Search results for "Inequalities"
showing 10 items of 188 documents
Schools without measurements : towards a pedagogy of recognition
2017
Since the OECD launched the Program for International Student Assessment (PISA) in 2000, education measurements have mainly been concerned with recording and issuing results in terms of school success or failure based on items aimed at measuring academic achievement. A major consequence of this obsession with quantifiable results, which stems from a sort of statistical monoculture, has been a shift of our attention away from the seminal fact that, indeed, educational disparities are directly linked to social inequalities. Besides, the application of accountability criteria within systems of education tends to hide the increasing deregulation of the former. Contrary to its seeming appearance…
Limits of Sobolev homeomorphisms
2017
Let X; Y subset of R-2 be topologically equivalent bounded Lipschitz domains. We prove that weak and strong limits of homeomorphisms h: X (onto)-> Y in the Sobolev space W-1,W-p (X, R-2), p >= 2; are the same. As an application, we establish the existence of 2D-traction free minimal deformations for fairly general energy integrals. Peer reviewed
Shape optimization for monge-ampére equations via domain derivative
2011
In this note we prove that, if $\Omega$ is a smooth, strictly convex, open set in $R^n$ $(n \ge 2)$ with given measure, the $L^1$ norm of the convex solution to the Dirichlet problem $\det D^2 u=1$ in $\Omega$, $u=0$ on $\partial\Omega$, is minimum whenever $\Omega$ is an ellipsoid.
New isoperimetric estimates for solutions to Monge - Ampère equations
2009
Abstract We prove some sharp estimates for solutions to Dirichlet problems relative to Monge–Ampere equations. Among them we show that the eigenvalue of the Dirichlet problem, when computed on convex domains with fixed measure, is maximal on ellipsoids. This result falls in the class of affine isoperimetric inequalities and shows that the eigenvalue of the Monge–Ampere operator behaves just the contrary of the first eigenvalue of the Laplace operator.
Infinite games and chain conditions
2015
We apply the theory of infinite two-person games to two well-known problems in topology: Suslin's Problem and Arhangel'skii's problem on $G_\delta$ covers of compact spaces. More specifically, we prove results of which the following two are special cases: 1) every linearly ordered topological space satisfying the game-theoretic version of the countable chain condition is separable and 2) in every compact space satisfying the game-theoretic version of the weak Lindel\"of property, every cover by $G_\delta$ sets has a continuum-sized subcollection whose union is $G_\delta$-dense.
Minimal Morse flows on compact manifolds
2006
Abstract In this paper we prove, using the Poincare–Hopf inequalities, that a minimal number of non-degenerate singularities can be computed in terms only of abstract homological boundary information. Furthermore, this minimal number can be realized on some manifold with non-empty boundary satisfying the abstract homological boundary information. In fact, we present all possible indices and types (connecting or disconnecting) of singularities realizing this minimal number. The Euler characteristics of all manifolds realizing this minimal number are obtained and the associated Lyapunov graphs of Morse type are described and shown to have the lowest topological complexity.
Maximal function estimates and self-improvement results for Poincaré inequalities
2018
Our main result is an estimate for a sharp maximal function, which implies a Keith–Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces. peerReviewed
Mapping geographical inequalities in access to drinking water and sanitation facilities in low-income and middle-income countries, 2000-17.
2020
Background: Universal access to safe drinking water and sanitation facilities is an essential human right, recognised in the Sustainable Development Goals as crucial for preventing disease and improving human wellbeing. Comprehensive, high-resolution estimates are important to inform progress towards achieving this goal. We aimed to produce highresolution geospatial estimates of access to drinking water and sanitation facilities. Methods: We used a Bayesian geostatistical model and data from 600 sources across more than 88 low-income and middle-income countries (LMICs) to estimate access to drinking water and sanitation facilities on continuous continent-wide surfaces from 2000 to 2017, and…
Overcoming the crisis : the changing profile and trajectories of Latvian migrants
2016
The work was funded by the National Research Programme [grant number 5.2.4] and the Latvian Council of Sciences [grant number 514/2012]. Taking mobility between Latvia and Western Europe as an empirical lens, this analysis explores the complex relationship between spatial disparities in earning potential and migration. The very dramatic shifts in the economic and political context against which migration from Latvia has occurred over the period 2004-2012 make it an especially apposite focus of research investigating the link between mobility and labour market circumstances. As an analytical starting point, conventional economic theory broadly explains the movement of workers from lower to h…
A Multisite Preregistered Paradigmatic Test of the Ego-Depletion Effect
2021
We conducted a preregistered multilaboratory project ( k = 36; N = 3,531) to assess the size and robustness of ego-depletion effects using a novel replication method, termed the paradigmatic replication approach. Each laboratory implemented one of two procedures that was intended to manipulate self-control and tested performance on a subsequent measure of self-control. Confirmatory tests found a nonsignificant result ( d = 0.06). Confirmatory Bayesian meta-analyses using an informed-prior hypothesis (δ = 0.30, SD = 0.15) found that the data were 4 times more likely under the null than the alternative hypothesis. Hence, preregistered analyses did not find evidence for a depletion effect. Ex…