On expenditure functions

In this paper we present complete characterizations of the expenditure function for both utility representations and preference structures. Building upon these results, we also establish under minimal assumptions duality theorems for exıpenditure functions and utility representations, and for expenditure functions and preference structures. These results generalize previous work in this area; moreover, in the case of preferences structures they apply to non-completeı preorders

New results on q-positivity

In this paper we discuss symmetrically self-dual spaces, which are simply real vector spaces with a symmetric bilinear form. Certain subsets of the space will be called q-positive, where q is the quadratic form induced by the original bilinear form. The notion of q-positivity generalizes the classical notion of the monotonicity of a subset of a product of a Banach space and its dual. Maximal q-positivity then generalizes maximal monotonicity. We discuss concepts generalizing the representations of monotone sets by convex functions, as well as the number of maximally q-positive extensions of a q-positive set. We also discuss symmetrically self-dual Banach spaces, in which we add a Banach space structure, giving new characterizations of maximal q-positivity. The paper finishes with two new examples.Comment: 18 page

On the Structure of Higher Order Voronoi Cells

The classic Voronoi cells can be generalized to a higher-order version by considering the cells of points for which a given $k$-element subset of the set of sites consists of the $k$ closest sites. We study the structure of the $k$-order Voronoi cells and illustrate our theoretical findings with a case study of two-dimensional higher-order Voronoi cells for four points.Comment: Minor correction

On expenditure functions.

In this paper we present complete characterizations of the expenditure function for both utility representations and preference structures. Building upon these results, we also establish under minimal assumptions duality theorems for exıpenditure functions and utility representations, and for expenditure functions and preference structures. These results generalize previous work in this area; moreover, in the case of preferences structures they apply to non-completeı preorders.Expenditure functions; Utility representations; Duality; Non-complete preorders;

Risk Aversion over Incomes and Risk Aversion over Commodities

This note determines the precise connection between an agent's attitude towards income risks and his attitude over risks in the underlying consumption space. Our results follow a general mathematical theory connecting the curvature properties of an objective function with the ray-curvature properties of its dual.risk aversion, concavity, duality

Effect of verb argument structure on picture naming in children with and without specific language impairment (SLI)

Background: This study investigated verb argument structure effects in children with specific language impairment (SLI). Aims: A picture-naming paradigm was used to compare the response times and naming accuracy for nouns and verbs with differing argument structure between Spanish-speaking children with and without language impairment. Methods & Procedures: Twenty-four children with SLI (ages 5;3-8;2 [years;months]), 24 age-matched controls (ages 5;3-8;2), 24 MLU-w controls (ages 3;3-7;1 years), and 31 adults participated in a picture-naming study. Outcomes & Results: The results show all groups produced more correct responses and were faster for nouns than all verbs together. As regards verb type accuracy, there were no differences between groups in naming one-argument verbs. However, for both two- and three-argument verbs, children with SLI were less accurate than adults and age-matched controls, but similar to the MLU-matched controls. For verb type latency, children with SLI were slower than both the agematched controls and adults for one- and two-argument verbs, while no differences were found in three-argument verbs. No differences were found between children with SLI and MLU-matched controls for any verb type. Conclusions & Implications: It has been shown that the naming of verbs is delayed in Spanish children with SLI. It is suggested that children with SLI may have problems encoding semantic representations