteration dedicated to rigorous sensibility
analysis of parametric systems of equations
On construction of the smallest one-sided confidence interval for the difference of two proportions
For any class of one-sided confidence intervals with a certain
monotonicity ordering on the random confidence limit, the smallest interval, in
the sense of the set inclusion for the difference of two proportions of two
independent binomial random variables, is constructed based on a direct
analysis of coverage probability function. A special ordering on the confidence
limit is developed and the corresponding smallest confidence interval is
derived. This interval is then applied to identify the minimum effective dose
(MED) for binary data in dose-response studies, and a multiple test procedure
that controls the familywise error rate at level is obtained. A
generalization of constructing the smallest one-sided confidence interval to
other discrete sample spaces is discussed in the presence of nuisance
parameters.Comment: Published in at http://dx.doi.org/10.1214/09-AOS744 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Leray's fundamental work on the Navier-Stokes equations: a modern review of "Sur le mouvement d'un liquide visqueux emplissant l'espace"
This article offers a modern perspective which exposes the many contributions
of Leray in his celebrated work on the Navier--Stokes equations from 1934.
Although the importance of his work is widely acknowledged, the precise
contents of his paper are perhaps less well known. The purpose of this article
is to fill this gap. We follow Leray's results in detail: we prove local
existence of strong solutions starting from divergence-free initial data that
is either smooth, or belongs to , (with ),
as well as lower bounds on the norms ,
() as approaches a putative blow-up time. We show global
existence of a weak solution and weak-strong uniqueness. We present Leray's
characterisation of the set of singular times for the weak solution, from which
we deduce that its upper box-counting dimension is at most .
Throughout the text we provide additional details and clarifications for the
modern reader and we expand on all ideas left implicit in the original work,
some of which we have not found in the literature. We use some modern
mathematical tools to bypass some technical details in Leray's work, and thus
expose the elegance of his approach.Comment: 81 pages. All comments are welcom
On the classification of Kahler-Ricci solitons on Gorenstein del Pezzo surfaces
We give a classification of all pairs (X,v) of Gorenstein del Pezzo surfaces
X and vector fields v which are K-stable in the sense of Berman-Nystrom and
therefore are expected to admit a Kahler-Ricci solition. Moreover, we provide
some new examples of Fano threefolds admitting a Kahler-Ricci soliton.Comment: 21 pages, ancillary files containing calculations in SageMath; minor
correction
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