The Concept of Multidimensional Poverty: Accounting for Dimensional Poverty

Increasing efforts have recently been directed towards the question of how to incorporate the idea of a multidimensional poverty concept into traditional poverty measurement. In response, several suggestions have been made to derive different classes of multidimensional poverty measures. In this paper we focus on five axiomatically derived classes of multidimensional poverty measures. Each of these classes follow the unidimensional approach to progressively weight the respective distances to the threshold levels in order to account for poverty intensity. In this paper we claim that this approach, though reasonable in a unidimensional setting, does not suffice in a multidimensional setting. An additional aspect of poverty intensity should be considered which we denote as dimensional poverty: the number of dimensions in which individuals are deprived. There exists no luminous explanation why a weighting scheme should account for one aspect of poverty intensity while at the same time ignoring the other one. In this paper we introduce a multiple cutoff method to identify the poor which allows us to extent the five classes of poverty measures to include an additional weighting scheme in order to account for dimensional poverty. We find that the additional weight has no effect on the axiomatic basis of the classes of poverty measures other than a partial violation of the well-known subgroup decomposability axiom.Multidimensional Poverty, Multidimensional Poverty measures, Axiomatic Approach, Poverty Intensity

Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis

We consider the Lie group $\mathbb{R}^D_\kappa$ generated by the Lie algebra of $\kappa$-Minkowski space. Imposing the invariance of the metric under the pull-back of diffeomorphisms induced by right translations in the group, we show that a unique right invariant metric is associated with $\mathbb{R}^D_\kappa$. This metric coincides with the metric of de Sitter space-time. We analyze the structure of unitary representations of the group $\mathbb{R}^D_\kappa$ relevant for the realization of the non-commutative $\kappa$-Minkowski space by embedding into $(2D-1)$-dimensional Heisenberg algebra. Using a suitable set of generalized coherent states, we select the particular Hilbert space and realize the non-commutative $\kappa$-Minkowski space as an algebra of the Hilbert-Schmidt operators. We define dequantization map and fuzzy variant of the Laplace-Beltrami operator such that dequantization map relates fuzzy eigenvectors with the eigenfunctions of the Laplace-Beltrami operator on the half of de Sitter space-time.Comment: 21 pages, v3 differs from version published in Fortschritte der Physik by a note and references added and adjuste

Fuzzy Algebrae of the General Kaehler Coset Space G/H\otimesU(1)^k

We study the fuzzy structure of the general Kaehler coset space G/S\otimes{U(1)}^k deformed by the Fedosov formalism. It is shown that the Killing potentials satisfy the fuzzy algebrae working in the Darboux coordinates.Comment: 8 pages, LaTex, no figur

D0 Matrix Mechanics: New Fuzzy Solutions at Large N

We wish to consider in this report the large N limit of a particular matrix model introduced by Myers describing D-brane physics in the presence of an RR flux background. At finite N, fuzzy spheres appear naturally as non-trivial solutions to this matrix model and have been extensively studied. In this report, we wish to demonstrate several new classes of solutions which appear in the large N limit, corresponding to the fuzzy cylinder,the fuzzy plane and a warped fuzzy plane. The latter two solutions arise from a possible "central extension" to our model that arises after we account for non-trivial issues involved in the large N limit. As is the case for finite N, these new solutions are to be interpreted as constituent D0-branes forming D2 bound states describing new fuzzy geometries.Comment: revised version: references added, derivation of "central extensions" improved upon. To appear in JHE