This paper introduces an inequality on vectors in $mathbb{R}^n$ which compares vectors in $mathbb{R}^n$ based on the $p$-norm of their projections on $mathbb{R}^k$ ($kleq n$). For $p>0$, we say $x$ is $d$-projectionally less than or equal to $y$ with respect to $p$-norm if $sum_{i=1}^kvert x_ivert^p$ is less than or equal to $ sum_{i=1}^kvert y_ivert^p$, for every $dleq kleq n$. For...

BACKGROUND Employment is a priority in the European Union, and it is essential to address the needs of individuals disadvantaged at the labour market on grounds such as ethnicity, age, gender or disability, to increase the opportunities for these groups to gain employment. The Council of the European Union recognize the important role of national organisations in increasing gender equality and ...

We show that for any graph G, by considering “activation” through the strong product with another graph H , the relation αpGq ď θpGq between the independence number and the Lovász number of G can be made arbitrarily tight: Precisely, the inequality αpG ˆHq ď θpGˆHq “ θpGqθpHq becomes asymptotically an equality for a suitable sequence of ancillary graphs H . This motivates us to look for other p...

A novel equality relating the rate of energy dissipation to a degree of violation of the fluctuation-response relation (FRR) in non-equilibrium Langevin systems is described. The FRR is a relation between the correlation function of the fluctuations and the response function of macroscopic variables. Although it has been established that the FRR holds in equilibrium, physical significance of vi...

The nature and significance of equity and equality in relation to health and healthcare policy is discussed in the light of a recent article by Culyer. Culyer makes the following claims: (a) the importance of equity in relation to the provision of health care derives from the human need for health in order to flourish; and (b) for the sake of equity, equality of health among the members of part...

Comparative preference statements are the basic ingredients of conditional logics for representing users’ preferences in a compact way. These statements may be strict or not and obey different semantics. Algorithms have been developed in the literature to compute a preference relation over outcomes given a set of comparative preference statements and one or several semantics. These algorithms a...

Behavioural theories are a generalization of rst-order theories where the equality predicate symbol is interpreted by a behavioural equality of objects (and not by their identity). In this paper we rst consider arbitrary behavioural equalities determined by some (partial) congruence relation and we show how to reduce the behavioural theory of any class of-algebras to (a subset of) the standard ...

of thesis The prospect of a justification defence in cases of direct sex discrimination is universally criticised by academic commentators on the ground that it would subvert the goal of equality that underlies sex discrimination and equal treatment legislation. At the outset the thesis examines the differences between the sexes, how these differences can be used to explain the distinction betw...

The nature and significance of equity and equality in relation to health and healthcare policy is discussed in the light of a recent article by Culyer. Culyer makes the following claims: (a) the importance of equity in relation to the provision of health care derives from the human need for health in order to flourish; and (b) for the sake of equity, equality of health among the members of part...