Search results for "Applied Mathematics"

Monotonicity of Bayes estimators

2013

Let X = (X1; : : : ;Xn) be a sample from a distribution with density (x;θ), θ∈Θ⊂R. In this article the Bayesian estimation of the parameter is considered.We examine whether the Bayes estimators of are pointwise ordered when the prior distributions are partially ordered. Various cases of loss function are studied. A lower bound for the survival function of the normal distribution is obtained.

A space on which diameter-type packing measure is not Borel regular

1999

We construct a separable metric space on which 1-dimensional diameter-type packing measure is not Borel regular.

Deuring’s mass formula of a Mumford family

2015

We study the Newton polygon jumping locus of a Mumford family in char p p . Our main result says that, under a mild assumption on p p , the jumping locus consists of only supersingular points and its cardinality is equal to ( p r − 1 ) ( g − 1 ) (p^r-1)(g-1) , where r r is the degree of the defining field of the base curve of a Mumford family in char p p and g g is the genus of the curve. The underlying technique is the p p -adic Hodge theory.

Vertices for characters of $p$-solvable groups

2002

Suppose that G is a finite p-solvable group. We associate to every irreducible complex character X ∈ Irr(G) of G a canonical pair (Q, δ), where Q is a p-subgroup of G and δ ∈ Irr(Q), uniquely determined by X up to G-conjugacy. This pair behaves as a Green vertex and partitions Irr(G) into families of characters. Using the pair (Q, δ), we give a canonical choice of a certain p-radical subgroup R of G and a character η ∈ Irr(R) associated to X which was predicted by some conjecture of G. R. Robinson.

Quasianalytic Denjoy-Carleman classes and o-minimality

2003

We show that the expansion of the real field generated by the functions of a quasianalytic Denjoy-Carleman class is model complete and o-minimal, provided that the class satisfies certain closure conditions. Some of these structures do not admit analytic cell decomposition, and they show that there is no largest o-minimal expansion of the real field.

Analytic extension of non quasi-analytic Whitney jets of Roumieu type

1997

Let (Mr)r∈ℕ0 be a logarithmically convex sequence of positive numbers which verifies M0 = 1 as well as Mr≥ 1 for every r ∈ ℕ and defines a non quasi-analytic class. Let moreover F be a closed proper subset of ℝn. Then for every function ƒ on ℝn belonging to the non quasi-analytic (Mr)-class of Roumieu type, there is an element g of the same class which is analytic on ℝnF and such that Dα ƒ(x) = Dαg(x) for every σ ∈ ƒ0n SBAP and x ∈ F.

Classification générique de synthèses temps minimales avec cible de codimension un et applications

1997

In this article we consider the problem of constructing the optimal closed loop control in the time minimal control problem, with terminal constraints belonging to a manifold of codimension one, for systems of the form v = X + uY, v ϵ R2, R3, |u| ≤ 1 under generic assumptions. The analysis is localized near the terminal manifold and is motivated by the problem of controlling a class of chemical systems.

Asymptotics for thenth-degree Laguerre polynomial evaluated atn

1992

We investigate the asymptotic behaviour of ? n (n),n?? where ? n (x) denotes the Laguerre polynomial of degreen. Our results give a partial answer to the conjecture ?? n (n)>1 forn>6, made in 1984 by van Iseghem. We also show the connection between this conjecture and the continued fraction approximants of $$6\sqrt {{3 \mathord{\left/ {\vphantom {3 \pi }} \right. \kern-\nulldelimiterspace} \pi }} $$ .

An algorithm to find all paths between two nodes in a graph

1990

On Brauer’s Height Zero Conjecture

2014

In this paper, the unproven half of Richard Brauer’s Height Zero Conjecture is reduced to a question on simple groups.