INEQUALITY AND DISABILITY: IN STATISTICAL TERMS, WHAT ELSE DO WE NEED TO KNOW?

Social inequality is the phenomenon that differentiates between people in the context of the same society, placing some individuals in structurally more advantageous conditions than others. It manifests itself in all aspects: political, economic among others. The main causes of inequality are investment lack in social areas, health and education. Among the consequences of inequality, we highlight: increased violence, poverty, delay in economic progress; hunger, destruction and infant mortality; young marginalization people, and finally; rising unemployment. Among the main inequality types, we highlight: people with and without disabilities, regions, races; income and sex. To measure this inequality, we highlight HDI, Theil and MPI. A person with a disability is any person who presents a loss or abnormality that generates an inability to perform one or more activities, and these characteristics hinder their social inclusion, access to the labor market, transportation, education, financing and training; urban and environmental barriers, and finally; ignorance of employers. Situations like these provide disabilities people with lower wages when employed, worse purchasing power, less social participation providing greater exclusion and disadvantaged situations when compared to those without disabilities. For this work we used exploratory analysis techniques considering data sets from the 2010 IBGE Census and UNDP.

Inequalities in utilization and provision of dental services: a scoping review

Background There are many determinants that can affect inequality in oral and dental health. This study is aimed to explore the main determinants of inequality in both utilization and provision of dental services in Organization for Economic Co-operation and Development (OECD) countries. Methods Four databases including PubMed, ISI WOS, Scopus, and ProQuest were searched up to 8 Aug 2020, applying the relevant keywords. Thematic analysis was used for synthesizing and extracting data. Trend analysis was applied to determine the trends of the inequality determinants. Results Thematic analysis led to 6 main themes, 13 sub-themes, and 53 sub-sub-themes. The main themes represent the main inequality determinants for both utilization and provision of dental services. The streamgraph illustrated that fewer studies have been conducted on social and cultural determinants, and for almost all determinants the trend of published articles has been increasing since 2007, with the exception of health policies. Conclusions Inequality in the utilization and provision of dental services is addressed by various factors including individual, social, cultural and economic determinants, health policies, and availability of services. The first four determinants are related to utilization and the last two are related to the provision of services. All these aspects must be considered to reduce inequality in dental services.

Local behavior of mappings of metric spaces with branching

The local behavior of mappings with the inverse Poletsky inequality between metric spaces is studied. The case where one of the spaces satisfies the condition of weak sphericalization, is similar to the Riemannian sphere (extended Euclidean space), and is locally linearly connected under a mapping is considered. It is proved that the equicontinuity of the corresponding families of mappings of two domains, one of which is a domain with a weakly flat boundary, and another one is a fixed domain with a compact closure, the corresponding weight in the main inequality being supposed to be integrable.

Further inequalities and properties of p-inner parallel bodies

A. R. Martínez Fernández obtained upper bounds for quermassintegrals of the p-inner parallel bodies: an extension of the classical inner parallel body to the $L_p$ -Brunn-Minkowski theory. In this paper, we establish (sharp) upper and lower bounds for quermassintegrals of p-inner parallel bodies. Moreover, the sufficient and necessary conditions of the equality case for the main inequality are obtained, which characterize the so-called tangential bodies.

Bootstrapping Inequality of Opportunity in Europe. Are changes significant?

The aim of this article is to shed some light on the behaviour of income inequality and inequality of opportunity over time for 26 European countries. The analysis is carried out using microdata collected by the European Union Statistics on Income and Living Conditions (EU-SILC), which incorporate a wide variety of personal harmonised variables, allowing comparability between countries. The availability of this database for the years 2004 and 2010 is particularly relevant to assess changes over time in the main inequality indices and the contribution of “circumstance” to inequality of opportunity. Bootstrap methodology is used with the aim of testing if the differences between the two years are statistically significant. Results show that observed changes in inequality of opportunity and income inequality are in most cases significant and also prove the robustness of the bootstrap methods to analyse the evolution of income inequality and inequality of opportunity.

A sharp interpolation between the Hölder and Gaussian Young inequalities

We prove a very general sharp inequality of the Hölder–Young-type for functions defined on infinite dimensional Gaussian spaces. We begin by considering a family of commutative products for functions which interpolates between the pointwise and Wick products; this family arises naturally in the context of stochastic differential equations, through Wong–Zakai-type approximation theorems, and plays a key role in some generalizations of the Beckner-type Poincaré inequality. We then obtain a crucial integral representation for that family of products which is employed, together with a generalization of the classic Young inequality due to Lieb, to prove our main theorem. We stress that our main inequality contains as particular cases the Hölder inequality and Nelson’s hyper-contractive estimate, thus providing a unified framework for two fundamental results of the Gaussian analysis.

Application of Functionals in Creating Inequalities

The paper deals with the fundamental inequalities for convex functions in the bounded closed interval. The main inequality includes convex functions and positive linear functionals extending and refining the functional form of Jensen’s inequality. This inequality implies the Jensen, Fejér, and, thus, Hermite-Hadamard inequality, as well as their refinements.