Describing orbitopes by linear inequalities and projection based tools

Magdeburg, Univ., Fak. für Mathematik, Diss., 2011

Lattice point inequalities and face numbers of polytopes in view of central symmetry

Magdeburg, Univ., Fak. für Mathematik, Diss., 2012

Social inequalities in health among children and adolescents in Germany : an investigation of political approaches

The present diploma thesis analyses the German political understanding of social inequalities in health (SIH) among children and adolescents, and explores the political strategies that are perceived as most effective to tackle SIH. The study is based on the qualitative content analysis of official political documents developed at different political levels, which were the national level as well as two purposefully selected counties, Mecklenburg-Vorpommern and Niedersachsen. The study's findings indicate a beginning awareness of the existence of SIH in Germany. Nevertheless, this judgement refers to few publishing ministries only, both at national and county levels. The suggested approaches to tackle SIH vary significantly among the analysed documents, and no consensus can be identified with regard to the preference of upstream or downstream policies. The existence of the social gradient is not criticised in any of the analysed data. However, there seems to be a common agreement on the importance of setting related interventions and the contribution of both the national, regional, and local politic levels. As the absence of a central coordinator can explain these highly heterogeneous findings, key recommendations concern the establishment of a nation-wide coordinator and a nation-wide collection of best practice examples. Here, the Federal Centre for Health Education has an adequate position and the required competences to act as a coordinator and facilitator. Further requirements for a successful reduction of SIH in Germany are the extension of a continuous communication between all actors, the adoption of the planned German Prevention Law, and the nation-wide and early promotion of children as part of education policies in the federal states.

Regional income inequalities in Europe: an updated measurement and some decomposition results

In this paper well-known summary inequality indexes are used to explore interregional income inequalities in Europe. In particular, we mainly employ Theils’population-weighted index because of its appealing properties. Two decomposition analysis are applied. First, regional inequalities are decomposed by regional subgroups (countries). Second, intertemporal inequality changes are separated into income and population changes. The main results can be summarized as follows. First, data confirm a reduction in crossregional inequality during 1982-97. Second, this reduction is basically due to real convergence among countries. Third, currently the greater part of European interregional disparities is within-country by nature, which introduce an important challenge for the European policy. Fourth, inequality changes are due mainly to income variations, population changes playing a minor role.

Norm inequalities in multidimensional Lorentz spaces

In this paper we obtain necessary and sufficient conditions for double trigonometric series to belong to generalized Lorentz spaces, not symmetric in general. Estimates for the norms are given in terms of coefficients.

Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Convolution inequalities in Lorentz spaces

In this paper we study boundedness of the convolution operator in different Lorentz spaces. In particular, we obtain the limit case of the Young-O'Neil inequality in the classical Lorentz spaces. We also investigate the convolution operator in the weighted Lorentz spaces. Finally, norm inequalities for the potential operator are presented.

Accounting for the dead in the longitudinal analysis of income-related health inequalities

This paper develops an accounting framework to consider the effect of deaths on the longitudinal analysis of income-related health inequalities. Ignoring deaths or using inverse probability weights (IPWs) to re-weight the sample for mortality-related attrition can produce misleading results, since to do so would be to disregard the most extreme of all health outcomes. Incorporating deaths into the longitudinal analysis of income-related health inequalities provides a more complete picture in terms of the evaluation of health changes in respect to socioeconomic status. We illustrate our work by investigating health mobility in Quality Adjusted Life Years (QALYs) as measured by the SF6D from 1999 till 2004 using the British Household Panel Survey (BHPS). We show that for Scottish males explicitly accounting for the dead, rather than using IPWs to account for mortality-related attrition, changes the direction of the relationship between relative health changes and initial income position, while for other population groups it increases the strength of this relationship by up to 14 times. When deaths are explicitly incorporated into the analysis it is found that over this five year period for both Scotland and England & Wales the relative health changes were significantly regressive such that the poor experienced a larger share of the health losses relative to their initial share of health and a large amount of this was related to mortality.

Development of tools to measure and explain changes in health inequalities in Scotland and benchmark performance

This project will develop a modelling framework to explain changes in income-related health inequalities and benchmark the performance of Scotland in tackling income-related health inequalities, both over time and relative to that of England and Wales.

Inequalities in Child Mortality in India: A District-Level Analysis

This paper measures the degree of inequality in child mortality rates across districts in India, using data from the 1981, 1991 and 2001 Indian population censuses. The results show that child mortality is more concentrated in less developed districts in all three census years. Further, between 1981 and 2001, the inequality in child mortality seems to have increased to the advantage of the more developed districts (i.e., there was an increasing concentration of child mortality in less developed districts). However, the inequality in female child mortality rates seems to have declined between 1991 and 2001, even as it increased – albeit at a slower rate than before – for male child mortality rates. In the decomposition analysis, it is found that while a more equitable distribution of medical facilities and safe drinking water across districts did contribute towards reducing inequality in child mortality between 1981 and 1991, different levels of structural change among districts were responsible for a very large part of the inequality in child mortality to the advantage of the more developed districts in all three census years. Other variables which played important roles in increasing inequality included a measure of infrastructure development, female literacy, and a social group status variable. The paper concludes with some brief comments on the policy implications of the findings.

My Group Beats Your Group: Evaluating Non-Income Inequalities

This paper proposes a new methodology, the Domination Index, to evaluate non-income inequalities between social groups such as inequalities of educational attainment, occupational status, health or subjective well-being. The Domination Index does not require specific cardinalisation assumptions, but only uses the ordinal structure of these non-income variables. We approach from an axiomatic perspective and show that a set of desirable properties for a group inequality measure when the variable of interest is ordinal, characterizes the Domination Index up to a positive scalar transformation. Moreover we make use of the Domination Index to explore the relation between inequality and segregation and show how these two concepts are related theoretically.

Norm convolution inequalities in Lebesgue spaces

We obtain upper and lower estimates of the (p; q) norm of the con-volution operator. The upper estimate sharpens the Young-type inequalities due to O'Neil and Stepanov.

Some variational problems from image processing

"Vegeu el resum a l'inici del document del fitxer adjunt."

A characterization of two weight norm inequalities for maximal singular integrals

"Vegeu el resum a l'inici del document del fitxer adjunt."