Search results for "Asymptotic"

On Limits at Infinity of Weighted Sobolev Functions

2022

We study necessary and sufficient conditions for a Muckenhoupt weight $w \in L^1_{\mathrm{loc}}(\mathbb R^d)$ that yield almost sure existence of radial, and vertical, limits at infinity for Sobolev functions $u \in W^{1,p}_{\mathrm{loc}}(\mathbb R^d,w)$ with a $p$-integrable gradient $|\nabla u|\in L^p(\mathbb R^d,w)$. The question is shown to subtly depend on the sense in which the limit is taken. First, we fully characterize the existence of radial limits. Second, we give essentially sharp sufficient conditions for the existence of vertical limits. In the specific setting of product and radial weights, we give if and only if statements. These generalize and give new proofs for results of…

Double index recursive models

1994

The purpose of this document is to study the model belongs to the family of structural equation models with data varying both accross individuals (sectors) and in time. A complete theoretical analysis is developed in this work for the case of a recursive structure. Maximum likelihood estimation and Zellner's "seemingly unrelated equations" estimators (iterated or not) are presented and their asymptotic properties are carefully derived.The application of the estimation methods to the economy morocco produced statistically significant and economic meaningful results. Through a test of exogeneity, the recursivity of the system is confirmed. Policy recommendations are discussed and analyzed.

Global representation and multiscale expansion for the Dirichlet problem in a domain with a small hole close to the boundary

2019

For each pair (Formula presented.) of positive parameters, we define a perforated domain (Formula presented.) by making a small hole of size (Formula presented.) in an open regular subset (Formula presented.) of (Formula presented.) ((Formula presented.)). The hole is situated at distance (Formula presented.) from the outer boundary (Formula presented.) of the domain. Thus, when (Formula presented.) both the size of the hole and its distance from (Formula presented.) tend to zero, but the size shrinks faster than the distance. Next, we consider a Dirichlet problem for the Laplace equation in the perforated domain (Formula presented.) and we denote its solution by (Formula presented.) Our ai…

Multiplicity of solutions for asymptotically linear $n$-th order boundary value problems

2007

In this paper we investigate existence and multiplicity of solutions, with prescribed nodal properties, to a two-point boundary value problem of asymptotically linear $n$-th order equations. The proof follows a shooting approach and it is based on the weighted eigenvalue theory for linear $n$-th order boundary value problems

Extremal Irregular Digraphs

2018

A digraph is called irregular if its distinct vertices have distinct degree pairs. An irregular digraph is called minimal (maximal) if the removal of any arc (addition of any new arc) results in a non-irregular digraph. It is easily seen that the minimum sizes among irregular n-vertex whether digraphs or oriented graphs are the same and are asymptotic to (√2/3) n3/2; maximum sizes, however, are asymptotic to n2 and n2/2, respectively. Let s stand for the sum of initial positive integers, s = 1, 3, 6, . . . . An oriented graph Hs and a digraph Fs, both large (in terms of the size), minimal irregular, and on any such s vertices, s ≥ 21, are constructed in [Large minimal irregular digraphs, Op…

Asymptotic mean value formulas for parabolic nonlinear equations

2021

In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge–Ampère equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from a probabilistic point of view in terms of dynamic programming principles for certain two-player, zero-sum games. peerReviewed

On the asymptotic behaviour of gaussian spherical integrals

1983

Model selection using limiting distributions of second-order blind source separation algorithms

2015

Signals, recorded over time, are often observed as mixtures of multiple source signals. To extract relevant information from such measurements one needs to determine the mixing coefficients. In case of weakly stationary time series with uncorrelated source signals, this separation can be achieved by jointly diagonalizing sample autocovariances at different lags, and several algorithms address this task. Often the mixing estimates contain close-to-zero entries and one wants to decide whether the corresponding source signals have a relevant impact on the observations or not. To address this question of model selection we consider the recently published second-order blind identification proced…

Branching Ratios and Spectral Functions of $\tau$ Decays: final ALEPH measurements and physics implications

2005

The full LEP-1 data set collected with the ALEPH detector at the $Z$ pole during 1991-1995 is analysed in order to measure the $\tau$ decay branching fractions. Extensive systematic studies are performed, in order to match the large statistics of the data sample corresponding to over 300 000 measured and identified $\tau$ decays. Branching fractions are obtained for the two leptonic channels and eleven hadronic channels defined by their respective numbers of charged particles and $\pi^0$'s. Using previously published ALEPH results on final states with charged and neutral kaons, corrections are applied to the hadronic channels to derive branching ratios for exclusive final states without kao…

Large number asymptotics of two-component systems

2012

We shall analyze the asymptotics of two-component systems with at least one particle component when the number of particles becomes large; choosing suitable scalings for the parameters, we find the set of coupled partial differential equations modeling those systems in the limit.