Search results for "equality"

Neumann p-Laplacian problems with a reaction term on metric spaces

2020

We use a variational approach to study existence and regularity of solutions for a Neumann p-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincare inequality. Trace theorems for functions with bounded variation are applied in the definition of the variational functional and minimizers are shown to satisfy De Giorgi type conditions.

Sobolev Spaces and Quasiconformal Mappings on Metric Spaces

2001

Heinonen and I have recently established a theory of quasiconformal mappings on Ahlfors regular Loewner spaces. These spaces are metric spaces that have sufficiently many rectifiable curves in a sense of good estimates on moduli of curve families. The Loewner condition can be conveniently described in terms of Poincare inequalities for pairs of functions and upper gradients. Here an upper gradient plays the role that the length of the gradient of a smooth function has in the Euclidean setting. For example, the Euclidean spaces and Heisenberg groups and the more general Carnot groups admit the type of a Poincare inequality we need. We describe the basics and discuss the associated Sobolev sp…

Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems

2013

In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ1(Ω) for the p-Laplace operator (p > 1) in a Lipschitz bounded domain Ω in ℝn. Our estimate does not require any convexity assumption on Ω and it involves the best isoperimetric constant relative to Ω. In a suitable class of convex planar domains, our bound turns out to be better than the one provided by the Payne—Weinberger inequality.

Admissibility versus Ap-Conditions on Regular Trees

2020

We show that the combination of doubling and (1, p)-Poincaré inequality is equivalent to a version of the Ap-condition on rooted K-ary trees. peerReviewed

Qualidade docente e eficácia escolar

2008

Este texto visa a explorar uma faceta do funcionamento do sistema escolar que permite associar a implementação de políticas públicas, no caso, a distribuição dos professores pelas escolas e salas de aula, e à avaliação dos impactos dessa distribuição do ponto de vista da busca por maior igualdade de oportunidades. Para discutir essa questão, usaremos os dados de pesquisa realizada no Brasil, na Argentina, no Chile e no México, com informações de 96 escolas e professores, assim como de 2048 alunos de 4ª série que estudavam em escolas situadas em bairros pobres de Belo Horizonte, Buenos Aires, Santiago e Guanajuato. Inicialmente, discutimos alguns dos elementos das políticas educacionais lati…

Nonequilibrium critical scaling in quantum thermodynamics

2016

The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work produced in a quench exhibits finite-size scaling at quantum criticality. This scaling faithfully …

Hall–Post inequalities: Review and application to molecules and tetraquarks

2019

A review is presented of the Hall–Post inequalities that give lower-bounds to the ground-state energy of quantum systems in terms of energies of smaller systems. New applications are given for systems experiencing both a static source and inner interactions, as well as for hydrogen-like molecules and for tetraquarks in some quark models. In the latter case, the Hall–Post inequalities constrain the possibility of deeply-bound exotic mesons below the threshold for dissociation into two quark–antiquark mesons. We also emphasize the usefulness of the Hall–Post bounds in terms of 3-body energies when some 2-body subsystems are ill defined or do not support any bound state.

Asymptotic values and hölder continuity of quasiconformal mappings

1987

The impact of study design and diagnostic approach in a large multi-centre ADHD study. Part 1: ADHD symptom patterns

2011

Contains fulltext : 96439.pdf (Publisher’s version ) (Open Access) BACKGROUND: The International Multi-centre ADHD Genetics (IMAGE) project with 11 participating centres from 7 European countries and Israel has collected a large behavioural and genetic database for present and future research. Behavioural data were collected from 1068 probands with the combined type of attention deficit/hyperactivity disorder (ADHD-CT) and 1446 'unselected' siblings. The aim was to analyse the IMAGE sample with respect to demographic features (gender, age, family status, and recruiting centres) and psychopathological characteristics (diagnostic subtype, symptom frequencies, age at symptom detection, and com…

Mapping inequalities in exclusive breastfeeding in low- and middle-income countries, 2000-2018

2021

Exclusive breastfeeding (EBF)—giving infants only breast-milk for the first 6 months of life—is a component of optimal breastfeeding practices effective in preventing child morbidity and mortality. EBF practices are known to vary by population and comparable subnational estimates of prevalence and progress across low- and middle-income countries (LMICs) are required for planning policy and interventions. Here we present a geospatial analysis of EBF prevalence estimates from 2000 to 2018 across 94 LMICs mapped to policy-relevant administrative units (for example, districts), quantify subnational inequalities and their changes over time, and estimate probabilities of meeting the World Health …