Family-type subsistence incomes

Different family types may have a fixed flow of consumption costs, related to subsistence needs. We use a survey method in order to identify and estimate such a fixed component of spending for different families. Our method involves making direct questions about the linkup between aggregate disposable family income and well-being for different family types. Conducting our survey in six countries, Germany, France, Cyprus, China, India and Botswana, we provide evidence that fixed costs of consumption are embedded in welfare evaluations of respondents. More precisely, we find that the formalized relationship between welfare-retaining aggregate family incomes across different family types, suggested by Donaldson and Pendakur (2005) and termed Generalized Absolute Equivalence Scale Exactness, is prevalent and robust in our data. We use this relationship to identify subsistence needs of different family types and to calculate income inequality. --subsistence,equivalence scales,survey method,generalized equivalence scale exactness

Affine Hecke algebras and generalisations of quiver Hecke algebras for type B

We define and study cyclotomic quotients of affine Hecke algebras of type B. We establish an isomorphism between direct sums of blocks of these algebras and a generalisation, for type B, of cyclotomic quiver Hecke algebras which are a family of graded algebras closely related to algebras introduced by Varagnolo and Vasserot. Inspired by the work of Brundan and Kleshchev we first give a family of isomorphisms for the corresponding result in type A which includes their original isomorphism. We then select a particular isomorphism from this family and use it to prove our result.Comment: 37 page

The characteristic function of the discrete Cauchy distribution

A new family of integer-valued Cauchy-type distributions is introduced, the {\it Cauchy-Cacoullos family}. The characteristic function is evaluated, showing some interesting distributional properties, similar to the ordinary (continuous) Cauchy scale family. The results are extendable to discrete Student-type distributions with odd degrees of freedom. Keywords: Fourier series; discrete Student distribution; Cauchy-Cacoullos family.Comment: Dedicated to Professor Theo Cacoullos (13 pages, 1 Figure

On a family of integral operators of Hankel type

In this paper we perform an explicit diagonalization of Hankel integral operators $K^{(0)}, K^{(1)}, K^{(2)}, ...$ It turns out that each of these operators has a simple purely absolutely continuous spectrum filling in the interval $[-1,1]$. This generalizes a result of Kostrykin and Makarov (2008).Comment: 20 page